"If you are wearing a hat, you are a baseball fan." and "If you are not a baseball fan, you are not wearing a hat." It's called a [B]contrapositive[/B]. definition: : a proposition or theorem formed by contradicting both the subject and predicate or both the hypothesis and conclusion of a given proposition

$1,100 per month for 10 years, if the account earns 2% per year What the student or parent is asking is: If they deposit $1,100 per month in a savings/investment account every month for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? Deposits are monthly. But interest crediting is annual. What we want is to match the two based on interest crediting time, which is annual or yearly. 1100 per month. * 12 months in a year = 13,200 per year in deposit Since we matched interest crediting period with deposits, we now want to know: If they deposit $13,200 per year in a savings/investment account every year for 10 years, and they earn 2% per year, how much will the account be worth after 10 years? This is an annuity, which is a constant stream of payments with interest crediting at a certain period. [SIZE=5][B]Calculate AV given i = 0.02, n = 10[/B] [B]AV = Payment * ((1 + i)^n - 1)/i[/B][/SIZE] [B]AV =[/B]13200 * ((1 + 0.02)^10 - 1)/0.02 [B]AV =[/B]13200 * (1.02^10 - 1)/0.02 [B]AV =[/B]13200 * (1.2189944199948 - 1)/0.02 [B]AV =[/B]13200 * 0.21899441999476/0.02 [B]AV = [/B]2890.7263439308/0.02 [B]AV = 144,536.32[/B]

2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're given two equations: [LIST=1] [*]a = 2b + 3 [*]a + b = 60 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: 2b + 3 + b = 60 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get: b = [B]19 [/B] To solve for a, we substitute b = 19 into equation (1): a = 2(19) + 3 a = 38 + 3 a = [B]41[/B]

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2000 people attended a baseball game 1300 of the people attending supported the home team while 700 supported the visiting team what percentage of people attending supported the home team We want the percentage of 1300 out of 2000. [URL='https://www.mathcelebrity.com/perc.php?num=1300&den=2000&pcheck=1&num1=+16&pct1=+80&pct2=+35&den1=+90&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']We go to our search engine and type 1300 out of 2300 as a percent[/URL] and we get: [B]65%[/B]

5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member Let the full salary of the union members be s. Since 17% is 0.17, We're given: 0.17s = 108000000 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get: s = 635,294,117.65 Calculate the average annual pay of a single union member: Average Pay = Total Pay / Number of Union Members Average Pay = 635,294,117.65 / 5000 Average Pay = [B]127,058.82[/B]

A 13 ft. ladder is leaning against a building 12 ft. up from the ground. How far is the base of the ladder from the building? This is a classic 5-12-13 pythagorean triple, where the hypotenuse is 13, and the 2 sides are 5 and 12. The building and the ground form a right triangle. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=12&hypinput=13&pl=Solve+Missing+Side']You can see the proof here[/URL]...

A 5 foot ladder is leaning against a wall. If the bottom of the ladder is 3 feet from the base of the wall, how high up the wall is the top of the ladder? The answer is [B]4[/B]. Since we have a right triangle, with special ratio 3-4-5. The ladder represents the hypotenuse.

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need? The difference between the 70 foot and 50 foot pole is: 70 - 50 = 20 foot height difference. So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse. Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get: hypotenuse = [B]36.06 feet[/B]

A 74 inch rake is Leaning against a wall. The top of the rake hits the wall 70 inches above the ground. How far is the bottom of the rake from the base of the wall? We have a right triangle. Hypotenuse is the rake length fo 74 inches. One of the legs is 70. We [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=70&hypinput=74&pl=Solve+Missing+Side']use our right triangle calculator to solve for the other leg[/URL]: [B]24 inches[/B]

A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]

a baseball park charges $4.50 per admission ticket. the park has already sold 42 tickets. how many more tickets would they need to sell to earn at least $441? Let the number of tickets above 42 be t. A few things to note on this question: [LIST] [*]The phrase [I]at least[/I] means greater than or equal to, so we have an inequality. [*]Earnings = Price * Quantity [/LIST] We're given: Earnings = 4.50 * 42 + 4.5t >= 441 Earnings = 189 + 4.5t >= 441 We want to solve this inequality for t: Solve for [I]t[/I] in the inequality 189 + 4.5t ≥ 441 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 189 and 441. To do that, we subtract 189 from both sides 4.5t + 189 - 189 ≥ 441 - 189 [SIZE=5][B]Step 2: Cancel 189 on the left side:[/B][/SIZE] 4.5t ≥ 252 [SIZE=5][B]Step 3: Divide each side of the inequality by 4.5[/B][/SIZE] 4.5t/4.5 ≥ 252.4.5 [B]t ≥ 56[/B]

A baseball player gets 12 hits in 40 at bats. What percent are hits, and what percent are not hits? Percent Hits = 12/40 Using our [URL='http://www.mathcelebrity.com/perc.php?num=12&den=40&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']percent calculator[/URL], we get [B]30%[/B] Since you either get a hit or you don't, we subtract 30% from 100% to find the percent of not hits: Percent Not Hits = 100 - 30% = [B]70%[/B]

A baseball player gets 3 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? We set up a proportion of hits to games where h is the number of hits the player gets in 45 games: 3/15 = h/45 [URL='https://www.mathcelebrity.com/prop.php?num1=3&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']Enter this into our search engine[/URL], and we get [B]h = 9[/B].

A baseball player gets 7 hits in the first 15 games of the season. If he continues hitting at the same rate, how many hits will he get in the first 45 games? Let's find the proportion of hits to games. Using h as the number of hits in 45 games, we have: 7/15 = h/45 Using our [URL='http://www.mathcelebrity.com/prop.php?num1=7&num2=h&den1=15&den2=45&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get h = 21

a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400? Let the amount of consecutive hits needed be h. We have: hits / at bats = Batting Average Plugging in our numbers, we get: (9 + h)/60 = 0.400 Cross multiply: 9 + h = 60 * 0.4 9 + h = 24 To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get: h = [B]15[/B]

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last. (This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.) First 8 positions: [URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200 For the pitcher, we can have 10 different possibilities for the 9th player: 259,459,200 x 10 = [B]2,594,592,000 ways[/B]

A baseball team won 40% of its first 30 games. The team then won 65% of its next 60 games. Approximately what percent of the games did the team win? Using our percentage calculators, we type the following statements into our search engine and get: [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=45&den1=30&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']45% of 30[/URL] = 13.5 [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=65&den1=60&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']65% of 60[/URL] = 39 For a total of 52.5 games won The team played 30 + 60 = 90 games. So we want to know the pecent: [URL='https://www.mathcelebrity.com/perc.php?num=52&den=90&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']52/90[/URL] = [B]57.78%[/B]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree? So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg. The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides Rearranging this equation to isolate a, we get a^2 = c^2 - b^2 Taking the square root of both sides, we get a = sqrt(c^2 - b^2) a = sqrt(15^2 - 12^2) a = sqrt(225 - 144) a = sqrt(81) a = [B]9 meters[/B]

A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given? 582 passengers on the boat Let r be the number of rides So we want to find r when: 582r = 13105 To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get: r = 22.517 If we round this down, setting 0.517 rides as the first ride, we get: r = [B]22 [MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]

A company’s number of personnel on active duty (not on sick leave or vacation leave) during the period 2000 - 2013 can be approximated by the cubic model f(x) = 2.5x^3 - 15x^2 - 80x + 1025, where x = 0 corresponds to 2000. Based on the model, how many personnel were on active duty in 2010? What is the domain of f? If x = 0 corresponds to 2000, when 2010 is 2010 - 2000 = 10. We want f(10): f(10) = 2.5(10)^3 - 15(10)^2 - 80(10) + 1025 f(10) = 2.5(1000) - 15(100) - 800 + 1025 f(10) = 2500 - 1500 - 800 + 1025 f(10) = [B]1,225[/B]

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X. We have: [B]y = 21x + 5[/B] Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family. We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.

A ladder 25 feet long is leaning against a wall. If the base of the ladder is 7 feet from the wall, how high up the wall does the ladder reach? We have a right triangle, where the ladder is the hypotenuse, and we want the measurement of one leg. Set up the pythagorean theorem with these given items using our P[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=7&hypinput=25&pl=Solve+Missing+Side']ythagorean Theorem Calculator[/URL]. We get Side 1 = [B]24 feet.[/B]

A ladder rests 2.5 m from the base of a house. If the ladder is 4 m long, how far up the side of the house will the ladder reach? We have a right triangle with the hypotenuse as 4, the one leg as 2.5 We want to solve for the other leg length. We use our [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=2.5&hypinput=4&pl=Solve+Missing+Side']right triangle solver[/URL] to get [B]3.122[/B]

A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages? Set up the cost function y = C(x) [B]C(x) = 4.95 + 11.90x[/B]

A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angle of elevation of the top of the building from the man. Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of the building. Using right triangle calculations, we want Angle A which is the angle of elevation. [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=20&angle_b=&b=45&c=&pl=Calculate+Right+Triangle']Angle of Elevation[/URL] which is [B]23.9625°[/B]

A mountain with a base 6684 feet below sea level rises 22304 feet. What is the elevation above sea level of its peak? Below sea level is written as a negative, so we have: -6684 + 22304 = [B]15,620 feet above sea level[/B]

A person places $230 in an investment account earning an annual rate of 6.8%, compounded continuously. Using the formula V = Pe^{rt}V=Pe^rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 20 years Using our [URL='http://www.mathcelebrity.com/simpint.php?av=&p=230&int=6.8&t=20&pl=Continuous+Interest']continuous compounding calculator[/URL], we get: V = [B]896.12[/B]

A person places $96300 in an investment account earning an annual rate of 2.8%, compounded continuously. Using the formula V=PertV = Pe^{rt} V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 7 years. Substituting our given numbers in where P = 96,300, r = 0.028, and t = 7, we get: V = 96,300 * e^(0.028 * 7) V = 96,300 * e^0.196 V = 96,300 * 1.21652690533 V = [B]$117,151.54[/B]

A rectangular fish tank has a base that is 8 inches by 7 inches. How much water will it take to a depth of 5 inches The volume (V) or a rectangular solid is: V = lwh Using l = 8, w = 7, and h = 5, we have: V = 8(7)(5) V = [B]280 cubic inches[/B]

A sales clerk receives a monthly salary of $750 plus a commission of 4% on all sales over $3900. What did the clerk earn the month that she sold $12,800 in merchandise? [U]Calculate Commission Sales Eligible Amount:[/U] Commission Sales Eligible Amount = Sales - 3900 Commission Sales Eligible Amount = 12800 - 3900 Commission Sales Eligible Amount = 8900 [U]Calculate Commission Amount:[/U] Commission Amount = Commission Sales Eligible Amount * Commission Percent Commission Amount = [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=4&den1=8900&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']8900 * 4%[/URL] Commission Amount = 356 [U]Calculate total earnings:[/U] Total Earnings = Base Salary + Commission Amount Total Earnings = 750 + 356 Total Earnings = [B]1106[/B]

A salesperson receives a base salary of $300 per week and a commission of 15% on all sales over $5,000. If x represents the salesperson’s weekly sales, express the total weekly earnings E(x) as a function of x and simplify the expression. Then find E(2,000) and E(7,000) and E(10,000). 15% as a decimal is written as 0.15. Build our weekly earnings function E(x) = Commission + Base Salary E(x) = 0.15(Max(0, x - 5000)) + 300 Now find the sales salary for 2,000, 7,000, and 10,000 in sales E(2,000) = 0.15(Max(0,2000 - 5000)) + 300 E(2,000) = 0.15(Max(0,-3000)) + 300 E(2,000) = 0.15(0) + 300 [B]E(2,000) = 300 [/B] E(7,000) = 0.15(Max(0,7000 - 5000)) + 300 E(7,000) = 0.15(Max(0,2000)) + 300 E(7,000) = 0.15(2,000) + 300 E(7,000) = 300 + 300 [B][B]E(7,000) = 600[/B][/B] E(10,000) = 0.15(Max(0,10000 - 5000)) + 300 E(10,000) = 0.15(Max(0,5000)) + 300 E(10,000) = 0.15(5,000) + 300 E(10,000) = 750+ 300 [B][B]E(10,000) = 1,050[/B][/B]

A Septon said that he had 100 rocks. How many rocks does he have in base 10? 100 in base 7 is: 1 * 7^2 + 0 * 7^1 + 0 * 7^0 = [B]49[/B]

A Septon said that he has 3 eyes. Does that mean he really has 3 eyes in base 10? 3 in base 7 is: 3 * 7^0 = 3 * 1 = 3 So [B]Yes[/B]

A Septon said that he has a collection of 1,000,000 stones in his house. How many stones is that in base 10? The 1 is in decimal position 7, or 6th power. [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=7%5E6&pl=Calculate']1 * 7^6[/URL] = [B]117,649[/B]

A Septon who visited Earth used an Earth scale and found that he weighed 125 pounds. He is horrified that he lost so much weight. Translate 125 pounds base 10 into base 7. Using our [URL='https://www.mathcelebrity.com/binary.php?num=125&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we see that: 125 = [B]236[/B] (in base 7)

A Septonian said that his exact weight is 250.346 pounds (base 7). Translate this into base 10. Start the conversion: 2 * 7^2 + 5 * 7^1 + 0 * 7^0 + 3 * 1/7 + 4 * (1/7)^2 + 6 * (1/7)^3 2 * 49 + 5 * 7 + 0 * 1 + 3/7 + 4 * 1/49 + 6 * 1/343 98 + 35 + 3/7 + 4/49 + 6/343 [B]133 & 181/343[/B]

A Septonian won the lottery in the United States and won $1,000,000. How many dollars in that in base 7? Using our [URL='https://www.mathcelebrity.com/binary.php?num=1000000&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we get: 1,000,000 in base 7 = [B]11,333,311[/B]

A shop tech earns a base PayPal $15.68 per hour, plus "time-and-a-half" for overtime (time exceeding 40 hours). If he work 44.5 hours during a particular week, what is his gross pay? Gross pay = Regular Pay + Overtime Pay Calculate regular pay: Regular Pay = 40 hours * $15.68 = $627.20 Calculate overtime pay Overtime pay = (44.5 - 40) * 1.5 * $15.68 Overtime Pay = 4.5 * 1.5 * $15.68 Overtime Pay = $105.84 Gross pay = $627.20 + $105.84 Gross pay = [B]$733.04[/B]

A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box? The volume of the box is l x w x h. We're given l and w = 4. So we want height: 56 = 4 x 4 x h 16h = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get: h = [B]3.5[/B]

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid? Setup measurements: [LIST] [*]Small base = n [*]Large base = 1.2n [*]sides = n/2 [*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4 [/LIST] Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (1 + 1.2 + 0.5 + 0.5)n = 3.2n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 3.2n = + 54.4 [SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE] 3.2n/3.2 = 54.4/3.2 n = [B]17[/B] [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

A triangle has an area of 60 square inches and a base of 10 inches. What is its height? A = bh/2 b = 2A/h b = 2(60)/10 b = 120/10 b = [B]12 inches[/B]

A triangular garden has base of 6 meters amd height of 8 meters. Find its area Area (A) of a triangle is: A = bh/2 Plugging in our numbers, we get: A = 6*8/2 A = [B]24 square meters[/B]

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true? The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway. Imagine a third post midway between the two goal posts. It has the same height as the two goalposts. From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

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Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3577.00 for 1197 paid admissions. How many of each ticket were sold? Let g be the number of tickets for general admission Let r be the number of tickets for reserved seats We have two equations: [LIST=1] [*]g + r = 1197 [*]2g + 5.50r = 3577 [/LIST] We can solve this a few ways, but let's use substitution using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=g+%2B+r+%3D+1197&term2=2g+%2B+5.50r+%3D+3577&pl=Substitution']simultaneous equations calculator[/URL]: [LIST] [*][B]r = 338[/B] [*][B]g = 859[/B] [/LIST]

Alex sells cars at Keith Palmer ford. He earns 400 dollars a week plus 150 dollars per car he sells. If he earned 1450 dollars last week, how many cars did he sell? Subtract the base salary of $400 $1,450 - 400 =$1,050 Divide this by 150 per car $1,050/$150 = [B]7 cars[/B]

Free Algebraic Expressions Calculator - This calculator builds algebraic expressions based on word representations of numbers using the four operators and the words that represent them(increased,product,decreased,divided,times) Also known as Mathematical phrases

Alonzo needs to buy some pencils. Brand A has a pack of 36 pencils for $8.52. Brand B has a pack of 48 pencils for $9.98. Find the unit price for each brand. Then state which brand is the better buy based on the unit price. Round your answers to the nearest cent. Using our [URL='http://www.mathcelebrity.com/betterbuy.php?p1=8.52&p2=9.98&q1=36&q2=48&pl=Better+Buy']better buy calculator[/URL], we see the following unit prices: [LIST] [*][B]Brand A = $0.24[/B] [*][B]Brand B = $0.21[/B]. [*][B]Brand B has the better unit price by 3 cents.[/B] [/LIST]

Answer an electrician charges a base fee of $75. plus a $50 for each hour of work. The minimum the electrician charges is $175. Create a table that shows the amount the electrician charges for 1,2,3, and 4 hours of work. The hourly cost for h hours worked is C(h): C(h) = Max(175, 50h + 75) 1 hour cost: C(1) = Max(175, 50(1) + 75) C(1) = Max(175, 50 + 75) C(1) = Max(175, 125) [B]C(1) = 175[/B] 2 hour cost: C(2) = Max(175, 50(2) + 75) C(2) = Max(175, 100 + 75) C(2) = Max(175, 175) [B]C(2) = 175[/B] 3 hour cost: C(3) = Max(175, 50(3) + 75) C(3) = Max(175, 150 + 75) C(3) = Max(175, 225) [B]C(3) = 225[/B] 4 hour cost: C(4) = Max(175, 50(4) + 75) C(4) = Max(175, 200 + 75) C(4) = Max(175, 275) [B]C(4) = 275[/B]

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As a salesperson, Laura earns a base salary of $72 per week plus a commission of 20% of sales. If she had $75 in sales last week, what was her total pay? Total Pay = Base Pay + Commission Calculate Commission: Commission = Commission Percent x Sales Commission = 20% * 75 Commission = 15 Total Pay = Base Pay + Commission Total Pay = 72 + 15 Total Pay = [B]$97[/B]

As a salesperson, Lauren earns a base salary of $94 per week plus a commission of 10% of sales. If she had $90 in sales last week, what was her total pay? [B][U]Use the Base plus Commission formula above[/U][/B] Salary = Base Salary + 10%(Total Sales) Salary = $94 + 0.1(90) Salary = $94 + $9 Salary = [B]$103[/B]

Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph. a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit? b. What proportion of the vehicles would be going less than 50 mph? c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion? d. In what way do you think the actual distribution of speeds differs from a normal distribution? a. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=65&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<65) = [B]22.66%[/B] b. Using our [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+50&mean=71&stdev=8&n=+1&pl=P%28X+%3C+Z%29']z-score calculator[/URL], we see that P(x<50) = [B]0.4269%[/B] c. [URL='http://www.mathcelebrity.com/zcritical.php?a=0.9&pl=Calculate+Critical+Z+Value']Inverse of normal for 90% percentile[/URL] = 1.281551566 Plug into z-score formula: (x - 71)/8 = 1.281551566 [B]x = 81.25241252[/B] d. [B]The shape/ trail differ because the normal distribution is symmetric with relatively more values at the center. Where the actual has a flatter trail and could be expected to occur.[/B]

At Billy’s Baseball Dugout, they are having a sale on merchandise. All bats cost $45.00, sunflower seeds, $1.50, and cleats $85.00. Write an expression if you bought b bats, s sunflower seeds, and c cleats. Since amount = cost * quantity, we have a cost of: [B]45b + 1.50s + 85c[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years. At any time t, the Bangladesh population at year t is: [B]y = 170,000,000(1.015)^t[/B]

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based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: [LIST=1] [*]Benny buys 8 new cards, so we add 8 to get b + 8 [*]The dog ate half of his cards the next day, so Benny has (b + 8)/2 [*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47 [/LIST] (b + 8)/2 = 47 [B][U]Cross multiply:[/U][/B] b + 8 = 47 * 2 b + 8 = 94 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].

Bills car rental charges a base fee of 50$ and then $0.20 per mile. Set up the cost function C(m) where m is the number of miles driven: [B]C(m) = 50 + 0.20m[/B]

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Blanca works as a salesperson and earns a base salary of $72 per week plus a commission of 12% of all her sales. If Blanca had $75 in weekly sales, how much did she make? [U]Find the commission on her sales[/U] Commission = Sales * 12% Commission = 75 * 0.12 = 9 [U]Now add in her base salary[/U] Total Salary = Base Salary + Commission Total Salary = 72 + 9 Total Salary = [B]81[/B]

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Caleb has a complicated and difficult research paper due soon. What should he do to keep from feeling overwhelmed and procrastinating? A. work on the paper every day but save the bulk of the work for the night before it's due B. break down the paper into several small steps and start with the smallest one C. write down the deadline for the paper where he can see it every day so he doesn't forget D. work on the hardest parts of the paper first and take multiple breaks until he's finished Caleb wants to avoid both overwhelm and procrastination. Let's review each option: [LIST] [*]A is out because saving a majority of the work will cause overwhelm [U]and[/U] demonstrates procrastination [*]B is a good option as small steps reduce overwhelm [*]C looks nice on paper, but will he follow through with seeing the deadline everyday? [*]D is a good option as well. Finishing the tough parts first makes the rest of the journey seem like a downhill cruise [/LIST] Based on these, I'd take [B]B or D[/B]

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Carter is going away to college and is giving his collection of 531 baseball cards to his cousins. If he gives 227 cards to Lewis, 186 cards to Benny, and 18 cards to Seven, how many cards are left over? When Carter gives away cards, he subtracts from his collection. So we have: 531 - 227 - 186 - 18 = [B]100 cards leftover[/B]

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Change Base 10 number of 25 into base 2 Using our [URL='https://www.mathcelebrity.com/binary.php?num=25&check1=7&bchoice=2&pl=Convert']base change calculator[/URL], we get: 25 = [B]11001[/B] (in base 2)

Change the base 10 number 100 into base 5 Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=5&pl=Convert']base change calculator[/URL], we get: 100 = [B]400 (Base 5)[/B]

Change the base 2 number 1000 into base 10 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 0 * 2^0 8 + 0 + 0 + 0 = [B]8[/B]

Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to? Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations: [LIST=1] [*]6f + 5 = n [*]8f - 7 = n [/LIST] Since both equations equal n, we set these equations equal to each other 6f + 5 = 8f - 7 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get: f = [B]6 [/B] To check our work, we plug in f = 6 into each equation: [LIST=1] [*]6(6) + 5 = 36 + 5 = 41 [*]8(6) - 7 = 48 - 7 = 41 [/LIST] So this checks out. Clark has 41 total cards which he gives to 6 friends.

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cscx-cotx*cosx=sinx A few transformations we can make based on trig identities: [LIST] [*]csc(x) = 1/sin(x) [*]cot(x) = cos(x)/sin(x) [/LIST] So we have: 1/sin(x) - cos(x)/sin(x) * cos(x) = sin(x) (1 - cos^2(x))/sin(x) = sin(x) 1 - cos^2(x) = sin^2(x) This is [B]true[/B] from the identity: sin^2(x) - cos^2(x) = 1

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Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with? Let the starting amount of cards be s. We're given: [LIST] [*]Dan bought 7 new cards: s + 7 [*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2 [*]Now, he's got 26 cards left. So we set up the following equation: [/LIST] (s + 7)/2 = 26 Cross multiply: s + 7 = 26 * 2 s + 7 = 52 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get: s = [B]45[/B]

Dan bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 30 cards left. How many cards did Dan start with? Let the original collection count of cards be b. So we have (b + 8)/2 = 30 Cross multiply: b + 8 = 30 * 2 b + 8 = 60 [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B8%3D60&pl=Solve']Use the equation calculator[/URL] [B]b = 52 cards[/B]

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George has 600 baseball cards and Joy has one fifth as many baseball cards as George. How many baseball cards does joy have? Let j = Joy's cards and g = George's cards. We have the following equation: g = 600 j = 1/5g So j = 600/5 [B]j = 120[/B]

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Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck? Set up the equation where x is the amount of miles he drove: 0.76x + 16.95 = 152.99 [URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]: x = 179 miles

Harjap is a salesperson at an electronic store earning a base salary of $420 per week. She also earns 2.0% commission on sales each month. This month she had $131600 in sales. What was harjaps gross income for this month? [U]Calculate Monthly Gross Income:[/U] Gross Income = Monthly Base Salary + Commissions [U]Calculate Monthly Base Salary:[/U] Monthly Base Salary = Weekly Base Salary * 4 Monthly Base Salary = $420 * 4 Monthly Base Salary = $1,680 [U]Calculate Commissions:[/U] Commissions = Sales * Commission Percent Commissions = $131,600 * 2% Since 2% as a decimal is 0.02, we have: Commissions = $131,600 * 0.02 Commissions = $2,632 [U]Calculate Monthly Gross Income:[/U] Gross Income = Monthly Base Salary + Commissions Gross Income = $1,680 + $2632 Gross Income = [B]$4,312[/B]

Hayden bought 48 new trading cards. Three-fourths of the new cards are baseball cards. How many baseball cards did Hayden buy? We want 3/4 of 48. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=48&frac2=3/4&pl=Multiply']type this statement into our calculator[/URL] and we get: [B]36[/B]

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How many fingers would you guess a Septon has? We have 10 fingers in base 10 So Septons have [B]7 fingers[/B] in base 7

How many possible batting orders are there for a baseball team with 9 players? 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = [B]362,880 batting orders[/B]

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If a person from Septon at .1 of their cookie, what fraction of the cookie did they eat using base 10 (1/7)^1 = 1/7

If Bill's salary is $25 and he gets a 20¢ commission on every newspaper he sells, how many must he sell to make $47 Set up bills Earnings function E(n) where n is the number of newspapers he sells: E(n) =. Cost per newspaper * number of newspapers sold + base salary E(n) = 0.2n + 25 We're asked to find n when E(n) = 47, so we set E(n) = 47 and solve for n: 0.2n + 25 = 47 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=0.2n%2B25%3D47&pl=Solve']equation solver[/URL], we get: n = [B]110[/B]

if Logb(5)=3.56 and logb(8)=4.61 then what is logb(40) There exists a logarithmic identity which says log(xy) = log(x) + log(y). Since the two logs above have the same base b, we have: x = 5 and y = 8. So we have: logb(40) = logb(5) + logb(8) logb(40) = 3.56 + 4.61 logb(40) = [B]8.17[/B]

In 1 year, a baseball player got 195 hits in 600 times. What is his batting average? Batting Average = Hits / Times at Bat Batting Average = 195 / 600 [URL='https://www.mathcelebrity.com/perc.php?num=196&den=600&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']Batting Average[/URL] = [B]0.327[/B]

In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have: b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already [/I] We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get: b = [B]6[/B]

In base 10 the number 25.12 actually means 20 + 5 + 1/10 + 2/100. What does the base 7 number 25.12 mean? 2 groups of 7 5 groups of 1 1 group of 1/7 2 groups of 1/49 (1/7)^2 14 + 5 + 1/7 + 2/49

In base 10, the number .1111... approaches 1/9. What does .111111 base 2 approach in base 10? Base 2 .11111 means: (1/2)^1 + (1/2)^2 + + (1/2)^3 + (1/2)^4 1/2 + 1/4 + 1/8 + 1/16 [B]This approaches 1[/B]

Is someone has $1,000,000 in base 2, how much money does she have in base 10? 1 is in 7th digit place, so we raise it to the 6th power: [URL='https://www.mathcelebrity.com/powersq.php?sqconst=+6&num=2%5E6&pl=Calculate']1 * 2^6 [/URL]= [B]64[/B]

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Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]

Juliana answered 42 times correctly on an 80-item quiz, while her sister Angela answered 21 items correctly on a 40-item quiz. Do they have the same portion of correct answers? Let's compare based on correct answers to questions: Juliana = 42/80 = 0.525 Angela = 21/40 = 0.525 So yes, they do have the same portion of correct answers. But there's another way to solve this: [LIST=1] [*]Divide Juliana's the top and bottom of Juliana's fraction by 2. [*]We picked 2 as a GCF shown in our calculator. [*]Type [URL='https://www.mathcelebrity.com/gcflcm.php?num1=42&num2=80&num3=&pl=GCF']GCF of 42 and 80[/URL]. [/LIST] Divide top and bottom of Juliana's fraction by the GCF of 2 42/2 = 80/2 = 21/40 This ratio equals Angela's.

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Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000 Let the Sales amount be s. We have: Sales over 1,500 is written as s - 1500 11% is also 0.11 as a decimal, so we have: 0.11(s - 1500) + 650 = 3000 Multiply through: 0.11s - 165 + 650 = 3500 0.11s + 485 = 3500 To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=0.11s%2B485%3D3500&pl=Solve']we type it in our search engine[/URL] and we get: s = [B]27,409.10[/B]

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mark has a drawer full of 12 yellow baseball caps and 18 white baseball caps. What is the probability of the next cap he chooses at random will be yellow? P(yellow) = yellow caps / Total caps P(yellow) = 12/(12 + 18) P(yellow) = 12/30 [URL='https://www.mathcelebrity.com/fraction.php?frac1=12.%2F30&frac2=3%2F8&pl=Simplify']Simplifying this fraction,[/URL] we get: P(yellow) = [B]2/5[/B]

A box in the shape of a rectangular prism is used in a movie scene. The base of the box measures 6 feet by 5 feet. The box has a volume of 195 cubic feet. The director hires an actor who is 6 feet 4 inches tall. Can the actor stand up straight in the box? Also I do need to show my work so please write down the work to solve this. Thanks!

Melinda is paid 17000 per year. She is also paid a sales commission of 5% of the value of her sales. Last year she sold 344000 worth of products. What percent of her total income was her commission? Calculate Melinda's commission: 344,000 * 0.05 = 17,200 Calculate her total income for the year Total Income = Base Pay + Commission Total Income = 17,000 + 17,200 Total Income = 34,200 Calculate the percent of her income which is commission: Commission Income Percent = 100 * 17,200/34,200 Commission Income Percent = 100 * 0.5029 [B]Commission Income Percent = 50.29%[/B]

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Oliver and Julia deposit $1,000.00 into a savings account which earns 14% interest compounded continuously. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent. [URL='https://www.mathcelebrity.com/simpint.php?av=&p=1000&int=3&t=14&pl=Continuous+Interest']Using our continuous interest calculator[/URL], we get: A = [B]1,521.96[/B]

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Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun. We want a sales function p where c is the number of copies of Math is Fun p = Price per sale * c + Base Salary [B]p = 40c + 1900 [/B] Now, we want to know Total pay if c = 22 p = 40(22) + 1900 p = 880 + 1900 p = [B]2780[/B]

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Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If the hook is 4 meters from the base of the flagpole, how tall is the flagpole? We have a right triangle, with hypotenuse of 9 and side of 4. [URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=4&hypinput=9&pl=Solve+Missing+Side']Using our Pythagorean Theorem calculator[/URL], we get a flagpole height of [B]8.063[/B].

Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. whats is the equation. Let S(c) be the equation for the money Sarah makes selling (c) cookies. We have: S(c) = Cost per cookies * c cookies + Base Salary [B]S(c) = 50c + 500[/B]

Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers. If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is: Commission = Total Pay - Base Pay Commission = 100 - 90 Commission = $10 Assuming the commission for each computer is equal, we need to find the commission per computer: Commission per computer = Total Commission / Number of Computers Sold Commission per computer = 10/4 Commission per computer = $2.50 Now, we build the Total pay function P(x): Total Pay = Base Pay + Commission * Number of Computers sold [B]P(x) = 90 + 2.5x[/B]

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based on a sample of size 41, a 95% confidence interval for the mean score of all students,µ, on an aptitude test is from 60 to 66. Find the margin of error

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. We randomly sample 49 fly balls. a. If X = average distance in feet for 49 fly balls, then X ~ _______(_______,_______)
b. What is the probability that the 49 balls traveled an average of less than 240 feet? Sketch the graph. Scale the horizontal axis for X. Shade the region corresponding to the probability. Find the probability.
c. Find the 80^th percentile of the distribution of the average of 49 fly balls a. N(250, 50/sqrt(49)) = [B]0.42074[/B] b. Calculate Z-score and probability = 0.08 shown [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+240&mean=+250&stdev=+7.14&n=+1&pl=P%28X+%3C+Z%29']here[/URL] c. Inverse of normal distribution(0.8) = 0.8416. Use NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL] Using the Z-score formula, we have 0.8416 = (x - 250)/50 x = [B]292.08[/B]

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 250 feet and a standard deviation of 50 feet. a. If X = distance in feet for a fly ball, then X ~ b. If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 220 feet? Sketch the graph. Scale the horizontal axis X. Shade the region corresponding to the probability. Find the probability. c. Find the 80th percentile of the distribution of fly balls. Sketch the graph, and write the probability statement. a. [B]N(250, 50/sqrt(1))[/B] b. Calculate [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+220&mean=250&stdev=50&n=+1&pl=P%28X+%3C+Z%29']z-score[/URL] Z = -0.6 and P(Z < -0.6) = [B]0.274253[/B] c. Inverse of normal distribution(0.8) = 0.8416 using NORMSINV(0.8) [URL='http://www.mathcelebrity.com/zcritical.php?a=0.8&pl=Calculate+Critical+Z+Value']calculator[/URL] Z-score formula: 0.8416 = (x - 250)/50
x = [B]292.08[/B]

The base of a triangle with a height of 7 units is represented by the formula b=2/7A. The base of the triangle is less than 10 units. Write and solve an inequality that represents the possible area A of the triangle We're given: b=2/7A We're also told that b is less than 10. So we have: 2/7A < 10 2A/7 < 10 Cross multiply: 2A < 7 * 10 2A < 70 Divide each side of the inequality by 2 to isolate A 2A/2 < 70/2 Cancel the 2's on the left side and we get: A < [B]35[/B]

The baseball coach bought 2 new baseballs for $1 each. The basketball coach bought 7 new basketballs for $10 each. How much more did the basketball coach spend than the baseball coach? [U]Baseball coach spend:[/U] Spend = Number of baseballs * cost per baseball Spend= 2 * $1 Spend = $2 [U]Basketball coach spend:[/U] Spend = Number of basketballs * cost per basketball Spend= 7 * $10 Spend = $70 [U]Calculate the difference in spend:[/U] Difference = Basketball coach spend - Baseball coach spend Difference= $70 - $2 Difference= [B]$68[/B]

the basketball coach bought 8 new basketballs for 2$ each. the baseball coach bought 8 new baseballs for 25$ each. how much more did the basketball coach spend than the baseball coach. [LIST] [*]Basketball Coach Spend: 8 basketballs * $2 = $16 [*]Baseball Coach Spend: 8 baseballs * $25 = $200 [/LIST] The Baseball Coach spent $200 - $16 = [B]$184[/B] more than the Basketball coach

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base? We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130 The distance from home to first is 90 feet. Our hypotenuse is the distance from the outfielder to first base. [URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get: d = [B]158.11 feet[/B]

The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 231 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer. Digit, Probability 1, 0.301 2, 0.176 3, 0.125 4, 0.097 5, 0.079 6, 0.067 7, 0.058 8, 0.051 9, 0.046 [B][U]Fradulent Checks[/U][/B] Digit, Frequency 1, 36 2, 32 3, 45 4, 20 5, 24 6, 36 7, 15 8, 16 9, 7 Complete parts (a) and (b). (a) Using the level of significance α = 0.05, test whether the first digits in the allegedly fraudulent checks obey Benford's Law. Do the first digits obey the Benford's Law?
Yes or No Based on the results of part (a), could one think that the employe is guilty of embezzlement? Yes or No Show frequency percentages Digit Fraud Probability Benford Probability 1 0.156 0.301 2 0.139 0.176 3 0.195 0.125 4 0.087 0.097 5 0.104 0.079 6 0.156 0.067 7 0.065 0.058 8 0.069 0.051 9 0.03 0.046 Take the difference between the 2 values, divide it by the Benford's Value. Sum up the squares to get the Test Stat of 2.725281277 Critical Value Excel: =CHIINV(0.95,8) = 2.733 Since test stat is less than critical value, we cannot reject, so [B]YES[/B], it does obey Benford's Law and [B]NO[/B], there is not enough evidence to suggest the employee is guilty of embezzlement.

The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly observed the bartender and found that he used the CORRECT amounts in only 9 out of the 39 margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified at α = 0.10. Let p represent the proportion of all margaritas made by the bartender that have INCORRECT amounts of the three ingredients. Use Table 1. a. Select the null and the alternative hypotheses. [B]H0: p ≤ 0.50; HA: p > 0.50[/B] [B][/B] b. Calculate the sample proportion. (Round your answer to 3 decimal places.) 9/39 = [B]0.231 [/B] c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=9&n=39&ptype=%3C&p=+0.5&alpha=+0.10&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL], we get: [B]Test Stat = -3.36[/B] [B][/B] d. Calculate the critical value. (Round your answer to 2 decimal places.) Using the link above, we get a critical value of [B]1.2816 [/B] e. What is the conclusion? [B]The manager’s suspicion is not justified since the value of the test statistic does not fall in the rejection region. Do not reject H0[/B] [B][/B]

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000. [LIST] [*]h = b + 70 [*]A = 1/2bh = 3000 [/LIST] Substitute the height equation into the area equation 1/2b(b + 70) = 3000 Multiply each side by 2 b^2 + 70b = 6000 Subtract 6000 from each side: b^2 + 70b - 6000 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: b = 50 and b = -120 Since the base cannot be negative, we use b = 50. If b = 50, then h = 50 + 70 = 120 The perimeter is b + h + hypotenuse Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02 Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The price of a baseball glove is no more than $38.95. Let p be the price of the baseball glove. The phrase "no more than" means less than or equal to. Our inequality is: p <= $38.95

The ratio of the measures of the 3 angles of a triangle is 1:2:3. What is the measure of the largest angle in degrees? Let the smallest angle be x. Then we have 3 angles based on the ratio: x, 2x, 3x We know the sum of the angles of a triangle equals 180. So we have: x + 2x + 3x = 180 6x = 180 Divide each side by 6: 6x/6 = 180/6 x = 30 The largest angle is 3(30) = [B]90 [MEDIA=youtube]l8Lc6YtK9dg[/MEDIA][/B]

There are 377 baseball teams at the tournament and each team has 228 players. How many players are at the tournament? Key words are "There are", "each team", and "how many". We multiply teams by players per team to get number of players. 377 * 228 = [B]85,956[/B]

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What is the base 10 number 100 in base 7? Using our [URL='https://www.mathcelebrity.com/binary.php?num=100&check1=7&bchoice=7&pl=Convert']base change calculator[/URL], we see that: 100 in base 10 = [B]202[/B] in base 7

Which of the following is the probability that subjects do not have the disease, but the test result is positive? a. Miss rate b. False positive rate c. Base rate d. Disease rate [B]b. [URL='http://sites.stat.psu.edu/~lsimon/stat250/sp00/solutions/misc/diagtests.htm']False positive rate[/URL][/B]

Yesterday, Boris had 144 baseball cards. Today, he got m more. Using m, write an expression for the total number of baseball cards he has now. 144 and m more means we add [B]144 + m[/B]

Yesterday, Kareem had n baseball cards. Today, he got 9 more. Using n, write an expression for the total number of baseball cards he has now. 9 more means we add 9 to n [B]n + 9[/B]

Youre setting sales goals for next month. You base your goals on previous average sales. The actual sales for the same month for the last four years have been 24 units, 30 units, 23 units, and 27 units. What is the average number of units you can expect to sell next month? Find the average sales for the last four years: Average Sales = Total Sales / 4 Average Sales = (24 + 30 + 23 + 27) / 4 Average Sales = 104 / 4 Average Sales = [B]26 units[/B]