A candidate for mayor wants to gauge potential voter reaction to an increase recreational services by estimating the proportion of voter who now use city services. If we assume that 50% of the voters require city recreational services, what is the probability that 40% or fewer voters in a sample of 100 actually will use these city services? First, let's do a test on the proportion using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+40&n=+100&ptype=%3D&p=+0.5&alpha=+0.05&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL]: We get Z = -2 Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28z%3C-2%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(z<-2) = [B]0.02275[/B]

A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years? Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the starting value at time t: B(t) = 19,000(1-0.3)^t Simplifying this, we get: B(t) = 19,000(0.7)^t <-- I[I]f an asset decreases by 30%, it keeps 70% of it's value from the prior period[/I] The problem asks for B(4): B(4) = 19,000(0.7)^4 B(4) = 19,000(0.2401) B(4) = [B]4,561.90[/B]

A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]

Free Bond Flat Price-Accrued Coupon-Market Price Calculator - Calculates the flat price, accrued coupon, and market price for a bond between valuation dates using the following methods:
1) Theoretical Method
2) Practical Method
3) Semi-Theoretical Method

CCP Stat Club is sending a delegate of 2 members to attend the 2015 Joint Statistical Meeting in Seattle. There are 10 qualified candidates. How many different ways can the delegate be selected? 10C2 = [B]45[/B] shown on our [URL='http://www.mathcelebrity.com/permutation.php?num=10&den=2&pl=Combinations']Combinations Calculator[/URL]

Free Date and Time Difference Calculator - Calculates the difference between two dates using the following methods
1) Difference in dates using year/month/day/hour/minute/second as the primary unit of time
2) Difference in dates in the form of years remaining, months remaining, days remaining, hours remaining, minutes remaining, seconds remaining.

Free Date Calendar Calculator - Shows a calendar for a month and year

Free Date Information Calculator - This calculator takes a date in mm/dd/yyyy format, and gives the following information about it:
* Weekday
* Day number in the year
* Week number in the year
* Number of days in the month containing that date
* Leap Year (Yes or No)
* Zodiac Sign
* Julian Date

Edna plans to treat her boyfriend Curt to dinner for his birthday. The costs of their date options are listed next to each possible choice. Edna plans to allow Curt to choose whether they will eat Mexican food ($25), Chinese food ($15), or Italian food ($30). Next, they will go bowling ($20), go to the movies ($30) or go to a museum ($10). Edna also is deciding between a new wallet ($12) and a cell phone case ($20) as possible gift options for Curt. What is the maximum cost of this date? Edna has 3 phases of the date: [LIST=1] [*]Dinner [*]Event after dinner [*]Gift Option [/LIST] In order to calculate the maximum cost of the date, we take the maximum cost option of all 3 date phases: [LIST=1] [*]Dinner - Max price is Italian food at $30 [*]Event after dinner - Max price is movies at $30 [*]Gift Option - Max price option is the cell phone cast at $20 [/LIST] Add all those up, we get: $30 + $30 + $20 = [B]$80[/B]

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible? We want 8 choose 5, or 8C5. [URL='http://www.mathcelebrity.com/permutation.php?num=8&den=5&pl=Combinations']Typing this into the search engine[/URL] we get [B]56[/B].

Lois is purchasing an annuity that will pay $5,000 annually for 20 years, with the first annuity payment made on the date of purchase. What is the value of the annuity on the purchase date given a discount rate of 7 percent? This is an annuity due, since the first payment is made on the date of purchase. Using our [URL='http://www.mathcelebrity.com/annimmpv.php?pv=&av=&pmt=5000&n=20&i=7&check1=2&pl=Calculate']present value of an annuity due calculator[/URL], we get [B]56,677.98[/B].

Free Percentage of Completion Calculator - Given a sales price, total costs, and costs per period, this determines the gross profit to date using the percentage of completion method.

Update, this has been added to our shortcuts. You can type any expression in the form, positive numbers less than x where x is any integer. You can also type positive numbers greater than x where x is any integer. Same with less than or equal to and greater than or equal to.

Simplify the monomial in parentheses: 2^3x^2*3y^3 8x^6y^3 Now we update the multiplication: 6x^2y^3(8x^6y^3) 6*8 x^(2 + 6)y^(3 + 3) [B]48x^8y^6[/B] [MEDIA=youtube]rmuDx027gL4[/MEDIA]

Suppose that Candidates A and B have moderate political positions, while Candidate C is quite liberal. Voter opinions about the candidates are as follows. 35% want A as their first choice, but would also approve of B. 31% want B as their first choice, but would also approve of A. 20% want B as their first choice, and approve of neither A nor C. 10% want C as their first choice, and approve of neither A nor B. [LIST=1] [*]If all voters could vote only for their first choice, which candidate would win by plurality? [*]Which candidate wins by an approval vote? [/LIST] [U]Plurality Voting:[/U] [LIST] [*]A: 35% [*]B: 31% + 20% = 51% [*]C: 10% [/LIST] [B]Candidate B wins[/B] using the plurality voting method and a majority [U]Approval Voting:[/U] [LIST] [*]A: 35% + 31% = 2 approvals [*]B: 35% + 31% + 20% = 3 approvals [*]C: 10% = 1 approval [/LIST] Therefore, [B]Candidate B wins[/B] using the approval voting method

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]

Free Unix Time Translation Calculator - Translates a unix time to date and time information

The calculator is updated to handle shortcuts like these.