Math Questions

After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x? A.y-300 = 4(x - 100) B. y+ 300 = 2.5(x + 100) C. y+ 300 = 4(x + 100) D. y 300 = 2.5(x - 100)

Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 4 inches to the volume of a sphere with a radius of 8 inches. The ratio is. (Type an integer or a simplified fraction.)

An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is $13,000. The probability of being awarded the bid is 0.4. If the architect is awarded the bid, she will make $32,500 minus the $13,000 cost for plans and a model. Complete parts a. through b. below. a. What is the expected value in this situation? (Round to the nearest dollar.)

An oil company is considering two sites on which to drill. The sites are described in the following table. Complete parts (a) through (b) below. Site A: Profit if oil is found: $90 million Site B:Loss if no oil is found: $12 million Probability of finding oil: 0.2 Profit if oil is found: $135 million Loss if no oil is found: $25 million Probability of finding oil: 0.1 a. Which site has the larger expected profit? Site A has the larger expected profit. Site B has the larger expected profit. The expected profits for both sites are the same. b. If the expected profit for both sites is not the same, by how much is the expected profit larger? million (Round to the nearest tenth as needed.)

Give the slope of y+2=3(x-7) and a point on the line. A. The slope is 7 and (3, 2) is on the line. B. The slope is 3 and (7, -2) is on the line. C. The slope is 2 and (7,3) is on the line. D. The slope is 3 and (-7, 2) is on the line.

Customers can pick their own blueberries at Blueberry Hill. They pay $5 to enter the patch and $4 per pound for the blueberries they pick. Write an equation to model the total cost, y, for x pounds of blueberries. A. y = 5x +4 B. y = 4x + 5 C. y = x(5+4) D. y = 4(x + 5)

A game is played using one die. If the die is rolled and shows 2, the player wins $10. If the die shows any number other than 2, the player wins nothing. Complete parts (a) through (b) below. a. If there is a charge of $2 to play the game, what is the game's expected value? $(Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. A. This value represents the expected loss over the long run for each game played. B. The player can expect to break even over the long run. C. This value represents the expected win over the long run for each game played.

Construct the dotplot for the given data. A manufacturer records the number of errors each work station makes during the week. The data are as follows. 6323520254201 5 10 → 10 10 10

Answer the question, considering an event to be "unlikely" if its probability is less than or equal to 0.05. Is it unlikely to get 11 when a pair of dice is rolled? Yes No

Watching TV: In 2012, the General Social Survey asked a sample of 1314 people how much time they spent watching TV each day. The mean number of hours was 2.85 with a standard deviation of 2.62. A sociologist claims that people watch a mean of 3 hours of TV per day. Do the data provide sufficient evidence to conclude that the mean hours of TV watched per day is less than the claim? Use the a= 0.05 level of significance and the P-value method with the TI-84 Plus calculator. Part 1 of 4 (a) State the appropriate null and alternate hypotheses. Ho: This hypothesis test is a (Choose one) test. O<O DO X O<O L 0-0 3

TV sets: According to the Nielsen Company, the mean number of TV sets in a U.S. household in 2013 was 2.24. Assume the standard deviation is 1.1. A sample of 90 households is drawn. Part 1 of 5 (a) What is the probability that the sample mean number of TV sets is greater than 2? Round your answer to at least four decimal places. The probability that the sample mean number of TV sets is greater than 2 is 9809 Part: 1/5 Part 2 of 5 (b) What is the probability that the sample mean number of TV sets is between 2.5 and 3? Round your answer to at least four decimal places. The probability that the sample mean number of TV sets is between 2.5 and 3 is

The mathematics department of a college has 14 male professors, 6 female professors, 8 male teaching assistants, and 9 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female. (Type an integer or a fraction. Simplify your answer.) The probability is

The mathematics department of a college has 9 male professors, 9 female professors, 8 male teaching assistants, and 15 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male. (Type an integer or a fraction. Simplify your answer.) The probability is

There are 9 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances? ways (Type a whole number.)

You need to arrange seven of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? ways (Type a whole number.)

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is ud = 0. Compute the value of the t test statistic. Round intermediate calculations to four decimal places as needed and final answers to three decimal places as needed. 29 31 23 27 26 26 34 30 27 27 29 27 27 31 34 29 t = -0.185 t = 0.690 t = -0.523 t = -1.480

Determine whether the quantitative variable is discrete or continuous. the number of bottles of juice sold in a cafeteria during lunch continuous discrete

Calibrating a scale: Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be a=2.0. They weigh this weight on the scale 55 times and read the result each time. The 55 scale readings have a sample mean of x = 1000.6 grams. The scale is out of calibration if the mean scale reading differs from 1000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration. Use the a=0.10 level of significance and the P-value method with the TI-84 calculator. Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses. Ho H₁ This hypothesis test is a (Choose one) test.

Determine the mean, median, mode and midrange of the set of data. 59, 52, 39, 50, 60, 47, 63 The mean is (Round to the nearest tenth as needed.) The median is Select the correct choice below and fill in any answer boxes within your choice. OA. The mode is OB. There is no mode. The midrange is (Use a comma to separate answers as needed.)

Heavy children: Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) taken between 1999 and 2002 reported that the mean weight of six-year-old girls in the United States was 49.3 pounds. Another NHANES survey, published in 2008, reported that a sample of 205 six-year-old girls weighed between 2003 and 2006 had an average weight of 50.2 pounds. Assume the population standard deviation is a = 15.3 pounds. Can you conclude that the mean weight of six-year-old girls in 2006 is different from what it was in 2002? Use the a = 0.05 level of significance and the P-value method with the TI-84 calculator. Part 1 of 4 State the appropriate null and alternate hypotheses. Ho:u= 49.3 H₁: = 49.3 The hypothesis test is a two-tailed ▼test. Part: 1/4 - Part 2 of 4 Compute the P-value. Round your answer to at least four decimal places. P-value=

Use the given data to construct a frequency distribution. Lori asked 24 students how many hours they had spent doing homework during the previous week. The results are shown below. 10 10 10 8 10 10 14 13 10 8 12 10 10 12 10 10 12 10 10 13 10 12 13 8 Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 8 for

Assume that X has a normal distribution, and find the indicated probability. The mean is μ = 60.0 and the standard deviation is o = 4.0. Find the probability that X is less than 53.0. 0.0802 0.9599 0.0401 0.5589

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 8 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen. Not binomial: there are too many trials. Procedure results in a binomial distribution. Not binomial: there are more than two outcomes for each trial. Not binomial: the trials are not independent.

The given tessellation formed by two or more regular polygons is shown. a. Name the type of regular polygons that surround each vertex. b. Determine the number of angles that come together at each vertex, as well as the measures of these angles. c. Use the angle measures from part (b) to explain why the tessellation is possible. 88 a. Choose the correct answer below. OA. triangle, pentagons B. triangles, octagons OC. triangle, dodecagons

Find the standard deviation, o, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 38; p = 0.4 o = 7.14 σ = 6.29 σ = 3.02 σ = 0.61

A circular backyard pool has a diameter of 24 feet and is 3 feet deep. One cubic foot of water has a capacity of approximately 7.48 gallons. If water costs $4 per thousand gallons, how much, to the nearest dollar, will it cost to fill the pool? It will cost approximately $ to fill the pool. (Round to the nearest dollar as needed.)

Assume that a sample of bivariate data yields the correlation coefficient, r, indicated. Use the table on the right for the specified sample size and level of significance to determine whether a linear correlation exists. r=0.81 when n=10 at a = 0.01 Does a linear correlation exist? A linear correlation does not exist. OA linear correlation exists. C4567668 n 9 10 Correlation Coefficient, r α=0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 α = 0.01 0.990 0.959 0.917 0.875 0.834 0.798 0.765

A man earned wages of $33,600, received $1700 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. He was entitled to a personal exemption of $3000 and had deductions totaling $5480. Find his gross income, adjusted gross income, and taxable income. His gross income was $ (Simplify your answer.)

A certain pyramid has a square base measuring 819 feet on a side and a height of 486 feet. a. What is the volume of the pyramid, in cubic yards? b. The stones used to build the pyramid were blocks with an average volume of 1.5 cubic yards. How many of these blocks were needed to construct the great pyramid?

Solve the problem. Round the point estimate to the nearest thousandth. Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 898 people, 46 people had hearing aids. 0.050 0.949 0.049 0.051

A woman is in the 15% tax bracket and itemizes her deductions. How much will her tax bill be reduced if she qualifies for a $300 tax credit? Her tax bill will be reduced by $ (Simplify your answer.)

Lottery: In the New York State Numbers lottery, you pay $2 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.08, and if you win, you win $10, which is a profit of $8. If you lose, you lose $2. Part: 0/2 Part 1 of 2 (a) What is the expected value of your profit? Round the answer to two decimal places. The expected value of profit is

The four sequential sides of a quadrilateral have lengths a = 5.3, b = 7.2, c = 9.7, and d = 10.9 (all measured in yards). The angle between the two smallest sides is a = 116°. What is the area of this figure? area = yd²

When a national sample of heights of kindergarten children was taken, a student was told that she was in the 25th percentile. Explain what that means. Choose the correct interpretation below. A. She is shorter than 25 percent of all kindergarten children. B. She is taller than 75 percent of all kindergarten children. C. She is taller than 25 percent of all kindergarten children. D. She is taller than 25 kindergarten children.

One circular table has a diameter of 8 ft, and another circular table has a diameter of 12 ft. How much greater is the area of the larger table? Round to the nearest whole number. about 31 ft2 about 6 ft2 about 63 ft2 about 13 ft2

Is there a doctor in the house? A market research firm reported the mean annual earnings of all family practitioners in the United States was $178,258. A random sample of 43 family practitioners in Los Angeles had mean earnings of x = $193,010 with a standard deviation of $42,777. Do the data provide sufficient evidence to conclude that the mean salary for family practitioners in Los Angeles is greater than the national average? Use the a= 0.05 level of significance and the P-value method with the TI-84 Plus calculator. Part 1 of 4 State the appropriate null and alternate hypotheses. Ho H₁ : This hypothesis test is a (Choose one) test.

A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. 0.428 0.844 0.484 0

Write the following rate as a simplified fraction. 26 dogs to 34 cats

Determine how much the following individual will save in taxes with the specified tax credits or deductions. Rosa is in the 15% tax bracket and claims the standard deduction. How much will her tax bill be reduced if she makes a $500 contribution to charity? www. Her tax bill will be reduced by $. (Simplify your answer.)

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The amount of time (in hours) that Sam studied for an exam on each of the last five days is given below. Find the mean study time. 1.5 8.3 6.9 1.8 5.3 4.76 hr 23.80 hr 4.96 hr 5.45 hr

Efficient manufacturing: Efficiency experts study the processes used to manufacture items in order to make them as efficient as possible. One of the steps used to manufacture a metal clamp involves the drilling of three holes. In a sample of 95 clamps, the mean time to complete this step was 55.3 seconds. Assume that the population standard deviation is = 12 seconds. Round the critical value to no less than three decimal places. Part 1 of 2 (a) Construct an 80% confidence interval for the mean time needed to complete this step. Round the answer to at least one decimal place. An 80% confidence interval for the mean is < <

In a survey of 2752 adults, 1429 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is 0. (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. B. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. C. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.

A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: A-B-3 C-2 D-1 and F-a Compute the grade point average (GPA) and round the result to two decimal places. 1.37 2.37 9.00 3.46

Write the following number in decimal notation. Seventy-eight hundredths

Find the P-value for the indicated hypothesis test. A random sample of 139 forty-year-old men contains 26% smokers. Find the P-value for a test to reject the claim that the percentage of forty-year-old men that smoke is 22%. 0.2542 0.2802 0.1271 0.1401

Find the P-value for the indicated hypothesis test. Round all proportions and standard scores to two decimal places. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%. 0.9946 0.0045 0.0054 0.0027

A woman eamed wages of $31,200, received $2800 in interest from a savings account, and contributed $3200 to a tax-deferred retirement plan. She was entitled to a personal exemption of $2600 and had deductions totaling $5220. Find her gross income, adjusted gross income, and taxable income.

Write the indicated product in decimal form and round your answer to the nearest thousandth, if necessary.

Use the graph to determine the following. a. the function's domain b. the function's range c. the x-intercepts, if any d. the y-intercept, if any e. the function value indicated below.

Each dimension of a rectangular family room is 3.5 times larger than a rectangular bedroom. If it costs $312 to carpet the bedroom, how much would it cost to carpet the family room with same carpet? $3,822 $1,092 $4,914 $2,184