Math Questions

What is the length of the arc that subtends a central angle of 82° for a circle with a radius of 9 centimeters? Use 3.14 for π when necessary. A. 12.60 cm B. 12.87 cm C. 6.56 cm D. 14.60 cm

A rectangular prism is changed by doubling its length, halving its width, and tripling its height. How will these changes affect its volume? [Hint: draw a picture] A. The volume is multiplied by 6. B. The volume is multiplied by 3. C. The volume is increased by 3. D. The volume is doubled.

4.2.1: You have saved $400, $350, and $340 so far. After your next and final week of saving, you want to have saved an average of $375 per week. How much do you have to save to get a four week average of $375 per week?

A piece of string that is 132 inches long is cut into 3 pieces. The second piece of string is twice as long as the first piece. The third piece of string is three times as long as the first piece. Find the length of the longest piece of string.

Points A and B are on opposite sides of a lake. A point C is 81.3 meters from A. The measure of angle BAC is 78.33°, and the measure of angle ACB is determined to be 34.167°. Find the distance between points A and B (to the nearest meter). A. 54 m B. 49 m C. 35 m D. 25 m

What is the circumference of a circle whose radius is 13? A. 26 B. 13 C. 13π D. 26π

Use the confidence interval to find the estimated margin of error. Then find the sample mean. A biologist reports a confidence interval of (3.5,4.3) when estimating the mean height (in centimeters) of a sample of seedlings.

13. Which steps would transform the parent function f(x) = x to f(x) = -2(x-4)² + 5? a. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the right and up 5 units. b. A stretch by a factor of 2, translate 4 units to the left and up 5 units. c. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the left and down 5 units. d. Reflect across the x-axis, stretch by a factor of 2, translate 4 units to the left and up 5 units.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $90,000 loan. Option 1: a 30-year loan at an APR of 7.65%. Option 2: a 15-year loan at an APR of 7.25%. Find the monthly payment for each option. The monthly payment for option 1 is $638.56. The monthly payment for option 2 is $ 821.58 (Do not round until the final answer. Then round to the nearest cent as needed.) Find the total amount paid for each option. The total payment for option 1 is $ The total payment for option 2 is $ (Use the answers from the previous step. Round to the nearest cent as needed.)

Solve the following system of equations. 5a - 30b= 3 10a + 30c = 34 60b + 20c = 22 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one solution. The solution is (Type integers or simplified fractions.) B. There are infinitely many solutions. The solutions are (, ,c). (Type integers or simplified fractions.) C. There is no solution.

Answer parts a through c based on a study showing that late in the semester, procrastinating students reported more symptoms of physical illness than their nonprocrastinating peers. a. At the beginning of the semester, procrastinators reported an average of 2.75 symptoms, increasing at a rate of 0.35 symptoms per week. Write a function that models the average number of symptoms after x weeks. y= 2.75 +0.35x (Use integers or decimals for any numbers in the expression.) b. At the beginning of the semester, nonprocrastinators reported an average of 3.75 symptoms, increasing at a rate of 0.15 symptoms per week. Write a function that models the average number of symptoms after x weeks. y= 3.75 +0.15x (Use integers or decimals for any numbers in the expression.) c. By which week in the semester did both groups report the same number of symptoms of physical illness? For that week, how many symptoms were reported by each group? By week in the semester both groups reported the same number of symptoms of physical illness. Each group reported symptoms.

In a random sample of 8 people, the mean commute time to work was 36.5 minutes and the standard deviation was 7.2 minutes. A 98% confidence interval using the t-distribution was calculated to be (28.9,44.1). After researching commute times to work, it was found that the population standard deviation is 8.7 minutes. Find the margin of error and construct a 98% confidence interval using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.

A baseball player hit 59 home runs in a season. Of the 59 home runs, 17 went to right field, 21 went to right center field, 8 went to center field, 12 went to left center field, and 1 went to left field. (a) What is the probability that a randomly selected home run was hit to right field? (b) What is the probability that a randomly selected home run was hit to left field? (c) Was it unusual for this player to hit a home run to left field? Explain.

Consider the function f(x) = 7x² - 7x. a.Determine, without graphing, whether the function has a minimum value or a maximum value. b.Find the minimum or maximum value and determine where it occurs. c.Identify the function's domain and its range. a. The function has a value. b. The minimum/maximum value is It occurs at x = c. The domain off is. (Type your answer in interval notation.) (Type your answer in interval notation.) The range of fis

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 146. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of restaurant-purchased meals eaten in a restaurant, the number eaten in a car, and the number eaten at home.

You need a loan of $155,000 to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices. Choice 1: 15-year fixed rate at 5% with closing costs of $2400 and no points. Choice 2: 15-year fixed rate at 4.5% with closing costs of $2400 and 4 points. What is the monthly payment for choice 1? $1,225.73 (Do not round until the final answer. Then round to the nearest cent as needed.) What is the monthly payment for choice 2? $1,185.74 (Do not round until the final answer. Then round to the nearest cent as needed.) What is the total closing cost for choice 1?

12. An object is launched at 19.6 meters per second from a 58.8 meter tall platform. The equation for the object's height s at time t seconds after launch is h(t) = -4.91² + 19.6t+ 58.8, where his in meters. When does the object strike the ground? a. t= -2 sec and t = 6 b. t=0 sec c. t = 2 sec d. t = 6 sec

Use Cramer's rule to solve for y. 2x + 5y + 5z = -15 3x+4y-5z = 17 4x-3y-2z= -21

Use the confidence interval to find the margin of error and the sample mean. (1.62,1.96) The margin of error is 0.17. (Round to two decimal places as needed.) The sample mean is ………..

The coordinates of three vertices of parallelogram ABCD are A(-3,-2), B(0,2), and C(2,2). What are the coordinates of vertex D? A. (1,-2) B. (1,2) C. (-1,2) D. (-1,-2)

Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 80 yd from B and 104 yd from A, with angle ACB measuring 51.2°. How far apart are A and B (to the nearest yard)? A. 82 yards B. 109 yards C. 100 yards D. 101 yards

What is the radius of a circle whose circumference is 36π? A. 36 B. 12 C. 18 D. 9

SW is the diameter of circle C. Point S is located at (6,-1) and point W is located at (10,-7). What are the coordinates of the center of this circle? A. (8,-4) B. (7,-5) C. (9,-3) D. (8, -3)

Give the domain and range of the quadratic function whose graph is described. The vertex is (-8, -7) and the parabola opens down. The domain off is. (Type your answer in interval notation.) The range of the function is (Type your answer in interval notation.)

Find the center of a circle with the equation: x² + y² - 2y - 8x - 19 = 0 A. (4,1) B. (2, 3) C. (3, 4) D. (3,7)

The exponential model A = 520.1e0.006 describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003. The population of the country in 2003 was million.

A nutritionist claims that the mean tuna consumption by a person is 3.2 pounds per year. A sample of 90 people shows that the mean tuna consumption by a person is 2.9 pounds per year. Assume the population standard deviation is 1.21 pounds. At a= 0.07, can you reject the claim? (a) Identify the null hypothesis and alternative hypothesis. A. Ho: μ=3.2 Ha: μ≠3.2 B. Ho: μ> 3.2 Ha: μ≤3.2 C. Ho: μ≠2.9 Ha: μ=2.9 D. Ho: ≤2.9 Ha: μ>2.9 E. Ho: μ> 2.9 Ha: μ≤2.9 F. Ho: ≤3.2 Ha:p>3.2

Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equation y=1.5x+5 intersect the circle with radius 5 and center (0, 5)?

The Tennis Club has 5 new members. Each member buys a racket and a tube of balls. If 6 rackets cost $186.00 and 6 tubes of balls cost $27.00, how much do the 5 people pay for rackets and balls?

The angle of elevation to the top of a Building in New York is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle. A. 496.08 ft² B. 153.45 ft² C. 494.35 ft² D. 107.24 ft²

What is the circumference of a circle (to the nearest whole number) whose diameter is 12? A. 12 B. 19 C. 38 D. 113

If the coordinates of a parallelogram are Q(3, -2), R(7, -2), S(9,3), and T(5,3), the area of the parallelogram is: A. 30 units² B. 10 units² C. 20 units² D. 40 units²

Find the critical value ze necessary to form a confidence interval at the level of confidence shown below. c=0.86 Zc =

When estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? Explain your reasoning. Choose the correct answer below. A. If n ≤30 an interval estimate is more accurate. If n > 30 a point estimate is more accurate. B. You are more likely to be correct using a point estimate because an interval estimate is too broad and contains many possible values. C. You are more likely to be correct using an interval estimate because it is unlikely that a point estimate will exactly equal the population mean. D. There is no difference between an interval estimate and a point estimate in terms of accuracy.

What is the number of square units in the area of the triangle whose vertices are points A(2,0), B(6,0), and C(8,5)? A. 30 units² B. 6 units² C. 15 units² D. 10 units²

Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance a, and sample size n. Two-tailed test, a=0.02, n=17

4. A Ferris wheel with a diameter of 40 m rotates every 40 seconds. A passenger gets on at a point 1 m above the ground. a) Sketch a graph showing the passenger's height during the first rotation. Be sure to label important numbers along each axis. b) Write an equation which expresses the height of the passenger with respect to time in seconds.

Suppose you want to borrow $95,000 and you find a bank offering a 20-year loan with an APR of 5%. a. Find your regular payments if you pay n = 1, 12, 26, 52 times a year. b. Compute the total payout for each of the loans in part (a). c. Compare the total payouts computed in part (b). a. The payment for n = 1 would be $ 7,623.05. The payment for n = 12 would be $ 626.96. The payment for n = 26 would be $289.18. The payment for n = 52 would be $144.55. (Do not round until the final answer. Then round to the nearest cent as needed.) b. For n = 1, the total amount paid is $, for n = 12, the total amount paid is $, for n = 26, and for n = 52, the total amount paid is $ the total amount paid is $ (Round to the nearest dollar.)

Among all pairs of numbers whose sum is 20, find a pair whose product is as large as possible. What is the maximum product?

A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume? Radius= Height =

Find the minimum sample size n needed to estimate µ for the given values of c, σ, and E. c=0.95, σ=6.4, and E= 2 Assume that a preliminary sample has at least 30 members.

Consider a student loan of $17,500 at a fixed APR of 9% for 25 years. a. Calculate the monthly payment. b. Determine the total amount paid over the term of the loan. c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest. a. The monthly payment is $ (Do not round until the final answer. Then round to the nearest cent as needed.)

Two four-sided dice with sides numbered from 1 through 4 are tossed. What is the sample space for the sum of the two dice? a. {4} b. {1, 2, 3, 4) c. {2, 3, 4, 5, 6, 7, 8} d. {1, 2, 3, 4, 5, 6, 7, 8)

Write the following number in decimal notation. Ninety-two and seven hundredths

Which sets of points represent one-to-one functions? Select all the correct answers. f= {(1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,8)} g = {(1,2), (3,3), (5,4), (7,4), (9,4), (11,4), (13,4), (17,4)} h = {(1,6), (2,3), (3,16), (4,21), (5,27), (6,36), (7,48), (8,56)} i= {(0,1), (1,3), (3,5), (5,3), (7,4), (9,6), (11,9), (13,10)} j = {(2,6), (4,16), (6,26), (8,36), (10,16), (12,56), (14,66), (16,16)} k={(2,6), (4,16), (6,26), (8,36), (10,46), (12,56), (14,66), (16,76)}

If all other quantities remain the same, how does the indicated change affect the width of a confidence interval? (a) Increase in the level of confidence (b) Increase in the sample size (c) Increase in the population standard deviation

Approximate the area under the graph of F(x) = 0.9x³ +9x² -0.9x-9 over the interval [-6, -1] using 5 subintervals. Use the left endpoints to find the heights of the rectangles. The area is approximately square units.

Find the center of a circle with the equation: x² + y² + 10x - 16y + 75 = 0 A. (5,-8) B. (8,5) C. (5,8) D. (-5, 8)

For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. Choose the correct answer below. 99%, because as the level of confidence increases, Zc decreases. 90%, because as the level of confidence decreases, zo increases. 90%, because as the level of confidence decreases, Zc decreases. 99%, because as the level of confidence increases, zc increases.