Math Questions

Convert the equation to standard form by completing the square on x or y. Then find the vertex, focus, and directrix of the parabola. Finally, graph the parabola. x² +10x-4y+5=0

The mean annual tuition and fees for a sample of 10 private colleges was $36,000 with a standard deviation of $4900 A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $37,900. State a conclusion regarding H0. Use the a = 0.10 level of significance. A) Reject H0. The mean annual tuition and fees appears to be different from $37,900. B) There is not enough information to draw a conclusion. C) Do not reject H0 There is insufficient evidence to conclude that the mean annual tuition and fees is different from $37,900.

Let the sample space be S=(1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E="an odd number less than 10."

Let the sample space be S= (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Suppose the outcomes are equally likely. Compute the probability of the event E={3, 5, 9}

Convert the degree measurement to radians. Express answer as multiple of π: 45° A.π/5 B. π/4 C. π/6 D.π/3

Suppose you have the following three student loans: $12,000 with an APR of 8.5% for 15 years, $17,000 with an APR of 9% for 20 years, and $14,500 with an APR of 10% for 10 years. a. Calculate the monthly payment for each loan individually. b. Calculate the total you'll pay in payments during the life of all three loans. c. A bank offers to consolidate your three loans into a single loan with an APR of 9% and loan term of 20 years. What will your monthly payments be in that case? What will you total payments be over the 20 years? a. The monthly payment of the $12,000 loan is $118.17. The monthly payment of the $17,000 loan is $152.95. The monthly payment of the $14,500 loan is $ 191.62. b. The total you'll pay in payments during the life of all three loans is $.

Water weighs 62.4 pounds per cubic foot. How much does the water in a tank that measures 7 ft x 4 ft x 9 in, weigh? A. 1,310 lbs B. 1,316 lbs C. 1,573 lbs D. 1,574 lbs

Which of the following statements is false? A. The diagonals of a rectangle are perpendicular. B. The base angles of an isosceles trapezold are congruent. C. A quadrilateral is a polygon with four angles. D. The dlagonals of a rhombus are perpendicular and bisect each other.

A bag contains four red marbles, three blue marbles, and three yellow marbles. You randomly pick three marbles without replacement. The first marble is red, the second marble is blue, and the third marble is red. Find the probability of this occuring. A. 25/546 B. 1/96 C. 1/20 D. 1/256

In a random sample of six people, the mean driving distance to work was 24.1 miles and the standard deviation was 7.5 miles. Assuming the population is normally distributed and using the t-distribution, a 95% confidence interval for the population mean μ is (16.2, 32.0) (and the margin of error is 7.9). Through research, it has been found that the population standard deviation of driving distances to work is 6.3. Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, find the margin of error and construct a 95% confidence interval for the population mean μ. Interpret and compare the results.

A sample of sulfur hexafluoride gas occupies 7.97 L at 242°C. Assuming that the pressure remains constant, what temperature (in °C) is needed to reduce the volume to 3.18 L? Report your answer to the proper number of significant figures.

Find the area of a triangle with legs that are: 15 m, 25 m, and 20 m. A. 150 m² B. 42.4 m² C. 106.1 m² D. 38.2 m²

If each interior angle of a regular polygon measures 108°, how many sides does it have? A. 6 sides B. 5 sides C. 7 sides D. 10 sides

If the diameter of a sphere is 4 ft, then what is its surface area? Leave your answers in terms of π A. 14π m² B. 16 m² C. 2π m² D.16π m²

Enter your answer in the provided box. A 86-L sample of dry air cools from 107°C to -24°C while the pressure is maintained at 2.88 atm. What is the final volume?

A line segment that goes from one side of the circle to the other side of the circle and doesn't go through the center is: A. a secant B. a diameter C. a tangent D. a chord

A sandwich shop offers a choice of 5 meats, 3 cheeses, and 4 different breads. How many different combinations of sandwiches are there to choose from which contain one kind of meat, one kind of cheese, and one type of bread? a. 12 b. 15 c. 28 d. 60

You just bought an aquarium for your fish, which is 39.75 inches wide and 11.375 inches deep. The salesman told you to keep the water 2 inches from the top of the tank so the filter to works properly. If the tank is 14 inches high, how many cubic inches of water will it contain once it's filled? A. 5,426 in³ B. 5,087 in³ C. 4,688 in³ D. 5,552 in³

oblems A plumber wishes to cut a piece of pipe 32 inches long into two parts so that the larger part is 4 inches less than three times the smaller part. What are the lengths of the two parts of the pipe?

The half-life of the radioactive element unobtanium-41 is 20 seconds. If 178 grams of unobtanium-41 are initially present, how many grams are present after 20 seconds? 40 seconds? 60 seconds? 80 seconds? 100 seconds?

You have a choice between a 30-year fixed rate loan at 3.5% and an adjustable rate mortgage (ARM) with a first year rate of 2%. Neglecting compounding and changes in principal, estimate your monthly savings with the ARM during the first year on a $175,000 loan. Suppose that the ARM rate rises to 11.5% at the start of the third year. Approximately how much extra will you then be paying over what you would have paid if you had taken the fixed rate loan? What is the approximate monthly savings with the ARM during the first year?

Casey buys a bracelet. She pays for the bracelet and pays $0.72 in sales tax. The sales tax rate is 6%. What is the original price of the bracelet, before tax?

A stained glass window is going to be installed in a semi-circular opening, which is above a 30 inch wide door. If the stained glass window costs $1.40 per square inch, how much will the window cost? Use 3.14 for π as necessary. A. $494.55 B. $1,724.17 C. $389.10 D. $989.10

Find the area of a triangle with legs that are: 9 mm, 6 mm, and 12 mm. A. 12.3 mm² B. 11.6 mm² C. 37 mm² D. 26.1 mm²

The domain, range, and Intercepts of a function are shown. Which set of Information could be characteristics of the function's Inverse? domain: x≥-1 y-Intercept: (0,-1) range: y≥-2 x-intercept: (1,0) A. domain: x= -1; range: y = -2; y-intercept: (0,-1); x-intercept: (1,0) B.domain: x= -2; range: y=-1; y-intercept: (0,1); x-intercept: (-1,0) C.domain: x ≥ 1; range: yz 2; y-intercept: (0,1); x-intercept: (-1,0) D.domain: x= -1; range: ye -2; y-intercept: (1,0); x-intercept: (0,-1)

The half-life of the radioactive element unobtanium-37 is 5 seconds. If 80 grams of unobtanium-37 are initially present, how many grams are present after 5 seconds? 10 seconds? 15 seconds? 20 seconds? 25 seconds? The amount left after 5 seconds is 40 grams. The amount left after 10 seconds is grams.

Enter your answer in the provided box. A sample of carbon monoxide occupies 7.36 L at 296.0 K and 772 torr. Find its volume at -47°C and 417 torr.

Enter your answer in the provided box. If 1.97 × 10-3 mol of argon occupies a 96.3-mL container at 31°C, what is the pressure (in torr)?

Use a graphing utility that gives a matrix in a row-echelon form or a matrix in a reduced row-echelon form, if available, to solve the system of equations given to the right. {3a-b+4c = 1 {2a-b+5c= -3 {a+2b-3c= 2

Solve using the elimination method. Also determine whether the following system is consistent or inconsistent and whether the equations are dependent or independent. 12x - 10y = 3 6x - 5y = 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is one solution. The solution of the system is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions of the form (x.). (Simplify your answer.) C. There is no solution. Choose the correct type of solution below. consistent and dependent consistent and independent inconsistent and independent

Enter your answer in the provided box. A sample of sulfur hexafluoride gas occupies 7.97 L at 242°C. Assuming that the pressure remains constant, what temperature (in °C) is needed to reduce the volume to 3.18 L? Report your answer to the proper number of significant figures.

Find the circumference given the area =437.4 in². Use 3.14 for π as necessary. A. 74.1 in B. 76 in C. 75.4 in D. 77.9 in

In a random sample of eight cell phones, the mean full retail price was $449.00 and the standard deviation was $225.00. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean u. Interpret the results.

Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 17 mortgage institutions, the mean interest rate was 3.45% and the standard deviation was 0.38%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a normal distribution because n∠30 and the interest rates are normally distributed. B. Use a normal distribution because the interest rates are normally distributed and σ is known. C. Use a t-distribution because it is a random sample, σ is unknown, and the interest rates are normally distributed. D. Use a t-distribution because the interest rates are normally distributed and σ is known. E. Cannot use the standard normal distribution or the t-distribution because σ is unknown, n<30, and the interest rates are not normally distributed.

Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,30); Directrix: y=-30 The equation of the parabola is

Jose wants to cover his rectangular bathroom floor in tile. The floor measures 3 units by 5 units. Each tile is 1 square unit and costs $4. How much will it cost Jose to cover his entire bathroom floor in tile? Choose 1 answer: A $15 B $20 C $45 D $60

Jack wants to plant a border of flowers in the shape of an arc along the edge of a circular walkway. If the circle has a radius of 5 yards and the angle subtended by the arc measures 1.5 radians, what is the length of the curved border? A. 5 yds B. 7.5 yds C. 2 yds D. 0.5 yds

The weight of an organ in adult males has a bell-shaped distribution with a mean of 350 grams and a standard deviation of 45 grams. Use the empirical rule to determine the following. (a) About 95% of organs will be between what weights? (b) What percentage of organs weighs between 305 grams and 395 grams? (c) What percentage of organs weighs less than 305 grams or more than 395 grams? (d) What percentage of organs weighs between 260 grams and 485 grams? (a) and grams (Use ascending order.)

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.