Math Questions

Simplify cos(11t) + cos(5t)/sin(11t)+ sin(5t) to an expression involving a single trigonometric function.

Choose the best answer. The diagonals of a square: A. are the same length and Intersect at different angles B. are the same length and Intersect at a right angle C. do not bisect each other and Intersect at right angles D. bisect each other at different angles

NASA is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before launch, and has a diameter of 4.7 feet, what is the total weight in pounds of the satellite on Earth? Use π = 3.14. A. 950 lbs B. 921 lbs C. 774 lbs D. 815 lbs

Company A pays $24,500 yearly with raises of $1,700 per year. Company B pays $28,500 yearly with raises of $850 per year. Which company will pay more year 10? How much more? Which company pays more in year 10? Both companies pay the same. Company B pays more. Company A pays more. There is not enough information.

A sample of Freon-12 (CF₂Cl₂) occupies 10.0 L at 365 K and 111.40 kPa. Find its volume at STP.

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. 5x + 17y + 4z = 14 2x + 7y+ 3z=-6 x + 3y - 2z = 2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution set is {( )}. (Simplify your answers.) B. There are infinitely many solutions. The solution set is {( , , z)}, where z is any real number. (Type expressions using z as the variable. Use integers or fractions for any numbers in the expression.) C. There is no solution. The solution set is Ø.

The formulas below are the cost and revenue functions for a company that manufactures and sells small radios. C(x) = 70,000+32x and R(x) = 39x a. Use the formulas shown to write the company's profit function, P. from producing and selling x radios. b. Find the company's profit if 17,000 radios are produced and sold. a. The company's profit function is P(x) = (Simplify your answer.)

Roberto's train runs every 45 minutes. If he arrives at the train stop at a random time, what is the probability that he will have to wait at least 30 minutes? Round to the nearest percent. A. 75% B. 67% C. 50% D. 33%

If the equation y = 4(2) is plotted on a semilog scale graph, then the linearized equation will be log(y) = mx + b where

Solve sin(6x) cos(9x) - cos(6x) sin(9x) = -0.7 for the smallest positive solution. Give your answer accurate to two decimal places.

Consider the standard form of the equation x²/25 + y²/36 = 1 The value of a² is, so the y-intercepts are The graph passes through the ordered pairs which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs The value of a² is, so the y-intercepts are The graph passes through the ordered pairs , which are the vertices. The value of b² is, so the x-intercepts are The graph passes through the ordered pairs

A sports recreation company plans to manufacture a beach ball with a surface area of 7238 in². Use the formula A = 4r, to find the radius of the beach ball. A represents the surface area r represents the radius of the sphere a. 24 in b. ±24 in c. 288 in d. 576 in

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.)