Basic Math Questions and Answers

If 0 ≤ θ < 2π and 1 - 7cos θ = 8, determine the values of θ. Enter your answer(s) in radians. If necessary, separate multiple values by commas.

Samir is preheating his oven before using it to bake. Samir created the following linear graph to predict the final temperature after a minutes. What is the meaning of the point (1,90)?

In what form is the following quadratic function? f(x) =3x²-7x+4 Vertex Form Standard Form Maximum Form Intercept Form

What is the image point of (2, 9) after the transformation T-1,-4° ry=x ?

For each pair of functions and g below, find f(g(x)) and g(/(x)). Then, determine whether fand g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the compos You do not have to indicate the domain.)

Teagan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

Subtract the following rational expressions and make sure to state the restrictions on the variable:

Brent Pickett borrowed $3000 from his brother Dave. He agreed to repay the money at the end of 4 years, giving Dave the same amount of interest that he would have received if the money had been invested at 3.75% compounded quarterly. How much money did Brent repay his brother?

Use the present value formula to determine the amount to be invested now, or the present value needed. The desired accumulated amount is $85,000 after 10 years invested in an account with 6% interest compounded semiannually. The amount to be invested now, or the present value needed, is $ (Round to the nearest cent as needed.)

Use the compound interest formula to compute the total amount accumulated and the interest earned. $2500 for 3 years at 6% compounded quarterly

If P(E)= 0.19, find the odds against E. What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are to (Type integers or decimals.) B. The odds are (Type an integer or a decimal.)

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Wind farms are a source of renewable energy found around the world. The power P (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second). If a turbine generates 500 kW in a 10 m/s wind, how much power does it generate in a 12 m/s wind?

Match each of the following equations according to their slope and y-intercept. y=-1.5x-4 m = -1.5, b = -4 y = 3x m = -3, b = 4 y = 1.5x-7 m = 0, b = 7 y=-3x+4 m = 3, b=0 y=7 m = 1.5, b = -7

Find the average value of the function f over the interval [0, 10]. f(x)=5/x+1

Enter the next three numbers of the repeating decimal produced by the fraction 3/9. 0.333333...

A large snowball is melting so that its radius is decreasing at the rate of 4 inches per hour. How fast is the volume decreasing at the moment when the radius is 5 inches? [Hint: The volume of a sphere of radius r is V = 7³.] (Round your answer to the nearest integer.)

The function h (t) = -25 cos(4nt) + 29 represents the height above the ground of a chair on a Ferris Wheel where t=0 represents the time the ride started. If h(t) is in feet and t is in minutes, answer the following: Be sure to include units and justify your answers. A. How long does it take to complete one full revolution? B. What is the highest point on the ride? C. If the ride stops after 15 seconds, how high is the chair above the ground? D. What is the radius of the Wheel?

Write a rule for 9 described by the transformations of the graph of f(x) = x² A vertical stretch by a factor of 3 and a reflection in the x-axis, followed by a translation 5 units down. a. g(x) = 3x² + 5 b. g(x) = (-3x)² - 5 c. g(x) = (3x)² - 5 d. g(x) = -3x² - 5

Solve the following inequality. (x - 1)(x-2)(x-4) ≤0 The solution is (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.)

Nick's telephone company charges $0.04 per minute for weekend calls and $0.08 per minute for calls made on weekdays. This month Nick was billed for 627 minutes. The charge for these minutes was $37.84. How many minutes did he talk on weekends and how many minutes did he talk on weekdays?

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by S = 405, 000e-0.32, where S is the weekly sales and is the number of weeks that have passes since the end of the sales promotion. Round each answer to 2 decimal places. a) What will the sales 5 weeks after the end of the promotion? $ b) How many weeks after the end of the promotion will sales drop below 15,000, if no new campaign is started?

For states that cover a particular region, the average poverty rate in 2013 was 12.84% with a standard deviation of 1.54%. A second source found that for these states, the average poverty rate in 2013 was 13.66% with a standard deviation of 3.31%. Which set of data has more relative variability? What is the coefficient of variation for the first data set? CV = % (Round to one decimal place as needed.) What is the coefficient of variation for the second data set? CV= % (Round to one decimal place as needed.)

An alligator's tail length is proportional to its body length. An alligator with a body length of 4.6 feet has a tail length of 5.1 feet. What is the tail length of an alligator whose body length is 8.4 feet? Complete the proportion below, where the ratios are tail length to body length. x/ = (Do not simplify.) .... The tail length of an alligator whose body length is 8.4 feet is approximately feet. (Round to two decimal places as needed.)

How many ways can a student pick five questions from an exam containing nine questions? There are ways to pick five questions from an exam containing nine questions. Part 2 of 2 How many ways are there if he is required to answer the first question and the last question? There areways if he is required to answer the first question and the last question.

Let the graph of g be a translation 2 units to the left and 6 units up of the graph of f(x)=(x-4)² - 4. Identify the vertex of the graph of 9. a(-2,2) b(6,2) c(2, 2) d(2,6)

A bus travels two different routes: the Green Route and the Blue Route. The routes are diferent lengths. . On Monday the bus traveled the Green Route 6 times and the Blue Route 5 times, traveling a total of 52 miles. On Tuesday the bus traveled the Green Route 12 times and the Blue Route 13 times, traveling a total of 119 miles. What is the length of the Green Route in miles? O F 4.4 mi H 6.4 mi G 4.5 mi • ) 6.8 mi

Divide the following rational expression and state the restrictions on the variable: I²-25 4x = x+5 81² O 2x(x - 5), x = 0 O 2x(x - 5), no restrictions O 2x(x - 5), x = -5,0,5 O 2x(x - 5), x = -5,0

In Exercises 50-160, find the focus and directrix of the parabola with the given equation. Then graph the parabola. 5. y² = 16x 6. y² = 4x 7. y² = -8x 8. y² = -12x 9. x² = 12y 10. x² = 8y 11. x² = -16y 12. x² = -20y

Solve the following expression when k = 12 and v= 6 V + 5 - 4v + 12

Rocket League Incorporated finds that the cost of producing a rocket cars costs C(x) = 200x + 1500. The revenue function is R(x) 500x 5x2, where R is the revenue (in dollars) at which exactly a rocket cars will be sold. Find the quantity Rocket League should produce to maximize profit. Also find the maximum profit. (Recall Profit= Revenue - Cost)

A clerk's weekly salary varies directly with the number of hours he works. For 12 hours of work, the clerk earns $114 How much will he earn for 19 hours of work? The steps to solve this problem were written on note cards below, but they got mixed up.

Your friend states that quadratic functions with the same x-intercepts have the same equations, vertex, and axis of symmetry. Is your friend correct? Explain your reasoning. (2 points)

Solve the following inequality for n. Write your answer in simplest form. n 13 6n −(n+1) < 3n −2+5n Submit Answer

Determine the remaining sides and angles of the triangle ABC. a = 150 m, A = 33° 54', C = 24° 34' What is the measure of angle B? B = 121 32 What is the length of side b? b= m (Do not round until the final answer. Then round to the nearest meter as needed.)

A bag contains 1 gold marbles, 6 silver marbles, and 24 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $3. If it is black, you lose $1. What is your expected value if you play this game? S

Considering only the values of 3 for which sec 3(1 + cos 6) (1 - cos 3) is defined, which of the following expressions is equivalent to sec 3(1 + cos 6) (1 - cos 3)? Select the correct answer below: 0 1 O sec ßtan B O cos B O sec B O sin ßtan B

You have 550-grams of an an unknown radioactive substance that has been determined to decay according to D(t) = 550e-0.006359-t where t is in years. How long before half of the initial amount has decayed? It will take amount to decay. (Round to 1 decimal place) years for half of the initial

Solve the following for 0, in radians, where 0 ≤ 0 < 2T. Enter your answers in radians, rounded to two decimal places. Provide your answer below: 0 = = -4 sin² (0)-7 sin(0)+7= 0 and 0 =

Karen Gaines invested $12,000 in a money market account with an interest rate of 3.25% compounded semiannually. Six years later, Karen withdrew the full amount to put toward the down payment on a new house. How much did Karen withdraw from the account? Karen withdrew $ (Round to the nearest cent as needed.)

The Mendez family is going to see a play. Adult tickets cost $9 and children's tickets cost $6. There are 6 people in the family, and they spend a total of $48 on tickets. Which system of equations can be solved to determine a, the number of adult tickets, and c, the number of children's tickets?

A youth sports league held various fundraisers. They received $320 from a car wash, $209 from a bake sale, and $554 from a used equipment sale. The league decides to invest this money in a 5 year CD that pays 2.5% interest compounded daily. How much will the league receive from the CD in 5 years? The league will have $ in this account after 5 years. (Round to the nearest cent as needed.)

A simple formula can help you estimate the number of years required to double your money. It's called the rule of 72. You simply divide 72 by the interest rate (without the percent sign). For example, with an interest rate of 4%, your money would double in approximately 72+4, or 18 years. Complete parts (a) through (e). a) How many years would it take $1000 to double at an interest rate of 2%? years

You mix soda water, fruit punch concentrate, and ginger ale in the ratio of 1: 2:5 to make fruit punch. How many pints of each ingredient should you use to make 4 gallons of fruit punch?

Find the number of distinguishable permutations of the given letters "AAABBBCD". Your answer is:

Which function represents the widest parabola? a y = -x² +6 b y=x²-5 c y = 0.5(x - 1)² + 1 d y = 2(x+3)²

In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function 7(t) = 53-2.8t+ 0.43t2 -0.018³. Find the average temperature during the period from 9 AM to 9 PM. (Round your answer to one decimal place.) X °F Submit Answer

A metal circular disk whose area is 143 cm² is used as a knockout on an electrical service in a factory. Use your calculator value of 7 to find the radius of the disk to the nearest tenth of a centimeter.

Complete the factored form. 12x²² +4x-5=(6x+5)( ) 12x² + 4x-5 = (6x+5))

Question 4 A tree is 8.5 feet high. A shrub is 2 feet high. If the tree is depicted as 3 inches in a scaled drawing, the shrub should be how many inches? O O 0.55 1.03 0.71 2.61

To help pay for new costumes for a play, a theater invests $1100 in a 42-month CD paying 2.5% interest compounded monthly. Determine the amount the theater will receive when it cashes in the CD after 42 months. The theater will receive $ when it cashes in the CD. (Round to the nearest cent as needed.)