Basic Math Questions and Answers

If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from your starting point? Round your answer to the nearest tenth of a mile. If a 12-foot ladder is leaned against the top of a 10-foot high wall, how far will the base of the ladder be from the bottom of the wall? Round your answer to the nearest tenth of a foot.

Cabinet X costs $60, requires 12 sq ft of floor space, and holds 24 cu ft of files. Cabinet Y costs $50, requires 6 sq ft of floor space, and holds 24 cu ft. To get maximum storage, how many of each should be purchased with a budget limit of $600 and floor space of 96 sq ft?

Which of the following is true about the graph of f(x) = 6x³ - 12x² + 6x - 7? a) f(x) has a local minimum at the point (1/3 , -55/9) b) f(x) is decreasing on the interval (1/3, 1). c) f(x) has a local maximum at the point (1, -7). d) f(x) is increasing on the interval(2/3 ,infinity) e) f(x) has a point of inflection at the point (1, -7).

For a given input value x, the function h outputs a value y to satisfy the following equation. 6x + y = 4x + 11y Write a formula for h(x) in terms of x. h(x) =

Christine is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges an initial fee of $77.50 and an additional 30 cents for every mile driven. Company B charges an initial fee of $45 and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.

Identify the transformation equation below for the following function: f(x) = x²→ shifted 2 units right & up 2 units Select one: a. f(x) = (x + 2)² + 2 b. f(x) = (x - 2)² + 2 c. f(x) = (2x)² - 2 d. f(x) = 2(x)² +2

Simplify the following rational expression by subtracting, then identify the simplified form below. 6/x2-1 - 3/x+1 Select one: a. x²+1 / (x-3)(x+3) b. 3x²/ (x-1)(x+1) c. x-3 / (x²-1)(x²+1) d. -3x+9 / (x-1)(x+1)

List the roots of the parabola: y = -x² + 20x - 7 In other words, list the solutions of the equation: 0= -x² + 20x - 7 x= Your answers must be in exact form, do not give their decimal values. Separate multiple roots with a comma.

This polynomial is not factorable, so you need to use the complete the square method. Solve the equation for x. x² + 2x - 12 = 0

An exponential function f(x) = ab^x passes through the points (0, 4000) and (3, 108). What are the values of a and b? a = b=

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.) y = 18(1.15)^x y = 18(0.15)^x y = 20.7(1.15)^x y = 20.7(0.15)^x

Write an expression that represents the total cost of making roughly 16 coffees at home and occasionally going to Starbucks (use x to represent the number of mochas). What does each part of your expression represent? Don't forget to define your variable.

Mr. Parker had $86 to buy school supplies for his class. He bought 32 boxes of pencils and 32 packages of notebook paper. Each package of paper cost $1.09, and each box of pencils cost $0.75. How much money did Mr. Parker have left?

f(x)=√(x-4) Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.

Greg is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A has no initial fee but charges 70 cents for every mile driven. Company B charges an initial fee of $55 and an additional 20 cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m.

Bloomington is a growing industrial town. Every year, the level of CO₂ emissions from the town increases by 6%. If the town produced 186,000 metric tons of CO₂ this year, how much will be produced 5 years in the future? If necessary, round your answer to the nearest whole number.

The rabbit population in a forest area grows at the rate of 9% monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use y-160(2.7)^0.09t 481 455 468 467

You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business, how much it will cost you to make each item, and how much you're going to charge for each item. Research something that would be reasonable to make and sell with the start- up investment you have determined. a. What is the total amount of money you are willing to invest in this business? b. What item are you going to make and sell? Why? c. Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for? d. Do you think your business will be profitable? Explain your answer.

A geneticist conducts an experiment with peas, one sample of offspring consisted of 458 green peas and 149 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green. Report the answer as a percent with one decimal place accuracy. (You need not enter the "%" symbol) Probability Is the result reasonably close to the value of 3/4 that was expected? yes no

Raina is choosing between two exercise routines. In Routine #1, she burns 21 calories walking. She then runs at a rate that burns 10.25 calories per minute. In Routine #2, she does only running, burning 15.5 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3 mph greaterbthan the speed of the eastbound train. After 3.5 hours, they are 567 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions. AnswerHow to enter your answer (opens in new window) westbound train: eastbound train:

James receives a gross pay of $1,550 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive.

A fish tank of 82 fish is made up of three types of fish. There are 41 betta fish, 18 goldfish and some rainbow fish. How many rainbow fish are in the tank?

Amanda is earning extra money over the summer mowing lawns around her neighborhood. She would like to earn at least $450. She charges $15 for a small yard and $26 for a larger yard. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. . x = the number of small yards mowed . y = the number of larger yards mowed 15x - 26y> 450 26x + 15y > 450 15x + 26y ≥ 450 15x + 26y≤ 450

Kenneth invested his savings in shares of a new company. The company's share price dropped by $1.00 at the end of the first year, and by a further $0.75 at the end of the second year. The share price was $21.63 at the end of the second year. a. Calculate the original share price (at the beginning of the first year). b. Calculate the percent change in the share price over the two-year period.

Marwin is selling handmade toys in an online craft boutique. She hopes to earn more than $150 by selling toy planes for $8 each and toy tractors for $12 each. Use the following variables to write an inequality that represents the scenario. . x = the number of toy planes . y = the number of toy tractors

Vail Ski Shop received a $1,210 invoice dated July 17 with 3/10, 2/15, n/60 terms. On July 31, Vail sent a $494 partial payment. a. What credit should Vail receive? (Round your answer to the nearest cent.) b. What is Vail's outstanding balance? (Round your answer to the nearest cent.)

Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below. y = − x + 4

A video rental company offers a plan that includes a membership fee of $5 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $25 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? Write a system of equations, graph them, and type the solution.

Macy of New York sold LeeCo. of Chicago office equipment with a $7,100 list price. Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?

G. Zach deposited $3,000 in a new account at his bank. The bank pays 7.5% interest compounded annually on this account. Zack makes no additional deposits or withdrawals. What will be the balance of Zack's account at the end of 3 years?

There are a total of 19,153 IRSC students, 61% of which are under the age of 22. In a random sample of 655 students, 68% are found to be under the age of 22. Determine how many students in the population and the sample, respectively, are under the age of 22. Round solutions to the nearest whole number, if necessary. IRSC students are under the age of 22. students in the random sample of 655 IRSC students are under the age of 22:

Verizon offers to sell cellular phones listing for $100.24 with a chain discount of 15/10/5. Cellular Company offers to sell its cellular phones that list at $103.49 with a chain discount of 25/5. If Irene is to buy six phones, how much could she save if she buys from the lower-priced company? (Do not round intermediate calculations. Round all dollar amounts to the nearest hundredth. Round your final answer to the nearest cent.)

How did advances in physics and chemistry dramatically change manufacturing? made large multinational companies possible forced companies to share control of the production process employed fewer workers created research and development divisions

In 2004, the highest spaceplane flight was made in SpaceShipOne. A flight with this altitude can be modeled by the function below, where h is the altitude in meters and t is flight time in seconds. Approximately how long did the flight last? h(t) = -0.17t² + 187t +61,000 t≈1101.3 seconds t≈1363 seconds t≈261.7 seconds t≈1596 seconds

Victoria invests $300 into an account with a 2.5% interest rate that is compounded semiannually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar.

The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science fiction books to the number of biographies is 4: 5. If there are 48 science fiction books, find the total number of books.

Two cities have nearly the same north-south line of 97° W. The latitude of the first city is 27° N, and the latitude of the second city is 37° N. Approximate the distance between the cities if the average radius of Earth is 6400 km. The cities are approximately (Round to the nearest integer as needed.) kilometers apart.

An astronaut is returning to Earth in a spacecraft. If the spacecraft is descending at a rate of 13.81 kilometers per minute, what will be its change in height after 51/2 minutes? Round your answer to the nearest kilometer. 76 km -76 km 760 km -760 km

The function fis defined as follows. f(x) = -x² +6 If the graph of fis translated vertically downward by 3 units, it becomes the graph of a function g. Find the expression for g (x).

Angle is in standard position and (-6, -4) is a point on the terminal side of θ What is the exact value of secθ in simplest form with a rational denominator?

Solve the equation for x. x² - 12x +32 = 0

Carmen is choosing between two exercise routines. In Routine #1, she burns 44 calories walking. She then runs at a rate that burns 16.3 calories per minute. In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 18.5 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t

Using the verbal description below, write the original function and it's inverse. Explain your solution strategy. 1. Starting with a number x, subtract 5 2. Take the square of that quantity 3. Divide by 3

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4,720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?

A coach bought 3 jerseys and 2 pairs of shorts for each of the 14 players on her soccer team. The jerseys cost $15 each, and the shorts cost $12 each. The coach used a $100 coupon to hel pay for the uniforms. Rewrite the numerical expression with parentheses to model the total cost, $866. 14 x 3 x 15 +2 x 12 + 100

A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with a full time workers can be found using the function f(x) = 234. Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function. f(-1) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. of the problem. f(2)= meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. f(6.5) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is

In Fall 2020, 10.5 million undergraduate students attended a 4-year institution full- time. Of those, 9,240,000 were under age 25, 945,000 were ages 25-34, and 315,000 were age 35 and older. Answer the questions below. Label your answers with a, b, c. a. What percent of the students were under age 25? b. What percent of the students were ages 25-34? c. What percent of the students were age 35 and older?

Express 9.603603603... as a rational number, in the form p/q where p and q have no common factors.