Basic Math Questions and Answers

For the function f(x) = 1/10x,construct and simplify the difference quotient f(x+h)-f(x) / h

A water park has pools, slides, and rides that, in total, make use of 4.1 × 106 gallons of water. They plan to add a ride that would make use of an additional 91, 000 gallons of water. Use scientific notation to express the total gallons of water made use of in the park after the new ride is installed.

Jon recently drove to visit his parents who live 270 miles away. On his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 hours driving, find the two rates.

Each day, Caleb feeds his horse 2.25 lb of oats. He also feeds it hay. The weight of hay is 6.5 times the weight of oats. What is the combined weight of oats and hay Caleb feeds his horse in one week? A 61.250 lb B 102.375 lb C 118.125 lb D 259.875 lb Naomi chose C as the correct answer. How might she have gotten that answer?

Researchers in Antarctica discovered a warm sea current under a glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate of 0.06 m per day. Which function can be used to find the thickness of the ice shelf in meters x days since the discovery? t(x)= 450 -0.06x t(x)= -0.06(x+450) t(x)= 450+ 0.06x t(x)= 0.06 (x+450)

Use f(x) and g(x) to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) (a) (fog)(x) (b) (gof)(x) (c) (fof)(x) f(x)=x². g(x)=√1-x (a) (fog)(x) = 1-x (Simplify your answer.) The domain of (fog)(x) is (-∞0.1). (Type your answer in interval notation.) (b) (gof)(x) = (Simplify your answer.)

You earn $11 per hour working at a grocery store during the summer. The function p(x) = 11x represents the amount you earn for working x hours. a. You work 18 hours. How much do you earn? b. How many hours do you have to work to earn $275?

A street sign company is making street signs in the shape of equilateral triangles. The side length of each sign is 22 inches. What is the exact altitude length so that the company will be able to know what size box to ship them in?

Factor the expression. -36x-32 The positive GCF of -36x and 32 is 4. Complete each equation with an expression or integer factor. The expression with 4 factored out is.

The fuel efficiency rating for a certain car is 28 miles per gallon on the highway and 20 miles per gallon in the city. During one week the car traveled 220 miles and used 9 gallons of fuel. How much fuel was used for city driving? How much fuel was used for highway driving?

For what value of x is the following true? log(x+11) = log x + log 11 Your answer is: x= You may enter the exact value or round to 4 decimal places.

If e7x = 20, then x =

In one question on a history test, a student is asked to match 10 dates with 10 events; each date can be matched with only 1 event. In how many ways can this question be answered?

You go to the doctor and he gives you 17 milligrams of radioactive dye. After 24 minutes, 5 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.

Three friends are going fishing. They will share 4 1/3 gallons of water equally. How much water will each friend get? Answer the question in the following order and number your answers 1. What is the improper fraction that 4 1/3 equals? 2. What is the multiplication expression you need to find the quotient? 3. How much water will each friend get?

Answer parts (a), (b), and (c) for a cylinder with a radius of 5 inches and height of 9 inches. (a) Compute the volume of the cylinder if the height were increased by 3 inches and the radius stayed the same. (b) Compute the volume of the cylinder if the radius were increased by 3 inches and the height stayed the same. (c) Which causes the volume to increase more, increasing its radius or height? Explain.

HOW MANY DIFFERENT 4 LETTER CALL LETTERS ARE POSSIBLE FOR A RADIO STATION IF: a) THE FIRST LETTER MUST BE K OR W AND REPEATS ARE ALLOWED? b)THE FIRST LETTER MUST BE K OR W, IT MUST END IN R, AND NO REPEATS ARE ALLOWED?

The odds against Muffy beating her friend in a round of golf are 1:6. Find the probability that Muffy will lose.

Two boats leave the same dock in Cairo, IL at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels 4 miles per hour. The southbound boat goes 8 miles per hour. How long will it take them to be 54 miles apart?

Find out how long it takes a $2700 investment to earn $300 interest if it is invested at 7% compounded quarterly. Round to the nearest tenth of a year. Use the formula A=P(1+r/n)nt 1.7 years 1.5 years 1.9 years 1.3 years

Terry is feeling crafty and wants to put a ribbon border on her boring clock to jazz it up a bit. If the clock has a radius of 15 inches, how many inches of ribbon will Terry need to use to surround the clock? Your answer should be a number only. Use 3.14 for pi. Round your answer to the nearest hundredth.

Quadrilateral ABCD is mapped to quadrilateral A'B'C'D'. Which of the following transformations would not result in the two quadrilaterals being congruent? (1) a translation along side AB by a distance of twice AB (2) a dilation from point d by a factor of one-half (3) a rotation about point C by 90 counterclockwise (4) a reflection across side BC

A child starts a piggy bank with $2. Each day, the child receives 25 cents at the end of the day and puts it in the bank. If A represents the amount of money and d stands for the number of days then 4(d)=2+0.25d gives the amount of money in the bank as a function of days (think about this formula). (a) Evaluate 4(1), 4(7), and 4(30) (b) For what value of d will 4(d) = $10.50 (c) Explain why the domain does not contain the value d = 2.5. (d) Explain why the range does not include the value A = $3.10.

Factor the expression. - 40y-15 The positive GCF of -40y and -15 is 5. Complete each equation with an expression or integer factor.

The staircase to a home's second story rises to 15 ft, and spans 20 ft along the first floor. How long will be banister be? Round your answer to the nearest tenth of a foot. 25 ft 35 ft 22.5 ft 17.5 ft

Find the domain of the function f(x)=1/4x + 2 .What is the only value of a not in the domain?

Consider the differential equation y' (t) = (y-2)(2+ y). a) Find the solutions that are constant, for all t20 (the equilibrium solutions). b) In what regions are solutions increasing? Decreasing? c) Which initial conditions y(0) = A lead to solutions that are increasing in time? Decreasing? d) Sketch the direction field and verify that it is consistent with parts a through c.

Suppose Rita borrows $6500 at an interest rate of 11% compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding. (a) Find the amount owed at the end of 1 year. $0 (b) Find the amount owed at the end of 2 years. $0

9.4 × 104 bacteria are measured to be in a dirt sample that weighs 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 23 grams.

A painter is painting the triangular gable of a home, with two sides measuring 8'-4" by 8'-4". The gable is shaped like a right triangle. What is the total area the painter needs to paint? Round your answer to the nearest hundredth. 16.67 sqft 43.52 sqft 64.44 sqft 34.72 sqft

The given angle is approximate. Find the value of the given trigonometric function by finding the reference angle and attaching the proper sign. sec 945.78° Express in terms of the reference angle. sec 945.78° = (Type a decimal rounded to two decimal places as needed.) Evaluate. sec 945.78° = (Round to three decimal places as needed.)

Determine if the given ordered pair is a solution to the equation. x = -2; (-2,7) The ordered pair (-2, 7) is not a solution. The ordered pair (-2, 7) is a solution.

The number of new skin cells on a revolutionary skin graft is growing at a rate of 5% per hour. How many hours will it take for 200 skin cells to become 298 skin cells? Use the equation A = A₁ ert, where time t is measure in hours, Ao is the number of skin cells at t=0, r is the hourly growth rate, and A is the number of skin cells at time t.

Julian borrowed some money from his friend in order to help buy a new video game system. Julian originally borrowed $100 and agreed to pay back his friend $20 per week. Write an equation for L, in terms of t, representing the amount Julian owes his friend after t weeks!

Simplify the expression by using a double-angle formula.

For f(x)=9x-8 and g(x) = (x+8), find (fog)(x) and (gof)(x). Then determine whether (fog)(x) = (gof)(x). What is (fog)(x)?

For the function f(x)=10-x², construct and simplify the difference quotient f(x+h)-f(x) h (Simplify your answer. Use integers or fractions for any numbers in the expression.) ne f(x+h)-f(x) h H

Write as a sum of logarithms. log 85y Choose the correct answer below. A. log 85y-log 85+ log gy B. log 85y = log 58+ log ,8 C. log 85y-log 85 - log gy D. log 85y-log 58-logy8

In a race in which twelve automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

The manufacturer of a CD player has found that the revenue R (in dollars) is R(p)=-5p2+ 1310p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar?

A company has decreased the weight of its boxes of macaroni by 8%. If the new weight of the box is 15.4 ounces, what was the original weight of the box?

For f(x)= (a) fog X X-7 (a) (fog)(x) = and g(x)= (b) gof A. 6 7x+6 (b) (gof)(x) = -6 X Select the correct choice below and, if necessary, fill in the answer box within your choice. find the following composite functions and state the domain of each. 1 (c) fof (d) gog 42-6x X (Simplify your answer.) The domain of fog is x x#0,x# is {x\ (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of f o g is all real numbers. 6 ..... (Simplify your answer.) Select the correct choice below and, if necessary, fill in the answer box within your choice. ⒸA. The domain of g of is {x|x#0,x #7}. (Type an inequality. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. The domain of g of is all real numbers. (c) (fof)(x) = (Simplify your answer.)

The magnitude of an earthquake (amount of energy released) is described by the formula R = log(I/I0), where I is the intensity of the earthquake and lo is the minimum measurable intensity. If one earthquake had a magnitude of 7.4 and another one measured 8.1, how many times more intense was the second earthquake than the first? The second earthquake was about times more intense than the first. (Round to the nearest tenth as needed.)

Write the following function in simplified form. List all restrictions on the domain. g(y) =(y³+ 5y/(y²-25))/(y2 + 5y- 14/(y² + 2y-35))

Jennifer knows that 3,312 x 15 = 49,680. Based on this fact, Jennifer claims that 33.12 X 0.15 = 0.4968. She says that the product has four digits after the decimal point because a product of two decimals in the hundredths should be a decimal in the ten-thousandths. Describe Jennifer's error.

Statistics indicate that the world population since world war II has been growing exponentially. If we assume exponential growth, the world population can be modeled by P(t) = 5(1.051) where P(t) is the world population in billions and t is the time in years since 1985. When (which year) will the population reach 15 billion? Round to the nearest year. {your answer input will be number only}

The population of White Oak decreased from 20,000 to 17,250. What was the percent of decrease in the population of the town?

What is the flow rate, in mL/hour, of 1.3 L delivered over 6 hours? Round to the tenth.

What are some reasons a person might decide to leave his or her country? Check all that apply. to be with family to build a better life to flee from violence Oto try something new to take an extended vacation to seek opportunities for education

The function f(x) = x² - 16/4x2 , x>0, is one-to-one. (a) Find its inverse and check your answer. (b) Find the domain and the range of f and f 1