Basic Math Questions and Answers

GDP is the sum of: a. personal consumption, investment, government purchases of goods and services, exports, and imports. b. personal consumption, investment, government purchases of goods and services, and net exports. c. personal consumption, investment, government purchases of goods and services, and net imports. d. value added, net imports, and government purchases of goods and services.

The three sides of a triangle are n, 3n - 1, and 2n + 1. If the perimeter of the triangle is 42 inches, what is the length of each side? Separate multiple entries with a comma.

Solve the equation. 2x-(7x+5)=5x-45 Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is B. There is no solution.

The coordinate on a map for San Francisco are (57,13) and those for Sacramento are (127,72). Note the coordinate represent miles. Find the distance between the two cities to the nearest mile.

A certain forest covers an area of 2800 km². Suppose that each year this area decreases by 7.75%. What will the area be after 9 years? Use the calculator provided and round your answer to the nearest square kilometer.

A restaurant manager wants to purchase 200 sets of dishes. One design costs $15 per set, while another costs $45 per set. If she wants to use her entire budget of $6600, how many of each design should be ordered? Select the correct choice below and fill in any answer boxes in your choice A. She should buy of the $15 sets. She should buy of the $45 sets. (Type whole numbers.) B. There are infinitely many solutions. C. There is no solution.

Find a value for k such that the graph will have the specified number of - intercept y = x² + k If the graph were to have 2 - intercept(s),

A principal of $4200 is invested at 3.25% interest, compounded annually. How much will the investment be worth after 15 years? Use the calculator provided and round your answer to the nearest dollar.

Given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function.

The Riley and Brown families decided to go to a concert together. The Riley's live 6 miles west and 3 miles north of the concert. The Browns live 2 miles east and 4 miles south. How far apart do they live?

A car is purchased for $29,500. After each year, the resale value decreases by 25%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

In Exercises 7 and 8, write a rule for g and then graph each function. Describe the graph of g as a transformation of the graph of f. 7. f(x) = x³ + 2, g(x) = f(x - 1) 8. f(x)= x - 3x + 1, g(x) = 2f(x)

At a math contest, 12 problems were given. Five points were awarded for each correct answer, and two points were deducted for each incorrect answer. Matt's score was 39. How many correct answers did he have?

Problem number one. You are rolling a fair nine sided dice. The sample space is {1,2,3,4,5,6,7,8,9). We define E to be the event that the number rolled is even and T to be that the number rolled is a multiple of three. A) Find P(E) B) Find P(TIE).

In Chapter 1, we modeled the world population from 1900 to 2010 with the exponential function P(t) = (1436.53) - (1.01395)* where t = 0 corresponds to the year 1900 and P(t) is measured in millions. Use this model, to find the rate of change of world population (in million/yr) in 1920, 1959, and 2000. (Round your answers to two decimal places.)

Assume the point (2,7) is on the graph of y=f(x). Determine the value of n in the following situations: 1. (2,n) is on the graph of y=3f(x) with respect to x 2. (2,n) is on the graph of y=-2-5f(x) with respect to x 3. (2,n) is on the graph of y=f(x)+3 with respect to x.

What is the precision of the measurement 4.006 inches? 1 significant digit hundredth of an inch oneth of an inch thousandth of an inch tenth of an inch 3 significant digits

The range R of a projectile is shown below, where v0 is the initial velocity in feet per second and is the angle of elevation. R = V02/32 (sin 2θ) Use differentials to approximate the change in the range when v0= 2500 feet per second and is changed from 10° to 9º. (Round your answer to the nearest whole number.) ft

Identify the constant term b and coefficient m in the expression b + mt for the linear function q(t) = 3x + 17/4 Enter the exact answers.

The distance, d, in meters from the shore, of a surfer riding a wave is given by d = 150 - 7t, where t is the number of seconds since she caught the wave. Identify the initial value and the rate of change, and explain their meanings in practical terms using units. The initial value is The rate of change is

A circle has the equation x² + y² + 4x-6y - 23=0. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any, of the graph.

A city has a population of 240,000 people. Suppose that each year the population grows by 5.25%. What will the population be after 14 years? Use the calculator provided and round your answer to the nearest whole number.

When Sebastian left his house in the morning, his cell phone battery was partially charged. Let B represent the charge remaining in Sebastian's battery, as a percentage, t hours since Sebastian left his house. The table below has select values showing the linear relationship between t and B. Determine how much battery life Sebastian's phone would have 4 hours after leaving his house.

11. The numbers below follow a pattern. 0.006 0.06 0.6 6 A. What are the next two numbers in the pattern? B. What is the relationship between the terms in the pattern?

Write the conditional statement, the converse, the inverse, and the contrapositive of the statement. 10. 2t+3= 13 when t = 5. 11. The dog gets a treat when it performs the trick. 12. An isosceles triangle has two sides with the same length.

Evaluate the polynomial function for the given values of the variable. P(c)=4c²-17c+5; find P(4) and P(0).

Which sentence contains transitional words or phrases? A. As you can see, I am a better writer than a speaker. B. I am a better writer than a speaker. C. I am a good speaker. I am a better writer. D. I am a good speaker; I am a better writer.

Find the average rate of change of f(x) = 4x² - 6 on the interval [2, b]. Your answer will be an expression involving b.

Given the polynomial functions j(x) and k(x), find j(x)+k(x). j(x)=x²-x k(x) = 2x³ + x² – 1 2x³ + 2x²+x+1 -x³ +x-1 -2x³+2x² − x + 1 2x³+2x²-x-1

Find the average rate of change of g(x) = 2x³ + 6/x4 on the interval [-1, 1].

A bucket is the shape of a frustum of a cone. One base has a radius of 6 in., the top has a radius that is 8 in., and the bucket is 12 in. high. Using = 3.14, what is the area of the 6 in base? A₁ = sq in Using = 3.14, what is the area of the 8 in base? V = sq in Rounded to three decimal places, what is the volume of the bucket in cubic inches? A₂ = cu in Using 1 gal = 231 cu in, to the nearest whole gallon, how many gallons will the bucket hold?

The following rational equation has denominators that contain variables. For this equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2x / x+2 =4- 4/x+2 X= ***** a. What are the value or values of the variable that makes the denominators zero?

Find the average rate of change of g(x) = 4x³ + 5/x2 on the interval [-1, 2].

For a certain product, the revenue is given by R = 30x and the cost is given by C(x) = 10x + 1700. To obtain a profit, the revenue must be greater than the cost. For what values of x will there be a profit?

A rectangular sandbox is surrounded on all sides by a strip of grass that is 5 feet wide on all sides. The length of the sandbox is 4 feet more than the width, and the total area for the sandbox and the grass is 189 square feet. Find the dimensions of the sandbox. The length of the sandbox is feet and the width is feet.

A city has a population of 250,000 people. Suppose that each year the population grows by 8%. What will the population be after 8 years? Use the calculator provided and round your answer to the nearest whole number.

Kendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? Explain how you decided.

Soybean meal is 12% protein; cornmeal is 6% protein. How many pounds of each should be mixed together in order to get 240-lb mixture that is 8% protein? How many pounds of cornmeal should be in the mixture? pounds

Use a calculator to solve the equation. Round your answer to three decimal places. 3.251x 8.632= -3.1(8.628x + 4.915) X =

Consider the following function. 4x + 2, x ≤ -1 x² - 3, x>-1 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.)

Of all the numbers whose difference is 40, find the two that have the minimum product. The two numbers whose difference is 40 and that have the minimum product are

Junior is saving money in his piggy bank. He starts with 10 cents and adds two pennies each day. Create a table. draw a complete graph, and write an equation to model this situation, where x represents the number of days and y represents the amount of money.

A retired woman has $200,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $20,000 per year from her investments? 9% fund $ 13% fund $

Find the x-intercept and y-intercept of the graph of - 2x + 4y = - 8. Then graph. x-intercept = ( ,0) y-intercept = (0, )

Norio is running to raise money for charity. He finds 2 people who have pledged to donate money based on the distance he runs. His neighbor says he will donate $0.25 fe every 40 feet Desmond runs. His aunt also says that she will donate $20 for every mile runs. If Desmond runs a total of 4 miles during the cancer awareness run, how much money will he have raised based on these two donations? (1 mile = 5,280 feet)

Solve the system of equations below using the Desmos calculator: -14-20y-7x 10y + 4 = 2x The solution to the system of equations is

The percent P of the U.S. population with Internet access is given by 25P - 34t = 1378 where t is the number of years past 1990.+ (a) What percent of the U.S. population had Internet access in 2005? (Round your answer to one decimal place.) P = % (b) In what year will 90% have Internet access?

Carolyn walked 3 miles from her house to the library and then 2 1/2 miles farther to the grocery store. Returning home by the same route, she walked 1 2/3 miles before stopping at a friend's house. How many miles did Carolyn have left to walk home?

The following rational equation has denominators that contain variables. For this equation, a. Write the value or values of the variable that make a denominator zero. These are the restrictions on the variable, b. Keeping the restrictions in mind, solve the equation. 1/ x-4 - 3/x+2 = 6/x²-2x-8 ***** a. What is/are the value or values of the variable that make(s) the denominators zero? X= (Simplify your answer. Use a comma to separate answers as needed.)

Find the average rate of change of g(x) = - 4x³ + 2 from x= -1 to x = 3.