Basic Math Questions and Answers

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent at hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 more than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

- The capture-recapture method is used to find the number of turtles in a small stream. Forty- two turtles are captured. Their shells are marked with green paint. Then the turtles are released back into the stream. Later in the summer, 56 turtles are captured. Of those captured, 7 had green paint on their shells.

Given the function f(x) = -2 log3 (x-1) + 4and the function g(x) = -log5 (x+13) — 1, what is the distance between the vertical asymptotes of the two graphs f(x) and g(x)? 14 units 12 units 5 units 13 units

Solve the absolute value equation: | 15 + 8x | +3 = 24

The function represents an inverse proportion. If for a set of points (,y) generated for this function, V( y-axis) was plotted versus r-axis), the resulting graph would give a straight line. The statement is true. The statement is false.

Which function below represents the inverse function of y =2³x-4? y¹ =1/3 log₂ (x+4) y-¹ =3 log₂ (x) + 4 y¹ = log₂ (3x + 4) y¹ =1/3 log₁ (2x)

A certain substance has a half-life of 2 minutes. A fresh sample of the substance weighing 60 mg was obtained. After how many minutes will there be 14 mg of the substance remaining? 4.6 minutes 8.4 minutes 2.5 minutes 4.2 minutes

Solve the compound inequality. 3x+1 <13 and 2x+4>-2 Graph the solution on the number line.

Find the slope and the y-intercept of the graph of the equation. y= x/7 + 3/7 Slope = (Type an integer or a fraction.) y-intercept = (Type an integer or a fraction.)

For the following description of data, identify the W's from what's given, name the variables, specify for each variable whether its use indicates that it should be treated as categorical or quantitative, and, for any quantitative variable, identify the units in which it was measured (or note that they were not provided). A polling organization conducted a poll of registered American voters in 2017 to gauge people's levels of concern about a variety of issues, including environmental issues. The data collected for each voter included his or her gender, age, race, education, and party affiliation, and whether he or she was "worried a great deal" about climate change, about air pollution, and about pollution of waterways. Identify the Who. O A. All registered American voters in 2017 who were "worried a great deal" about climate change, air pollution, and pollution of waterways B. All registered American voters in 2017 C. A group of registered American voters in 2017 D. A group of registered American voters in 2017 who were "worried a great deal" about climate change, air pollution, and pollution of waterways E. The Who for this situation cannot be determined from the given information.

Sophia, Malcolm, and Oren are playing a money game. Their bank balances are shown in the table. Complete the table by writing the absolute value of each bank balance to show how much each player owes. Who owes the greatest amount?

A couple has a credit card debt of $ 18,000.00. In your checking account, you have $ 2,000.00, and on a 401 (k), you have $ 6,000.00. The balance on your home mortgage of $ 180,000.00 is $ 120,000.00. His two cars are worth a total of $ 19,000.00, but the loan balances on them total $ 23,000.00. Find her net worth. Response option group 6:51 PM ✔

Writing your answer in simplest form, solve the Area of a Trapezoid formula for b₁ : A =1/2 (b₁ + b₂) h

The __ is used to determine whether the graph represents y as a function of x Select your answer horizontal line test greatest integer test relative maximum test vertical line test even/odd function test relative minimum test

For which point (x,y) is the slope of the line between (6,8) and (x,y) equal to the slope of the line between (6,8) and (-3,5). (Use the interactive figure to find your answer.) Click here to launch the interactive figure. Choose the correct answer below. A. (8,6) B. (11,15) C. (-2,2) D(15,11)

For a ride on a rental scooter, Pablo paid a $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Pablo's ride was $13.12. For how many minutes did Pablo ride the scooter?

a-bed In order to solve the equation above for c, you must multiply both sides of the equation by the same expression: a * __= -bed x The resulting equation is:

Dot products: Find the indicated quantity, assuming that u = 2 i + j, v=i-3 j, and w = 4i-8 j. a. u.v b. v w C. W u d. u. (v + w) e. (u + v) (u-v) f. Are any of the vectors u, v, or w perpendicular to each other? Justify your reasoning.

Given the following equation, solve for x. 32x-333x+1 x=4 no solution x=-4 X-2

olve the compound inequality. Give the solution set in both interval and graph forms. x-2≤3 and x+1≥5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Type your answer in interval notation.) B. The solution set is Ø.

Eric rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 93 cents for each mile driven. Eric had to pay $165.72 when he returned the truck. For how many miles did he drive the truck?

You are buying shirts for the math club members. The t-shirt company will charge you according to the number of shirts you purchase. If you purchase less than 10 the cost is $15.00 per shirt. If you purchase 10 or more but less than 50 you pay $12.00 per shirt. . If you purchase 50 or more you pay $10.00 per shirt. Which function models the cost of the shirt, C(x), based on the number of shirts, x, you purchase?

Evaluate the function f(x) = 6x + 4 at the given values of the independent variable and simplify. f(-3) b. f(x+1) c. f(-x) f(-3)=

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, David has scored 76, 80, and 84 on the first three. What range of scores on the fourth test will give David a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.

Use graphs to find the set. (-8,0) n[-6.1] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set is B. The set is the empty set.

A farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. Use x- for number of corn acres and y-for number of wheat acres. How many of each crop should the farmer plant. equation1: 180= equation2: Number of corn acres: Number of wheat acres:

Find the surface area of a sphere with d= 14 in. Express your answer in terms of .

Solve the compound inequality. 0<2x+2≤8 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is B. The solution set is the empty set.

Solve the equation using the quadratic formula. 2x² = 2x+3 The solution set is

Solve the equation by the method of your choice. (5x−4)? =16 The solution set is .

Solve the compound inequality. 7<x+5<9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. The solution is Ø.

Find all x-Intercepts and y-Intercepts of the graph of the function. f(x)=2x³-2x²-84x If there is more than one answer, separate them with commas. Click on "None" if applicable. x-Intercept(s): y-intercept(s):

For which point (x,y) is the slope of the line between (2,5) and (x,y) equal to the slope of the line between (2,5) and (-3,5). Choose the correct answer below. A. (-3,3) B. (7,5) C. (5,2) D. (5,7)

Solve the following exponential equation: log(3x+1)+1=3 no solution x=333 x=1 x=33

In countries where businesses are government owned: a. there is less incentive to work hard. b. the right amount of each good is produced. c. profits tend to be higher. d. the quality of goods is high but profits are low.

Determine the point (x,y) for which the slope of the line between (-4,10) and (x,y) the largest. (Use the interactive figure to find your answer.) A. (-10,8) B. (-9,1) C. (4,13) D. (1,7)

Surface Areas and Volumes of Spheres If you know the surface area of a sphere, you can find its volume. First, use the surface area formula, S.A. = 4r², to determine the radius of the sphere. Next, substitute the value of its radius into the formula for the volume of a sphere, V = ³. Type your answer and then click or tap Done. The surface area of a sphere is 144 Express your answer in terms of . cm³ Text to Spe cm². What is the volume of the sphere?

Determine the open intervals on which the function is increasing, decreasing, or constant. (Enter you answers using interval notation. If an answer does not exist, enter DNE.) * f(x) = x² - 4x

A population has a mean µ = 70 and a standard deviation o= 21. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 49. Px = ox

Determine whether the statement is true or false. If it is false, rewrite it as a true statement. As the size of a sample increases, the standard deviation of the distribution of sample means increases. Choose the correct choice below. A. This statement is true. B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases." C. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means does not change." D. This statement is false. A true statement is, "As the size of a sample decreases, the standard deviation of the distribution of sample means decreases.

A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score? Choose the correct answer below. A. The student scored higher than 78% of the students who took the actuarial exam. B. 78% of students scored higher than this particular student. C. The student scored a 78% on the exam. D. About 78% of students achieved the same score as this particular student.

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think Congress is doing a good or excellent job. Her estimate must be accurate within 2% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 34% of the respondents said they think Congress is doing a good or excellent job. (c) Compare the results from parts (a) and (b). (a) What is the minimum sample size needed assuming that no prior information is available? (Round up to the nearest whole number as needed.) (b) What is the minimum sample size needed using a prior study that found that 34% of the respondents said they think Congress is doing a good or excellent job? n = (Round up to the nearest whole number as needed.) (c) How do the results from (a) and (b) compare? n = A. Having an estimate of the population proportion has no effect on the minimum sample size needed. B. Having an estimate of the population proportion reduces the minimum sample size needed. C. Having an estimate of the population proportion raises the minimum sample size needed.

Use graphs to find the set. [-5, ∞0) n (2,00) Select the correct choice below and fill in any answer boxes within your choice. A. The set is (Type your answer in interval notation.) B. The answer is the empty set.

If the rate of inflation is 1.9% per year, the future price p (t) (in dollars) of a certa number of years from today. p(t)=3000 (1.019) Find the current price of the item and the price 9 years from today. Round your answers to the nearest dollar as necessary. Current price: Price 9 years from today:

Find the average rate of change. Fuel Efficiency On Friday, you left for a weekend camping trip with 110 miles on the odometer and 14.5 gallons of gas in the tank of your car. When you returned on Sunday, the odometer read 299 miles and you still had 7.5 gallons of gas left. What was the fuel efficiency of your car on this trip?

A sphere has a surface area of 144 ft². Find the volume of the sphere. A. 324л ft³ B. 288 ft³ C. 216 ft³ D. 144 ft³

Suppose that the polynomial function f is defined as follows. f(x)=9(x-4)²(x-13)³(x+7)³ List each zero of f according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there is no answer, click on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity two: Zero(s) of multiplicity three:

Research whether it is possible to trisect a segment using only construction tools. If possible, use construction tools to trisect WZ and explain your steps. If not possible, explain why.

A regular box of cereal holds 14 ounces. If an economy box is made by doubling all the dimensions of the regular-sized box, how many ounces will the economy box hold? 28 oz 196 oz 56 oz 112 oz

What is the difference between an observational study and an experiment? Choose the correct answer below. A. In an experiment, a treatment is applied to an entire population and responses are observed. In an observational study, a researcher measures characteristics of interest of an entire population but does not change existing conditions. B. In an experiment, a researcher measures characteristics of interest of an entire population but does not change existing conditions. In an observational study, a treatment is applied to an entire population and responsesare observed. C. In an experiment, a researcher measures characteristics of interest of a part of a population but does not change existing conditions. In an observational study, a treatment is applied to part of population and responsesare observed. D. In an experiment, a treatment is applied to part of a population and responses are observed. In an observational study, a researcher measures characteristics of interest of a part of a population but does not changeexisting conditions.