Basic Math Questions and Answers

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.

In a binomial experiement, what does it mean to say that each trial is independent of the other trials? Choose the correct answer below. A. Each trial is independent of the other trials if the outcome of one trial affects the outcome of another trial. B. Each trial is independent of the other trials if the outcome of one trial does not affect the outcome of any of the other trials. C. Each trial is independent of the other trials if no more than one trial occurs at a time. D. Each trial is independent of the other trials if the sum of all the possible trial outcomes equals 1.

Of the cartons produced by a company, 10% have a puncture, 8% have a smashed corner, and 0.5% have both a puncture and a smashed comer. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner.

The mean scores for students in a statistics course (by major) are shown below. What is the mean score for the class? 9 engineering majors: 92 5 math majors: 94 13 business majors: 85 The class's mean score is

Solve the equation by the method of your choice. x² +8x=1

Solve the equation by the square root property. (x-3)² = 1 What is the solution set? (Use a comma to separate answers as needed.)

A depressant puts more emphasis on the inhibitory part of the brain, which can cause you to be more A. aroused B. stimulated C. dispirited

Determine whether the study is an observational study or an experiment. Explain. In a survey of 1081 adults in a country, 53% said the country's leader should release all medical information that might affect their ability to serve. The study is because it a treatment to the adults.

Friendship's soccer team purchased uniforms and equipment for a total cost of $912. equipment cost $612, and the uniforms cost $25 each. How many uniforms did the school purchase? 1. Variable: 2. Constant: 3. Rate: 4. Equation and solve:

Quadratic Equations Solve the equation by the method of your choice. (2x + 1)(x+3) = -1 The solution set is. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)

Members of the track team can run one mile in an average of 7.32 minutes. The fastest and slowest times varied from the average by 1.04 minutes. Which absolute value inequality below models the one mile running times of the track team? |x+8.36| ≤ 7.32 |x-7.32|≤ 1.04 |x+7.32| ≤ 1.04 |x-1.04| ≤ 7.32

Solve the following system of three equations and three unknowns using either substitution or linear combination. Be sure to check that your solution satisfies all three of the original equations! x-y +z = 10 3x + y + 2z = 34 -5x + 2y-z = -14

Two trains leave stations 374 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other travels at 95 miles per hour. How long will it take for the two trains to meet? Do not do any rounding.

You are shopping for school supplies. A store is offering a 10% discount on binders and a 20% discount on packages of paper. You want to buy 5 binders originally marked $2.50 each and 10 packages of paper originally marked $1.30 each. Write an expression that shows how much you will save after the discounts.

There are 750 toothpicks in a regular-size box. A jumbo-size box is made by doubling the length, width, and height of the regular box. How many toothpicks will the jumbo box hold? 6000 toothpicks 1500 toothpicks 2250 toothpicks 3000 toothpicks

u= <- 4,6 > and v= < 2,- 3 > a. Sketch u, v, and u + v on a pair of coordinate axes below: b. Find | u + v | and label it on your graph above. c. Find the angle that u + v makes with the positive or negative x-axis and label it on your graph above. d. Sketch u, v, and u- v on a pair of coordinate axes below:

Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the graph of f(x) = 5√x -4about the y-axis on the interval [4, 5]. Note: Round to the nearest hundredth.

The access code for a garage door consists of three digits. Each digit can be any number from 1 through 6, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is 216 (b) What is the probability of randomly selecting the correct access code on the first try? The probability of randomly selecting the correct access code is 0.005 (Round to three decimal places as needed.) (c) What is the probability of not selecting the correct access code on the first try? The probability of not selecting the correct access code is (Round to three decimal places as needed.)

Find the domain of the function. (10 Points) f(t) = √√√r +2 all real numbers t such that 1 ≥ 2 all real numbers t except t = 2 all real numbers t O all real numbers t such that t ≤ 2 all real numbers t except t = - 2

Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 19 people can line up in a row for concert tickets. Does the situation involve permutations, combinations, or neither? Choose the correct answer below. A. Permutations. The order of the 19 people in line matters. B. Combinations. The order of the 19 people in line does not matter. C. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.

A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 600 cubic centimeters of soup. The sides and bottom of the containe will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.06 cents per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information: h: height of cylinder, r: radius of cylinder Volume of a cylinder: V = Tr²h 2πrh Area of the top/bottom: A = ² To minimize the cost of the package: Radius: Area of the sides: A Height: Minimum cost: = cm cm cents