Basic Math Questions and Answers

At a carnival, each game has a cost of x dollars to play. Which situation can be represented by this inequality? 8x>5x+6 The cost to play 8 games is less than the cost to play 5 games and a $6 snack. The cost to play 8 games is greater than the cost to play 6 games and a $5 snack. The cost to play 8 games is greater than the cost to play 5 games and a $6 snack. The cost to play 8 games is $6 greater than the cost to play 5 games.

Solve the inequality 5x-4<-8x-69. Write your answer as an inequality and in interval notation, then graph the solution set on the number line.

Out of 4,500 colleges surveyed, 40% reported that SAT scores were not used as a high consideration in viewing their applications. How many schools view the SAT as important in screening applicants?

The following equation is given. Complete parts (a)-(c). x³-3x²-25x+75=0 a. List all rational roots that are possible according to the Rational Zero Theorem. (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is (Simplify your answer.) c. Use the root from part (b) and solve the equation. The solution set of x³-3x²-25x+75=0 is O. (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as neec

Pedro has scores of 92, 85, 68, and 73 after four tests. What score must he make on his fifth test to have an average of 78 or greater? The score that Pedro needs on his fifth test to get an average of at least 78 is (Round to the nearest integer as needed.)

Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used. Order each step and justification that is needed to solve the equation below.

Graph the polynomial function f(x) = -2(x-3)²(x²-16) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = -2x for large values of [x]. (b) Find the x- and y-intercepts of the graph of the function. The x-intercept(s) is/are 3,4,-4. The y-intercept is 288. (Simplify your answer. Type an integer or a fraction.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. The real zero(s) of f is/are 3,4,-4.

Given f(x)=3x+6, (a) Find f(x+h) and simplify. (b) Find f(x+h)-f(x)/h and simplify.

Determine the total amount and the interest paid on $3000 with interest compounded semiannually for 5 years at a) 1%. b) 2%. c) 4%. d) Is there a predictable outcome in either the amount or the interest when the rate is doubled?

In a recent year, person A and person B had the two top-grossing concert tours, together generating about $314 million in ticket sales. If person B took in $28 million less than person A, how much did each tour generate?

Sarah Yost took out a 48-month fixed installment loan of $17,000 to open a gift shop. She began making monthly payments of $423.05. Sarah's business does better than expected and instead of making her 12th payment, Sarah decides to repay her loan in full. How much interest will Sarah save (use the actuarial method)? $1926.35 $1872.84 $2205.29 $1907.97

An island has some portion submerged in water. Point A on the island is at -5/4 feet from the surface of the sea. Point B on the island is at -2/3 feet from the surface of the sea. Because -2/3 feet > -5/4 feet what is true about the distance of the two points from the surface of the sea? Point A is closer to the surface of the sea than point B. Point B is closer to the surface of the sea than point A. Both points are 1 11/12feet from the surface of the sea. Both points are 7/12feet from the surface of the sea.

Construct a Binomial probability distrubtion table using n= 5 and p = 0.22. Next, record the mean a standard deviation of the distribution below. Where necessary, round all numbers to four decimal place

Analyze the polynomial function f(x) = 2x (x² - 9) (x + 4) using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y = for large values of |x|.

Two ships leave a port at the same time. The first ship sails on a bearing of 39° at 18 knots (nautical miles per hour) and the second on a bearing of 129° at 12 knots. How far apart are they after 1.5 hours? (Neglect the curvature of the earth.) After 1.5 hours, the ships are approximately (Round to the nearest nautical mile as needed.) nautical miles apart.

Use the substitution method to solve the system -x+y=2 4x-3y=-8 Your answer is x= y=

Luggage Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) Are the first flight leaving on time and the luggage making the connection independent events? Explain. b) What is the probability that her luggage arrives in Denver with her?

Which is an equation with a degree of 4, zeros located at (5, 0), (−8, 0) and (3, 0) and a y- intercept located at (0, -120)? Select the correct answer below: y = (x - 5)(x + 8)(x − 3)(x - 1) y = (x - 5)(x + 8)(x − 3)(x + 1) y = (x + 5)(x + 8)(x − 3)(x - 1) y = (x + 5)(x-8)(x+3)(x + 1)

Admission to a baseball game is $4.00 for general admission and $6.00 for reserved seats. The receipts were $6120.00 for 1348 paid admissions. How many of each ticket were sold? (Round to nearest integer if necessary.)

Multiply 9.5 x 1.3 First, write your factors as whole numbers to multiply: 95 13 Now write your final answer with your decimal:

The System of linear equation given by a11x1 + a12x2 + a13x3 = b₁ a21x1 + a22x2 + a23x3 = b₂ a31x1 + a32x2 + a33x3 = b3 Possess infinite solution if : Select one: a. Rank(A) = Rank(A:B) < 3 b. Rank(A) = Rank(A:B) = 3. c. Rank(A) = Rank(A:B) ≥ 3 d. Rank(A) = Rank(A:B)>3

The velocity function for an object is given to the right. Assuming that the object is at the origin at time t=0, find the position at time t = 20. v(t)= 1/10 if 0≥t≤ 10 1 if 10 <1≤20 The position of the object at time t=20 is

One safe investment pays 6% per year, and a more risky investment pays 14% per year. a. How much must be invested in each account if an investor of $94,000 would like a return of $7,400 per year? b. Why might the investor use two accounts rather than put all the money in the 14% investment? a. is invested in the 6% account. is invested in the 14% account. b. Why might the investor use two accounts? A. The 14% account does not earn as much interest as the 6% account B. Investing in two accounts always yields more money than investing in just one account. C. The 14% investment is riskier than the 6% investment. There is a greater chance the investor will lose money if it is all placed in the 14% account. D. Although the 14% account earns more interest, the 6% account has no hidden fees.

A dolphin jumped from 5 feet below the surface of the sea. Jane wrote -5 to represent the depth from which the dolphin jumped. What does 0 represent in this situation? the floor of the sea the surface of the sea the level to which the dolphin jumped the level from which the dolphin jumped

Write an equation of the line that passes through (-3,-1) and is parallel to the line defined by 4x+y=-3. Write the answer in slope-intercept form and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable. The equation of the line in slope-intercept form:

A construction company plans to invest in a housing project. There is a 30% chance that the company will lose $200,000 a 30% chance it will lose $100,000, and a 40% chance of a $300,000 profit. Based ONLY on this information, what should the company do? The expected value is $60,000, so the company should proceed with the project. The expected value is -$90,000, so the company should not proceed with the project. The expected value is $30,000, so the company should proceed with the project. The expected value is $90,000, so the company should proceed with the project.

The base of a triangle exceeds the height by 4 feet. If the area is 142.5 square feet, find the length of the base and the height of the triangle.

Working her way through school, Kathy works two part-time jobs for a total of 22 hours a week. Job A pays $6.20 per hour, and Job B pays $6.50 per hour. How many hours did she work at each job the week that she made $140.60? (Round to two decimal places if necessary.)

One number is 7 more than another. The difference between their squares is 161. What are the numbers? smaller number = larger number =

The length of a rectangle is 7 more than the width. The area is 744 square centimeters. Find the length and width of the rectangle.

The points (-8, 3) and (-9, 5) fall on a particular line. What is its equation in point- slope form? Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.

A student at Pine Valley high school would like to find the mean number of extra credit points her fellow students earned on a statistics chapter test. She collects data from 11 students in her class. The graph shows the frequency for the number of extra credit points earned by her fellow classmates. Find the mean number of extra credit points earned by the 11 students, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.

The volume of a hexagonal prism is given by The area of the base is given by. Find an expression for the height of the hexagonal prism.

Suppose a bounty hunter captures a certain type of fugitive 62% of the time. On average the apprehension of this type of criminal costs him $9,000 in expenses, but if he captures the criminal he receives a bounty(monetary reward) of $50,000. Based on this information, should the bounty hunter take the job? The expected value is -$27,580, so the bounty hunter should not take the job. The expected value is $22,000, so the bounty hunter should not take the job. The expected value is $27,580, so the bounty hunter should take the job. The expected value is $22,000, so the bounty hunter should take the job.

Analyze the polynomial function f(x) = − 3(x + 2)(x-4)³ using parts (a) through (e). (a) Determine the end behavior of the graph of the function. The graph of f behaves like y =__for large values of |x|

Imagine that you work for a company that sells hardware to various businesses. You receive a commission based on your monthly sales, and your goal for commissions this month is $1,500. You receive a $10 commission for every tablet you sell, and $30 for every computer you sell. Part A Write a linear inequality to model this situation.

The formula for the volume of a pyramid is A.h/3 where A is the area of the pyramid's base and h is its height. The base of the Great Pyramid of Giza is about 53,000 square meters, and its height is about 150 meters. What calculation will give us the estimated volume of the Great Pyramid of Giza in cubic meters?

The total amount of money (in cents) in x nickels, (x + 3) dimes, and 2x quarters. (Hint: The value of a nickel is 5 cents, the value of a dime is 10 cents, and the value of a quarter is 25 cents.)

Determine which of the equations, y = 2x + 4 or y=0.5x+4, is the better fit for the data points. (0,4), (1,6.5), (2,8), (3,10.5) Which equation is a better fit for the data points? A. y=0.5x+4 B. y = 2x+4

Jamaal ran 6 miles in 30 minutes. Which expression shows how to correctly determine his speed in miles per minute? 6 miles 30 minutes 30 minutes = 6 miles 6 miles 1 minute 30 minutes + 1 mile

Solve the system using the substitution method. If there is exactly one solution, write as an ordered pair. If not, choose one of the other options.

A grocer stacks oranges in a pyramidke pille. If the bottom layer is rectangular with 5 rows of 20 oranges and the top layer has a single row of oranges, how many oranges are in the stack? There are ___oranges in the stack

A box, with rectangular sides, base and top is to have a volume of 2 cubic feet. It has a square base. a. Express the surface area A of the box in terms of the width w of the base. b. If the material for the base and top costs 20 dollars/ft² and that for the sides costs 30 dollars/ft², express the total cost C as a function of the width.

Suppose f(x) represents the total number of children that have bought a defective product, and x is the number of days since it came out. Step 2 of 2: Interpret the meaning of f'(42) = 12. 12 is the rate of change in children who have bought a defective product after 42 days. 12 is the total change between the first day and 42 days later. 12 is the average change in the number of children who have bought a defective product between the first day and 42 days later. After 42 days 12 children have bought a defective product.

There is a 60% chance that your math teacher will give a pop quiz tonight, and due to the fact that you have a soccer game, there is a 85% chance you will not be able to do your math homework. You decide that you will not do the homework if the probability of their being a pop quiz and your not doing the home is greater than 80%. What is the probability of there being a pop quiz and your not doing your homework? 0.51 0.34 0.06 0.09

If the density of New York City is 26,403 people per square mile, and the city is 302 square miles, how many people are living in New York City? 7,973,706 people 6,723, 874 people 880,000 people 1,346,395 people

Solve the following system of equations with the Write your answer as an Ordered Pair. on Hele If infinitely many solutions exist, enter ∞ (00). If no solution exists, enter DNE

Solve the equation for all values of x. -3(100x² - 49)(x² - 2) = 0

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only 1 hour 12 minutes. What is his speed in still air, and how fast is the wind blowing?

An airplane takes 7 hours to travel a distance of 6468 kilometers against the wind. The return trip takes 6 hours with the wind. What is the rat in still air and what is the rate of the wind?