Basic Math Questions and Answers

Solve the problem. Supply and demand functions, S(x) and D(x), are given for a particular commodity in terms of the level of production x. In each case: S(x) = 4x + 200 and D(x) = -6x + 460 a. For what values of x is there a market shortage? b. For what values of x is there a market surplus? Show all your work.

A 1000 gram sample of radioactive matter will completely decay (be undetectable) in 10 hours. There exists a set of ordered pairs (t, m), where t is the amount of time in hours that the substance has been decaying, and m is the mass in grams that has decayed. If t 0, what is the range of m? Om 1000 OmER Om 10 00 m 1000 Om > 0

A car enters an interstate highway 15 mi south of Youngstown. The car travels due south at an average speed of 62.5 mi/h. Write an equation to model the car's distance, d, from Youngstown after traveling h hours. How far south of Youngstown will the car be after 150 minutes?

In the number: 05629 determine the most significant digit = the least significant digit = The number of significant digits = I

Luke invests $4200 in an account that has an annual interest rate of 2.8% compounded semi-annually. Todd invests $3900 into an account that has an annual interest rate of 3.3% and is compounded continuously. After 8 years what is the difference between the two accounts? Todd has approximately $1.361 more in his account than Luke after 8 years. Luke has approximately $168 more in his account than Todd after 8 years. Luke has approximately $300 more in his account than Todd after 8 years. Both Todd and Luke have the same amount of money in their accounts after 8 years.

Potassium-42 has a half-life of 12.4 hours. Approximately how much of a 1202 mg sample of potassium-42 will be left after 36.8 hours? 953 mg 153 mg 300 mg 88 mg

The perimeter of the rectangular playing field is 370 yards. The length of the field is 7 yards less than triple the width. What are the dimensions of the playing field?

Maximum Capacity A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lb and each box of books weighs 50 lb. The maximum capacity of the elevator is 1000 lb. How many boxes of books can the delivery person bring up at one time?

6 Write the equation of the line passing through the point (7, - 7) with slope 7 The equation of the line is EE H-R

Write the equation of the line with slope 7 and y-intercept 1/8. The equation of the line is

#10 i The land area of the entire United States is 3,531,905 square miles. Use the current population of the United States to estimate the population per square mile. Explain. - T

Solve the problem. When starting a new job at a production facility, employees can be expected to assemble n items per hour after t weeks of work experience, where n(t) = 75 -130/t+ 20.88 Employees are paid 30 cents for each item they assemble. a. Find an expression for the amount of money A(t) earned per hour by an employee with t weeks of experience. b. How much money per hour should an employee expect to earn in the long run (as t→ ∞0)?

Use what you learned to solve these problems. Aimee works up to 50 hours a month and earns $12 per hour. She wants to save more than $240 to buy a computer. The inequality 12h 240, where h is the number of hours Aimee works this month, models this situation. Which values from 0 to 50 are solutions of the inequality? What do the solutions mean in this situation? Explain your reasoning.

In this Exercise, use what you've learned about linear functions and their properties to model real-world situations. 1. In science class, you learned about converting temperatures between degrees Celsius (°C) and Fahrenheit (°F), but recently you could not find a reference with the correct formulas. You then remembered that the relationship between °F and °C is linear. (a) Using this and the knowledge that 32°F = 0°C and 212° F = 100°C, find an equation that computes Celsius temperature in terms of Fahrenheit; i.e. an equation of the form C = "an expression involving only the variable F." (b) Analogously, find an equation that computes Fahrenheit temperature in terms of Celsius temperature; i.e. an equation of the form F = "an expression involving only the variable C."

1 point Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33% -67% split on grades between tests and homework where whichever average is higher will be the 67%. What will your final grade be if your homework average is 56 and your test average is 71?

We want to solve the equation 10x² + x3 = 0 First, factor 10x² + x - 3: By the zero product property we know: 5x+3 = = 0 OR 2x-1=0 And therefore we know that: X= 1 3/5 -B 2 OR= • Do not use decimal approximations in your answer. • Use fractions instead.

Hiroaki has 23 keychains in his collection. He has a goal of collecting at least 30 keychains. He uses the inequality 30 ≤ 23 + x, where x is a number of keychains, to represent how he can reach his goal. Which values in the set (6,7,8} are solutions of Hiroaki's inequality? Show your work.

Graph the given equation. -3 y = 2³x+3 4

On moving day, Guyton needs to rent a truck. The length of the cargo space is 11 ft, and the height is 2 ft less than the width. The brochure indicates that the truck can hold 385 ft³. What are the dimensions of the cargo space? Assume that the cargo space is in the shape of a rectangular solid. x-2 11 ft

Find the inverse of the one-to-one function f(x) = 5x/6 + 25. (Use integers or fractions for any numbers in the expression.)

6. Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this exercise, think of Sandy's wake as a line. m/1 = (2x + 2y)° and m/2 = (2x + y)°. Find x and y. X = y =

Solve the systems of equations. y = x + 3 y = -x + 1 x= y=

To use the quotient rule, write the given function as a quotient of two functions.

Express the fact that x differs from 10 by less than 5 as an inequality involving absolute value. Solve for x. Express the given sentence algebraically as an inequality involving absolute value.

Simplify the complex fraction: (3x5/4y6)/(x4/3xy)

The land area of the entire United States is 3,531,905 square miles. Use the current population of the United States to estimate the population per square mile. Explain.

Draw a tape diagram to represent each problem. Use numbers to solve, and write your answer as a statement. There were 22,869 children, 49,563 men, and 2,872 more women than men at the fair. How many people were at the fair?

Jenny is solving the equation 3x+5-4x42 using algebra tiles. She cannot decide if she should add 3 negative x-tiles or add 2 negative unit tiles to both sides first. Which explains which Jenny should do first? She should add 3 negative x-tiles first because that is the only way to isolate the variable. She should add 2 negative unit tiles first because that is the only way to get to the correct solution. She can do either one first because zero pairs will be created to isolate the variable either way, She should do neither one first because the first step is to add 4 negative tiles to both sides.

Graph the function f(x) = − −x+2, and then find and graph its inverse. 3 f-1(x) = (Simplify your answer.)

The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 94, the student scored 99. What is the student's new weighted mean? Homework Quiz Project Speech Final Exam The student's new weighted mean score is 20 (Simplify your answer.) Score 83 85 99 87 94 Percent of Final Grade 5 30 20 10 35 Weighted Mean Weighted Score 4.15 25.5 19.8 8.7 32.9 91.05 0

Substitution property of Equality: If AB = 20, then AB + CD = Symmetric property of Equality: If m1=m42, then Addition property of Equality: If AB = CD, then AB + EF = Multiplication property of Equality: If AB = CD, then 5. AB= Subtraction property of Equality: If LM = XY, then LM - GH = = 2 Distributive Property: If 5(x+8) = 2, then Transitive Property of Equality: If mz1 = m22, and m22=m23, then Reflexive Property of Equality: m<ABC=

Betsy, a recent retiree, requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year? The amount of money invested at 13% = $ The amount of money invested at 3% = $ Question 8, 1.6.19

A cell phone company charges $40 for a smart phone and $20 per month for its data package. Find the cost C(t) of operating a phone for t months. Use the function to find the cost of the plan for 2 months. Find the cost C(t) of operating a phone for t months.

A credit card company estimates that the average cardholder owed $7440 in the year 2005 and $9420 in 2010. Suppose average cardholder debt D grows at a constant rate. a. Express D as a linear function of time t, where t is the number of years after 2005. b. Draw the graph. c. Use the function in part (a) to predict the average cardholder debt in the year 2015.

When drawing a card from a deck, the P(face card and hearts) is: O 1/13 O 3/26 O 3/52 O 1/52

The distance, d, of an object in free fall for an amount of time in seconds, t, is given by the equation d = 9.81². Write the distance d as a function of t, and find the distance an object falls after 5 seconds The distance d as a function of t can be written as

Simplify s-³s-9 and write your answer without using negative exponents.

A taxi company charges an initial fee of $3 and a rate per mile of $0.71. Write C, the cost for a taxi ride, as a function of m, the number of miles ridden. Find the cost of a 11-mile taxi ride. The cost C for a taxi rides as a function of m can be witten as C(m). The cost is $ *****

Graph f(x)=2x.

A population of 420 bacteria is introduced into a culture and grows in number according to the equation below, where ti measured in hours. Find P'(t). P'(t) = P(t) = 420 3+ 5t 72 +² bacteria/hour Find the rate at which the population is growing when t = 3. (Round your answer to two decimal places.) P'(3) = bacteria/hour

Evaluate the discriminant and determine the number and type of solutions to the equation. 6x²-2x+8=0

A cell phone company charges $30 for a smart phone and $20 per month for its data package. Find the cost C(t) of operating a phone for t months. Use the function to find the cost of the plan for 8 months. Find the cost C(t) of operating a phone for t months. C(t)= (Simplify your answer.)

If we are told that (2x - 1)(5x + 3) = 0, then what can we infer? By the zero product property we know: And therefore we know that: • Do not use decimal approximations in your answer. Use fractions instead.

Solve by using the square root property. Express the solution set in exact simplest form. (z+3)²=28

A savings account had an initial deposit of $50 with $20 deposited each month after it was opened. The total amount in the account can be found by the function A(t) = 20t+50, where t is the time in months after the account was opened. If the total amount in the account is $390, find the length of time the account has been open. After months, the total amount in the account is $390. (Simplify your answer.)

A certain substance has a half-life of 4 minutes. A fresh sample of the substance weighing 90 mg was obtained. After how many minutes will there be 23 mg of the substance remaining? 1.9 minutes 7.9 minutes 5.5 minutes 31.6 minutes

A business uses straight-line depreciation to determine the value y of a piece of machinery over a 10-year period. Suppose the original value (when t= 0) is equal to $42,000 and its value is reduced by $4200 each year. Write the linear equation that models the value y of this machinery at the end of year t. The linear equation models the value y of the machinery at the end of year t (Type an equation. Do not factor.)

A group of test subjects is divided into twelve groups; then four of the groups are chosen at random. [Select] Par Idei or c [Select] Simple Random Stratified Systematic Cluster Convenient ✓ crete, quantitative continuous,

Mr. Morrison bought a cart to move boxes for $49.80 and furniture straps for $19.78. He helped the Greene family move and got paid $400. How much profit did Mr. Morrison make?

WHAT IF? The surface of a city playground is being covered with rubber mulch, which is shredded rubber made from recycle tires. A city worker measures the dimensions of the playground as shown. The recommended depth of the mulch is 4 inches. A 1-ton bag of mulch contains about 3 cubic yards of mulch. How many bags of mulch are needed to cover the surface of the playground? 40.5 ft bags 66.75 ft