Basic Math Questions and Answers

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

Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92? x+y = 15.98 x+y= 43.92 43.92x-2.99y = 12.99 2.99x+12.99y = 43.92

An internet provider charges a $150 set-up fee and a $70 monthly fee. Find the cost C(t) of having a contract with this provider for t months. If a person has paid $1130 to the internet provider, how many months has he had a contract with them? Find the cost C(t) of having a contract with this provider for t months. C(t)= (Simplify your answer.)

Convert 96°F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas. C= (F-32) F=C+32

The state of Michigan recorded an all-time high snowfall of 355.9 inches during the winter of 1978-79. Its lowest snowfall of 81.3 inches was recorded during the winter of 1930-31. How much more snowfall did Michigan receive during the winter of 1978-79 than in 1930-31?

For a ride on a rental scooter, Dante paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Dante's ride was $9.92. For how many minutes did Dante ride the scooter? minutes X 5 P

Frank invests $2,500 in an account that has an annual interest rate of 5.4% compounded continuously. Hannah invests $3,000 in an account that has an annual interest rate of 3.2% compounded quarterly. Which of the following statements is true when comparing the amount of money in the two accounts after 10 years? After 10 years Hannah has about $164 more than Frank. After 10 years Frank and Hannah have the same amount of money in their accounts. After 10 years Frank has about $164 more than Hannah. After 10 years Frank has about $500 more than Hannah.

Graph r(x) = -8. Use the graphing tool to graph the function.

The tangent line to the graph of y = g(x) at the point (4, 3) passes through the point (9, 4). Find g(4) and g'(4).

A class of 195 students went on a field trip. They took 7 vehicles, some cars and some buses. Each car holds 5 students and each bus hold 45 students. If x represents the number of cars and y represents the number of busses determine which of the following systems of equations model this scenario. x+y=195 7x + 5y = 45 x+y=7 5x + 45y = 195 x+y = 45 5x + 7y = 195 x+y = 745 x + 5y = 195

Using a calculator, simplify the following to the ten-thousandths place: A) log(768) B) In (135) 2.8853 4.9052 C) log4(225) 3.907 D) log (225) 5.4161

Is this equation an identity? 19p+ 16 = 2p + 17p + 16 yes no

Write the inequality using interval notation and illustrate the inequality using the real number line. -4≤x≤8

The population of Winnemucca, Nevada, can be modeled by P=6191(0.98)' where t is the number of years since 1990. What was the population in 1990? 6191 By what percent did the population change each year? [Select]

Determine if the following relation is a one-to-one function. S={(-6, -6), (4,4), (3,7), (7,3)} Is S a one-to-one function? Yes No

Use the Remainder Theorem and the Factor Theorem to determine whether (x+3) is a factor of the polynomial f(x) = 2x³ + 6x²+x+3. O It is not a factor because f(-3) = 0. O It is a factor because f(-3)-0. O It is a factor because f(3) = 0. It is not a factor because f(3) = 0.

How much water must be evaporated from 32 ounces of a 7% salt solution to make an 8% salt solution? To obtain a solution that is 8% salt,ounce(s) of water must be evaporated. (Simplify your answer)

Find the inverse of the one-to-one function. f(x) = 6x+5

The following table shows worldwide sales of a certain type of cell phone and their average selling prices in 2012 and 2013. Year q(p) = 2012 Selling Price ($) 395 Sales (millions) 702 2013 335 1,050 (a) Use the data to obtain a linear demand function for this type of cell phone. (Let p be the price, and let q be the demand). 29p 5 +2993 Use your demand equation to predict sales if the price is lowered to $235. 1630 ✔ million phones (b) Fill in the blank. For every $1 increase in price, sales of this type of cell phone decrease by 8 IVIT I X million units.

Given f(x) = 32x-3 +1 and g(x) = 4x, what is the x value(s) where f(x)=g(x)? O x-1.067 and x = 10 O x-0.267 and x -2.5 Ox=2 Ox-1.2 and x = 3.1

Ellie needs more than 10 packs of thread to make friendship bracelets for her classmates. She already has 6 packs of thread. She models this situation with the inequality 6 p> 10, where p is a number of packs of thread. Which values in the set (4, 5, 6, 7) are solutions of Ellie's inequality? Show your work,

Solve the inequality, and write the solution set in interval notation if possible. Write numbers as simplified fractions or integers. |4w-5| +6<3

The 2015 senior class from Puma High School raised funds for an end of the year party at Club Sizzle. It costs $4,000 to rent out Club Sizzle plus $20 per student for food and drinks. If the senior class raised $11,000 how many students can attend the end of year party?

- Multiply using the distributive property. a. 3(90+5) = 3. c. 4(a + b) = 4. e. 7(y + 3) = g. s(6+x) = i. 8(5+ b) = = +3. +4. ||

Assume that the growth of the membership of a country club was linear from 1996 to 2000 with a membership of 167 in 1996 and a rate of growth of 729 per year. a. Write an equation for the membership P of this country club as a function of the number of years x after 1996. b. Use the function to estimate the membership in 2002.

Find the derivative of the function. f(x)= = 10 √√x + 8cos x Step 1 Rewrite the function f(x) using an exponential expression for the radical. f(x) = 10x. + 8cos x

A local hamburger shop sold a combined total of 481 hamburgers and cheeseburgers on Saturday. There were 69 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Saturday?

Solve for x. x2+x-2=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

Factor the polynomial f(x) = x5 + 2x³ - 8x² - 16 and find its real zeros using the Zero Product Property. f(x) = (x³ - 8) (x² + 2); real zero at x = 2 f(x) = (x - 2) (x²+2x+4) (2²-2), real zeros at z = 2, ± √2 f(x) = (x − 2)(x² + 4x + 4) (²+2): real zeros at x = -2( multiplicity 2), 2 f(x) = (x - 2) (x² + 2x + 4) (x² + 2): real zero at x = 2

Identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. 3(8-8w)+2=-5w+3-19w Part 1 of 2 The equation is a conditional equation. a contradiction. an identity.

our final answer(s). The Toyota Camry and the Honda Civic were the top-selling passenger cars in the United States in 2016. Honda Civic sales were 22 thousand less than Toyota Camry sales, and 756 thousand of these two cars were sold. How many of each model of car were sold?

Solve for u. u²-6u+9=0 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution."

An employee has two options for positions in a large corporation. One position pays $13.30 per hour plus an additional unit rate of $0.95 per unit produced. The other pays $12.10 per hour plus a unit rate of $1.15. (a) Find linear equations for the hourly wages W in terms of x, the number of units produced per hour, for each option. option 1 W₁ = option 2 W₂ (b) Use a graphing utility to graph the linear equations and find the point of intersection. (x, y) = (

Given the parent function f(x) = x³, choose the function g(x) that first reflects f(x) over the x-axis and then shifts f(x) up by 2 and left by 1. g(x) = (x + 1)³ +2 g(x) = -(x + 1)³ +2 g(x) = -(2-1)³ + 2 g(x) = -(x - 1)³ - 2

Which polynomial has a zero at x=5, a zero with multiplicity two at x=-1, two imaginary zeros, and a y intercept at (0,4)? O f(x) = (x - 1)(x + 1)(x + 5) (x² - 4) O f(x) = (x + 1)²(x - 5) (x²+4) O f(x) = -(x + 1)(x - 1)(x - 5) (x² + 4) O f(x) = (x - 1)²(x + 5) (x² + 1)

The distance from Boston, Massachusetts, to Phoenix, Arizona, is approximately 1,690 mi. Estimate to find how long it would take to drive from Boston to Phoenix if you average 58 mi./hr. 0 20 1 C₂

Trent can deliver his newspapers in 60 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together? It will take minutes.

Ethanol fuel mixtures have "E" numbers that indicate the percentage of ethanol in the mixture by volume. For example, E10 is a mixture of 10% ethanol and 90% gasoline. How much E2 should be mixed with 5250 gal of E10 to make an E8 mixture? The amount of E2 needed is gal. X 5