Basic Math Questions and Answers

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

Which of the following is not a law of exponents? When dividing like bases subtract the exponents 1 to any power is 1 Anything to the 0th power is 1, except 0 When adding like bases multiply the exponents.

Bradley High School was the winner in Saturday's track meet with the help of 20 individual-event placers earning a combined 68 points. A first place finish earns 5 points, a second place finish earns 3 points, and a third place finish earns 1 point. Bradley had a strong second-place showing, with as many second place finishers as first- and third- place finishers combined. If x = # of first-place finishers, y = # second-place finishers, and z = # of third-place finishers which of the following systems represents this scenario? Ox+y+z= 68 5x + 3y +z = 68 Z = x + y Ox+y+z= 20 5x + 3y + z = 68 y=x+z Ox+y+z=20 5x + 3y + z = 68 x = y + z

Write the equation of the line with slope 5 and y-intercept 1/2 The equation of the line is

A Hamilton multitouch watch was originally priced at $475. At a closing of the Alpha Omega Jewelry Shop, the watch is being reduced by What is the new selling price?

Critique Reasoning A cube-shaped box has a volume of 27 cubic inches. Bethany says each side of the cube measures 9 inches because 9 x 3=27. Is Bethany correct? Explain your reasoning. MP.3

Lacoste Middle School surveyed its student population about their favorite mobile apps. The 786 students who listed Facebook as their favorite app represented 32 fewer students than two times the number of students who listed Instagram as their favorite app. How many students listed Instagram as their favorite app? students

5 A triangle has sides 46 yards, 8 yards, and 38 yards. What is the perimeter (distance around the edges) of the triangle in yards? Express your answer in mixed number form, and reduce if possible.

Which of the following functions has a restricted domain? f(x) = 3x² - 2x + 1 f(x) = 3√2-1 f(x) = -32-3+1 f(x) = ln(x - 3)

Keiko, Jose, and Michael have a total of $97 in their wallets. Keiko has $7 more than Michael. Jose has 4 times what Michael has. How much does each have? Amount in Keiko's wallet: Amount in Jose's wallet: Amount in Michael's wallet: $ $

Lara rents a car while spending her vacation traveling in Chile. When she returns the car, she has driven 850 miles and used about 34 gallons of gas. If gas costs an average of $5.889 per gallon, estimate how much she spent on fuel.

Solve the following using substitution. If one solution, type that point in for both points. If no solution, type in "NS": y = 3x² - 4x -1 x + y = 5 Solution 1: x = Solution 2: x =

Jina received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.63 per pound. After buying the coffee, she had $28.22 left on her card. How many pounds of coffee did she buy?

Tempco Corporation has a machine that produces 11 baseball gloves each hour. In the last 2 days, the machine has run for a total of 30 hours. How many baseball gloves has Tempco produced? Number of baseball gloves

Translate the following sentence into a mathematical equation. Be sure to identify the meaning of all symbols. The area of a rectangle equals length times width. Let A represent area of a rectangle, L represent length, and W represent width. The mathematical equation is

Kaina has two jobs at two different pharmacies. At Walgreen's, she earns $13 dollars per hour. At CVS, she earns $14 dollars per hour. She needs $300.00 to pay her weekly bills. a. Create an inequality to describe the number of hours she could work at each pharmacy to earn this amount. b. If she works 5 hours at Walgreen's next week, how many hours does she needs to work at CVS to be able to pay her bills?

Which formula defines the sequence f(1) = 2, f(2)= 6, f(3) = 10, f(4) = 14, f(5) = 18? O f(1) = 2, f(n) = 4+ f(n-1) for n ≥ 2 O f(1) = 2, f(n) = 6 + f(n-1) for n ≥ 2 O f(1) = 6. f(n) = 4+ f(n-1) for n ≥ 2 O f(1) = 2, f(n) = 2 + f(n-1) for n 2 thy

On the walk home from school, Meg stopped at the library for 22 minutes and at her grandmother's house for 38 minutes. She spent 17 minutes walking. She left at 3:00 and was supposed to be home by 4:00. a. Did Meg make it home on time? 7:00 How did you get your answer?

The length of a rectangle is 5 yd more than twice the width x. The area is 738 yd². (a) Write an equation in terms of x that represents the given relationship. The equation is 738 = 7 Correct Answer: The equation is x (2x+5)=738. Part: 1/3 Part 2 of 3 (b) Solve the equation to find the dimensions of the given shape.

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? Dapublicans. There

Find the equation that represents the volume of a large shipping container in the shape of a rectangular prism with length x, width that is 2 meters more than the length, and height that is one third of the length. V=2(2-2)(3x) V=2(2-4) (=) V=1(1+2) (3z) V=2(2+2) (²)

A translation takes the point (2, -5) and moves it to (-3, -1). If the image of another point under the same translation is (1,14), what are the coordinates of it- pre-image? Explain your process (that means to write in sentences!)

PROBLEM SOLVING You travel on the highway at a constant speed of 70 miles per hour for 1 hour 45 minutes. Your vehicl travets miles per gallon and gasoline costs $2.90 per gallon. How much do you spend on fuel for the trip? You spend $ on fuel for the trip.

Miyoko was putting her wrenches away and discovered that one was missing. Her missing wrench is near the center of her 1/16-inch set. She had the following wrenches: 1/4, 7/16, 3/8, 3/16, and 1/8. Which wrench was missing? Record your answer as a simplified fraction.

The density of steel is 8,050 kilograms per cubic meter. A construction company is using a steel beam in the shape of a rectangular prism that measures 12 meters long, 1/5 of a meter wide, and 1/3 meter deep. What is the weight of the steel beam? O 6,440 kilograms O 8,050 kilograms O 3,220 kilograms O 1,610 kilograms

Tiffani Lind got her new weekly course schedule from Roxbury Community College in Boston. Following are her classes and their length: Business Math, 6 hours; Introduction to Business, 3 hours; Microeconomics, 3 hours; Spanish, 24 hours: Marketing, 2 hours; and Business Statistics, 14 hours. How long will she be in class each week? Number of hours

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. If x represents the number of children that came to the fair and y represents the number of adults that came to the fair which of the following systems of equations model this scenario. O 1.50x + 2200y = 5050 2200x + 4.00y = 5050 Ox+y= 2200 1.5x + 4.00y = Ox+y= 2200 = 5050 4.00x +1.50y = 5050 1.50x + 4.00y = 2200 2200x+2200y = 5050

Lacey and Haley are rewriting expressions in an equivalent, simpler form. a. b. Haley simplified x³ x² and got x5. Lacey simplified x³ + x² and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know? Haley simplifies 35.45 and gets the result 1210, but Lacey is not sure. Is Haley correct? Be sure to justify your answer.

Identify the end behavior of the polynomial function. y = -x5-x³ + 4x + 6 O Asz-∞, f(x)→-∞o; As a → ∞, f(z) →-00 O As x-x, f(x) → -∞; As xx, f(z) → ∞ Asa-∞, f(x) → ∞; Asz →x, f(x) - - As a →-∞, f(x) →∞; Aszx, f(x) →∞ O -X

Molly's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 6 adult tickets and 8 student tickets for a total of $60. The school took in $48 on the second day by selling 7 adult tickets and 2 student tickets. Find the price of an adult ticket and the price of a student ticket.

The indoor climbing gym is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 12 buses with 744 students. High School B rented and filled 5 vans and 6 buses with 381 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?