Basic Math Questions and Answers

Suppose that a guitar company estimates that its monthly cost is C(x) = 400x² + 600x and its monthly revenue is R(x) = -0.4x³ + 600x²200x + 500, where x is in thousands of guitars sold. The profit is the difference between the revenue and the cost. What is the profit function, P(x)? A. P(x) = 0.4x³ + 200x² 800x +500 B. P(x) = -0.4x³ + 1000x² + 400x +500 c. P(x) = 0.4x³ 200x² +800x 500 D. P(x) = 0.4x³ + 200x² 800x + 500

Solve |x- 4 + 6 = 15. A. x= 13 and x = -13 B. x = 13 and x = -5 C. x= -13 and x = 5 D. x= -13 and x = -5

A 60 ft. long swimming pool is to be constructed. The pool will be 3 ft. deep at one end and 12 ft. deep at the other. To the nearest degree, what will be the measure of the acute angle the bottom of the pool makes with the wall at the deep end? 78° 83° 81° 80° 84°

The Thompson family took a $300,000 mortgage loan, with no down payment, at an annual rate of 3.6% compounded monthly for 30 years. Calculate the family's monthly payment. Round the answer to the nearest hundredth.

Which expression is the simplest form of 5(2x-3) - 3(x+4) / 9 A. 7x-27 /9 B. 13x - 27/9 C. 7X - 3 / 9 D. 7x - 3

We created this inequality to represent how Amy can meet her revenue goals: -100x² +15,750x + 212,500 ≥ 243,600 In this activity, you'll solve this inequality to find the minimum ticket price Amy should charge to meet her minimum revenue goal.

Find an ordered pair (x, y) that is a solution to the equation. 4x+y=5

Which one of the following describes the solution set of |x + 7| <3? The interval from -co to 4 together with the interval from 10 to ∞ The interval from 4 to 10. The interval from -10 to -4. The interval from -∞ to -10 together with the interval from -4 to ∞. The interval from -4 to 10.

Which of the following statements is true of a reflection? Select all that apply. It is an isometry. It slides a plane. The transformation is done over a line of reflection. It flips a plane about a fixed line. It changes the size of the figure being reflected.

A 61/4-inch circular power saw rotates at 4,800 revolutions per minute. (Round your answers to two decimal places.) 4 (a) Find the angular speed of the saw blade in radians per minute. rad/min (b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut. ft/min

The drug concentration in the bloodstream t hours after injection is given approximately by C(t) = 4.95 e ¹,0sts5, where C(t) is the concentration in milligrams per milliliter. (A) What is the rate of change of concentration after 1 hour? After 5 hours? (B) Graph C.

Noah creates a scatter plot showing the relationship between number of free throws made in a basketball game and the number of points scored. The correlation coefficient for the line of best fit is 0.76. Are the two variables correlated? Explain your reasoning. b. Do either of the variables cause the other to change? Explain your reasoning.

There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If the total number of swans and ducks in the pond is 12, find the number of ducks. 16 9 3 4

A store is offering 25% off all shoes. Declan purchases shoes and clothes. The expression representing his total cost (including 8% tax) is c+(1-0.25)s+0.08[e+ (1-0.25) s). Which term represents the cost of the shoes after the discount? A. (1-0.25) B. 0.08[c+ (1-0.25) s] C. le+ (1-0.25) s] D. (1-0.25)s

A pyramid is 24 ft tall. A scaled model has a height of 2 ft and is 1 foot wide at the base. Identify the scale factor that was used to create the model. A. 1/12 C. 12 B. 1/24 D. 22

The equation y = -143x³ + 1810x² - 187x+2231 where x represents the time in years since January 1, 1983 is a mathematical model for the number of AIDS cases, y, in some population between the years 1983 and 1991. According to this model, how long after January 1, 1983 was the number of AIDS cases in this population 26,488? Round your answer to one decimal place. 4.4 years 04.3 years 4.6 years 04.7 years 05.1 years

Triangle ABC is translated onto its image, triangle A'B'C'. Use the given vertices of the triangles to answer parts A and B. A(-6, 0) B(-1, 0) C(-5, 3) A'(-2, 4) B'(3, 4) C'(-1, 7) Part A: Use the distance formula to prove that the translation was an isometric transformation. Include all of your work in your final answer. Part B: Use complete sentences to describe the translation that maps triangle ABC onto its image.

Solve 4ax + 5ax = 6ax +9 for x. Assume a ≠ 0. A. x = 3/a B. x = 2a C. x = 1/2a D. x= 3a

Solve |2x - 7 ≥ 11. A. x≤-2 or x ≥ 7 B. x≤-2 or x ≥ 8 C. x≤-2 or x ≥ 9 D. x≤ 3 or x ≥ 6

Select the correct answer. What is the simplest form of4m-17/m^2-16 + 3m-11/m^2-16, assuming no denominator equals zero? A. 7/m+4 B. 7m/m+4 C. 7/m-4 D. 7m-6/m^2-16

In a reflection along the x-axis a given coordinate (2, -1) transforms itself into which of the following? (2,1) (-2,1) (-2, 0) (0, 1)

Which expression is equivalent to the given expression? (3m²n)³/mn^4 A. 9m^5/n B. 9m^4n C. 27m^4n D. m27m^5/n

A coffee shop begins the day with 75 bagels and sells an average of 10 bagels each hour. Function bmodels the bagel inventory, (*), x hours after opening. b(x) = 75 - 10x If the coffee shop wants to make a graph of function b, which values of x should it include on the graph to include the relevant domain within the context? A. 0≤ x ≤ 7.5 B. 0≤ x ≤ 75 C -∞ ≤x ≤ ∞ D. 0≤x ≤ ∞

Samantha is a waitress and earns a weekly paycheck of $350 plus any tips she earns throughout the week. One week, Samantha noticed that she earned about $12 in tips each hour. Let x represent the number of hours Samantha works during a week where her average hourly earnings is $22.

Marci earns $8 an hour. Write an equation that shows the direct proportionality between hours (h) and money earned (m). A. 8h=m C. 8mh B. 8m = h D. none of the above

The equation t = -1/1.008 ln(12.3/W - 0.5) is a mathematical model for the relationship between the weight W (in grams) of an individual leaf of a wheat plant and the number of days t since the leaf unfolded from the stalk of the plant. The weight of a certain leaf is 13.1 grams. According to this model, how many days ago did the leaf unfold? (Round to the nearest tenth of a day.) 0.4 days 1.5 days 1.4 days 0.8 days 0.5 days

Which of the following represents x = 1/3y written in general form? 3x - y = 0 x- 1/3y=0 1/3x-y=0

If you rolled a die, what is the probability that you would roll a 4 or a 5?

Grace is traveling to an island for vacation. She drives from home at a constant rate for the first 154 miles, then takes a ferry to travel the last 35 miles from the coast to the island. The ferry travels at a constant rate that is half the rate at which Grace drives. Given that the entire trip takes 4 hours, complete the statement below. Grace drives at a rate of miles per hour.

Let u = i +6j and v=-4i +4j. Decompose u into two vectors u₁ and u₂, where u₁ is parallel to v and u₂ is orthogonal to v. Write your answers in the form ai+bj.

Solve |2x + 2| = 10. A. x = 4 and x = 6 B. x = 4 and x = -6 C. x = 4 and x = -4 D. x = -4 and x = -6

Write a direct proportion equation that shows the price (y) for any number of posters (x) that are $2.50 each. A. y = kx B. 2.50x=y C. $2.50 = yx D. 2.50y = x

Which of these is a factor in this expression? 6z^4 - 4+9 (y³+6) A. (y³ + 6) B. 9 (y³ + 6) C. -4+9 (y³ + 6) D. 6z^4-4

Solve 4|x + 5| = 16. A. x= -1 and x = 9 B. x = -1 and x = − 9 C. x= 1 and x = -9 D.x= 1 and x = -1

Theo's kitchen is 192 square feet. A blueprint of his kitchen is created with the scale 1 inch: 4 feet. What is the area of the kitchen on the blueprint?

Which of the following is a name for an isometry that moves or maps every point of the plane the same distance and direction? Select all that apply. flip glide rotation slide translation

Solve |6x + 3| = 27. A. x = -4 and x = -5 B. x = -4 and x = 5 C. x = 4 and x = -5 D. x = 4 and a = - 4

Solve 9 ax + 10ax = 11ax + 32 for x. Assume a 0. A. x = 4a B. x = 8a C. x = 4/a D. x = 1/8a

Mia has 50 feet of fencing to make a rectangular kennel for her dog. She decides to use a part of her house as one side of the kennel. She needs a minimum enclosed area of 300 square feet. Of the inequalities listed, which forms of the inequality represent this situation? -2/² +50/-300 ≥ 0 (/-15)(/-10) ≥ 0 /(50-20/) ≥ 300 (/-15)(/-10) ≤ 0 /(2/-50) ≥ 300 -2/² + 50/- 300 ≤ 0

For a candy-making competition, Tanya made 3 kinds of candies. She made 3 times as many orange candies as pineapple candies. She made 30 more lemon candies than pineapple candies. The ratio of orange candies to lemon candies was 2 to 1. Which equation could be used to find the number of pineapple candies Tanya made for the competition? 3n+ 2n = 30 3n/n+30 = 2 2.3n = 1.(n + 30) n+30/3n = 2

Which value of r indicates a stronger correlation: r=0.837 or r= -0.921? Explain your reasoning. Choose the correct answer below. A. r=0.837 represents a stronger correlation because | -0.921|> |0.837|. B. r= -0.921 represents a stronger correlation because | -0.921|> |0.837|. C. r=0.837 represents a stronger correlation because 0.837> - 0.921. D. r= -0.921 represents a stronger correlation because 0.837> -0.921.

Click on the graphic to select the figure that would make the following "a reflection in line k."

A car purchased for $25,000 depreciates annually at a rate of 11%. The value of the car t years after its purchase is given by the expression 25,000(0.89). Which expression represents the quarterly depreciated value at the rate at which the car is depreciating? A. 25,000(0.89^4 )^4t B. 25,000(0.89^4)^1/4 t C. 25,000(0.89^1/4)^1/4 t D. 25,000(0.89^1/4)^4t

Evaluate 4(x − 3) + 5x − x² for x = 2. A. 2 B. 11 C. 16 D. -2

Consider this equation. 10x +25/3x + 12=5x/x+4 How many valid solutions does the equation have? The equation has valid solution(s).

A map that was created using a scale of 1 inch : 3 miles shows a lake with an area of 4.5 square inches. What is the actual area of the lake?

Jason hired a luxury car service. The service charges a fixed rate of $4.92, regardless of the number of miles traveled, plus an additional $3.79 per mile. If Jason wants to spend no more than $4.20 per mile, what is the minimum number of miles he should travel? 12 1 6 0

A rotation is an isometry that moves a plane across a line of symmetry moves a plane in a straight line motion moves a plane as a nor image moves a plane about a fixed point

Consider this product. x^2-3x-10/x^2-6x+5 . x-2/x-5 The simplest form of this product has a numerator of and a denominator of The expression has an excluded value of x =

Finance. Suppose that $4,100 is invested at 3.2% annual interest rate, compounded monthly. How much money will be in the account in (A) 10 months? (B) 20 years? (A) Amount after 10 months: $ (Round to the nearest cent.)