Basic Math Questions and Answers

The number of research articles in Physical Review that were written by researchers in the United States from 1983 through 2003 can be approximated by A(t) = -0.01t² + 0.24t+ 3.4 hundred articles (t is the time in years since 1983). (a) Find an appropriate domain of A. (Enter your answer using interval notation.) Is t ≤ 20 an appropriate domain? Yes No (b) Compute A(16). hundred articles. What does the answer say about the number of research articles? Since t= 16 represents, the answer tells us that, in , approximately x 100 = T research articles in Physics Review were written by researchers in the U.S.

An inground swimming pool contains 2.3 x 10^4 units of water. Which unit of measure was used? teaspoons cubic centimeters fluid ounces gallons

The height h (in feet) of a water balloon can be modeled by h(x) = -3x² + 24x + 11, where x is the horizontal distance (in feet) from the launch pad. The launch pad is adjusted so that the water balloon lands exactly 9 feet away from the launch pad. Write a function that models the new path of the water balloon. Use Extra Example 5. The launch pad is adjusted so that the water balloon lands 8 feet from the launch pad. V/rite a function to model the new path of the water balloon.

Use technology to graph the pairs of functions on the same set of axes with -3 ≤ x ≤ 3. f₁(x) = 1.6^x, f₂(x) = 1.8^x Identify which graph corresponds to which function. f₁(x) starts lower than f₂(x), but finishes higher than f₂(x). f₁(x) is identical to f₂(x). f₁(x) starts higher than f₂(x), but finishes lower than f₂(x). f₁(x) is always lower than f₂(x). f₁(x) is always higher than f₂(x).

Factor the following expression completely: xy + 4y - 6x - 24

Factor the polynomial f(x)=x³-3x²-9x+27 and find all its real zeros using the Zero Product Property. f(x) = (x - 3)² real zero at x=3 (multiplicity 2) f(x) = (x - 3)³ real zeros at x=3 (multiplicity 3) f(x) = (x - 3)²(x + 3) real zeros at x=-3.3 (multiplicity 2) f(x) = (x - 3)(x + 3)(x - 2) real zeros at x=-3.3

Factor the following expression completely: 70p+q - 10 - 7qp

The value V of an item after 7 years is given by the following formula, assuming linear depreciation, V = C-Crt, where C is the original cost and r is the rate of depreciation expressed as a decimal. If you buy a car for $7830 and it depreciates linearly at a rate of 17% per year, what will be its value after 9 months? Round your answer to the nearest cent.

What electrical changes occur in muscles as they get tired? Student subjects hold their arms above their shoulders until they have to drop them. Meanwhile, the electrical activity in their arm muscles is measured. This is an uncontrolled experiment. an observational study. matched pairs experiment. a randomized comparative experiment.

If f(x) is a linear function, f(-1) = 1, and f(5) = -3, find an equation for f(x). f(x) =

Factor the following expression completely: 24p + q-3-8qp

Determine whether y is a function of x. x² + y = 3 Yes, y is a function of x. No, y is not a function of x. It cannot be determined whether y is a function of x.

The domain of the piecewise function is (-∞,∞). f(x) = x+4 if x < -2 x-4 if x ≥ -2 a. Graph the function. b. Use your graph to determine the function's range. a. Choose the correct graph below.

At a golf club the demand equation for the number of members of the club, q is given by q=-10p+200 where p is the yearly price for membership in the club a) Find the revenue function b) What would be the yearly price that would maximize revenue

Add the following polynomials (Write answers in descending order): 1. (7j³-2) + (5j³-j-3) 2. (8a5-4) + (3a² + a-2) 3. (6m5 + 1) + (2m5 + 9m - 1) 4. (3m5 + 1) + (9m5 +3m - 2) 5. (-5x²-x+4) + (-3x² - 5x+2) 6. (-4x + 4x³ + 7) + (3x³-9-3x) 7. (3x² - 2x + 1) + (-x² + 3x + 1)

Graph the equation y = -x² + 12x - 35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation -² + 12x - 35 = 0.

For a recent year, the monthly snowfall (in inches) for Chicago, Illinois, for November, December, January, and February was 2, 8.4, 11.2, and 7.9 respectively. How much snow would be necessary in March for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months?

A car rental agency advertised renting a car for $24.95 per day and $0.28 per mile. If Shawn rents this car for 2 days, how many whole miles can he drive on a $150 budget? miles (Round down to the nearest whole mile.)

The dollar value v (t) of a certain car model that is / years old is given by the following exponential function. v (t)=32,000(0.95)^t Find the initial value of the car and the value after 11 years. Round your answers to the nearest dollar as necessary. Initial value: Value after 11 years:

Tell whether each sentence below is true or false. The formula for calculating the sum of any finite geometric sequence is n/2 (a₁ + an). Standard deviation is a popular (and accurate) measure of the spread or distribution of a group of data.

Solve the polynomial inequality. (x + 1)(x-2)(x - 5) >0 (-∞, -1) U (2,5) (-1,2) U (5,∞) [-1,2] U [5,∞) (-∞, -1] U [2,5]

A bacteria culture starts with 960 bacteria and grows at a rate proportional to its size. After 6 hours there will be 5760 bacteria. (a) Express the population after t hours as a function of t. population: (function of t) (b) What will be the population after 2 hours? (c) How long will it take for the population to reach 1090?

Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product? The pair of numbers whose difference is 14 and whose product is as small as possible is (Use a comma to separate answers.)

Factor the polynomial f(x)= x³ - 2x² - 9x +18 given that x=2 is a zero of f(x). f(x) = (1-3)(x + 3) f(x) = (x-2)(x-3)(x+3) f(x) = (x + 2)(x − 3)(x+3) f(x) = (x-2)(x - 3)²

PLAT has vertices P(-1,1), L(0.2), A(1,2), T(0,1). P'L'A'T' is the image of PLAT for the translation (x,y) → (x+3, y-2), Show that PP', LI', AA', and TT' are all parallel. Two segments are parallel if are Find the coordinates of the images of the vertices by each x-coordinate andy-coordinate and each

A cylinder with surface area 300 square inches and a height equal to 10 inches has what volume? Round to the nearest cubic inch. 391 cubic inches. 782 cubic inches 498 cubic inches 738 cubic inches

You start a small baking business, and you want to earn a profit of at least $250 in the first month. The expenses in the first month are $155. What are the possible revenues that you need to earn to meet the profit goal? Write and solve an inequality to model this situation.

Factor the following expression completely: -4w² - 4w - 6w-6

Katie was asked to solve the following inequality and show all of her work. She made an error when solving. x/3 +2≤6 x + 2 ≤ 18 X ≤ 16

Members of the student council are taking a trip to the state legislature. The student council must pay a $1000 entry fee plus $140 per student. What is the average total cost per student if 25 students attend? Do not include the dollar sign ($) in your answer. Provide your answer below:

A certain forest covers an area of 1900 km2. Suppose that each year this area decreases by 8%. What will the area be after 11 years? Use the calculator provided and round your answer to the nearest square kilometer.

An entry level machinist's annual pay is $40,872 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its machinists. If the firm cuts the work year to 50 weeks but keeps the same rate of pay, how much should the machinist expect his annual pay to decrease? Round your answer to the nearest dollar.

Graph the function. h(x)=-3x²+5 Plot five points on the graph of the function: one point with x=0, two points with negative x-values, and two points with positive x-values. Then click on the graph-a-function button.

Suppose that we want to examine the relationship between high school GPA and college GPA. We collect data from students at a local college. The linear regression predicted college GPA = 1.07 +0.62* high school GPA. One student has a high school GPA of 3.00 and a college GPA of 3.15. What is the residual for this student? 0.15 -0.15 -0.22 0.22

Clay's hair is 10 2/7 inches long. The barber trims off 1/4 inch. About how long is his hair now? A 9 in. B 10 in. C 11 in. D 12 in.

A social networking site recorded that 80% of the people who became members of the site one month were between 30 and 40 years old. The equation below represents this information, where x represents the total number of people who became members of the site that month: x=0.8x + 72 How many people who became members of the site that month were between 30 and 40 years of age? a. 112 b. 288 c. 360 d. 432

Kelly has 4 times as many songs on her music player as Lou. Tiffany has 6 times as many songs on her music player as Lou. Altogether, they have 682 songs on their music players. How many songs does Kelly have?

A rectangular field is to have an area of 225 m² and is to be surrounded by a fence. The cost, C, of the fence is 2 dollars per meter of length. Express the total cost of the fence in terms of the width of the field (use the variable 'w' for width). C(w) = $

Factor the following expression completely: z²+9z-1z - 9

AB has coordinates A(-3, 9) and B(6, -12) After a dilation with scale factor of 2/3 centered at the origin, the coordinates of A', are The preimage and the image are to each other. parallel not parallel

Find the domain of the function f(x) = 2x² + 3x + 1 Use interval notation to express your answer.

Factor the following expression completely: 9w(3w+1) + 3w+1

A hair stylist makes $67 each day that she works and makes approximately $13 in tips for each hair cut that she gives. If she wants to make at least $184 in one day, at least how many hair cuts does she need to give?

Devante has some quarters and dimes. He has 23 coins worth a total of $3.05. How many of each type of coin does he have? Number of quarters: Number of dimes:

If the total precipitation (rainfall and snow) for the year at a mountain town is expected to be 37.9 inches and it has already rained 26.82 inches, how many more inches of precipitation are expected?

Add the polynomials: (-x^4 - 2x² + 5) + ( -11x³ - 12x² - 1)

Let f(x) = 5x + 3 and g(x)= 2x² + 2x. Find (f + g)(x). (f+g)(x) =

Find the associated exponential decay or growth model. (Round all coefficients to three significant digits.) Q = 1,700 when t = 0; half-life = 1 Q =

Subtract the polynomials: (-x^5 +7x^4-3x³-4x) - (12x^5 - 6x³ + 2x² - 11x)

Solve the system of equations: -4/5 x - 5/3 = -7/60 3/2 x - 2/5y = 11/10