Basic Math Questions and Answers

Suppose a ball is thrown upward to a height of h0 meters. Each time the ball bounces, it rebounds to a fraction r of its previous height. Let hn be the height after the nth bounce. Consider the following values of h0 and r. Complete parts (a) and (b) below. h0=45, r=0.5 a. Find the first four terms of the sequence of heights {hn}.

While attending a major league baseball game, you think you can guess the attendance within 10% of the actual value. If the announced attendance is 35,000, within what number of people would your guess have to be in order for you to support your claim?

A house is advertised as having 1500 square feet under roof. What is the area of this house in square meters?

Given the function f(x)=x²-21, x20, complete parts a through c. (a) Find an equation for f¹(x). (b) Graph f and f¹ in the same rectangular coordinate system. (c) Use interval notation to give the domain and the range of f and f¹. (a) Find f¹(x). (Type an exact answer, using radicals as needed.)

Sand falls from a conveyor belt at a rate of 11 m³/min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 2 m high? The height is changing at a rate of cm/min when the height is 2 m. (Type an integer or decimal. Round to the nearest hundredth.)

Find the quotient and remainder using long division. 25x³ + 45x² + 30x + 8/5x+4 The quotient is The remainder is

The function A = Age-0.00866x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 800 pounds of the material are placed in the vault, how much time will need to pass for only 218 pounds to remain?

Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation).

A Food Marketing Institute found that 28% of households spend more than $125 a week on groceries. Assume the population proportion is 0.28 and a simple random sample of 193 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.25? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.25. Round the answer to 4 decimal places.

A professional soccer player kicked a ball across the field. The ball's height, in meters, is modeled by the function graphed below. What's the average rate of change between the point when the ball reached its maximum height and the point where it hit the ground? -1/3 meters per second meters per second 3 meters per second meters per second

A prism of angle 6° made from a crown glass of refractive index 1.5 is placed in contact with another prism, made of flint glass of refractive index 1.6. A ray of light falling normally passes through the two prisms without deviation. The angle of flint glass prism is A 2.0 B 5.0 C 6.6 D 7.2°

TV PURCHASES-AT A CIRCUIT CITY STORE, OF THOSE PURCHASING COLOR TELEVISIONS PURCHASE A LARGE-SCREEN TV. FIND THE PROBABILITY THAT NONE OF THE NEXT FOUR PEOPLE WHO PURCHASE A COLOR TELEVISION AT CIRCUIT CITY PURCHASES A LARGE-SCREEN TV.

Mr. and Mrs. Brown anticipate that they will need $60,000 for their child's education in 18 years. If their savings account earns 4% compounded quarterly, how much would they need to deposit now to reach their goal? (Round to the nearest dollar) $54,000 $34,884 $2327 $29,310

View the video found on page 1 of this journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations.

Sydney Dukes-Miller deposited $2,430 at 6.75%. She made no other deposits or withdrawals. How much simple interest did she earn in 65 days? What is the final amount in the account? (2 points)

What is the center of the shape formed by the equation (x-3)²/49 - (y+5)²/25 = 1? (0,0) (-3,5) (3,-5) (9,25) (-9, -25) (x-3)²

Julio must invest a total of $6300 in two accounts, one paying 10% simple annual interest and the other paying 7% annual interest. If he wants to earn $534.00 annual interest, how much should be invested at each rate?

The length of a path going diagonally across a rectangular field is 100 yards, the width of the rectangular field is 50 yards. What is the measure of the angle these two lines form? (Round your measure to the nearest whole degree).

Consider the function f(x) = 25x² - 64. a) Determine the zeros of the function: Writing values as simplified fractions if necessary. If there are multiple values, separate the solutions with a comma. If there are no values, input "DNE". b) Determine the x-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple x-intercepts, separate them with a comma. If there are no x-intercepts, input "DNE". c) Determine the y-intercept(s) of the graph of the function: Write ordered pairs, writing any values as simplified fractions if necessary. If there are multiple y-intercepts, separate them with a comma. If there are no y-intercepts, input "DNE".

The polynomial of degree 4, P(x), has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x - 1. It goes through the point (5, 96). Find a formula for P(x). P(x) =

A car was valued at $40,000 in the year 1995. The value depreciated to $14,000 by the year 2007. A) What was the annual rate of change between 1995 and 2007? T= Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? T = C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012? value = $ Round to the nearest 50 dollars.

Given a function f (x) = 2x² + 3, what is the average rate of change of f on the interval [2, 2 + h]? 11 2h +8 2h² + 8h 2h² + 8h + 11

Consider the equation below. f(x) = 2x³ + 3x² = 120x (a) Find the interval(s) of increase and decrease. (b) Find the local minimum and maximum values of f. (c) Find the inflection point and the intervals on which fis concave up and concave down. (a) Find the interval(s) of increase and decrease. For f(x) = 2x³ + 3x2 - 120x, we have the following f'(x) = This factors into(__)(x+__)(x-4).

A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. How rapidly is the area enclosed by the ripple increasing when the radius is 1 feet?

A linear function is given. Complete parts (a)-(d). f(x)=1/5x-6 (a) Determine the slope and y-intercept of the function.

Select the correct answer from each drop-down menu. The barley plant has seven pairs of chromosomes. For a gamete, the number of genetic combinations that are possible through independent assortment is __. For a zygote produced by two barley parents, the number of possible genetic combinations is__

A right triangle has sides that measure 24 and 32, but the length of the hypotenuse is unknown. What is the perimeter measurement of this triangle? Round your answer to the nearest hundredth 85.23 96 89 94.79

A candy company claims that 25% of the candies in its bags are colored green. Steve buys 32 bags of 32 candies, randomly selects one candy from each, and counts the number of green candies. If there are 7, 8, or 9 green candies, Steve will conclude that the company's claim is correct. What is the probability of Steve agreeing with the company's claim? Use Excel to find the probability • Round your answer to three decimal places.

A gallon contains 231 cubic inches. A cylindrical barrel full of juice concentrate has a diameter of 3 feet and is 8 feet high. How many gallons of concentrate are in the barrel? Use π = 3.14. There are __ gallons of concentrate in the barrel. (Type an integer or a decimal. Round to two decimal places as needed.) .....

If y varies inversely with the square of x, and y = 12 when x = 3, find y when x = 0.5. y= (Simplify your answer. Type an integer or a decimal.) *****

Kevin the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 8 clients who did Plan A and 3 who did Plan B. On Tuesday there were 2 clients who did Plan A and 5 who did Plan B. Kevin trained his Monday clients for a total of 15 hours and his Tuesday clients for a total of 8 hours. How long does each of the workout plans last? Length of each Plan A workout: _hour(s) Length of each Plan B workout: _hour(s)

(a) Use one of DeMorgan's Laws to choose a negation of the following statement. Abdul is in art class or he has a test today. Negation: (Choose one) (b) Use one of DeMorgan's Laws to choose a statement equivalent to the following. It is not the case that "squares have seven sides and trapezoids have nine angles". Equivalent: (Choose one) Squares don't have seven sides and trapezoids don't have nine angles. Trapezoids have nine angles or squares have seven sides. Trapezoids have nine angles and squares have seven sides. Squares don't have seven sides or trapezoids don't have nine angles.

Solve the following equations for x, showing each step on a separate line. Check your answers. a) 5x - 3x = 8 b) 5x - 3 = 8 c) 5x - 3 = 8x d) 2x - 11 = 4-x e) 2x - 11 = 4+* f) 2x + 11 = 4 + x g) 7x 6 = 18 + 3x h) 7x + 6 = 18 - 3x

Solve for x. |2x - 3| ≤2 What is the solution? Select the correct choice below and fill in any answer boxes within your choice. A. x≤__ or x ≥__ (Simplify your answers.) B. _≤x≤_ (Simplify your answers.)

A mortgage is paid off in 30 years with a total of $124,000. It had a 2% interest rate that compounded monthly. What was the principal? Round your answer to the nearest cent and do not include the dollar sign. Do not round at any other point in the solving process; only round your final answer. Provide your answer below:

Determine if the function given below is increasing, decreasing, or constant. f(x) = 0 Select the correct answer below: The line is increasing. The line is constant. The line is decreasing.

Select a possible formula for the polynomial f(x), given that f(x) has degree three, f(-1) = f(3) = f(5) = 0, and limz⇒∞f(x) = -∞. A. -(x + 1)(x - 3)(x - 5) B. -(x + 1)2(x - 3)(x - 5) C. (x + 1)(x+3)(x - 5) D. -(x + 1)(x + 5)(x+3) Is there more than one possible solution? A. No, because there is only one function that meets all of the requirements. B. Yes, because the leading coefficient could be any negative number. C. Yes, because there could be different multiplicities for the roots. D. No, because we know the three roots and it is a degree three polynomial.

"Princess Tower" in Dubai is considered the world's tallest residential building, towering to 101 floors! T(n) models the number of tenants living on floor n of the tower. What does the statement T(20) = T(c) mean? Choose 1 answer: (A).Floor 20 and floor c have the same number of tenants. (B)The number of tenants on floor 20 is equal to C. (C)The number of tenants on floor C is equal to 20.

Quadrilateral ABCD has vertices A(-2, 1), B(4,4), C(5, 0), and D(-1, -2). Which side is the longest? CD DA AB BC

Subtract the polynomials: (-8x5 + 10x² - 10x) - (-7x5 - 8x² + 6)

Is the function below exponential? m(t) = (2.3t) ³ If so, write the function in the form m(t) = abt and enter the values you find for a and b in the indicated blanks below. If the function is not exponential, enter NONE in both blanks below. a b

A clothing business finds there is a linear relationship between the number of shirts, it can sell and the price, P, It cancharge per shirt. In particular, historical data shows that 3 thousand shirts can be sold at a price of $78 each, and that 7 thousand shirts can be sold at a price of $62 each. Find the equation of the form P(n) = mn + b that gives the price P they can charge for n thousand shirts. Select the correct answer below: P(n) = 0n + 78 P(n) = -4n +95 P(n) = -4n +90 P(n) = On +62 P(n) = -6n +104 P(n) = -6n +96

Using the slope formula, find the slope of the line through the given points. (6,7) and (9,4) What is the slope of the line? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is B. The slope of the line is undefined. (Type an integer or a simplified fraction.)

Mario has a 500-page novel which he is required to read over summer break for his upcoming language arts class. a. If Mario reads 24 pages each day, write a function to represent the number of pages that Mario has left to read p after d days.

The notation fog, called the of the function f with g, is defined by (fog)(x) =

You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? 3x-2y=7 Equation 1 3x+4y=17 Equation 2 A. Multiply equation 1 by 2. Then add the new equation to equation 2. B. Subtract the left side of equation 2 from the left side of equation C. Subtract equation 2 from equation 1.

A 12-sided die can be made from a geometric solid called a dodecahedron. Assume that a fair dodecahedron is rolled. The sample space is (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12). Find P(7). 1/12 1/2 5/12 7/12

When we throw a tennis ball into a lake for my dog she knows that if she swims straight for it she'll take longer to get to the ball. Instead, she runs along the beach for a short distance and then turns and swims for the ball. Let's say we throw the ball so that it lands 15 meters out into the water and 5 meters to the right of where we're standing. Draw a picture of this scenario. Finally, let's say that the dog runs at a rate of 2.5 meters per second and swims at a rate of 1 meters per second. (A) If the dog were to swim directly for the ball how long will it take? Recall that distance is equal to rate multiplied by time. Direct Swim Time = seconds. (B) If the dog were to run down the beach and make a 90 degree turn and then swim directly for the ball how long would it take to get to the ball? Time for longest run and 90 degree turn to swim = seconds. (C) My dog is smarter than either of the answers in parts (A) or (B). She knows that there is a better solution. Let be the amount of running that she does down the beach (clearly r is less than 5 and greater than 0). The trip has now been broken into two parts: a running leg of length x meters and a swimming leg at some angle to the beach. What is the length of the swimming leg as a function of r? Length of swimming leg = (D) Write a function T(r) that expresses the total time to get to the ball in terms of how far she runs down the beach. T(r):

At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the height of the tree. Find the height of the tree.

The side of a square floor tile is measured to be 16 inches, with a possible error of 1/32 inch. Use differentials to approximate the possible error and the relative error in computing the area of the square. Step 1 Recall that the formula for the area of a square is A = x2 where x is the side of the square. We are given that the side of the square floor tile is x = 16 inches and the possible error Δx = dx = ±1/32 Step 2 To approximate the possible propagated error in computing the area of the square, differentiate A =x² with respect to x. dA /dx= dA= Step 3 Substitute the given values of x and dx into the equation. dA = 2x dx Step 4 Assuming that ΔA=dA, we can conclude that the approximate possible propagated error in computing the area of the square is in².