Basic Math Questions and Answers

Complete the sentence below. If 9^x = 9^6, then x = If 9^3x = 9^6, then x =

The palm tree on the left is 10 years old. The palm tree on the right is 8 years old. The trees grow at the same rate. b. a. Estimate the height y (in feet) of each tree. Plot the two points (x, y), where x is the age of each tree and y is the height of each tree. c. What is the rate of growth of the trees? d. Write an equation that represents the height of a palm tree in terms of its age.

Make a conjecture. Choose the correct answer below. A. cos 4x - sin 4x = (cos x)² B. cos x - sin^x= cos x C. cosx- sin^x= cos 2x D. cos 4x - sin4x = (cos 2x)² cos 4x - sin 4x = (cos²x- sin2x) (cos²x+ sin²x)

An airline finds that if it prices a cross-country ticket at $500, it will sell 300 tickets per day. It estimates that each $10 price reduction will result in 30 more tickets sold per day. Find the ticket price (and the number of tickets sold) that will maximize the airline's revenue. ticket price number of tickets

In a laboratory, it was observed that a colony of bacteria increases at the rate of 30% per hour. If the original number of bacteria is 10 000 how many will there be, (a). after 15 minutes? (b). in 30 minutes? (c). in 5 hours?

What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box.

The point (a, b) is on the terminal side of angle C in the coordinate plane. If a is a positive integer and b is a negative integer, which of the following statements is correct? Select all that apply. A.Angle C is in Quadrant II B.tan C < 0 C.sin C <0 D.cos C <0

The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times its previous size in 2 years. Find the annual percentage rate according to the exponential growth function.Write your answer in exact form, using In (do not round). Note: When entering natural log in your answer, enter lowercase LN as "In". There is no "natural log" button on the Alta keyboard. Provide your answer below:

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