Math Questions

The profits for a company can be modeled by the logarithmic function P(t) = (3/2)log(2t + 1) With P in thousands of dollars and tin years. What is the average increase in profit from year 2 to 3? a) 219 dollars/year b) 0.23 dollars/year c) 4.39 dollars/year d) 4386 dollars/year

Solve 3 cos²(x) + 5 cos(x) - 2 = 0 for the interval 0≤x≤ 2π a) 1.231 and 5.052 b) 1.231 c) 1.231, 2.356, 2.759 and 5.052 d) 5.052

Since the relationship sin²(x) + cos²(x) = 1 is correct, it stands to reason that sec²(x) + csc²(x) = 1 must also be correct. This statement is: a) True for all values of x b) Never true c) True for the interval 0 ≤ x ≤ 2π d) Not true only for the interval 0 ≤ x ≤ 2π

Find the area and perimeter of the figure below. Do not forget units. Arc AB is a semicircle (half of a circle, ABC is a right triangle, AB = 16 yards, BC = 12 yards and AC = 20 yards. Area = Perimeter =

Solve the equation. 2/3x+1/5x-1/4=4/5x The solution is x = (Type an integer or a simplified fraction.)

How much more intense is an earthquake of magnitude 3.6 than an earthquake of magnitude 1.8? a) 63 times more intense b) twice as intense c) 100 times more intense d) 1.8 times more intense

We are now going to work with Conditional Probability with Percentages. We will use the information from question 1. This time you will take the number of men divided by the total group. Next we will take that percentage of men who prefer chocolate chip cookies which is 5.67% and divide it by the percentage of men. Show your work.

Which statement is TRUE for the graph of the logarithmic function f(x) = log₂x: a) There is a horizontal asymptote b) The graph only exists above the x-axis c) The graph only exists to the right of the y-axis d) There is no restriction on the domain

Find the point that is symmetric to the point (0, -3) with respect to the x-axis, the y-axis, and the origin The point symmetric to (0, -3) with respect to the x-axis is (Type an ordered pair.) The point symmetric to (0, -3) with respect to the y-axis is (Type an ordered pair.) The point symmetric to (0, -3) with respect to the origin is (Type an ordered pair.)

Express as a single logarithm and simplify; log₃6+log₃1.5 a) 0 b) 1 c) 2 d) log₃7.5

Write an exponential function y= abˣ whose graph passes through (1, 3) and (3, 75). a y = 0.6(x⁵) b y = 5(0.6ˣ) c y = 0.6(36ˣ) d y = 0.6(5ˣ)

Simplify the expression. 4³√2+³√2 a 10 b 5³√2 c 5⁶√2 d 5³√4

Expand the logarithmic expression. log₃ x⁶/5y 6log₃x - log₃5 + log₃y 6log₃x - log₃5-log₃ y 6log₃ x + log₃ 5 + log₃y 6log₃x - 5log₃y

Which of the following is equivalent to: tan (θ)/cos (θ) a) cos(θ)/cot (θ) b) csc(θ)/sin (θ) c) 1 d) sec (θ)/cot (θ)

Which of the following functions are linear? a. y = 4x² +3 b. 2x + 4y = 14 c. y = 1/x +5 Select all that apply. A. y = 4x² +3 B. y= 1/x +5 C. 2x + 4y= 14

Solve y=f(x) for x. Then find the input(s) when the output is -7. f(x) = 5/9 x+2 a x= 9y-2 /5 ; -13 b x= 9y-18 / 5 ; -81/5 c x= 9y/5 -2 ; -73/5 d x= -5/9 y -2 ; 17/9

Decide whether f is even, odd, or neither. f(x)=x²-3x² +6 Choose the correct statement. A. The function is even. B. The function is odd. C. The function is neither even nor odd.

Condense the logarithmic expression. log₅6+3log₅3-log₅9 a log₅153 b log₅24 c log₅6 d log₅18

Chase had $100 in his wallet. He spent $5.56 on lunch one day and $1.75 on coffee a few mornings a week. Write and solve an inequality to determine how many mornings he got coffee if he now has at most $85 in his wallet.

Determine whether the sequence is geometric, arithmetic, neither with a defined general term, or neither with an undefined term, in any case justify your answer. 3, 1, 4, 1, 5, 9, 2, 6, . . .

Suppose z is the standard normal variable. Draw the normal curve for each of the following probability statements to visualize the required area. Report answers accurate to at least 4 decimal places. a. P(Z < -0.03)= b. P(z > -1.19) = c. P(Z < 0) = d. P(Z < 4.33) = e. P(-1.55 < z < 0.31) = f. P(-1.63 < z < 0) = g. P(z<-0.9 given z < 0) = h. P(z < -1.51 or z > 0.31) =

A population of values has a normal distribution with μ=152.1 and σ= 6.7. You intend to draw a random sample of size n = 25. First calculate z, round it to two (2) decimal places, then use the rounded z-score to determine the required probability accurate to four (4) decimal places. 1. Find the probability that a single randomly selected value is less than 155.5. P(x < 155.5) = 2. Find the probability that a sample of size n = 25 is randomly selected with a mean less than 155.5. P(x < 155.5) =

Let u and u be two vectors in an inner product space so that ||u||= 6, |v||=2 and the angle between the two vectors is 30°. Find the angle between vector u+3v and vector u-4v

Suppose the monthly cost for the manufacture of golf balls is C(x) = 3310 + 0.51x, where x is the number of golf balls produced each month. a. What is the slope of the graph of the total cost function? b. What is the marginal cost (rate of change of the cost function) for the product? c. What is the cost of each additional ball that is produced in a month? a. What is the slope of the graph of the total cost function? b. What is the marginal cost (rate of change of the cost function) for the product? c. What is the cost of each additional ball that is produced in a month?

A man bought a length of rope at the hardware store. He used one-third of it to make a bow painter (a rope located at the front of the canoe) for his canoe and then used one-fourth of the remaining piece to tie up a roll of carpet. He now has 24 feet of rope left. What was the length of the rope he had originally purchased? Since it is often helpful to visualize a problem, obtain your answer pictorially by adding additional marks and labels to the following drawing. He had originally purchased (Type an integer or a simplified fraction.) feet of rope.

At a track-and-field meet, the winner of the pole vault event cleared a height of 3.25 meters. This was 0.1 meters more than the height cleared by the second-place pole- vaulter. The second-place height was 0.05 meters more than the third-place height. What height did the third-place pole-vaulter clear?

Decide whether the statement is true or false. ØE{0} Choose the correct answer below. A. True because (Ø) represents a set with one element, Ø. B. False because Ø contains 0 elements so the only element of (Ø) is 0. C. False because Ø contains no elements so nothing can belong to it. - D. True because (Ø) is a subset of Ø.

Samuel invested $28,000 in an account paying an interest rate of 5% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest dollar, would be in the account after 5 years?

Which property is demonstrated by the following equation? (12+8) + 11 = 12 + (8 +11) Select the correct answer below: Commutative Distributive Identity Inverse Associative

In a study of the cost of speeding tickets across the nation, the cost is reported to be Normally distributed with a mean of $152. A local newspaper believes that the cost of speeding tickets in her county is higher. She takes a SRS of 35 speeding tickets and finds a mean cost of $158 with a sample standard deviation of $15. Select the correct p-value that would be used for conducting an hypothesis test to determine if the mean cost of speeding tickets in her county is higher than the national average. 0.0119 0.0062 0.0090 0.0098 0.0015 0.0028

Valerie is deciding on her schedule for next semester. She must take each of the following classes: English 102, Music 101, History 102, and Math 120. If there are 15 sections of English 102, 10 sections of Music 101, 13 sections of History 102, and 13 sections of Math 120, how many different possible schedules are there for Valerie to choose from? Assume there are no time conflicts between the different classes.

How much material would be needed for the rungs of a ladder of 30 rungs, if the rungs taper uniformly from 20 inches to 30 inches? inches of material would be needed. (Simplify your answer.)

A particle moves in a straight line and has velocity given by v(t) = -6t² + 7t-2 m/s. Its initial displacement is s(0) = 4 m. Find its position function s(t). Provide your answer below:

Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t2, where t is time in seconds. The height of a certain tower is 1005 feet. How long would it take an object to fall to the ground from the top of the building? seconds

The surface areas of two similar solids are 441 cm² and 225 cm². If the approximate volume of the smaller solid is 250 cm³, what is the volume of the larger solid? A. 466 cm³ B. 932 cm³ C. 686 cm³ D. 500 cm³

Officer James has noticed a strong positive correlation between the speed of the vehicles on Main Street and the number of accidents. In order to determine if the speed is causing the accidents, which experiment would be best? Officer James could make cars go fast and see if they crash. Officer James could view traffic cameras to determine the speed of some cars and compare the speed of the cars that wrecked to the speed of those that did not. Officer James could survey everyone who is in an accident and ask how fast they were going. Officer James could try to find someone who got in an accident while driving slowly.

It takes Doug 7 minutes to fill a bucket of blueberries and Nathan 10 minutes to fill the same size bucket. How long will it take them to fill 8 buckets of blueberries if they are working together? Approximately 28 minutes. Approximately 40 minutes. Approximately 33 minutes. Approximately 36 minutes.

Suppose that $2900 is borrowed for four years at an interest rate of 9% per year, compounded continuously. Find the amount owed, assuming no payments are made until the end. Do not round any intermediate computations, and round your answer to the nearest cent.

Sumalee wants to make a 23% saline solution. She has already poured 9 qt. of a 18% saline solution into a beaker. How many qt. of a 32% saline solution must she add to this to create the desired mixture? 5 qt. 6qt. 1 qt. 2 qt. 9 qt.

The use of a tremendously large sample does not solve the question of quality for an estimator. What problems do you anticipate with very large samples? (Select all that ap increase in standard error cost of sampling difficulty in obtaining a very large sample Oless outlier data none of these

The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude R and intensity I, the formula is R = log(1). The September 20, 1999 earthquake in Taiwan measured 7.7 on the Richter scale. The Beverly Hills earthquake in January 23, 2002 measured 1.8 on the scale. How many times more intense was the Talwan earthquake than the Beverly Hills earthquake? Round your answer to two decimal places, if necessary.

The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A-9,1000056 By what percentage is the account increasing each year? A 6.1% B. 6.2% C. 5.7% D. 5.9%

At a particular restaurant, each onion ring has 40 calories and each mini hotdog has 80 calories. A combination meal with onion rings and mini hotdogs has a total of 19 onion rings and mini hotdogs altogether and contains 1080 calories. Write a system of equations that could be used to determine the number of onion rings in the combination meal and the number of mini hotdogs in the combination meal. Define the variables that you use to write the system.

9. The time required to deliver and install a computer at a customer's location is t = 4+, where t is time in hours, d is the distance, in miles, from the warehouse to the customer's location, and r is the average speed of the delivery truck. If it takes 6.2 hours for the employee to deliver and install a computer for a customer located 100 miles from the warehouse, what is the average speed of the delivery truck?

The exponential model A=363.1 e 0.027t describes the population, A, of a country in millions, t years after 2003. Use the model to determine when the population of the country will be 676 million. The population of the country will be 676 million in (Round to the nearest year as needed.)

5. Jessica is building a model rocket for her physics class. After studying the flight path of her rocket, she has concluded that she wants her rocket to achieve a maximum height of 50 ft. The equation for her rocket is -3x² + 6x + 48. Will Jessica's rocket clear 50 ft?: (Hint Find the vertex of the equation to find the maximum height of the rocket)

A high times interest earned ratio indicates a. no protection in the event of an earnings decline. b. mediocre protection in the event of an earnings decline. c. extremely good protection in the event of an earnings decline. d. nothing about protection in the event of an earnings decline.

(a) Estimate the area under the graph of f(x) = 1 + x² from x= -1 to x 2 using three rectangles and right endpoints. Then improve your estimate by using six rectangles. Sketch the curve and the approximating rectangles. (b) Repeat part (a) using left endpoints. (c) Repeat part (a) using midpoints. (d) From your sketches in parts (a)-(c), which appears to be the best estimate?

8. There are 9 red, 6 blue, and 5 green marbles in a bag. a. How many marbles are in the bag? b. What is the probability a marble chosen at random will be blue?

Which of the following represents the explicit formula for the Arithmetic Sequence? -33, -29, -25, -21, .... Hint: a₁ = -33, so when n = 1, a₁ = -33.... Find the formula for an. an-37 + 4n an-33 + 2n an-31 + 2n an-33 + 4n