Math Questions

If you drive 23 miles south, make a turn and drive 39 miles east, how far are you, in a straight line, from your starting point? Round your answer to the nearest tenth of a mile. If a 12-foot ladder is leaned against the top of a 10-foot high wall, how far will the base of the ladder be from the bottom of the wall? Round your answer to the nearest tenth of a foot.

Cabinet X costs $60, requires 12 sq ft of floor space, and holds 24 cu ft of files. Cabinet Y costs $50, requires 6 sq ft of floor space, and holds 24 cu ft. To get maximum storage, how many of each should be purchased with a budget limit of $600 and floor space of 96 sq ft?

The time that it takes for the next train to come follows a Uniform distribution with f(x) =1/30 where x goes between 4 and 34 minutes. Round answers to 4 decimal places when possible. a. This is a Select an answer distribution. b. It is a Select an answer distribution. c. The mean of this distribution is 19 d. The standard deviation is e. Find the probability that the time will be at most 8 minutes. f. Find the probability that the time will be between 14 and 24 minutes. g. Find the 32nd percentile. h. Find the probability that the time is more than 28 minutes given (or knowing that) it is at least 8 minutes.

Fill in the missing words for the following statement about functions: A function is a relationship between two sets of data, the input and output sets. and the set of outputs is called the___The set of inputs is called the___

Which of the following is true about the graph of f(x) = 6x³ - 12x² + 6x - 7? a) f(x) has a local minimum at the point (1/3 , -55/9) b) f(x) is decreasing on the interval (1/3, 1). c) f(x) has a local maximum at the point (1, -7). d) f(x) is increasing on the interval(2/3 ,infinity) e) f(x) has a point of inflection at the point (1, -7).

A regular octagon is inscribed inside a circle. The perimeter of the octagon is 96 units. A: What is the measure of a side of the octagon? B: What is the measure of a central angle of the octagon? C: What is the approximate measure of the apothem of the octagon (to the nearest hundredth of a unit)? D: Using your answer to part C, what is the approximate area of the octagon (to the nearest whole unit²)? B: 60* D: 120 units² C: 2.49 units B: 30* B: 45* C: 14.49 units D: 696 units² A: 12 units C: 5.54 units D: 753 units² D: 266 units² A: 16 units C: 15.69 units A: 6 units

For a given input value x, the function h outputs a value y to satisfy the following equation. 6x + y = 4x + 11y Write a formula for h(x) in terms of x. h(x) =

Christine is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges an initial fee of $77.50 and an additional 30 cents for every mile driven. Company B charges an initial fee of $45 and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.

Identify the Domain and Range for the following set of coordinates: (-4,2), (3,-5), (4,-2), (9,-7) Select one: a. D = {4, -3, -4, -9} and R = (-2, 5, 2, 7}. b. D = (-2, 5, 2, 7) and R = {4, -3, -4, -9}. c. D = {2, -5, -2, -7} and R = {-4, 3, 4, 9}. d. D={-4, 3, 4, 9) and R = {2, -5, -2, -7}.

Fill in the blanks to correctly complete the sentence below. Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ. The sampling distribution of x has mean µx= and standard deviation σx=

Identify the transformation equation below for the following function: f(x) = x²→ shifted 2 units right & up 2 units Select one: a. f(x) = (x + 2)² + 2 b. f(x) = (x - 2)² + 2 c. f(x) = (2x)² - 2 d. f(x) = 2(x)² +2

If two six-sided dice are rolled, then the sum of the dice is an example of a continuous random variable. true false

Simplify the following rational expression by subtracting, then identify the simplified form below. 6/x2-1 - 3/x+1 Select one: a. x²+1 / (x-3)(x+3) b. 3x²/ (x-1)(x+1) c. x-3 / (x²-1)(x²+1) d. -3x+9 / (x-1)(x+1)

The population P(t) of a culture of the bacterium Pseudomonas aeruginosa is given by P(t)=-1687t2 +83,000t+10,000, where it is the time in hours since the culture was started. (a) Determine the time at which the population is at a maximum. Round to the nearest hour.

List the roots of the parabola: y = -x² + 20x - 7 In other words, list the solutions of the equation: 0= -x² + 20x - 7 x= Your answers must be in exact form, do not give their decimal values. Separate multiple roots with a comma.

This polynomial is not factorable, so you need to use the complete the square method. Solve the equation for x. x² + 2x - 12 = 0

A ball is drawn randomly from a jar that contains 3 red balls, 7 white balls, and 4 yellow balls. Find the probability of the given event, and please show your answers as reduced fractions. (a) A red ball is drawn. P(red). (b) A white ball is drawn. P(white) (c) A yellow ball or red ball is drawn. P(yellow or red)

A poll showed that 59.9% of Americans say they believe that life exists elsewhere in the galaxy. What is the probability of randomly selecting someone who does not believe that life exists elsewhere in the galaxy. Probability=

An exponential function f(x) = ab^x passes through the points (0, 4000) and (3, 108). What are the values of a and b? a = b=

A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.) y = 18(1.15)^x y = 18(0.15)^x y = 20.7(1.15)^x y = 20.7(0.15)^x

Write an expression that represents the total cost of making roughly 16 coffees at home and occasionally going to Starbucks (use x to represent the number of mochas). What does each part of your expression represent? Don't forget to define your variable.

Plot the point (0.5, -2.5) in a rectangular coordinate system. Indicate in which quadrant the point lies. Plot the point (0.5, -2.5) on the graph to the right.

Mr. Parker had $86 to buy school supplies for his class. He bought 32 boxes of pencils and 32 packages of notebook paper. Each package of paper cost $1.09, and each box of pencils cost $0.75. How much money did Mr. Parker have left?

f(x)=√(x-4) Plot four points on the graph of the function: the leftmost point and three additional points. Then click on the graph-a-function button.

Greg is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A has no initial fee but charges 70 cents for every mile driven. Company B charges an initial fee of $55 and an additional 20 cents for every mile driven. For what mileages will Company A charge more than Company B? Use m for the number of miles driven, and solve your inequality for m.

A special deck of cards has 5 blue cards, and 3 yellow cards. The blue cards are numbered 1, 2, 3, 4 and 5. The yellow cards are numbered 1, 2, and 3. The cards are well shuffled and you randomly draw one card. A card drawn is yellow B = card drawn is even-numbered a) How many elements are there in the sample space? b) P(A) = Please enter a reduced fraction c) P(B) = Please enter a reduced fraction

Bloomington is a growing industrial town. Every year, the level of CO₂ emissions from the town increases by 6%. If the town produced 186,000 metric tons of CO₂ this year, how much will be produced 5 years in the future? If necessary, round your answer to the nearest whole number.

For a given input value n, the function g outputs a value m to satisfy the following equation. 3m - 5n = 11 Write a formula for g(n) in terms of n. g(n) =

The rabbit population in a forest area grows at the rate of 9% monthly. If there are 160 rabbits in July, find how many rabbits (rounded to the nearest whole number) should be expected by next July. Use y-160(2.7)^0.09t 481 455 468 467

In the spring of 2008, petrol cost £1.029 per litre in London. On the same day, the exchange rate was $1 = £0.498. What was the price of London petrol in dollars ($) per gallon? (1 gal = 3.7854 L) $1.83 /gal $7.82 /gal $3.90 /gal $7.60 /gal $1.94 /gal

You want to start a summer business to earn money. What will you do? You have to consider how much money you can afford to invest in this business, how much it will cost you to make each item, and how much you're going to charge for each item. Research something that would be reasonable to make and sell with the start- up investment you have determined. a. What is the total amount of money you are willing to invest in this business? b. What item are you going to make and sell? Why? c. Describe how your business will work. How much will it cost you to make each item? How much will you sell each item for? d. Do you think your business will be profitable? Explain your answer.

A group of people were asked if Marilyn Monroe had an affair with JFK. 467 responded "yes", and 487 responded "no". Find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with JFK. Probability (Please enter a reduced fraction.)

The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.6 mm. Round values to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the round off error for a jumper's distance is exactly 2.3 is P(x = 2.3) = d. The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.6 mm is P(1.4 < x < 4.6) = e. The probability that the jump's round off error is greater than 1.32 is P(x > 1.32) = f. P(x> 4.7 x > 0.6) = g. Find the 92nd percentile. h. Find the minimum for the upper quartile.

A geneticist conducts an experiment with peas, one sample of offspring consisted of 458 green peas and 149 yellow peas. Based on these results, estimate the probability of getting an offspring pea that is green. Report the answer as a percent with one decimal place accuracy. (You need not enter the "%" symbol) Probability Is the result reasonably close to the value of 3/4 that was expected? yes no

Raina is choosing between two exercise routines. In Routine #1, she burns 21 calories walking. She then runs at a rate that burns 10.25 calories per minute. In Routine #2, she does only running, burning 15.5 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train is 3 mph greaterbthan the speed of the eastbound train. After 3.5 hours, they are 567 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions. AnswerHow to enter your answer (opens in new window) westbound train: eastbound train:

For the polynomial below, -3 is a zero. h(x) = x³ + x² − 9x-9 Express h (x) as a product of linear factors. h(x) =

Suppose that the weight of an newborn fawn is Uniformly distributed between 1.5 and 3.6 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. a. The mean of this distribution is b. The standard deviation is c. The probability that fawn will weigh exactly 2.6 kg is P(x = 2.6) = d. The probability that a newborn fawn will be weigh between 1.6 and 2.9 is P(1.6 < x < 2.9) = e. The probability that a newborn fawn will be weigh more than 3.12 is P(x > 3.12) = f. P(x> 1.91 x < 2.6) = g. Find the 91st percentile.

For q (x) =-2x² +5x-5/x² +2 (a) Identify the horizontal asymptotes (if any). (b) If the graph of the function has a horizontal asymptote, determine the point (if any) where the graph crosses the horizontal asymptote(s). Separate multiple equations of asymptotes with commas as necessary. Select "None" if applicable. The graph has no horizontal asymptotes. The graph has at least one horizontal asymptote. Equation(s) of the horizontal asymptote(s): y = Crossover point(s):

James receives a gross pay of $1,550 bi-weekly from his employer. If his employer changed his pay period to monthly instead of bi-weekly, calculate the monthly payment that he would receive.

A fish tank of 82 fish is made up of three types of fish. There are 41 betta fish, 18 goldfish and some rainbow fish. How many rainbow fish are in the tank?

Amanda is earning extra money over the summer mowing lawns around her neighborhood. She would like to earn at least $450. She charges $15 for a small yard and $26 for a larger yard. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. . x = the number of small yards mowed . y = the number of larger yards mowed 15x - 26y> 450 26x + 15y > 450 15x + 26y ≥ 450 15x + 26y≤ 450

Kenneth invested his savings in shares of a new company. The company's share price dropped by $1.00 at the end of the first year, and by a further $0.75 at the end of the second year. The share price was $21.63 at the end of the second year. a. Calculate the original share price (at the beginning of the first year). b. Calculate the percent change in the share price over the two-year period.

Ajar contains 12 red marbles numbered 1 to 12 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event, please show your answers as reduced fractions. (a) The marble is red. P(red) = (b) The marble is odd-numbered. P(odd) = (c) The marble is red or odd-numbered. P(red or odd) = (d) The marble is blue or even-numbered. P(blue or even) =

Marwin is selling handmade toys in an online craft boutique. She hopes to earn more than $150 by selling toy planes for $8 each and toy tractors for $12 each. Use the following variables to write an inequality that represents the scenario. . x = the number of toy planes . y = the number of toy tractors

Vail Ski Shop received a $1,210 invoice dated July 17 with 3/10, 2/15, n/60 terms. On July 31, Vail sent a $494 partial payment. a. What credit should Vail receive? (Round your answer to the nearest cent.) b. What is Vail's outstanding balance? (Round your answer to the nearest cent.)

Find five solutions of the equation. Select integer values for x, starting with - 2 and ending with 2. Complete the table of values below. y = − x + 4

A video rental company offers a plan that includes a membership fee of $5 and charges $2 for every DVD borrowed. They also offer a second plan, that costs $25 per month for unlimited DVD rentals. If a customer borrows enough DVDs in a month, the two plans cost the same amount. How many DVDs is that? Write a system of equations, graph them, and type the solution.

Macy of New York sold LeeCo. of Chicago office equipment with a $7,100 list price. Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?

G. Zach deposited $3,000 in a new account at his bank. The bank pays 7.5% interest compounded annually on this account. Zack makes no additional deposits or withdrawals. What will be the balance of Zack's account at the end of 3 years?