Math Questions

Which line is parallel to the line y = 1/2x– 10 and passes through the point (8, -7)? Write your answer as y=mx+b with no spaces. Use parenthesis if your slope is a fraction. For example, if your answer is y = -3/4x + 1. you would type your answer as y=(-3/4)x+1

A principal of $3300 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 6 years? Use the calculator provided and round your answer to the nearest dollar.

A relation contains the points (1, 2), (2, -1), (3, 0), (4, 1), and (5,-1). Which statement accurately describes this relation? F The relation does not represent y as a function of x, because each value of x is associated with a single value of y. G The relation represents y as a function of x, because one value of y is associated with two values of x. H The relation does not represent y as a function of x, because each value of y is associated with two values of x. J The relation represents y as a function of x, because each value of x is associated with a single value of y.

You're constructing a ball pit for a local preschool. You find online that a circular ball pit with diameter 5 feet and depth 3 holds 456 balls. You want to build a 7 by 9 by 3 rectangular ball pit. How many balls will that ball pit hold? Round your answer to the closest whole number.

One hundred students out of 1100 at a school were surveyed. The results are recorded in each problem below. For the statements below, predict the number of students in the population that would answer similarly. Thirty-two students said they drove to school. Show the setup of the problem (blank 1) and the answer (blank 2). Blank # 1 Blank # 2

Mr. and Mrs. Steele deposited $8,000 to open a college savings account for their granddaughter on the day she was born. The account pays 5% simple interest annually. If they made no other deposits or withdrawals since then, how much money would be in the account after 18 years? A $7,200 B $8,000 C $15,200 D $19,253

A study determined that 5% of children under 18 years old lived with their father only. Find the probability that none of the children selected at random from 15 children under 18 years old lived with their father only.

Coast Guard Station Able is located L=120 miles due south of Station Baker. A ship at sea sends an SOS call that is received by each station. The call to Station Able indicates that the ship is located N55°E; the call to Station Baker indicates that the ship is located S60°E.

A triangle is bounded by the line y = 6 -3/4 x, the line passing through the origin that is perpendicular to the first line, and the y-axis.

11.9% of the population is 65 or older. Find the probability that the following number of persons selected at random from 25 people are 65 or older. The probability that at least 3 are 65 or older is (Round to three decimal places as needed.)

The square root of 105 would lie between which two consecutive integers? A 9 and 10 B 10 and 11 C 104 and 106 D 9 and 11

In a class of 28 students, 10 are female and 15 have an A in the class. There are 4 students who are female and have an A in the class. What is the probability that a student chosen randomly from the class is a female who has an A?

A basketball player has a 0.654 probability of making a free throw. If the player shoots 13 free throws, what is the probability that she makes less than 6 of them? Insert the correct symbol to represent this probability.

Suppose the demand function for a product is given by the function: D(q)=-0.012q + 52.8 Find the Consumer's Surplus corresponding to q = 3, 700 units. (Do not round the results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4, 400.)

A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research). What percentage of household incomes are between $25,000 and $40,000? 62.5% 53.93% 28.23% 37.22%

A water tank is in the shape of a cylinder with a height of 21 feet and a diameter of 8 feet. What is the volume, in cubic feet, of the water tank? 352 cubic feet 1,056 cubic feet 4,224 cubic feet 5,544 cubic feet

Find the flux of the vector field F (y, — z, x) across the part of the plane z = 2 + 4x + y above the rectangle [0, 4] × [0, 5] with upwards orientation.

The city council conducts a survey of the city's residents to determine which services are most used by the community. 60% of the residents say that they use the library, and 35% of the residents say they use the library and the recycling center. What is the probability that a resident uses the recycling center given that they use the library? Express your answer as a decimal rounded to three decimal places.

The function f(x) = 2x³ − 27x² +84x + 3 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at x = ___ with output value ___ and a local maximum at x = ___ value with output ___

Use the right triangle shown in the figure. Then, using the given information, solve the triangle. a=13, b=4; find c, A, and B

Which set of ordered pairs represents y as a function of x? A {(0, 0), (-1, 2), (-1, -2), (-2, 4), (-2,-4)} B {(0, 0), (1, 1), (2, 4), (3, 9), (3, 16)} C {(0, 0), (0, 1), (0, 2), (0, -1), (0, -2)} D {(0, 0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)}

Let f be a scalar field (a function) and F a vector field. For each expression, decide first if it's meaningful, and if so, whether the result is a scalar field or vector field.

The 35-member History Club is meeting to choose a student government representative. The members decide that the representative, who will be chosen at random, CANNOT be any of the 3 officers of the club. What is the probability that Hiroko, who is a member of the club but NOT an officer, will be chosen?

The current balance in Marianne's savings account is $525. The account pays 3.5% compounded annually. If she makes no deposits or withdrawals for the next 4 years, her savings account balance will be- A $588.00 B $590.89 C $598.50 D $602.45

A Formula 1 race car is re-created as a toy car, reduced by a scale of 1/12. If the model version is 7.8 cm tall, how tall is the race car? Hint: take note of the units a. 0.75 m b. 1.13 m c. 0.94 m d. 0.56 m

An equilateral triangle is shrinking, with its area decreasing at a rate of 2 m² per hour. The rate at which a side length of the triangle is changing, at the moment when the side length is 66 m, is: m/sec

Phoenix has a population density of 3,349 people per square mile. If the current population of the city is 1,733,630 people, what land area (in square miles) does Phoenix cover? Round to the tenths of a square mile. Show all work.

The radius and height of a cylinder are multiplied by 5. What is the effect on the volume? None of the other answers are correct The volume is multiplied by 125. The volume is multiplied by 1/5. The volume is multiplied by 5. The volume is multiplied by 25.

Find the critical numbers of the function f(x) = − 12x^5 + 75x^4 + 80x³ + 6 and classify them using a graph.

The radius of the moon is about 1.738 megameters. The formula for the volume of a sphere is V = 4/3πr³. Approximately what is the volume of the moon? (Use 3.14 as an approximation for pi.) 2.75 cubic megameters 5.49 cubic megameters 12.64 cubic megameters 21.98 cubic megameters

A 124 foot fir tree and a 70 foot redwood were growing side by side in northern California. The fir is growing at the rate of 3.2 feet per year. The redwood grows at the rate of 6.2 feet per year. When will the redwood pass the fir in height?

A particle moves along a line so that its velocity at time t is v (t) = t² + 3t - 11 in meters per second. Find the displacement of the particle (in meters) during the time period 0 ≤ t ≤7.

The total cost of attending a state university is $18,500 for the first year. Stephen's grandparents will pay one-half of this cost. A football scholarship will pay another $7,000. Which amount is closest to the minimum that Stephen will need to save every month in order to pay off the remaining cost at the end of 12 months? A $2,250.00 $187.50 $958.33 $770.83

The time, t (in minutes), you need to type a certain paper varies inversely with the rate, r (in words per minute), that you can type. When typing 40 words per minute, you can finish in 50 minutes. Find the constant of proportionality and write an equation relating t and r. t = ?/?

Michelle has a balance of $950 in a savings account that pays 3% interest compounded annually. If Michelle makes no deposits or withdrawals, how much money will be in her savings account after 2 years? A $954.81 B $1,004.00 C $1,007.00 D $1,007.86

Shaaron and her two sisters, Anna and Bonnie, have apps on their phones so that at any moment Shaaron can see the distance in kilometres between her and each of her two sisters. Shaaron looks at her phone and sees: Anna - 15 km away from you Bonnie - 20 km away from you Which of these cannot be the distance between Anna and Bonnie? A. 10 km B. 20 km C. 30 km D .40 km

The sun produces 3.8 x 10^27 joules of energy per second. How much energy is produced in a year? (NOTE: A year is approximately 31,000,000 seconds, or 3.1 x 10^7) 1.178 x 10^35 1178 x 10^30 11.78 x 10^34 1.178 x 10^34

King Neptune bought 200 shares of a stock at $35.25 a few years ago. His broker charged her a 0.4% commission. He then sold all of his shares at $41.29, using an online broker who charges $18 per transaction. What were King Neptune's capital gains, including broker fees?

Draw triangle JKL with right angle L. If Sin J = 8/17, find each of the following ratios. Give answers in fraction form. Cos J= Tan J = Sin K = Cos K = Tan K =

Brandon has saved $1,220 for college. He expects the total cost of his first year to be $9,850. He will receive a scholarship for $2,120. How much money should Brandon save each week in order to have enough money in 2 years to pay for his first year of college? A $62.60 C $103.37 B $74.33 D $271.25

Joe Biden and Donald Trump recently went skydiving. Each tested the given pair of hypotheses; Joe Biden committed a Type I error while Donald Trump committed a Type II error. Consequently, one of the skydivers died. Who was it? Explain your reasoning. Ho: My parachute will function properly. H₁: My parachute will not function properly.

Jonathan Deman's income this month is $2000 after taxes. He has $1000 in fixed expenses which include his car payment and rent and $600 in variable expenses including groceries, entertainment and clothing purchases. He deposits $100 in his savings account each month. Suppose that Jonathan's refrigerator breaks during the month and he has to decide whether to repair it for $500 or purchase a new refrigerator on credit for $300 a month over the next year. What should he do? a. He can purchase or repair the fridge now with no changes to his budget b. He does not have enough money to do either of these options c. He has enough money in his budget to repair the fridge, but not to purchase a new one d. He will need to make changes to his variable expenses in order to repair the fridge, but he could buy one on credit and still meet his budget.

A company packages apples by weight. One of the weight grades is Class A apples. Class A apples have a mean weight of 105 g, and there is a maximum allowed weight tolerance of 5% (7.5 g) above or below the mean for apples in the same consumer package. A batch of apples is selected to be included in a Class A apple package. Given the following apple weights of the batch, does the fruit company comply with the Class A grade weight tolerance requirements? Conducts the appropriate hypothesis test at the 1% level of significance. 158 g, 167 g, 149 g, 169 g, 164 g, 139 g, 154 g, 150 g, 157 g, 171 g, 152 g, 161 g, 141 g, 161 g, 172 g

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by 7.2% per year. Write an exponential function and use it to predict the rabbit population of Springfield in 2036. Rabbit population of Springfield in 2036:

Mike already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 10% interest, how much could the annuity provide each month (to the nearest dollar)? *

The volume of a gas varies directly with its temperature and inversely with its pressure. When the temperature is 125 Kelvin and the pressure is 15 lb/cm², the volume is 100 m³. What is the volume when the temperature is 275 Kelvin and the pressure is 25 lb/cm²? A. 118 m³ B. 125 m³ C. 132 m³ D. 148 m³

A data set of values has a mean of 45 and a standard deviation of 5. The z-score for a point A is 0. The z-score for a point B is 0.2. State the values of point A and point B. Point A = Point B =

A principal of $3000 is invested at 7.25% interest, compounded annually. How much will the investment be worth after 11 years?

Divide and simplify: x + 10 / x+7 / 2x+ 20 / 5x+35

The cost per year to lease a coffee shop in downtown Austin varies directly with the size of the shop. If a 1,425 square foot shop costs $45,600 to lease for the year, how expensive is it to lease a shop that is 1,820 square feet?