Basic Math Questions and Answers

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

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.

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?

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

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?

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

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

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?

A scientist models the number of grams of a radioactive substance with the expression 15.(1/2)^d/5, where d is the number of days since the sample was measured. 1. After how many days has half of the substance disappeared through radioactive decay? Explain your reasoning. 2. After 20 days, will there be more or less than 1 gram of the substance left? Explain your reasoning.

Marvin lives in Stormwind City and works as an engineer in the city of Ironforge. In the morning, he has 3 transportation options (teleport, ride a dragon, or walk) to work, and in the evening he has the same 3 choices for his trip home. If Marvin randomly chooses his method of travel in the morning and in the evening, what is the probability that he teleports at least once per day?

A random study reported that 70% of very-low-birth-weight babies graduate from high school by age 20. If 180 very-low-birth-weight babies are followed through high school, how many would you expect to graduate from tgh schod

The U-Drive Rent-A-Truck company plans to spend $13 million on 320 new vehicles. Each commercial van will cost 535 000, each small truck $30,000, and each large truck $80,000 Past experience shows that they need tance as many varsas malucks How many of each type of vehicle can they buy? They can buy vans.small trucks, and large trucks

What is the length of one side of a square whose area is 100 square meters? What is the perimeter of a rectangle whose base has a length of 15 inches and whose diagonal measure 17 inches?

Spongebob, Patrick, and Mr. Krabs are investing a total of $70,000 in the Krusty Krab at a ratio of 12:7:16. How much money did each of them invest? Spongebob: Patrick: Mr. Krabs:

The beachfront path was 4,848 feet long. A tropical storm caused waves that washed away 3,383 feet from the end. How long was the path after the storm? 1,475 feet 8,231 feet 1,465 feet 1,455 feet

Add and simplify: 5x+7 / x-6 + 4x / 6 - x Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number

Paul opens a savings account with $350. He saves $150 per month. Write a function that illustrates this situation. Function: p(x)= Slope/Meaning in context: m = y-intercept/Meaning in context: b= How much has he saved after 8 months? p= How long will it take Paul to save $2000 in the bank?

Suppose that y varies inversely with x, and y= 10 when x=2. (a) Write an inverse variation equation that relates x and y Equation: (b) Find y when x = 5. y =

In one day, a yoga instructor teaches 3 classes in the morning and 4 classes in the afternoon. The length of each class is m minutes. Which expression represents the total number of minutes the yoga instructor teaches in one day? A. 7m B. 7+ m C. 10m D. 10 + m

A motorboat travels 111 kilometers in 3 hours going upstream. It travels 171 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current? Note that the ALEKS graphing calculator can be used to make computations easier. Rate of the boat in still water: Rate of the current:

Hannah can paint a room in 12 hours. Destiny can paint the same room in 20 hours. How long does it for both Hannah and Destiny to paint the room it they are working together.

A researcher is hired by an alcohol manufacturer to study the connection between alcohol consumption and poor decision making. They approach college students at a bar, explain the study to them, and offer to pay them to participate. Half of the students are given 3 free drinks, while the other half are given free food and non-alcoholic beverages. The researcher then asks them to complete a short study of their decision making ability. Many of the students given alcohol don't complete the study, or write in joke answers, so they throw those results out. Afterwards, they find that there is no difference between the decision making capability of the students who drank and those who did not. Select all of the ethical/procedural mistakes which the researcher made, based on the information given above. You will lose credit if you select incorrect answers. The researcher had a conflict of interest. The researcher used a convenience sample. The researcher risked the health or safety of participants. The researcher did not conduct a blind study. The researcher cherry-picked data. The researcher did not use a control group. The researcher confused correlation with causation. The researcher failed to obtain informed consent.

Solve the rational equation: - 9m / m²-9 + 1 / m+3 = 1 / m-3

Two routes connect an origin-destination (OD) pair with performance functions t₁ = 5 + 4x1 and t2= 7+ 2x2 (with t's in minutes and x's in thousands of vehicles per hour). The total demand for the OD pair is 4000 vehicles. (a) Find the User Equilibrium (UE) flow. (b) Find the System Optimum (SO) flow.

How much heat is required to boil 45.0 g of water at it's boiling point? a. 50.2 J b. 102 J c. 18800 J d. 102000 J

The dollar value v (t) of a certain car model that is t years old is given by the following exponential function. v (t) = 26,000(0.92)^t Find the initial value of the car and the value after 12 years.

Scott is using a 12-foot ramp to help load furniture into the back of a moving truck. If the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck?

A company is considering expanding their production capabilities with a new machine that costs $60,000 and has a projected lifespan of 6 years. They estimate the increased production will provide a constant $11,000 per year of additional income. Money can earn 1.4% per year, compounded continuously. Should the company buy the machine?

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is 54, the cost per minute is $0.20, and the cost per mile is $1.30. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed $10.30 and remarked that the number of minutes was four times the number of miles. Find the number of minutes and the number of miles for this trip.

A fishbowl shaped like a sphere is filled with water. The fishbowl has a diameter of 16 inches. Which measurement is closest to the volume of water in the fishbowl in cubic inches? A 2,144.66 in.³ B 17,157.28 in.³ C 5,461.67 in.³ D 6,433.98 in.³

Carter bought a pair of shoes online for $64. He used a coupon code to get a 10% discount. The website also applied a 5% processing fee to the price after the discount. How much did Carter pay, in the end?

A plane can fly 340 miles in the same time as it takes a car to go 120 miles. If the car travels 110 mph slower than the plane, find the speed of the plane.

A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year. 1. Write an exponential function that models the value y of the car over x years. 2. To the nearest cent, what will be the value of the car after eight years?

An electrician charges a $20 house call fee plus $30 per hour of work. Which equation represents this relationship? A. y=20+30 B. y=20x + 30 C. y = 30x + 20 D. y = 50x

Frederick's salary varies directly with the hours he works. Last week he earned $328.30 and worked 33.5 hours. If he works 35 hours this week, what will be his salary? A $314.23 B $329.80 C $343.00 D $357.14

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 10 hours. How lo it take the pipe to fill the pool if the drain is left open?

Add and/or subtract and then simplify completely: 3p/p²-81 + p/p+9

Subtract and simplify: 7x + 5/5x² - 1x + 5/5x² Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Add and/or subtract and then simplify completely: 4p + 3/p² - 6p+8 + 1/P-4 Numerator preview: Denominator preview: Enter the numerator and denominator separately in the boxes below. If the denominator is 1, enter the number 1. Do not leave either box blank. Answer:

Simplify the expression 2x - 3 / x - 3 + 3 - x / x - 3 and give your answer in the form of f(x) / g(x) Your answer for the function f(x) is : Your answer for the function g(x) is :

A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3121 tickets overall. It has sold 222 more $20 tickets than $10 tickets. The total sales are $58,770 How many tickets of each kind have been sold? How many $10 tickets were sold? How many $20 tickets were sold?

Evaluate the sine, cosine, and tangent of the angle without using a calculator. (If an answer is undefined, enter UNDEFINED.) -135° sin θ = cos θ = tan θ =

Suppose that y varies directly with x, and y=8 when x = 20. (a) Write a direct variation equation that relates x and y. Equation: (b) Find y when x = 7. y =