Basic Math Questions and Answers

The density of seawater is about 0.001027 kg/cm³. A tropical fish tank measures 50.8 centimeters by 30.5 centimeters by 30.5 centimeters. What is the mass of the seawater in the tank? Round to the nearest hundredth if necessary. 48.53 kg 43.63 kg 47.26 kg 51.19 kg None of the other answers are correct

In a baseball stadium, there is a certain number of fans. In the football stadium down the street, there are 300 more than twice the number of fans in the baseball stadium. There are 16,344 fans combined between the two stadiums. How many fans are at each stadium?

The number of math problems Phaedra has completed varies directly with the amount of time she has been working on homework. She completed 8 in the first 6 minutes. How many will she have completed after 27 minutes? A 20 B 29 C 35 D 36

A phone company offers two monthly plans. Plan A costs $21 plus an additional $0.11 for each minute of calls. Plan B costs $9 plus an additional $0.16 for each minute of calls. For what amount of calling do the two plans cost the same? minutes What is the cost when the two plans cost the same? $0

Ellie is building a dollhouse. She has boards that are two different lengths. A long board is 17 inches longer than the short board. a. Draw a picture showing how the short and long boards are related. The length of the long board is 50 inches. The length of the short board is unknown. b. Write an equation that shows how the length of the long board is related to the length of the short board. Remember to define your variable first. c. Ellie estimates that the length of the short board is between 30 and 40 inches. Test at least three values in this range in your equation. Were any of the values you tested a solution? How do you know? d. What is the length of the short board? Is there more than one possible answer?

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.

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

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.

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

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 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.

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

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 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

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