Math Questions

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?

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

Kaleb has $850 saved for college. Kaleb expects the total cost of his first year to be $8,990. He has $850 in his savings account. He will receive grants and scholarships that total $1,445. Kaleb plans to save $210 every month. At this rate, how many months will Kaleb need to save until he has enough money to pay for the net price of his first year of college? A 31 months C 36 months B 32 months D 46 months

A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. Mrs. Cox picks one without looking, replaces it and picks another one. What is the probability that she picks two that are not orange?

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?

Write the standard form of the equation of a circle with radius 8 and center (-9,1)

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

A card is pulled from a deck of card and noted. The card is then replaced, the deck is shuffled, and a second card is removed and noted. What is the probability that both cards are Aces? * 1/13 1/52 2/13 1/169 1/26

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:

Among the students in a local school division, ACT scores were normally distributed this year with a mean score of 20.7 and a standard deviation of 5.9. SAT scores were normally distributed with a mean score of 1075 and a standard deviation of 168. Who scored better on their standardized test with respect to the other test takers in the school division, Jamal who took the ACT and score 29 or Shamar who took the SAT and scored 1240? Jamal Shamar Both Jamal and Shamar Neither Jamal or Shamar

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.

Kevin is an auto mechanic. He spends 3 hours when he replaces the shocks on a car and 2 hours when he replaces the brakes. He works no more than 42 hours a week. He routinely completes at least 2 shocks replacements and 6 brake replacements a week. If he charges $500 for labor replacing shocks and $200 in labor for replacing brakes, how many jobs of each type should he complete a week to maximize his income?

Find the present value of a continuous income stream F(t) = 20 + 6t, where t is in years and F is in thousands of dollars per year, for 30 years, if money can earn 1.9% annual interest, compounded continuously.

There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 5?