Basic Math Questions and Answers

Fabian is 1.65 meters tall. At 12 noon, he measures the length of a tree's shadow to be 18.35 meters. He stands 13.6 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Change the logarithmic equation to an equivalent equation involving an exponent. In x = 9 The equivalent exponential equation is

For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 13.65 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.7 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.65 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.

A newsletter publisher believes that 26% of their readers own a personal computer. Is there sufficient evidence at the 0.01 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario. Answer: Ho: Ha:

A half-century ago, the mean height of women in a particular country in their 20s was 62.4 inches. Assume that the heights of today's women in their 20s are approximately normally distributed with a standard deviation of 2.28 inches. If the mean height today is the same as that of a half-century ago, what percentage of all samples of 28 of today's women in their 20s have mean heights of at least 63.33 inches? About of all samples have mean heights of at least 63.33 inches. (Round to one decimal place as needed.)

A boxer needs to lose 3 1/2 kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight?

Solve the linear programming problem using the simplex method. Maximize P=2x₁ + 3x₂ + 4x3 X₁ + X3 ≤24 subject to x2 + x3 ≤18 X1, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of P is B. There is no optimal solution.

The formula D=20 e -0.6h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug was administered. When the number of milligrams reaches 4, the drug is to be administered again. What is the time between injections? The time between injections is hour(s). (Round to two decimal places as needed.)

Write inequalities to represent the situations below. To get the 10% discount, a shopper must spend more than $300. Used to represent the spending (in dollars) of a shopper who gets the discount. The temperature inside the lab refrigerator is no more than 35 °F. Use t to represent the temperature (in °F) of the refrigerator.

Type the missing number to complete the proportion. 18 plants in 1 row 72 plants in rows

A shipment of small lab mice arrives at an animal care facility. A sample of five mice is selected and weighed. The average weight of the sample is 10.2 g, and the standard deviation of weight among mice is 2 g. Find a 95% confidence interval for the mean weight of all the mice in the shipment. 10.2 ±2.48 10.2 ± 11 10.2 ± 2.30 10.2 1.75

A Potating, panoramic camera attached to a helium balloon can capture images of all the airspace below the balloon. The altitude, in feet, of the balloon m minutes after it is released, is equal to 4 more than the square root of the sum of 100m³ and m². A similar camera is attached to a drone and aimed upward to capture images of all the airspace above the drone. The altitude, in feet, of the drone m minutes after it is launched, is equal to the cube root of the sum of m² and 1,600m. Which system of inequalities represents the altitudes, in feet, of airspace which are captured by both cameras after m minutes?

On the graph of f(x) = sin x and the interval [-2π, 0), for what value(s) of x does the graph cross the x-axis? Choose all answers that apply. Select all that apply:

To pay for an $18,800 camper, Diane made a down payment of $3900 and took out a loan for the rest. On the loan, she paid monthly payments of $267.74 for 5 years. (a) What was the total amount Diane ended up paying for the camper (including the down payment and monthly payments)? How much interest did Diane pay on the loan? (b)

Consider the following polynomial. f(x) = 4x³ - 21x² + 21x - 4 Step 2 of 2: Use polynomial division and the quadratic formula, if necessary, to identify the actual zeros.

Suppose that events F and S are conditional independent events given D and ~D respectively with p(F|D)=p(S|D)=0.9, p(~F|~D)=p(~S~D)=0.9, and p(D)=0.2. Find p(D|F∩S).

Sandi weighs 175 lb, but she has started a new diet plan that promises she will lose 2 lb per month every month until she reaches her goal weight. Write a Iinear equation that describes how much Sandi weighs, , each month, and then use your equation to find out how many months it will take her to get to 125 lb. use X to denote the number of months since Sandi started her new diet. The linear equation that describes how much Sandi weighs each month is = According to the equation, it w take Sandi months to reach 125 lb

It is known that the function D(h) = 1.225√h models the distance a person can see to the horizon D(h), in miles, if the person is h feet above sea level. Suppose Gregory wanted to be able to see out 76 miles to the horizon. At what elevation would he need to be to see out that far? a) Write an equation that models this situation. Equation: b) Solve the equation to answer the question. Complete the sentence with a number in the first box and an appropriate unit in the second box. You may round your numerical response to two decimal places. Sentence: Gregory would need to be an elevation of

A guy wire runs from the top of a cell tower to a metal stake in the ground. Juan places a 9-foot tall pole to support the guy wire. After placing the pole, Juan measures the distance from the stake to the pole to be 7 ft. He then measures the distance from the pole to the tower to be 25 ft. Find the length of the guy wire, to the nearest foot.

Select the correct statement and rationale relating the interest rates of traditional banks to those of online banks. Traditional banks offer lower interest rates than online banks because they have higher building costs Traditional banks offer lower interest rates than online banks because they are less risky Traditional banks offer higher interest rates than online banks because they have been around longer Traditional banks offer higher interest rates than online banks because they are not as convenient

At noon, to begin a study, a petri dish had 1800 bacteria cells. Each hour since, the number of cells has increased by 12%. Let / be the number of hours since the start of the study. Let y be the number of bacteria cells. Write an exponential function showing the relationship between y and f.

For the given triangle, find the missing lengths. Give an exact answer and, where appropriate, an approximation to three decimal places. A. Using radicals, the exact length of the other leg is (Simplify your answers.) Find the length of the other leg. Select the correct choice below and fill in the answer box(es) to complete your choice. units. The approximate length of the other leg, up to three decimal places, is B. The exact length of the other leg is units. No approximation is necessary. (Type an integer or a decimal.) Find the length of the hypotenuse. Select the correct choice below and fill in the answer box(es) to complete your choice. units

A building contractor is to dig a foundation 42 feet long, 15 feet wide, and 3 feet deep. The contractor pays $5 per load for trucks to remove the dirt. Each truck holds 7 cubic yards. What is the cost to the contractor to have all the dirt hauled away?

An rock is thrown upward from a platform that is 156 feet above ground at 60 feet per second. Use the projectile formula h = - 16t² + vot + ho to determine when the rock hit the ground. [Recall that vo is the initial velocity of the object and ho is the inital height of the object.] Answer: The rock will hit the ground after Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.

An 8½" wide by 11" long piece of paper is to be enlarged to poster size. If the width is enlarged to be 34", what is the new measurement of the length? a. 26.2" c. 42" b. 26.3" d. 44"

In 2005, a city had a population of 310,000 people. Each year since, the population has grown by 4.3%. Let / be the number of years since 2005. Let y be the city's population. Write an exponential function showing the relationship between y and t.

A bag of M&M's has 6 red, 5 green, 7 blue, and 3 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? 2) a blue or green? 3) an orange?

Suppose that an individual has a body fat percentage of 13.1% and weighs 189 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.

A scientist estimated the number of bacteria in a sample every hour and recorded the estimates in the table above. Then the scientist used the data to create the scatterplot above. Based on the information, which of the following functions best models the number of bacteria, f(t), at time t, in hours? (A) f(t)=100(2¹) (B) f(t)=100+2t (C) f(t)=t² +220t+100 (D) ƒ(t)=120 log (t+1)

The width of a rectangular garden is x feet. If 300 feet of fencing is needed to enclose the garden, which of the following represents the length of the garden, in feet? (A) 300-x (B) 300-2x (C) 150-x (D) 150-2x

Let a, b, c, d are an increasing A.P. with integer terms and d = a² + b² + c2², then Common difference of A. P. is 2 The value of a + 2b + 3c+4d is 10 The value of 4a + 3b+2c + d is zero Common difference of A.P. is 1

A particle is moving along a straight line such that the distance traveled (in feet) after t seconds is given by the function s(t) = 8t² + 40t. At t = 6 seconds, what is the velocity of the particle?

The water in a pool is evaporating at a rate of 3% per day. If the pool has 21,200 gallons in it today, how many gallons will it have in 10 days? Round your answer to the nearest whole number, if necessary. Answer How to enter your answer (opens in new window) 2 Points

Karla wants to save up for a prom dress. She figures she can save $9 each week from the money she earns babysitting. If she plans to spend less than $150 for the dress, how many weeks will it take her to save enough money to buy any dress in her price range?

As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 150 milligrams of Medication A with 45 milligrams of Medication B. However this week, the doctor said to only use 6 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?

be worth more or less (including zero) depending on your answer. Esmerelda rents a car from a company that rents cars by the hour. She has to pay an initial fee of $50, and then they charge her $8 per hour. She has $150 available to spend on car rental. What is the greatest number of hours for which she can rent the car? (The car cannot be rented for part of an hour.) 12 hours 18 hours 13 hours 12.5 hours

You and your classmates create 25 self-portraits to sell at the PTA auction to raise money for your school. In order to pay for the materials you bought to make the self-portraits, you need to sell each of the self- portraits for $1.00. When transporting the self-portraits to the auction, one of your parents accidentally drops three of the self-portraits in the street and they are run over by a school bus. What is the new minimum price you need to set for the remaining self-portraits in order to pay for the materials?

Kala paid $14.75 for a 2.12-pound bag of shrimp at one store. The following week, she paid $24.99 for a 3.77-pound bag at another store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent. Unit price for the 2.12-pound bag: per pound Unit price for the 3.77-pound bag: per pound The better buy: The 2.12-pound bag The 3.77-pound bag Neither (They have the same unit price)

Find all zeros of f(x) = x³ + 2x² - 6x - 4. Enter the zeros separated by commas. Enter exact value, not decimal approximations.

- Manuel bought 9 pounds of apples. He has eaten 3/4 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

Arianna invests $5500 in a new savings account which earns 5.6 % annual interest, compounded daily. What will be the value of her investment after 7 years? Round to the nearest cent.

A damsel is in distress and is being held captive in a tower. Her knight in shining armor is on the ground below with a ladder. When the knight stands 15 feet from the base of the tower and looks up at his precious damsel, the angle of elevation to her window is 60 degrees. How long does the ladder have to be?

Find the average rate of change of f(x) = 2x² +5 over each of the following intervals. (a) From 4 to 6 (b) From 2 to 0 (c) From 0 to 3 (a) The average rate of change from 4 to 6 is. (b) The average rate of change from - 2 to 0 is (c) The average rate of change from 0 to 3 is

Explain what "80% confidence" means in a 80% confidence interval. What does "80% confidence" mean in a 80% confidence interval? OA. The confidence interval includes 80% of all possible values for the parameter. OB. The value of the parameter lies within 80% of a standard deviation of the estimate. OC. The probability that the value of the parameter lies between the lower and upper bounds of the interval is 80%. The probability that it does not is 20%. OD. If 100 different confidence intervals are constructed, each based on a different sample of size n from the san population, then we expect 80 of the intervals to include the parameter and 20 to not include the parameter.

Situation: A 50 gram sample of a substance that's used to treat thyroid disorders has a k- value of 0.1113. N = Noe^-kt No initial mass (at time t = 0) N = mass at time t k = a positive constant that depends on the substance itself and on the units used to measure time t = time, in days Find the substance's half-life, in days. Round your answer to the nearest tenth. Enter the correct answer.

A manufacturer produces three products, A, B, and C. The profits for each unit of A, B, and C sold are $1, S2, and $3, respectively. Fixed costs are $17,000 per year, and the costs of producing each unit of A, B, and C are $4, $5, and $7, respectively. Next year, a total of 8000 units of all three products is to be produced and sold, and a total profit of $12,000 is to be realized. If total cost is to be $54,000, how many units of each of the products should be produced next year?

Enrico deposited $2000 in a savings account. Each month he will deposit an additional $25. Which kind of function best models the relationship between time and the total amount in the savings account? Choose 1 answer: Linear Exponential

In the game of roulette, a wheel consists of 38 slots numbered 0, 00, 1, 2,..., 36. To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots. If the number of the slot the ball falls into matches the number you selected, you win $35; otherwise you lose $1. Complete parts (a) through (g) below. (a) Construct a probability distribution for the random variable X, the winnings of each spin. x P(x) 35 -1 (Type integers or decimals rounded to four decimal places as needed.)

A machine is valued at $10,000. If the depreciation at the end of each year is 20% of its value at the beginning of the year, find its value at the end of 4 years.

Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy = f'(x)dx. f(x)=e8x