Basic Math Questions and Answers

A flagpole 94.4 ft tall is on the top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 35.7°, while the angle of elevation of the bottom of the flagpole is 25.4°. Find the height of the building.

Automatic transmissions and manual transmissions achieve the same goal: They use power to turn the wheels of a car. However, there are some differences between the two. An automatic transmission makes a car easy to drive; but stick shift drivers believe that automatics aren't quite as fun. There are other differences as well. A car with a manual transmission usually uses less fuel. This is because the driver has greater control over the car; it is the driver, not the car, who is "in the driver's seat." A manual transmission also has more power and can accelerate faster. This is why race cars have manual transmissions. Which organizational pattern is used in the passage? A. Sequential B. Problem-solution C. Cause and effect D. Compare and contrast

For a project in her Geometry class, Tamika uses a mirror on the ground to measure the height of her school's football goalpost. She walks a distance of 14.15 meters from the goalpost, then places a mirror on flat on the ground, marked with an X at the center. She then walks 4.2 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.

Consider the trinomial x² - 11x + 18. In preparation for factoring it by grouping, write -11 as a sum or difference of factors of 18.

Anthony works as a salesperson at an electronics store and sells phones and phone accessories. Anthony earns a $8 commission for every phone he sells and a $4 commission for every accessory he sells. On a given day, Anthony made a total of $80 in commission and sold 5 more accessories than phones. Graphically solve a system of equations in order to determine the number of phones sold, al, and the number of accessories sold, y.

Arnold Brown has a Visa Card with an annual percentage rate of 16.8 %. The unpaid balance for his June billing cycle is $1,054.33. During the billing cycle he purchased a printer cartridge for $43.72, books for $291.59 and gasoline for $17.06. He made a payment of $1,000. If the account applies the unpaid balance method, what are the finance charge and the new balance?

A total of 568 tickets were sold for the school play. They were either adult tickets or student tickets. There were 68 more student tickets sold than adult tickets. How many adult tickets were sold?

Solve the system of equations using Cramer's Rule if it is applicable. 3x - y = 10 2x + 2y = 12 Write the fractions using Cramer's Rule in the form of determinants. Do not evalua

1/9+5/6 Least multiple that is the same: Add using renamed fractions:

Peg and Larry purchased "no contract" cell phones. Peg's phone costs $25 plus $0.25 per minute. Larry's phone costs $35 plus $0.20 per minute. After how many minutes of use will Peg's phone cost more than Larry's phone?

A school is organizing a cookout where hotdogs will be served. The hotdogs come in small packs and large packs. Each small pack has 12 hotdogs and each large pack has 24 hotdogs. The school bought 4 times as many small packs as large packs, which altogether had 144 hotdogs. Graphically solve a system of equations in order to determine the number of small packs purchased, z, and the number of large packs purchased, y.

Karen, Dan, and Josh sent a total of 109 text messages over their cell phones during the weekend. Josh sent 4 times as many messages as Dan. Dan sent 5 more messages than Karen. How many messages did they each send? Number of text messages Karen sent: Number of text messages Dan sent: Number of text messages Josh sent;

The families "a", "b" and "c" are invited to dinner. The probabilities that each family will come are 0.8, 0.6 and 0.9, respectively. In addition, each family's decision is independent of the decisions of the other families. Find the probability that NONE of the families come. Define Event A: the family "a" comes; Event B: the family "b" comes; Event C: the family "c" comes.

On an exam for a class with 54 students, the mean score was 77.2 points. The instructor rescored the exam by adding 6 points to the exam score for every student. What was the mean of the scores on the rescored exam?

Factor the following polynomial if possible. Hint: Using an identity will be helpful. 27x3+y³z³ Cannot be simply factored. (3x+yz) (9x²-3xyz + y²z²) (2x+yz)(4x²-2xyz + y²z²) (3x-yz) (9x²+3xyz + y²z²) (3x+yz) (9x²-3x²y²z²+²z²)

Which of the following sets of numbers could represent the three sides of a triangle? {10, 21, 32} {14, 24, 40} {13, 17, 32} {13, 16, 27}

A company manufactures electronic components that each must weigh from 29.5 grams to 30.5 grams, inclusive. Which of the following inequalities describes all acceptable weights x, in grams, for each component? (A) |30-x| ≤0.5 (B) |30-x| >0.5 (C) 30-x≤ 0.5 (D)30-x>0.5

Michael wishes to give his son a savings bond that will mature in 8 years. He would like the value of the savings bond to be $5,000 at maturity. If he can invest in a bond that has an annual interest rate of 4% compounded monthly, which of the following is the best approximation of the amount he should invest? (A) $3,200 (B) $3,350 (C) $3,500 (D) $3,650

Define a variable and write an inequality. Then sol Marlea received an inheritance of $10,000. She plans to invest some in a stock that pays 7% interest annually. She will deposit the remainder in a savings account that pays 5% interest annually. What is the least amount that Marlea can invest in stock if she wants to earn at least $550 on her investments for the year?

Caitlin had $402 in her bank account. She withdrew $15 each week to pay for a swimming lesson. She now has $237. a.Write an equation that can be used to find the number of swimming lessons that she paid for. b. Find the number of swimming lessons she paid for. C.The cost of a swimming lesson rises to $19. How many lessons can she pay for with the remaining $237?

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