Basic Math Questions and Answers

There are 350 eighth graders at Wilson Middle School. In the class president election, 224 students voted for Luke, 70 students voted for Alice, and 56 students voted for Chris. What percent of eighth graders voted for Luke?

A medical treatment has a success rate of 0.8. Two patients will be treated with this treatment. Assuming the results are independent for the two patients, what is the probability that both of them will be successfully cured? A. 0.64 B. 0.36 C. 0.04 D. 0.20

For the functions f(x)=√x-11 and g(x)=√11-x, find the functions f+g, f-g, fg, and The domain off + g is {11}. (Use a comma to separa answers as needed.) What is the domain of f+g? Select the correct choice below and, if necessary, fill in the answer box to complete yo B. The domain of f + g is (Type your answer in interval notation.) The domain of f + g is Ø. (f- g)(x) = Determine the domain

First find f+g, f-g, fg, and f/g Then determine the domain for each function. What is the domain of f-g? What is the domain of fg?

Which of these shows the result of using the first equation to substitute for y in the second equation, then combining like terms? y= 2x 2x+3y=16 A. 5y=16 B. 8x = 16 C. 5x = 16 D. 4x = 16

Suppose an investment of $14,000 is invested at an annual rate of 7.6%, compounded continuously. What is the value of the account after 14 years? Round your answer to the nearest cent/penny. dollars. (Round to two decimal places)

A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work table, the sitting knee height must be considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.2 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.4 in. and a standard deviation of 1.0 in. Use this information to answer the following questions. Determine if the following statement is true or false. If there is clearance for 95% of males, there will certainly be clearance for all women in the bottom 5%. A. The statement is false because some women will have sitting knee heights that are outliers. B. The statement is true because the 95th percentile for men is greater than the 5th percentile for women. C. The statement is true because some women will have sitting knee heights that are outliers. D. The statement is false because the 95th percentile for men is greater than the 5th percentile for women.

Find the original investment in an account if the final amount of money is $9998. It was invested in an account earning 4% interest compounded weekly and the money is left for 9 years. The original investment was $. Round answer to 2 decimal places

Find the final amount of money in an account if $3, 700 is deposited at 7% interest compounded quarterly (every 3 months) and the money is left for 9 years. Round answer to 2 decimal places The final amount is $

Select all numbers that have an absolute value of 1.8. Choose all answers that apply: A -1/8 B 1.8 C -1.8 D 18

Use mathematical induction to prove the statement is true for every positive integer n. 8+16+24+...+8n=4n(n+1) What is the first step in a mathematical induction proof? Show that So is true. Show that S₁ is true. Show that Sk is true. Show that Sk+1 is true. Let S be the statement 8 + 16 + 24 + ... +8n=4n(n + 1). Write the statement S₁. S₁: (Do not simplify.) Simplify S, on the right. S₁:8= Is S₁ a true statement? Yes No

In a medical experiment, the number of bacteria is halved every hour. What type of function represents this pattern? A. Exponential decay B. Exponential growth C. Decreasing linear D. Increasing linear

The expression 5(4+v) +6v is simplified in several steps below. For each step, choose the reason that best justifies it.

For f(x)=2x-5 and g(x) = x² - 2, find the following functions. a. (f o g)(x); b. (g of)(x); c. (f • g)(1); d. (g of)(1) a. (fog)(x) = 2x² -9 (Simplify your answer.) b. (g of)(x) = 4x² - 20x+23 (Simplify your answer.) c. (fog)(1) = − 7 (Simplify your answer.) d. (gof)(1) = (Simplify your answer.)

A car was valued at $28,000 in the year 1995. The value depreciated to $15,000 by the year 2007. A) What was the annual rate of change between 1995 and 2007? T= Round the rate of decrease to 4 decimal places. B) What is the correct answer to part A written in percentage form? T= %. C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2012? value = $ Round to the nearest 50 dollars.

Explain why the statement is incorrect. The probability of rain tomorrow is 152%. What makes the statment incorrect? A. An event needs to have more than one possible outcome. B. The probability of an event must be contained in the interval [1,100]. C. The probability of an event cannot exceed 100%. D. The chance of rain is always more than 100%.

Write the following rate as a unit rate. 1720 words to 40 minutes words per minute

There were 567 people at a concert when a band started playing. After each song, only one-third of the people stayed to hear the next song. How many people were left at the concert after x songs? Write a function to represent this scenario. A. f(x)=567 +( B. f(x)=567-(3) C. f(x)-(567)* D. f(x)=567

If the mean weight of 4 backfield members on the football team is 220 lb and the mean weight of the 7 other players is 203 lb, what is the mean weight of the 11-person team? The mean weight of the team is approximately (Round to the nearest tenth.)

TechWiz Electronics makes a profit of $35 for each MP3 player sold and $18 for each DVD player sold. Last week, TechWiz sold a combined total of 141 MP3 and DVD players. Let x be the number of MP3 players TechWiz sold last week. Write an expression for the combined total profit (in dollars) TechWiz made from MP3 and DVD players last week.

A statement S, about the positive integers is given. Write statements SK and Sk+ 1, simplifying statement Sk+1 completely. S: 8+16+24+...+ 8n=4n(n+1) Write statement Sk. Sk: 8+16+24+.. Write SK+1- (Do not simplify.) Sk+1: 8+16+24+...+0=0 (Type your answers in factored form.) ....

Maria invested $2000 in an account that earns 4.5% interest, compounded annually. The formula for compound interest is A(t) = P(1 + i)t How much did Maria have in the account after 5 years? A. $2450.00 B. $2492.36 C. $12,819.47 D. $10,450.00

Which of the x-values are solutions to both of the following inequalities? 1<x and x < 13 Choose all answers that apply: A x = 0 B x = 2 C x = 14

A student has gotten the following grades on his tests. What is the minimum grade he must get on the last test in order to have an average of 79? 73, 81, 89, 72 The minimum grade he must get on the last test in order to have an average of 79 is (Simplify your answer.)

The function f(x) = 12,419(1.4)x represents the number of visitors to a. website x years after it was launched. Each year, the number of visitors is the number the year before. A. 0.4 times B. 1.4 times C. 4 times D. 4 more than

If the annual number of retail drug prescriptions (in millions) can be approximated by the least squares line y = 82.51x + 2917.93 where x = 0 corresponds to the year 2018, find the approximate number of prescriptions in the year 2028. A. 2917.93 million B. 3743.03 million C. 3000.44 million D. 8763.03 million

For f(x) = 6x and g(x)=x+5, find the following functions. a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2) a. (fog)(x) = 6x +30 (Simplify your answer.) b. (gof)(x) = 6x + 5 (Simplify your answer.) c. (fog)(2) = 42 d. (gof)(2) =

Prehistoric cave paintings were discovered in a cave in France. The paint contained 28% of the original carbon-14. Use the exponential decay model for carbon-14, A=Age -0.0001211 to estimate the age of the paintings The paintings are approximately years old. (Round to the nearest integer.)

64% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is (a) exactly five, (b) at least six, and (c) less than four.

Find the area of the indicated region under the standard normal curve. Click here to view page 1 of the standard normal table. Click here to view page 2 of the standard normal table. The area between z = -0.7 and z = 1.4 under the standard normal curve is (Round to four decimal places as needed.)

Wally Chin, the owner of an ExxonMobil station, bought a used Ford pickup truck, paying $2,300 as a down payment. He still owes 75% of the selling price. What was the selling price of the truck?

A large apartment complex has 750 tenants. 68% of tenants who were surveyed said they are in favor of having tennis courts installed for tenants to use. Which of the following numbers of tenants best represents the likely number of tenants who would like to have the tennis courts installed? A. 750 B. 675 C. 510 D. 240

Assume that the population consists of all students currently in your statistics class. Describe how to obtain a sample of six students so that the result is a sample of the given type. a. Simple random sample b. Systematic sample c. Stratified sample d. Cluster sample

State whether the graph of - 4/X^2 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous. The function is continuous. The function has infinite discontinuity. The function has point discontinuity. The function has jump discontinuity.

During a huge snowstorm in the White Mountains last year, it snowed 400 centimeters in one week. How much did it snow in meters?

Mrs. Collins has two full rainwater catching barrels in her yard. Barrel A holds 150 gallons of water, and Barrel B holds 175 gallons of water. Barrel A releases water at a rate of 1.5 gallons per minute. Barrel B releases water at a rate of 2.5 gallons per minute. If Mrs. Collins releases water from both barrels at the same time, after how many minutes will both barrels have the same amount of water?

Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers. 2 logb (z+1)+ logb(3z + 4) Choose the correct answer.

Susan has 4.25 pounds of flour in her pantry. She needs 2/3 of a pound to make one serving of her favorite recipe. How many whole servings can she make?

Why does "How to Jump-Start a Car Battery include this image with the instructions? A. To explain that the negative cable should be attached first B. To show how to attach the jumper cables to each car battery C. To illustrate for the reader how the cars should be positioned D. To provide the overall objective for the set of instructions

Solve the system by using the addition method. 2x² + y² = 11 5x²−4y² =−31 There are infinitely many solutions. The solution set is the empty set, {}. The solution set is a finite set.

The expression - 7( – 2x − 6) simplifies to Ax + B, where A = B=

On the graph of f(x) = sin x and the domain 0 ≤ x < 2л, for which of the following intervals is f(x) strictly decreasing? Choose all correct answers. Select all that apply: (0, π/2) (π/4, π/2) (π/2, 3π/2) (3π/2, 2π)

The concentration C(t) of a certain drug in the bloodstream after f minutes is given by the formula C(t) = 0.06(1-e-0.2t). What is the concentration after 4 minutes? Round to three decimal places.

Expand the polynomial using the Binomial Theorem. (a+b)^5

From a group of 7 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group? Give your answer as a fraction

Describe a function g(x) in terms of f(x) if the graph of g is obtained by vertically stretching f by a factor of 9, then shifting the graph of f to the right 3 units and upward 2 units. g(x) = Af(x +B) + C where

Make Sense and Persevere Charlotte buys a ticket to go to a baseball game. The total includes a charge of 7% of the original price for extra fees. If Charlotte pays a total of $44.94, how much was the original price of the ticket?

The oldest child in a family of four children is twice as old as the yougest. The two middle children are 12 and 15 years old. If the average age of the children is 14.25, how old is the youngest child?

What is the basic ratio of ounces of peanuts to ounces of raisins for a mixture of 24 ounces of peanuts and 16 ounces of raisins?

Factorize the following number into prime factors Use * to multiply the factors and use exponents for multiple same factors where is used to indicate expontents 21 =