Basic Math Questions and Answers

A recipe for trail mix uses 7 ounces of almonds with 5 ounces of raisins. (Almonds and raisins are the only ingredients.) How many ounces of almonds would be in a one-pound bag of this trail mix? Explain or show your reasoning.

Which pair of linear equations could describe the opposite sides of a parallelogram? 5x5y = 30 and y = x + 16 0 2x + y 24 and y = 2x + 13 -9x9y = 18 and y = x - 4 x+2y =16 and y = 2x + 7

In a class of 25 students, 14 have a brother and 17 have a sister. There are 5 students who do not have any siblings. What is the probability that a student who has a brother also has a sister?

An object is dropped from a tower, 196 ft above the ground. The object's height above ground t sec into the fall is s=196-16t². a. What is the object's velocity, speed, and acceleration at time t? b. About how long does it take the object to hit the ground? c. What is the object's velocity at the moment of impact? The object's velocity at time t is .

For Valentine's Day, a company makes decorative cylinder-shaped canisters and fills them with cinnamon candies. Each canister is 10 in. high and has a radius of 2 in. They want to make 700 canisters and need to determine how much candy to buy. What is the total number of cubic inches that will be filled with candy? Use 3.14 for .

Madeline is going to invest in an account paying an interest rate of 4.4% compounded annually. How much would Madeline need to invest, to the nearest ten dollars, for the value of the account to reach $16,600 in 12 years?

At time t, the position of a body moving along the s-axis is s= - t³ + 12t² - 45t m. a. Find the body's acceleration each time the velocity is zero. b. Find the body's speed each time the acceleration is zero. c. Find the total distance traveled by the body from t = 0 to t = 4. a. What is the body's acceleration each time the velocity is zero? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. m/s2 (Simplify your answer. Use a comma to separate answers as needed.) OB. There is no solution.

Which equation has the same solution as x² - 8x+8 = -10? (x-4)² = -2 (x-4)² = -34 ○ (x+4)² = −34 (x+4)² = -2

A recipe for 2 dozen corn muffins calls for 3 cup of flour. The number of muffins varies directly with the amount of flour you use. Estimate how many cups of flour are needed to make 6 dozen muffins.

The formula used to convert between degrees Fahrenheit and degrees Celsius is "the sum of \(32\) and \(\frac95\) times the temperature in degrees Celsius". What is an equivalent algebraic expression? Use \(C\) to represent the degrees Celsius.

Assume that a hypothesis test will be conducted using significance level a = .01 and alternative hypothesis Ha: u: 19.3. Furthermore, we will use the following sample data: n = 12, x-bar = 18.8, and s= 2.1. Find the p-value for the test. 0.5730 0.4270 0.3810 0.8540

The Mitchells bought a $219,000 townhome. They made a down payment of $47,000 and took out a mortgage for the rest. Over the course of 30 years they made monthly payments of $1031.24 on their mortgage until it was paid off. (a) What was the total amount they ended up paying for the townhome (including the down payment and monthly payments)? (b) How much interest did they pay on the mortgage?

Winston made strawberry jam anc raspberry jam. He made enough strawberry jam to fill 1/2 of a jar. If he made 4 times as much raspberry jam as strawberry jam, how many jars will the raspberry jam fill?

Gerda discovers that the lifetime of light bulbs is normally distributed with mean 1000 hours and standard deviation 100 hours. If Gerda buys 50 bulbs, how many of them are expected to last less than 800 hours? Give your answer correct to the nearest integer.

An engineer estimated the weight of a steel beam to be 600 pounds. The actual weight of the beam was 63 pounds. Find the absolute error and the percent error of the engineer's estimate. If necessary, round your answers the nearest tenth.

A busload of campers stopped at a dairy stand for ice cream. They ordered 40 cones some soft-serve at $2.25 and the rest hard-pack at $2.75. If the total bill was $96, how many of each type of cone were ordered?

A small telecommunications company invested its 2010 net income of $539,900 in a savings account for 5 years and 1 months. Money was earning interest at a rate of 6.50% compounded monthly. a. Calculate the amount it would have in this account at the end of the period. b. Calculate the interest earned.

Ashley estimated the height of her office building to be 12 m. The actual height of her office building was 13.4 m. Find the absolute error and the percent error of Ashley's estimate. If necessary, round your answers to the nearest tenth.

In a clinical test with 1400 subjects, 420 showed improvement from the treatment. Find the margin of error for the 99% confidence Interval used to estimate the population proportion. 0.0240 0.0180 0.0315 0.0276

Mrs. Ashton buys journals for the students in her language arts class. She pays $64.48 for all of the journals. If there are 26 students in her class, how much does each journal cost?

The growth of a certain bacteria population can be modeled by the function A(t) = 850e0.0649t where A(t) is the number of bacteria and t represents the time in minutes. a. What is the initial number of bacteria? (round to the nearest whole number of bacteria.) b. What is the number of bacteria after 5 minutes? (round to the nearest whole number of bacteria.) c. How long will it take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

The daily rainfall in Newtown in April is normally distributed with mean 43 mm and standard deviation 22 mm. Given that there are 30 days in April, on how many days do we expect a rainfall of between 40 mm and 50 mm? Give your answer correct to the nearest integer.

Amy, Shen, and Rafael sent a total of 90 text messages during the weekend. Amy sent 5 fewer messages than Rafael. Shen sent 3 times as many messages as Rafael. How many messages did they each send? Number of text messages Amy sent: Number of text messages Shen sent: Number of text messages Rafael sent: 800 X

A sun in a distant galaxy has an estimated Mass of 1.73188 x 10³1 kg and the earth has a mass of 5.972 x 1024 kg, how many earths would it take to equal the mass of the sun? Write your answer in scientific notation. It would take earths to equal the mass of the sun.

Solve the equation in x over the interval [0,2x). Give exact solutions. 10 cos 2x = -5 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The solution set is {}. (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) OB. The solution set is Ø.

Which is greater, O 37 50 O 37% 37 50 or 37%?

Tommy's Tree Farm sold 7 red maple trees so far this month. They expect to sell some more red maple trees at their upcoming Fall Festival. The rule for this pattern is t = m + 7, where m is the number of red maple trees they sell at the Fall Festival and t is the total number of red maple trees they will have sold this month. llow the rule

Suppose an investor deposits $21,000 into a savings account for 4 years at 8.5% interest. Find the total amount of money in the account if the interest is: 1. Compounded annually, then the investment is worth 2. Compounded quarterly, then the investment is worth 3. Compounded monthly, then the investment is worth 4. Compounded weekly, then the investment is worth after 4 years. after 4 years. after 4 years. after 4 years. 5. Compounded daily, then the investment is worth after 4 years. Round your answers to the nearest cent. Use a dollar sign to indicate that your answer is a monetary value.

A certain disease has an incidence rate of 0.9%. If the false negative rate is 4% and the false positive rate is 1%, compute the probability that a person who tests positive actually has the disease. Give your answer accurate to at least 3 decimal places

Given f(x) is a polynomial function and the remainder for the quotient of true. A. The binomial (x + 2) is a factor of f(x). B. The binomial (x + 2) is not a factor of f(x). C. f(9) = 2 D. f(9) = -2 E. f(2)=9 OF. f(-2) = 9 f(x) x+2 is 9. Select all of the following statements that must be

Yolanda estimated the length of a room is her house to be 13 ft. The actual length of the room is 12 ft. Find the absolute error and the percent error of Yolanda's estimate. If necessary, round your answers to the nearest tenth. absolute error t percent error =

2) Order (4 or 5 fractions; least to greatest vs greatest to least is up to you)

Karen is estimating the volume of her bathtub. The actual volume of her bathtub is 44 gal. Karen's estimate is 48 gal. Find the absolute error and the percent error of Karen's estimate. If necessary, round your answers to the nearest tenth. absolute error gal = percent error = X S ?

Given f(x) = 8x and g(x)=3x² +6, find the following expressions. (a) (fog)(4) (b) (gof)(2) (c) (fof)(1) (d) (gog)(0) (a) (fog)(4) = (Simplify your answer.)

Solve the following system of equations by graphing. y = x - 1 y = - 2x + 8 Identify the type of system. O Exactly one solution: O Infinite solutions O No solution Solve the following system of equations by graphing.

There are 7 erasers in a set. Grace buys 9 sets. After giving some erasers away, Grace has 35 erasers left. How many erasers did she give away? 4 Solve on paper. Then, check your answer on Zearn. ➡ Grace gave away erasers.

The population of Nigeria can be modeled by the function P(t) = 279(1+0.0251)* where P(t) measures the population in millions and t represents the number of years since 2000. 1. Using this model, what was the population of Nigeria in 2006? 2. Predict the population of Nigeria in 2025. 3. If this growth rate continues, in what year will the population of Nigeria reach 2 billion people? Note: You can earn partial credit on this problem.

Damonii and Adrian have new jobs at Ms. Battle's Cotton Candy Confectionary. Damonii is Adrian's manager. In their first year, Damonii will be paid $20 per hour, and Adrian will be paid $11 per hour. They have been told that after every year with the company, they will each be given a raise of $4 per hour. Is the relationship between Damonii's pay and Adrian's pay rate proportional? Explain your reasoning using a table.

Rewrite the distance formula to solve for y₁. SOA. OB. 3₁ = √√√d² - (1₂ - 1)² - y₂ 3₂ - √d² - (x₂ - 1₂) ² 32 1 = OC. ₁ = OD. 3/₁ = 2 - 2 - 1 + 3₂ - - d ₁ + 3₂ - ² d = √(21)²+(2-31)

A ship is sailing due north. At a certain point, the bearing of a lighthouse 3.3 km away is N38.3°E. Later on, the captain notices that the bearing of the lighthouse has become $32.3°E. How far did the ship travel between the two observations of the lighthouse? The ship travelled km between the two observations. (Do not round until the final answer. Then round to the nearest tenth as needed.)

Find the domain of the function f(x)=√x - 2. Write your answer in interval notation.

Solve the problem. 25) A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 7400 feet. What is the length of the trail (to the nearest foot)?

22 What is n NOR n (nn) when n = 1 and when n = 0? On NOR n is 1 when n = 1 and 0 when n = 0 On NOR n is 1 when n = 1 and 1 when n = 0 rn NOR n is 0 when n = 1 and 1 when n = 0 n NOR n is 0 when n = 1 and 0 when n = 0

A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M. Then graph your equation using the axes below. Equation:

For a certain endangered species, the goal is to have 900 breeding adults in the wild by 2023. If progress toward this goal continues, the population of breeding adults in the wild in year x can be approximated by P(x) = 74 e 0.15x, where x = 12 corresponds to the year 2012. Use this model to find the following. (a) P(16) (b) P'(x) and P'(16) (c) Interpret the answers in parts (a) and (b). (a) P(16)= 816 (Round to the nearest integer as needed.) 0.15x (b) P'(x)= 11.1 e P'(16)= (Round to the nearest integer as needed.) *****

=. A track is to be constructed around the football field at a junior high school. If the straightaways are 100 yd in length, what length of radius is needed for each of the semicircles shown if the total length around the track is to be 440 yd? 100 yd 100

58. In 1988, Winchell's House of Donuts in Pasadena, California, made the world's largest donut. It weighed 5000 pounds and had a circumference of 298.3 feet. What was the donut's diameter to the nearest tenth? (Hint: С=лd)

The speed of light is 3 × 108 m/s. If a star is 51, 000, 000, 000, 000 meters from Earth, how many seconds does it take light to travel from the Earth to the star? Enter your answer in scientific notation.

A 9-microgram sample of a radioactive isotope decays to 7.61 micrograms in 7 min. What is the half-life of the radioactive isotope, in minutes? Use the exponential decay equation A = Ao where A is the amount of a radioactive material present after time t, k is the half-life of the radioactive material, and Ao is the original amount of radioactive substance. (Round your answer to two decimal places.) (¹) t/K, min

Solve the triangle. a=8.953 in c=6.808 in B=75.17° What is the length of side b? in (Round to the nearest thousandth as needed.) What is the measure of angle A? (Round to the nearest hundredth as needed.) What is the measure of angle C? (Round to the nearest hundredth as needed.)