Basic Math Questions and Answers

G. Zach deposited $3,000 in a new account at his bank. The bank pays 7.5% interest compounded annually on this account. Zack makes no additional deposits or withdrawals. What will be the balance of Zack's account at the end of 3 years?

There are a total of 19,153 IRSC students, 61% of which are under the age of 22. In a random sample of 655 students, 68% are found to be under the age of 22. Determine how many students in the population and the sample, respectively, are under the age of 22. Round solutions to the nearest whole number, if necessary. IRSC students are under the age of 22. students in the random sample of 655 IRSC students are under the age of 22:

Verizon offers to sell cellular phones listing for $100.24 with a chain discount of 15/10/5. Cellular Company offers to sell its cellular phones that list at $103.49 with a chain discount of 25/5. If Irene is to buy six phones, how much could she save if she buys from the lower-priced company? (Do not round intermediate calculations. Round all dollar amounts to the nearest hundredth. Round your final answer to the nearest cent.)

How did advances in physics and chemistry dramatically change manufacturing? made large multinational companies possible forced companies to share control of the production process employed fewer workers created research and development divisions

In 2004, the highest spaceplane flight was made in SpaceShipOne. A flight with this altitude can be modeled by the function below, where h is the altitude in meters and t is flight time in seconds. Approximately how long did the flight last? h(t) = -0.17t² + 187t +61,000 t≈1101.3 seconds t≈1363 seconds t≈261.7 seconds t≈1596 seconds

Victoria invests $300 into an account with a 2.5% interest rate that is compounded semiannually. How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar.

The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science fiction books to the number of biographies is 4: 5. If there are 48 science fiction books, find the total number of books.

Two cities have nearly the same north-south line of 97° W. The latitude of the first city is 27° N, and the latitude of the second city is 37° N. Approximate the distance between the cities if the average radius of Earth is 6400 km. The cities are approximately (Round to the nearest integer as needed.) kilometers apart.

An astronaut is returning to Earth in a spacecraft. If the spacecraft is descending at a rate of 13.81 kilometers per minute, what will be its change in height after 51/2 minutes? Round your answer to the nearest kilometer. 76 km -76 km 760 km -760 km

The function fis defined as follows. f(x) = -x² +6 If the graph of fis translated vertically downward by 3 units, it becomes the graph of a function g. Find the expression for g (x).

Angle is in standard position and (-6, -4) is a point on the terminal side of θ What is the exact value of secθ in simplest form with a rational denominator?

Solve the equation for x. x² - 12x +32 = 0

Carmen is choosing between two exercise routines. In Routine #1, she burns 44 calories walking. She then runs at a rate that burns 16.3 calories per minute. In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 18.5 calories per minute. For what amounts of time spent running will Routine #1 burn at most as many calories as Routine #2? Use t for the number of minutes spent running, and solve your inequality for t

Using the verbal description below, write the original function and it's inverse. Explain your solution strategy. 1. Starting with a number x, subtract 5 2. Take the square of that quantity 3. Divide by 3

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4,720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

Liz does screen-printing. When she screen-prints a batch of T-shirts, there is an initial set-up time of 15 minutes. After that, it takes 3 minutes to print each shirt. How long does it take to screen-print a batch of 14 shirts?

A coach bought 3 jerseys and 2 pairs of shorts for each of the 14 players on her soccer team. The jerseys cost $15 each, and the shorts cost $12 each. The coach used a $100 coupon to hel pay for the uniforms. Rewrite the numerical expression with parentheses to model the total cost, $866. 14 x 3 x 15 +2 x 12 + 100

A contractor is in charge of hiring people for a construction project. The number of days it would take to complete the project with a full time workers can be found using the function f(x) = 234. Assume once workers are assigned to the project, no workers may be added or taken off the project until it is finished. Find and interpret the given function values and determine an appropriate domain for the function. f(-1) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. of the problem. f(2)= meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. f(6.5) = meaning with full time workers, the project would be complete in days. This interpretation in the context of the problem. Based on the observations above, it is clear that an appropriate domain for the function is

In Fall 2020, 10.5 million undergraduate students attended a 4-year institution full- time. Of those, 9,240,000 were under age 25, 945,000 were ages 25-34, and 315,000 were age 35 and older. Answer the questions below. Label your answers with a, b, c. a. What percent of the students were under age 25? b. What percent of the students were ages 25-34? c. What percent of the students were age 35 and older?

Express 9.603603603... as a rational number, in the form p/q where p and q have no common factors.

Which of the following expressions is incorrect? |-12| = 12 |12| = 12 -|-12| = -12 -|12| = 12

The Thomas Jefferson Memorial is on 18.36 acres of land and the Franklin Delano Roosevelt Memorial is on 7.5 acres of land. How many more acres is the Jefferson Memorial than the Roosevelt Memorial? 9.86 acres 10.86 acres 11.31 acres 17.61 acres

A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $7.80 and then an additional 7 cents per minute of use. In Plan B, there is no monthly fee, but the customer pays 9 cents per minute of use. For what amounts of monthly phone use will Plan A cost at least as much as Plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.

The amount of water an electric dishwasher uses to wash dishes varies directly with the number of loads of dishes. The dishwasher uses 32 gallons of water to wash 4 loads of dishes. How many gallons of water will the dishwasher use to wash 10 loads of dishes? Record your answer. Be sure to use the correct place value.

If you solve a system of equations, and your final step ends with the following answer: 12= 12....how many solutions are there to the system of equations? infinite solutions no solution one solution

What does the graph of y=x+- 1/(x+2)²-3 look like? Graph the equation on your calculator. Use the trace and/or zoom buttons to find the r- and y-intercepts. What is the domain of this function? What is the range?

Match the amplitude, midline, period, and frequency for the cosine equation. f(x) = 5 cos(2x) + 3 1.5 2. π 3. 2 4. y = 3 a. Amplitude b. Frequency c. Midline d. Period

Find the exact value of the following expression. Do not use a calculator to enter a decimal approximation. sinπ/4

According to a recent Pew Research poll, 68% of Americans say that the U.S. economic system unfairly favors the powerful. In a recent sample of 830 Americans, 111 agreed that the U.S. economic system unfairly favors the powerful. Determine the values of p and p. Round solutions to two decimal places, if necessary. p= p^=

Write the equation that results in the desired transformation. The cube root function, vertically shrunk by a factor of 0.5, and reflected across the x-axis. y = (Type an expression using x as the variable.)

The mean weight of all Goliath grouper caught on the Treasure coast is 438 pounds, with a standard deviation of 49 pounds. Suppose a random sample of 92 Goliath Grouper from the Treasure Coast are aught and weighed. Determine the probability that the average weight of the sample of 92 Goliath Grouper is within 8 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast. Round the solution to four decimal places, if necessary. P( within 8 pounds of μ)

Suppose there are eight salespeople. If seven of the salespeople earned $2,400, $2,500, $2,800, $2,800, $3,400, $3,400, and $3,800, how much would the eighth person would need to earn for the median to be $3,000? $3,200 $3,000 $2,800 $3,100

Two groups of students on a fieldtrip is getting food in a fast food restaurant. The first group bought 8 burgers and 4 soft drinks for $34.08. The second group bought 5 burgers and 5 soft drinks for $25.25. How much does one burger cost? $1.58 per burger $2.97 per burger $3.47 per burger $2.08 per burger

Use the following information to answer the questions. The 6th term in the arithmetic sequence is 35 and the 9th term of the arithmetic sequence is 50. What is the common difference? What is a, ? What is the explicit formula? Write in the form 10+4(n-1) where 10 is 1st term, 4 is the common difference

A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation 3x+52 = y. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change per day in the road's length? What was the road's length when the crew started working?

Drag and drop an answer choice into each empty box below. -11 4 -4 11 Consider the points R(6,5) and U(-5,–6). RU undergoes the translation (x, y) → (x + h, y + k), such that R'(-5, 1) and U'(-16, -10). Complete the following algebraic description. Drag the corresponding values. (x, y) → (x+

Estimate the population mean by finding a 99% confidence interval given a sample of size 11, with a mean of 41.7 and a standard deviation of 11.2. Preliminary: a. Is it safe to assume that n < 0.05 of all subjects in the population? b. Is n > 30? Confidence Interval: What is the 99% confidence interval to estimate the population mean? Enter the tri-linear inequality values accurate to one decimal place.

Answer the following. (a) The signal from a certain satellite takes approximately 0.013 seconds to reach Earth. Write this number in scientific notation. (b) The total surface area of South America is approximately 6.89 x 106 square miles. Write this number in standard notation.

Two cities are 2000 km apart and lie on the same north-south line. The latitude of the northernmost city is 53° N. What is the latitude of the other city? The radius of the Earth is approximately 6400 km. The latitude of the other city is approximately N. (Do not round until the final answer.

An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $4600 and his stock in Company B was worth $1000. The stock in Company A has increased 25% since last year and the stock in Company B has increased 22%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).

A store is having a sale on trail mix and jelly beans. For 8 pounds of trail mix and 3 pounds of jelly beans, the total cost is $23. For 2 pounds of trail mix and 5 pounds of jelly beans, the total cost is $10. Find the cost for each pound of trail mix and each pound of jelly beans.

A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ=145° and r= 36 yd. The area of lawn that receives the water is square yards. (Round to the nearest integer as needed.)

Ben walks at a rate of 3 miles per hour. He runs at a rate of 5 miles per hour. In one week, the combined distance that he walks and runs is 170 miles. If Ben walks for 10 hours, how many hours does he run?

Fill in each blank with the appropriate response. (Remember that the vertical stretch or shrink factor is positive.) The graph of y=- 1/5 [x-8]-7 can be obtained from the graph of y = [x] by shifting horizontally units to the vertically shrinking by applying a factor of reflecting across the -axis, and shifting vertically units in the direction. (Type whole numbers.)

Last year, a baseball team purchased new equipment. The equipment manager paid $20 per bat and $12 per glove, spending a total of $552. The manager bought 34 pieces of equipment. Write a system of equations that can represent this situation.

A person's blood type is denoted with the letters A, B, and O, and the symbols + and -. The blood type A+ is read as A positive. The blood type B- is read as B negative. Use the data to write a ratio for the comparison in 3 different ways. AB- donors to AB+ donors

At the local dairy farm, Kareem buys a 32-oz container of yogurt for $2.56. Jonah buys a 6-oz container of yogurt for $0.48. Are the cost, y, in dollars and the amount of yogurt, x, proportional? Explain. Write an equation to represent this relationship.

Graph the data. Then find the slope of the line. Explain what the slope represents. At 6 A.M., the retention pond had 28 inches of water in it. The water receded so that at10 A.M. there were 16 inches of water left.

Find (fog)(1), (g o f)(1), (f o g)(x) and (gof)(x). f(x) = x² + 1; g(x) = 3x - 4 (fog)(1) =

As shown in the illustration, Alexa had a negative balance in her checking account before depositing a $47.00 check. What is the new balance of Alexa's checking account? What property did you use to find the sum?