Basic Math Questions and Answers

A chemist has three different acid solutions. The first acid solution contains 20% acid, the second contains 30% and the third contains 50 %. They want to use all three solutions to obtain a mixture of 80 liters containing 40 % acid, using 3 times as much of the 50 % solution as the 30% solution. How many liters of each solution should be used?

Match the one-to-one functions with their inverse functions. Inverse Function f^-1(x) = 5x f^-1(x) = x^3/2 f^-1(x) = x+10 f^-1(x) = 3(x+17)/2

Which statement describes the end behavior of the function? f(x)=x^2-100/x^2-3x-4 A. The function approaches 0 as x approaches -∞ and ∞ B. The function approaches 1 as x approaches -∞ and ∞ C. The function approaches 5 as x approaches -∞ and ∞ D. The function approaches 25 as x approaches -∞ and ∞

Which variable is plotted on the vertical axis when a graph of the function z = f(w) is created? Choose the correct answer below. A. f is plotted on the vertical axis because the horizontal axis is used for the dependent variable and the vertical axis is used for the independent variable. B. f is plotted on the vertical axis because the horizontal axis is used for the independent variable and the vertical axis is used for the dependent variable. C. z is plotted on the vertical axis because the horizontal axis is used for the dependent variable and the vertical axis is used for the independent variable. D. w is plotted on the vertical axis because the horizontal axis is used for the independent variable and the vertical axis is used for the dependent variable. E. z is plotted on the vertical axis because the horizontal axis is used for the independent variable and the vertical axis is used for the dependent variable. F. w is plotted on the vertical axis because the horizontal axis is used for the dependent variable and the vertical axis is used for the independent variable.

The domain of function f is (-∞, 6) U (6, ∞). The value of the function approaches -∞ as x approaches -∞, and the value of the function approaches ∞ as x approaches ∞. Which function could be function f? A f(x)=x²-36/x-6 B. f(x)=x-6/x²-36 C. f(x)=x+6/x-6 D. (x)=x-6/x+6

After you graduate from CSU, you get a job with the Dihedral Group earning $1,890 a week. Soon the company needs to make cutbacks so your pay is reduced by 10%. Later you get a 10% cost-of-living raise. What is your current weekly pay? Round your answer to the nearest whole dollar.

Change the following decimal to fraction form (or mixed number form) and reduce, if possible. 76.09

Find the indicated quotient to the nearest thousandth. 5.81/85.761

If a minivan travels 306 miles on 25 gallons of gas, how many miles per gallon does it average (to the nearest tenth)?

Find the indicated quotient to the nearest tenth. 3.3 / 3.24

The use of linear and exponential models to predict growth patterns in science and medicine is not new. However, scientists and researchers continue to find new applications of the models to explain and predict growth patterns. Seiki Hamada and Makoto Takamiya of Japan have studied the growth patterns of a specific heart aneurism to better predict the estimated growth of an aneurism as well as to assist in determining when to recommend surgery. Hamada and Takamiya have found that aortic aneurisms grow in an exponential pattern rather than the hoped for linear pattern. What shape best describes the graph of an exponential model? A. A curve that starts slowly but then grows rapidly B. A straight line that is decreasing in value C. A curve that starts rapidly but then grows slowly D. A straight line that is increasing in value

Carlos begins his workout by stretching. Then he spends an equal amount of time on each workout machine. The equation y=8x+10 represents the total time, in minutes, of Carlos' workout if he uses x workout machines. Explain what the slope and y-intercept of the equation represent in this situation. A. Carlos spends 10 minutes on one machine and 8 minutes on another. B. Carlos uses 8 workout machines for 10 minutes each. C. Carlos spends 8 minutes stretching and 10 minutes on each workout machine. D. Carlos spends 10 minutes stretching and 8 minutes on each workout machine.

The government of a large city needs to determine whether the city's residents will support the construction of a new gymnasium. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be the most appropriate for obtaining a sample of the city's residents? Survey a random sample of the future employees of the new gymnasium. Survey every tenth person to use the public restroom. Survey the last 100 residents listed in the telephone directory. Survey a random sample of persons within each neighborhood.

Which situation is most likely to show a constant rate of change? A. The amount of gasoline in a car's tank while driving on a highway at a constant speed compared with time B. The distance of a student from home during a school day compared with the time of day C. The speed of the wind on a stormy day compared with the time of day D. The number of customers in a grocery store compared with the day of the week

After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x? A.y-300 = 4(x - 100) B. y+ 300 = 2.5(x + 100) C. y+ 300 = 4(x + 100) D. y 300 = 2.5(x - 100)

Find the ratio, reduced to lowest terms, of the volume of a sphere with a radius of 4 inches to the volume of a sphere with a radius of 8 inches. The ratio is. (Type an integer or a simplified fraction.)

An architect is considering bidding for the design of a new museum. The cost of drawing plans and submitting a model is $13,000. The probability of being awarded the bid is 0.4. If the architect is awarded the bid, she will make $32,500 minus the $13,000 cost for plans and a model. Complete parts a. through b. below. a. What is the expected value in this situation? (Round to the nearest dollar.)

Give the slope of y+2=3(x-7) and a point on the line. A. The slope is 7 and (3, 2) is on the line. B. The slope is 3 and (7, -2) is on the line. C. The slope is 2 and (7,3) is on the line. D. The slope is 3 and (-7, 2) is on the line.

Customers can pick their own blueberries at Blueberry Hill. They pay $5 to enter the patch and $4 per pound for the blueberries they pick. Write an equation to model the total cost, y, for x pounds of blueberries. A. y = 5x +4 B. y = 4x + 5 C. y = x(5+4) D. y = 4(x + 5)

A game is played using one die. If the die is rolled and shows 2, the player wins $10. If the die shows any number other than 2, the player wins nothing. Complete parts (a) through (b) below. a. If there is a charge of $2 to play the game, what is the game's expected value? $(Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. A. This value represents the expected loss over the long run for each game played. B. The player can expect to break even over the long run. C. This value represents the expected win over the long run for each game played.

Construct the dotplot for the given data. A manufacturer records the number of errors each work station makes during the week. The data are as follows. 6323520254201 5 10 → 10 10 10

TV sets: According to the Nielsen Company, the mean number of TV sets in a U.S. household in 2013 was 2.24. Assume the standard deviation is 1.1. A sample of 90 households is drawn. Part 1 of 5 (a) What is the probability that the sample mean number of TV sets is greater than 2? Round your answer to at least four decimal places. The probability that the sample mean number of TV sets is greater than 2 is 9809 Part: 1/5 Part 2 of 5 (b) What is the probability that the sample mean number of TV sets is between 2.5 and 3? Round your answer to at least four decimal places. The probability that the sample mean number of TV sets is between 2.5 and 3 is

There are 9 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances? ways (Type a whole number.)

Determine whether the quantitative variable is discrete or continuous. the number of bottles of juice sold in a cafeteria during lunch continuous discrete

Calibrating a scale: Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be a=2.0. They weigh this weight on the scale 55 times and read the result each time. The 55 scale readings have a sample mean of x = 1000.6 grams. The scale is out of calibration if the mean scale reading differs from 1000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration. Use the a=0.10 level of significance and the P-value method with the TI-84 calculator. Part: 0/4 Part 1 of 4 State the appropriate null and alternate hypotheses. Ho H₁ This hypothesis test is a (Choose one) test.

Use the given data to construct a frequency distribution. Lori asked 24 students how many hours they had spent doing homework during the previous week. The results are shown below. 10 10 10 8 10 10 14 13 10 8 12 10 10 12 10 10 12 10 10 13 10 12 13 8 Construct a frequency distribution. Use 4 classes, a class width of 2 hours, and a lower limit of 8 for

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. Choosing 8 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen. Not binomial: there are too many trials. Procedure results in a binomial distribution. Not binomial: there are more than two outcomes for each trial. Not binomial: the trials are not independent.

The given tessellation formed by two or more regular polygons is shown. a. Name the type of regular polygons that surround each vertex. b. Determine the number of angles that come together at each vertex, as well as the measures of these angles. c. Use the angle measures from part (b) to explain why the tessellation is possible. 88 a. Choose the correct answer below. OA. triangle, pentagons B. triangles, octagons OC. triangle, dodecagons

Find the standard deviation, o, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. n = 38; p = 0.4 o = 7.14 σ = 6.29 σ = 3.02 σ = 0.61

A circular backyard pool has a diameter of 24 feet and is 3 feet deep. One cubic foot of water has a capacity of approximately 7.48 gallons. If water costs $4 per thousand gallons, how much, to the nearest dollar, will it cost to fill the pool? It will cost approximately $ to fill the pool. (Round to the nearest dollar as needed.)

Assume that a sample of bivariate data yields the correlation coefficient, r, indicated. Use the table on the right for the specified sample size and level of significance to determine whether a linear correlation exists. r=0.81 when n=10 at a = 0.01 Does a linear correlation exist? A linear correlation does not exist. OA linear correlation exists. C4567668 n 9 10 Correlation Coefficient, r α=0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 α = 0.01 0.990 0.959 0.917 0.875 0.834 0.798 0.765

A man earned wages of $33,600, received $1700 in interest from a savings account, and contributed $2700 to a tax-deferred retirement plan. He was entitled to a personal exemption of $3000 and had deductions totaling $5480. Find his gross income, adjusted gross income, and taxable income. His gross income was $ (Simplify your answer.)

A certain pyramid has a square base measuring 819 feet on a side and a height of 486 feet. a. What is the volume of the pyramid, in cubic yards? b. The stones used to build the pyramid were blocks with an average volume of 1.5 cubic yards. How many of these blocks were needed to construct the great pyramid?

Solve the problem. Round the point estimate to the nearest thousandth. Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 898 people, 46 people had hearing aids. 0.050 0.949 0.049 0.051

A woman is in the 15% tax bracket and itemizes her deductions. How much will her tax bill be reduced if she qualifies for a $300 tax credit? Her tax bill will be reduced by $ (Simplify your answer.)

When a national sample of heights of kindergarten children was taken, a student was told that she was in the 25th percentile. Explain what that means. Choose the correct interpretation below. A. She is shorter than 25 percent of all kindergarten children. B. She is taller than 75 percent of all kindergarten children. C. She is taller than 25 percent of all kindergarten children. D. She is taller than 25 kindergarten children.

One circular table has a diameter of 8 ft, and another circular table has a diameter of 12 ft. How much greater is the area of the larger table? Round to the nearest whole number. about 31 ft2 about 6 ft2 about 63 ft2 about 13 ft2

A bin contains 64 light bulbs of which 10 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. Round to the nearest thousandth if necessary. 0.428 0.844 0.484 0

Write the following rate as a simplified fraction. 26 dogs to 34 cats

Determine how much the following individual will save in taxes with the specified tax credits or deductions. Rosa is in the 15% tax bracket and claims the standard deduction. How much will her tax bill be reduced if she makes a $500 contribution to charity? www. Her tax bill will be reduced by $. (Simplify your answer.)

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. The amount of time (in hours) that Sam studied for an exam on each of the last five days is given below. Find the mean study time. 1.5 8.3 6.9 1.8 5.3 4.76 hr 23.80 hr 4.96 hr 5.45 hr

In a survey of 2752 adults, 1429 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is 0. (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. B. With 99% confidence, it can be said that the sample proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval. C. The endpoints of the given confidence interval show that adults pay bills online 99% of the time.

A student earned grades of B, B, A, C, and D. Those courses had these corresponding numbers of credit hours: 4, 5, 1, 5, 4. The grading system assigns quality points to letter grades as follows: A-B-3 C-2 D-1 and F-a Compute the grade point average (GPA) and round the result to two decimal places. 1.37 2.37 9.00 3.46

Write the following number in decimal notation. Seventy-eight hundredths

A woman eamed wages of $31,200, received $2800 in interest from a savings account, and contributed $3200 to a tax-deferred retirement plan. She was entitled to a personal exemption of $2600 and had deductions totaling $5220. Find her gross income, adjusted gross income, and taxable income.

Write the indicated product in decimal form and round your answer to the nearest thousandth, if necessary.

Each dimension of a rectangular family room is 3.5 times larger than a rectangular bedroom. If it costs $312 to carpet the bedroom, how much would it cost to carpet the family room with same carpet? $3,822 $1,092 $4,914 $2,184

Use synthetic division to divide f(x) = x² +8x²-3x-90 by x + 5. Use the result to find all zeros of f. (x² +8x²-3x-90) + (x+5)= x² + 3x - 18 (Do not factor. If there is a remainder, type your answer in the form quotient + The zeros off are (Use a comma to separate answers as needed.)

Use the table of English and Metric Equivalents for Capacity, along with dimensional analysis, to convert the given unit to the unit indicated 21 mL to tsp Click to check the table of English and Metric Equivalents for Capacity. 21 mL tsp (Round to two decimal places as needed.)

From 15°C, 35°C, 45°C, and 60°C, select the best estimate of the Celsius temperature of a warm winter day in Michigan. The average temperature in Michigan during the winter is about 30°F. Choose the temperature that best represents a warm winter day in Michigan. 35°C 45°C 15°C 60°C