Basic Math Questions and Answers

Find the x- and y-intercepts of the graph of x -6y = 32. State your answers as whole numbers or as improper fractions in simplest form.

In the lab, Latoya has two solutions that contain alcohol and is mixing them with each other. Solution A is 10% alcohol and Solution B is 50% alcohol. She uses 600 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 40% alcohol solution? Number of milliliters of Solution B:

Suppose a bathroom scale registers 2 lb with no load. An object is weighed repeatedly on this bathroom scale, and each results in a reading of 117 lb. What is the probable true weight of the object in pounds (lb)?

The midpoint of AB is M(-5,0). If the coordinates of A are (-8, 5), what are the coordinates of B?

A spherical balloon with radius r inches has volume V(r) 4/3πr3. Find an expression that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r +1 inches. (Express your answer in terms of and r.)

Graph the equation y = x² + 12x +32 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Describe how the graph y = 2(3) - 2 can be transformed to the graph y = 4(3)-x + 4 The graph has a vertical shift up 6 units, a reflection over the y axis and a vertical stretch by a factor of 2. The graph has a vertical shift down 6 units, a reflection over the y axis and a vertical stretch by a factor of 2. The graph has a vertical shift down 4 units, a reflection over the x axis and a vertical stretch by a factor of 4. The graph has a vertical shift up 4 units, a reflection over the x axis and a vertical stretch by a factor of 4.

Find the coordinates of the image. Ry-axis (S) Ry-axis (S) = (Type an ordered pair.)

A circular swimming pool at an apartment complex has diameter 18 meters and depth 2.5 meters throughout. The apartment manager needs to get the interior of the swimming pool painted. The paint she wants to use covers 40 square meters per can. How many cans of paint will she need to purchase? You may use 3.14 for π. 5 4 11 10

A survey of 70 college students was taken to determine where they got the news about what's going on in the world. Of those surveyed, 20 got the news from newspapers, 28 from television, and 8 from both newspapers and television. Construct a Venn diagram and determine the cardinality for each region. Use the completed Venn Diagram to answer the following questions. How many got the news from only newspapers? n(Newspapers only) = 12 How many got the news from only television? n(Television only) =

The winning height for the men's Olympic high jump has been increasing each year. A regression line of the data is y = 0.23x +70.8. where y is the height of the men's winning jump in inches and x is the number of years since the first Olympics in 1896. Which statement best describes the meaning of the y-intercept of the regression line? A. The winning men's high jump height of the first Olympics was about 0.23 inches. B. The winning men's high jump height of the first Olympics was about 70.8 inches. C. Each year the winning men's high jump height is predicted to increase by 0.23 inches, D. Each year the winning men's high jump height is predicted to increase by 70. 8 inches.

a. When 37.579 and 29.2 are divided, the answer should be based on Enter the answer with the correct number of digits. 37.579 29.2 = b. When 29.2 is subtracted from 37.579, the answer should be based on Enter the answer with the correct number of digits. 37.57929.2 =

Now determine the cost for the additional data you used. Your plan allowed 2.00 GB data. You used 2.59 GB. You therefore you do owe money for extra data usage. Each additional MB of usage costs 2 cents, or $0.02. Assume 1 GB 1000 MB. Enter your value as a decimal number, dollar and cents. For example, enter $13.45 as 13.45.

According to a local medical facility, 3 out of every 5 patients it serves are treated on an outpatient and are not admitted overnight. The medical facility serves 175,000 patients per year. Based on this statement, a total of ______________ patients are admitted to the facility medical facility serves each year.

The discriminant of a quadratic function is 0. What does this mean about the solutions? 1 real solution, 1 imaginary solution 2 real solutions 1 real solution 0 real solution, 2 imaginary solutions

Write the quadratic function in standard form. y = -2(x-3)² -3 (fill in the blanks with the correct coefficient. If the coefficient has a "minus sign" in front make the number negative that you enter. Do not enter a "+" for positive numbers.)

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 200 grams of an alloy that contains 44% copper with 56 grams of pure copper. Answer the questions below. Do not do any rounding. (a) How many grams of copper are in the resulting mixture? (b) What percentage of the resulting mixture is copper?

Determine the volume, in ft3, of 2 lb of a two-phase liquid-vapor mixture of Refrigerant 134A at 40°F with a qualit- of 30%. What is the pressure, in lbf/in.?? Determine the volume, in ft3, of 2 lb of a two-phase liquid-vapor mixture of Refrigerant 134A at 40°F with a quality of 30%. V =

Coach Kelly drew his football team's next play on a coordinate grid. He placed Jon at (4,2). He will be passing the ball to Martice at (-6,8). What is the distance, in yards, of the pass from Jon to Martice? Round to the nearest tenth of a yard.

A toll collector on a highway receives $8 for cars and $9 for trucks. At the end of a 4-hour period, she collected $376. How many cars and trucks passed through the toll booth during that period? List all possible solutions. Which of the choices below are possible solutions to the problem? Select all that apply. A. 11 cars and 32 trucks C. 5 cars and 37 trucks E. 47 cars and 0 trucks G. 38 cars and 8 trucks 41 cars and 5 trucks B. 2 cars and 40 trucks D. 29 cars and 16 trucks F. 23 cars and 21 trucks H. cars and 42 trucks J. 20 cars and 24 trucks

Graph the equation and identify the x and y-intercepts. y=-6

Write in standard form. y = 4(x + 2)(x-3) A) y = 4x² - 24 C) y = 4x² 20x + 24 B) y = 4x² + 20x + 24 D) y = 4x² - 4x - 24

Find the following for the given functions. f(x) = x², g(x) = 4x - 3 (a) (f+g)(x) = (b) (f- g)(x) = (c) (fg)(x) = (d) (f/g)(x) What is the domain of f/g? (Enter your answer using interval notation.)

Complete the sentence below. The distance d between two points P₁ = (x₁.y₁) and P₂ = (x₂,Y₂) is d= The distance d between two points P₁ = (x₁,Y₁) and P₂ = (x₂,Y₂) is d =

At one university, the mean distance commuted to campus by students is 17.0 miles, with a standard deviation of 4.2 miles. Suppose that the commute distances are normally distributed. Complete the following statements. (a) Approximately 68% of the students have commute distances between miles and miles. (b) Approximately 2 miles and 25.4 miles. of the students have commute distances between 8.6

Marissa and Tori can shovel a driveway together in 22 min. If Marissa can shovel the same driveway in 70 minutes by herself, how long would it take Tori by her self?

If the height of this box was 10in, how man 2in cubes could fit inside this box? If the volume of this box was 750in³, what would the value of h have to be? If the surface area of this box was 680in², what would the value of h have to be?

The figure shows a coordinate plane on a baseball field. The distance from home plate to first base is 90 feet. The pitching mound is the midpoint between home plate and second base. Find the distance from home plate to second base. Find the distance between home plate and the pitching mound. Explain how you found your answers.

Solve the following system of equations. State whether the system is consistent and independent, consistent and dependent, or inconsistent. -4x + 7y= 28 4x - 7y=32 consistent and independent consistent and dependent inconsistent

Kenya plans to make a down payment plus monthly payments in order to buy a motorcycle. At one dealer she would pay $2,450 down and $150 each month. At another dealer, she would pay $3,150 down and $125 each month. After how many months would the total amount paid be the same for both dealers? What would that amount be?

Un Monday, the rover traveled 330 cm. On Tuesday, it traveled 180 cm. If the rover stopped every 15 cm to recharge, how many more times did it need to recharge on Monday than on Tuesday? 24 12 22 10

Write an equation and solve it. Kira had already read 13 books this year before joining a book club, and she planned to read 1 book every month. If Kira has read 22 books so far, how many months has she been with her book club? *

Use the given sample data to find Q3. 49 52 52 52 74 67 55 55 A. 6.0 B. 67.0 C. 61.0 D. 55.0

If -3 and 5 are the coordinates of two points on the real number line, the distance between these points is _____

Write an equation and solve. Mr. Hewitt estimates the cost towards a fresh paint job for the exteriors of his home. He quotes 12 gallons of paint priced at x dollars per gallon. The cost of paint supplies and miscellaneous expenses are $2264. The total estimated cost for the paint job is $2624. What is the price of a gallon of paint?

Write the quadratic function in vertex form that has a vertex of (2, 0) and goes through the point (3, 1)

Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general? 38 36 35 29 21 19 16 14 13.8 The range of the sample data is The variance of the sample data is The standard deviation of the sample data is the standard deviation of the sample a good estimate of the variation of salaries of TV personalities in general? A. No, because there is an outlier in the sample data. B. Yes, because the sample is random. C. Yes, because the standard deviation is an unbiased estimator. D. No, because the sample is not representative of the whole population.

In the 1970s, due to world events, there was a gasoline shortage in the United States. There were often long lines of cars waiting at gas stations. If there were a million cars in line, bumper to bumper, with average length of 9.65 feet, how long would that line be in miles? Round your answer to the nearest mile.

You have a $50 gift certificate at a store. You want to buy a book that costs $8.99 and boxes of stationery for your friends. Each box costs $4.59. How many boxes can you buy with your gift certificate?

Given that f(x) = 2^x- 1and g(x) = log3(x + 5)determine the x value(s) where f(x)=g(x). x=0.004 or x = 2.794 x= -4.652 or x = 1.43 x = -3.744 or r = -0.51 no solution

Miguel needs to have a toilet repaired in his house. The cost of the new plumbing fixtures is $150 and the labor is $40/hr. (a) Write a model that represents the cost of the repair C (in $) in terms of the number of hours of labor

Evaluate each logarithm and then use order of operations to simplify 4 (3-log₂ (8) +2. In e) + log3 1/9 42 34 54 55.744

John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.35 per pound, and type B coffee costs $5.40 per pound. This month, John made 139 pounds of the blend, for a total cost of $662.40. How many pounds of type B coffee did he use?

Rewrite logx, 2y = 3 in exponential form. (2y)³ = x 3² = 2y 3x = 2y y = x³

Suppose that you plan on taking a summer job selling magazine subscriptions. The magazine company will pay you $1 for selling the first subscription. For each. additional subscription sold, the magazine company will pay you 10 cents more than what was paid for the previous subscription. How much will you earn by selling 150 magazine subscriptions?

Your neighbors are purchasing hot dogs for a backyard barbecue. They are expecting 48 guests and want to provide an average of 2 hot dogs per guest. The hot dogs are sold in packages of twelve. Set up the problem below and calculate the number of twelve-packs of hot dogs they will need. Place your conversion factors in order such that "guests" cancels first.

Solve the absolute value equation: 9 - 6x | +2 = 23 {-2, 5} {-4} {22/9, -32/9} {-4, 1}

8. A motorcycle accelerates from rest along a straight road with position function s(t) = t³ + t, where s(t) is measured in meters and t is measured in seconds. a) What is the average velocity of the motorcycle between 1 and 6 seconds? b) What is the velocity of the motorcycle at 4 seconds?

Evaluate the function f(x) = 9x-3 at the given values of the independent variable and simplify. a. f(9) b. f(x+8) c. f(-x)

Solve the absolute value equation: |-3x + 9| = 15 {-8, 54/5} {3, -6} {-2, 8} {7, -12}