Basic Math Questions and Answers

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}

Diane invested her savings in two investment funds. The $3000 that she invested in Fund A returned a 3% profit. The amount that she invested in Fund B returned a 10% profit. How much did she invest in Fund B, if both funds together returned a 7% profit? Amount invested in Fund B: $

Set up the problem below and calculate the number of days that are equivalent to exactly 21600 minutes. Place your conversion factors in order such that "minutes" cancels first. 21600 minutes

Solve the system by substitution. -9y+ 2 = x -x-3y = -8

Write an algebraic equation for the following problem and then solve it. A landscaping company needs 180 gallons of 24% fertilizer to fertilize the shrubs in an office park. They have in stock 30% fertilizer and 20% fertilizer. How much of each type should they mix together? Let x = the number of gallons of 30% fertilizer to be used. Write an expression, in terms of x, that is equal to "180 gallons of 24% fertilizer". (Use integers or decimals for any numbers in the expression.) They should use ______gallons of 30% fertilizer and______ gallons of 20% fertilizer.

The patient's chart indicates that he weighed 175 pounds at the end of September. He then gained 2½ pounds in October and lost 3/4 pound in November. He weighed at the end of November.

Solve for u. -1/ u+5=- 7 /3u+15 - 1 If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Consider just the first sentence of this multistep word problem. Sentence 1: The sum of the ages of a brother and sister is 26. Give an equation that represents this statement using b as the age of the brother and s as the age of the sister. Express your answer in terms of the symbols b and s.

y = f(3x) Shift the graph 3 units upward. Stretch the graph horizontally and vertically by a factor of 3. Shift the graph 3 units to the left. Stretch the graph vertically by a factor of 3. Shrink the graph horizontally by a factor of 3.

Greg invested his savings in two investment funds. The amount he invested in Fund A was 4 times as much as the amount he invested in Fund B. Fund A returned a 8% profit and Fund B returned a 2% profit. How much did he invest in Fund B, if the total profit from the two funds together was $3400? Amount invested in Fund B:

The angle of depression from the top of a building to a point on the ground is 45 degrees. How far is the point on the ground from the top of the building if the building is 280 m high? Round your answer to the nearest whole number.

Find the length of each side of the triangle determined by the three points P₁, P2, and P3. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P₁ =(4,4); P₂=(2,3); P3 = (6,0) The length of side P₁ P₂ is (Type an exact answer, using radicals as needed). The length of side P₁P3 is (Type an exact answer, using radicals as needed).

Write the quadratic in vertex form (fill in the "a", "h", and "k" values) y = x² - 2x + 3 y =

Write an equivalent expression by distributing the "-" sign outside the parentheses: -(-3k-4.7)

A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 110 units of A per day. Both products use one raw material, of which the maximum daily availability is 300 lb. The usage rates of the raw material are 2 lb per unit of A, and 4 lb per unit of B. The profit units for A and B are $40 and $90, respectively. Determine the optimal product mix for the company.

A football is kicked vertically upward from a height of 5 feet with an initial speed of 75 feet per second. The formula h=5+75t-161² describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to find the ball's height 3 seconds after it was kicked.

Evaluate the function f(x)=x² + 4x+6 at the given values of the independent variable and simplify. a. f(-6) b. f(x+3) c. f(-x)

Final grades are often computed using weighted averages. Some college professors use complicated weighted averages. Your college professor tells you he will give a 33% -67% split on grades between tests and homework where whichever average is higher will be the 67%. What will your final grade be if your homework average is 85 and your test average is 62?