Math Questions

Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour? 0.8 of an inspection in 1 hour 4 inspections in 5 hours 1.25 inspections in 1 hour 5 inspections in 4 hours

Greg deposited $4000 into an account with 4.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 3 years? Do not round any intermediate computations, and round your answer to the nearest cent.

Write the equation of the line passing through (-2,-4) that is parallel to 3x + 5y = 11.

A projection made in January of 2005 determined that x years later, the average property tax on a three-bedroom home in a certain community will be T(x) = 48x 3/2 + 40x + 1300 dollars. Estimate the percentage change by which the property tax will increase during the first half of the year 2012.

Find the zeros of the following polynomial. f(x) = x³ + 12x4 +36x³ List the zeros separated by commas. For example, if you found that the zeros were x = 1, x = 2, enter 1, 2, 3. Provide your answer below:

A fence is to have 3 1/2 wide boards between two posts that are 94 1/4 apart so that the space between each board is the same. Calculate the number of boards and the spacing so that the spacing between the boards is as small as possible. Round your answer for the spacing to the nearest 16th of an inch.

We determined R = 0.0825 and T = 9/15 The amount of the loan, the principal, was $70,000, giving P = Substitute these values into the formula to find the amount of interest earned (in $) at 8 1/4 % for 9 months. I = PRT

A particle moves according to the law of motion s = t³ - 8t2 + 3t, t ≥ 0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1,2] (b) Find the velocity at time t. (c) What is the velocity after 3 seconds? (d) What is the acceleration after 7 seconds? (e) Fort > 0, when is the particle moving in the positive direction?

Consider the parabola given by the equation: f(x) = 4x² + 14x -15 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two a -intercepts of the parabola and write them as a list, separated by

Google it: According to a report of the Nielsen Company, 82% of internet searches used the Google search engine. A sample of 100 searches is studied. Use the Cumulative Normal Distribution Table or technology. Round your answer to four decimal places. (a) Approximate the probability that more than 76 of the searches used Google. The probability that more than 76 of the searches used Google was approximately

After a baby was born, he began to gain weight at a rate of 1.5 pounds per month. The weight of the baby at birth was 10 pounds. Write an equation for W, in terms of t, representing weight, in pounds, of the newborn baby t months after birth.

Find the equation of the line through (3, 1) with slope 7. Enter your solution in the form y = mx + b. y =

If a single pane of glass obliterates 2% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function below. p(n)= 100(0.98)n (a) What percent of light will pass through 20 panes? (b) What percent of light will pass through 30 panes? (c) Explain the meaning of the base 0.98 in this problem.

A gray crayon is made with 5 mL of black wax for every 6 mL of white wax. Which of the following wax mixtures will create the same shade of gray? Choose 2 answers: 10 mL of black wax mixed with 24 mL of white wax 15 mL of black wax mixed with 18 mL of white wax 35 mL of black wax mixed with 42 mL of white wax 20 mL of black wax mixed with 26 mL of white wax 45 mL of black wax mixed with 48 mL of white wax

Sketch the graph of a function f that satisfies all of the following properties. Indicate all asymptotes. (a) f(x) is defined for all real numbers except x = 1. (b) f(x) is discontinuous at x = -2 and x = 1, but is continuous for all other z. (c) f(x) is not differentiable at x = -2, x = 1, and x = 4 but it is differentiable for all other . (d) lim f(x) = 3, (e) lim f(x) = -2, (f) lim f(x) = -0.

Fill in the blanks Enter intercepts as ordered pairs, aka points. Then Graph the parabola given in vertex form. Vertex Form: y = (x + 4)² - 1 1. Does the parabola open up or down? Up Down 2. Vertex (x, y) = 3. Equation of the Axis of Symmetry:

Below, one description, one graph, and one equation are equivalent. Choose the proper set. You start with 2 Xbox360 games and each month you buy 2 new games. You start with 3 Xbox360 games and each month you buy 3 new games.

A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 160 square yards. Find the length and the width The parking lot has a width of The parking lot has a length of yards. yards.

7. A catering company is setting up for a wedding. They expect 150 people to attend. They can provide small tables that seat 6 people and large tables that seat 10 people. a. Find a combination of small and large tables that seats exactly 150 people. b. Let x represent the number of small tables and y represent the number of large tables. Write an equation to represent the relationship between x and y. c. Explain what the point (20, 5) means in this situation. d. Is the point (20, 5) a solution to the equation you wrote? Explain your reasoning.

A lunar module weighs 12 tons on the surface of the Earth. How much work is done in propelling the module from the surface of the moon to a height of 55 miles? Consider the radius of the moon to be 1100 miles (from the center of the moon) and its force of gravity to be one-sixth that of Earth.

Henry made a shirt using 1/3 yards of red fabric and 3/4 yards of blue fabric. How many more yards of blue fabric did Henry use? Write your answer as a fraction in simplest form.

A school counts the number of students taking AMDM and find 205 students taking AMDM. They also count the number of students taking Physics and find 217 students taking the Physics. When they compare the two lists they find 86 student taking AMDM and Physics. What is the probability of a student taking AMDM given they are taking Physics. (Answer in decimal form rounded to the thousandth)

{(-9, 3), (5, -6), (3, -9), (-6, 5), ?} Which ordered pair can replace the missing value and create a function? (5,3) (9,3) (-6,-9) (-9,-6)

Graph the following quadratic function. f(x)=x²-9 Find the vertex of the function. The vertex is (Simplify your answer. Type an ordered pair.)

The coordinates of the endpoints of RT are R(-6,-5) and T(4,0), and point S is on RT. The coordinates of S are (-2,-3). Which of the following represents the ratio RS: ST? 1:2 2:3 3:2 3:4

You are playing a card game. If you pull an Ace you win $26, if you pull the King of hearts you win $204, if you pull a jack or a queen you win $13, all other pulls you lose. What price should you be charged to make this a fair game? $8 $7 $6 $5

The local bakery requires that Josh must spend at least $7 to be able to pay using a credit card. Cookies cost $2.10 each. A bottle of water costs $1.10. If c represents the number of cookies Josh would need to buy to pay for one bottle of water and the A cookies using a credit card, which of the following inequalities best models the situation described above?

A car has a 16-gallon fuel tank. When driven on a highway, it has a gas mileage of 30 miles per gallon. The gas mileage (also called "fuel efficiency") tells us the number of miles the car can travel for a particular amount of fuel (one gallon of gasoline, in this case). After filling the gas tank, the driver got on a highway and drove for a while. a. How many miles has the car traveled if it has the following amounts of gas left in the tank? i. 15 gallons ii. 10 gallons iii. 2.5 gallons

Lottery Prizes A lottery offers one $800 prize, two $500 prizes, two $400 prizes, and five $200 prizes. One thousand tickets are sold at $7 each. Find the expectation if a person buys two tickets. Assume that the player's ticket is replaced after each draw and that the same ticket can win more than one prize. Round to two decimal places for currency problems.

Find the equation of the line through (2, a) and (8, b). y =

Graph the following quadratic function. f(x) = 7x² Find the vertex of the function. The vertex is (0,0). (Simplify your answer. Type an ordered pair.) Find the y-intercept of the function. The y-intercept is (0,0). (Simplify your answer. Type an ordered pair.) Find the x-intercept(s) of the function, if any exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) is/are (0,0). (Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.) B. There are no x-intercepts.

Find dy/dx by implicit differentiation. 9x3 + x²y-xy³ = 8

Find the real solutions of the following equation. x4-17x² +16=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (Use a comma to separate answers as needed.) B. There are no real solutions.

What is the equation of the circle in center-radius form? x² + y² -20x + 32y = 78 (x-10)² + (y +16) = 104 (x +10) + (y +16)² = 434 (x-10) + (y +16)² = 434 (x-100) + (y-256)² = 104

Multiple Choice Which is not a possible classification of the zeros of f(x) = x4 + 2x³-7x² - 7x + 3 according to Descartes' rule of signs? A. 2 positive real zeros, 2 negative real zeros, and 0 imaginary zeros B. 0 positive real zeros, 2 negative real zeros, and 2 imaginary zeros C. 0 positive real zeros, 0 negative real zeros, and 4 imaginary zeros D. 1 positive real zero, 1 negative real zero, and 2 imaginary zeros

The average tuition, fees, and room and board rates charged per year for full-time students at a certain college is approximated by the polynomial C= 5x2 +38x+2876 for the years 1984 to 2006. Let x represent the number of years since 1984. Use this model to predict what the costs will be for a student at this college in 2018 (x=34) and 2032 (x = 48). The costs at this college in 2018 will be $ (Simplify your answer. Do not include the $ symbol in your answer.) The costs at this college in 2032 will be $ (Simplify your answer. Do not include the $ symbol in your answer.)

An object moves along a coordinate line, its position at each time t≥ 0 is given by x(t) = (t² - 2 t) (t² + 2 t). Find the acceleration at time to = 3. a) -4 b) 100 c) 84 d) -84 e) 816

Find the zeros of the polynomial function and state the multiplicity of each. f(x) = − 5(x - 1)4(x + 5)²x³ The zero 1 has multiplicity is a zero of multiplicity 2. The remaining zero is It has multiplicity

Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. You may not be able to click on an x or y intercept. y = -x² + 10x - 21 1. State whether the parabola opens up or down? 2. State the vertex as an ordered pair: 3. State the y-intercept as an ordered pair: 4. Write the Equation of the Axis of Symmetry: 5. Click on the vertex and then another point of the parabola that fits on the axes below.

Find the slope m and y-intercept b. (If an answer is undefined, enter UNDEFINED. If an answer does not exist, enter DNE.) y = 7

Solve the problem. Records indicate that x years after 2008, the average property tax on a three bedroom home in a certain community was T(x)=20x^2 + 60x + 600 dollars. At what rate was the property tax increasing with respect to time in 2008?  $60 per year $600 per year  $100 per year $ 40 per year

Suppose that from 2020 to 2060, the number of females in the U.S. under the age of 18, in millions, can be modeled by N=0.150x + 36.4 where x is the number of years after 2020. (a) Viewing N as a function of x, what is the slope m of the graph of this function? (b) Interpret the slope as a rate of change. The slope m represents the number of females in the U.S., under age 18, in millions, in year 2060. Every m years, the population of females in the U.S., under age 18, in millions, is predicted to increase by 1. The slope m represents the number of females in the U.S., under age 18, in millions, in year 2020. Every year, the population of females in the U.S., under age 18, in millions, is predicted to increase by m. (c) What does the model predict the population of females under 18 (in millions) will be in 2040?

A Food Marketing Institute found that 27% of households spend more than $125 a week on groceries. Assume the population proportion is 0.27 and a simple random sample of 391 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.26? There is a probability that the sample proportion of households spending more than $125 a week is less than 0.26. Round the answer to 4 decimal places.

Find the equation of the line through (8,-1) which meets the x-axis at x = 3. Enter your solution in the form y = mx + b.

inches is rated at R-11 and 6 inches is rated at R-19. Assuming that this relationship is linear, The R-value of insulation is a measure of its ability to resist heat transfer. For fiberglass insulation, 3(1/2) write the equation that gives the R-value of fiberglass insulation R as a function of its thickness t (in inches). (Give an answer using exact values. Do not round.)

Find the equation of the line that is tangent to the graph of the given function at the specified point. y = x^4 - 5x^3 + 4x + 4; (1, 4) y=-11x - 7 y = -7x-3 y=-7x + 11 y = -11x + 15

Find the slope m of the line passing through the given pair of points. (Give an exact answer. Do not round. If an answer is undefined, enter UNDEFINED.) (3,-3) and (-1, 3) m=

A fair coin is flipped 13 times. Find the probability that more than 5 of the flips turn up tails. 0.757636 0.709473 0.683847 0.573194 0.734094 0.657303

a. Rewrite the given equation 4x +9y-36=0 slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function.

Car A leaves Santa Barbara at noon traveling south toward Los Angeles at 60 mph. At 1pm car B leaves Los Angeles traveling north toward Santa Barbara at 85 mph. The distance between the cars at noon was 100 miles. If car B does not get pulled over, how many minutes after car B leaves will they pass each other?