Math Questions

What is the vertex of this function? f(x) = -4(x - 2)² +9 ([?], []) Hint: Vertex form, y = a(x-h)2 + k, helps us quickly identify the vertex of a quadratic.

Graph n(x) = |x| on the Cartesian plane to the right. The domain of n(x) is: The range of n(x) is: If any of the above do not exist, leave the answer box blank.

The length of a rectangle is 5 less than twice its width. Find the perimeter of this rectangle if its area is 273 yd².

Solve the system of equations by the addition method. x - 2y = -3 -x+6y=-1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is B. There are infinitely many solutions. C. There is no solution. (Simplify your answer. Type an ordered pair.)

Let p, q and r represent the following simple statements: p: I get an A. q: The play is boring. r: The stove is hot. Write the following compound statement in its symbolic form. If I get an A or the play is not boring, then the stove is hot. Write the symbolic form of the statement below.

The revenue (in dollars) from the sale of x car seats for infants is given by the following function. R(x)=56x -0.020x² 0≤x≤2800 (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. (B) Use the four-step process to find R'(x). (C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results. (A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats. 15 (Round to one decimal place as needed.) (B) R'(x) =

The line graph shows the goals per game average for a sporting series during the years shown. Find the average number of goals per game in 1981. The average number of goals per game in 1981 was (Round to the nearest tenth as needed.)

If 3 gallons of paint covers 925 ft², how many gallons would be needed to cover 2775 ft²? [?] gallons Enter the number that belongs in the green box.

Select all the correct answers. Grey's Labs is testing a new growth inhibitor for a certain type of bacteria. The bacteria naturally grows exponentially at a rate of 4.7% each hour. The lab technicians know that the growth inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. The current sample contains 90 bacteria. Once a standard tube contains more than 270 bacteria, the sample will stop growing. So, to analyze the effect of the inhibitor over longer spans of time, the lab technicians move the bacteria to larger containers, essentially increasing the container size at a constant rate. This adaptation accommodates 100 more bacteria each hour. The research team wants to track the number of bacteria over time given these two conditions. Select the two inequalities they can use to model this situation. P ≥ 90e0.047t P ≤ 270 + 100t P ≤ 270 - 100t P≤ 0.047e90t P≤ 90e0.047t

By inspecting the graph of the function, find the absolute maximum and absolute minimum on the given interval. n(x)=3√x - 1 on [8,27] Choose the correct graph below.

What is the minimum number of x-intercepts that a polynomial of degree 6 can have? Explain. The minimum number of x-intercepts is 0. (Type a whole number.) Explain. With a positive leading coefficient, an .... polynomial will start .... Vand end ... With a negative leading coefficient, an .... polynomial will start ... and end ...

Joan has received scores of 64%, 79%, and 75% on the first three tests in a class. What score does she need to get on the fourth test to have an average of 75%? [?]%

Becky has quarters, dimes, and nickels in her pocket. The value of her money is $2.25. There are 2 more nickels than dimes and there are a total of 19 coins. How many dimes does Becky have? [?] dimes

In a study on the speed of muscle contraction in a certain species of frogs under various loads, researchers found that the speed of contraction decreases with increasing loads. In particular, they found that the relationship between speed of contraction v (in centimeters per second) and load x (in grams) is given approximately by v(x) = 29+0.05x/x, x≥5 (A) What does v(x) approach as x increases? (B) Sketch a graph of the function v. (A) As x increases, v(x) approaches

Patrick is given the following point and slope: Slope = -3 y-intercept = (0,6) He answers the following questions. Identify if he got each problem correct or Incorrect. If he answers a problem wrong, please do the problem correctly with explanation. 1) Write the equation for the line in Slope-Intercept Form y=-3x+6 2) What is the x-intercept of the line? The x-intercept of the line would be 6, because you are given (0,6) 3) Write the equation for the line in Standard Form -3x+y = 6 4) Using the point (1,3), write the equation for the line in point-slope form y-3 = -3(x-1)

The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.72, the probability that a car brought into the shop requires brake repair is 0.28, and the probability that a car requires both an oil change and brake repair is 0.13. For a car brought into the shop, determine the probability that the car will require an oil change or brake repair. The probability that the car requires an oil change or brake repair is (Type an integer or a decimal.)

A die is rolled 100 times and recorded each outcome. If 1 occurred ten times, 2 twenty times, 3 fifteen times, 4 fifteen times and 5 twenty times, then what is the probability of getting a 6? (a) 1/6 (c) 1/4 (b) 1/5 (d) 1/3

Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (-12, 5), (12,5) (-12, 5), (-12,-5) (-12, 5).(-5, 12) (-12, 5), (12,-5)

Select all the correct answers. Rachel and Jeffry decided to start saving for college. Rachel has $1,500 to start her savings account, and Jeffery has $1,200. Rachel's bank offered her an interest rate of 7.5% compounded annually. Jeffery decided to keep his money in a safe in his bedroom, and he adds $200 to his safe each year. Suppose that A represents the accumulated money in each one's savings fund and t represents the number of years. Choose the equations that form the system that best models this situation. A = 200t + 1,200 A = 1,200(1.2)t A = 7.5t + 1,500 A = 1,500(1.075) A = 1,200(1.075)t

Find each item listed below for the data provided. Test Scores: 50, 69, 70, 75, 75, 90, 85, 80, 70, 60, 100, 95, 90, 80, 85, 50 (all answers should be rounded to the nearest tenth) Mean: Median: Range: IQR:

Jon starts out on a trip at 45 mph. If 1/1/2 hours later, Joel starts out on the same route at 60 mph, which equation may be used to determine how long it will take Joel to overtake Jon? Enter a, b, c, d, or e.

The hypotenuse of a right triangle is 12 centimeters, and the shorter leg is 6 centimeters. Find the length of the other leg. 6 √3 cm 8 cm 6 √5 cm

A certain phone call costs 75 cents for the first three minutes plus 15 cents for each additional minute. If the call lasted x minutes and x is an integer greater than 3, which of the following expresses the cost of the call in dollars? Enter a, b, c, d, or e. a. 0.75(3) + 0.15x b. 0.75(3) + 0.15 (x+3) c. 0.75 +0.15(3-X) d. 0.75 +0.15(x - 3) e. 0.75 +0.15x

Twenty out of every fifty CDs produced in a factory are scratched. What is the ratio of unscratched to scratched CDs? Enter a, b, c, d, or e. a. 2:5 b. 3:5 c. 2:3 d. 3:2 e. 5:2

Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The caloric content and the sodium content (in milligrams) for 6 beef hot dogs are shown in the table below. Find the regression equation.

What is the solution set of the following equation? -5x + x + 9 = -4x + 12 (1/7) ∅ (all reals)

You borrow $500 from a friend and offer to pay it back in two months at 6% simple interest. How much interest will you pay?

If y is 2.5 when x is 5 and y varies directly with x, find y when x is 14. 12.5 7 28 7.5

Find the volume of the cone. Diameter: 10 m, Height: 10 m Round to the nearest whole number. Volume = [?] m³

Beverley has quarters and dimes in her pocket. She has 21 coins with a total value of $3.00. How many of each type of coin does she have? [?] quarters [] dimes Enter the number that belongs in the green box.

A homeowner purchases a riding lawn mower for $3600. Its value is expected to depreciate (decrease) by $400 each year. How many years will it take for the lawn mower to lose all its value (that is, have a value of $0)?

This month a city has 50 street lights installed. Next month it plans to have 54 lights installed, and 58 the following month. If this rate of change continues each month, what is the value of d (the growth factor) in the explicit linear growth equation that models this?

Which of the following is not a prime number? Enter a, b, c, d, or e. a. 49 b. 2 C. 67 d. 17 e. 53

Complete the following statement with the correct number. The sum of the three angles of any triangle is [?]°.

What is the distance between the points (-6, -2) and (2, 4)? 10 2 √10 2 √5 4 √5

Plot the intercepts to graph the equation. x + 2y = 2 Use the graphing tool to graph the equation. Use the intercepts when drawing the line. If only one intercept exists, use it and another point to draw the line.

Give the following number in Base 10. 62 8 = [?]10 Enter the number that belongs in the green box.

Find the volume of the cone. Diameter: 20 m, Slant Height: 26 m Round to the nearest whole number. Volume = [?] m³

A bottle of soda contains 350 mL. a) How many milliliters are contained in a six-bottle carton? b) How many liters does the amount in part (a) equal? c) At $2.25 for the carton of soda, what is its cost per liter? a) There are .... milliliters of soda in a six-bottle carton.

Certain birth defects and syndromes are polygenetic in nature. Typically, the chance that an offspring will be born with a polygenetic affliction is small. However, once an offspring is born with the affliction, the probability that future offspring of the same parents will be born with the same affliction increases. Let's assume that the probability of a child being born with affliction A is 0.005. If a child is born with this affliction, the probability of a future child being born with the same affliction becomes 0.03. Are the events of the births of two children in the same family with affliction A independent? Yes No A couple plans to have one child. Determine the probability that the child will be born with this affliction. 0.005 (Type an integer or a decimal.) Another couple plans to have two children. Determine the probability that both children will be born with the affliction. 0.00015 (Type an integer or a decimal.) Determine the probability that the first will be born with the affliction and the second will not. 0.00485 (Type an integer or a decimal.) Determine the probabilily that the first will not be born with the affliction and the second will. 0.004975 (Type an integer or a decimal) Determine the probabilily that neither will be born with the affliction. (Type an integer or a decimal.)

Red and blue ceramic tiles are laid according to a pattern such that for every 16 red tiles used, 9 blue tiles are used. If a total of 300 tiles are used, how many of them are blue?

There are 5 different math books, 1 social studies book, and 2 different science books on the shelf. How many different ways can the books be arranged?

Diane has quarters, dimes, and pennies in her pocket. The value of her money is $1.55. There are 4 more dimes than quarters and the number of pennies equals the sum of the number of quarters and dimes. How many pennies does Diane have? [?] pennies

After the govermnent takes a census, it is determined that the population of a country is 52% female. 52% is an example of a(n). parameter statistic population sample

There are 18 different drinks for a graduation. Sandra randomly selects 6. How many different combinations are there?

Two dice are rolled. What is the probability that both die will show even numbers? Give your answer as a decimal.

If the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on a number greater than 1, given that the color is red or purple. Note that the red sectors are the sectors numbered 5, 6, and 7, and the purple sectors are numbered 2, 4, 9, 11, and 12. What is the probability? (Type an integer or a simplified fraction.)

A house worth $120,000 is in an area where real estate is increasing in value at the rate of 8% per year. How much will the house be worth in 1 year?

Two cylinders are similar. The volume of one is 64 cm³, and the volume of the other is 729 cm³. Find the scale factor between them. Enter the smaller number first. scale factor = [?]:[ ]

A bag has 45 yellow, green, and blue jellybeans. 2/5 of the jellybeans are green and 1/3 are blue. How many yellow jellybeans are there?