Math Questions

When the function f(x) is divided by x + 2, the quotient is x² - 5x + 8 and the remainder is 8. Find the function f(x) and write the result in standard form.

Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym after x months and spends the rest of the year, y months, with the second gym. The membership to the first gym costs $50 per month, while the membership for the second gym costs $45 per month. If she ended up spending a total of $550 over the course of the year, how much time did she spend at each gym? Enter a system of equations to represent the situation, then solve the system. The system of equations is Jan spent and months at the first gym and months at the second gym.

Mrs. Lakshi asks her geometry students to describe how to create a right prism with a volume of 24 cubic units. Dorothee says that the prism could be a right rectangular prism where the base is 2 x 3 square units and the height is 4 units. Bai says that the prism could be a right triangular prism where the base is a 3-4-5 right triangle and the height is 4 units. Which of the following statements best explains which student described a correct prism with a volume of 24 cubic units? A. Both students described a prism with the correct volume because the product of the area of the base of the prism and the height of the prism is 24 cubic units for both prisms. B. Neither student described a prism with the correct volume because the product of the area of the base of the prism and the height of the prism is not 24 cubic units for either prism. C. Only Bai described a prism with a volume of 24 cubic units because Dorothee's prism has a volume that is half of the area of the base times the height. D. Only Dorothee described a prism with 24 cubic units because Bai's prism has a base with area 3 x 4 x 5, which is 60 square units.

Let f(x) = x²+3x-5/ x²-8x+15 What is the domain of f(x)? A. All real numbers except x = 3, x = -5 B. All real numbers except x = 3, x = 5 C. All real numbers except x = 2 D. All real numbers

The hypotenuse of a right triangle is 11 inches. If one leg is 7 inches, find the degree measure of each angle. The angle opposite the 7-inch leg is (Do not round until the final answer. Then round to one decimal place as needed.) The third angle of the right triangle is (Do not round until the final answer. Then round to one decimal place as needed.)

Given the two events: Event A is drawing a queen. Event B is drawing a red card. Calculate the probability that you draw a queen or a red card? P(AUB)

If you have 140 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose? Area = (include units)

Suppose the line of best fit is being found for some data points that have an r-value of 0.793. If the standard deviation of the x-coordinates is 5.591, and the standard deviation of the y-coordinates is 2.772, what is the slope of the line to three decimal places? A. 0.625 B. 2.543 C. 0.393 D. 1.599

Given f(x) = 10x² - 5x + 11 and m(x) = 20x - 5: a) Write the equation of the tangent line to f(x) when x = 2. b) At what ordered pair does f(x) have a tangent slope of zero? c) Write the equation of the normal line to f(x) at the point where f(x) has slope of -15

Let f(x) = x²+3x-5/x² - 8x+15 What is the domain of f(x)? A. All real numbers except x = 3, x = -5 B. All real numbers except x = 3, x = 5 C. All real numbers except x = 2 D. All real numbers

Choose the best definition of compound events Consists of two or more simple events. None of the other answers are correct A selection of objects in which the order of the objects matters. Combining the elements of two or more sets The product of a given integer and all smaller positive integers

Simplify the complex fraction: 9/y2 + 1/y / 81/y2 - 1

What would you do to isolate the variable in the equation below, using only one step? x + 9 = 55 Add 9 to both sides of the equation. Subtract 9 from the left side of the equation only. Subtract 9 from both sides of the equation. Add 55 to both sides of the equation.

A baseball stadium offers tickets with different prices, depending on the location of the seats. If it decreases the prices of all tickets by $15, what will happen to the median price of the tickets? A. There is not enough information to answer the question. B. It will increase by $15. C. It will stay the same. D. It will decrease by $15.

Juan Carlos has been asked to find the distance between two points on a coordinate grid. Using the distance formula, calculate the distance between points (-3, 2) and (12, 10). 15 units 16 units 17 units 20 units

Simplify the complex rational expression. 1/ x + 3 / 1/x²-2x-15 + 1/x-5

Marcus reads in a magazine article that 62% of teenagers prefer Batman over Iron Man. He decides to test this so he takes a simple random sample of 50 people at Wal-Mart on a Saturday afternoon. 1. What is the probability that he finds exactly 40 Batman fans? 2. What is the probability that he finds fewer than 30 Batman fans? 3. What is the probability that Marcus will find more than 35 Batman fans?

I can calculate the conditional probability of A, given B, and interpret the answer in context. In New England, 84% of the houses have a garage and 65% of the houses have a garage and a back yard. What is the probability that a house has a backyard given that it has a garage? Enter you answer a decimal rounded to the nearest hundredth.

A guy is on top of a building looking down to his girl friend on the ground. The building is 12 feet high, and the girl friend is 25 feet away from the base of the building. What is the angle of depression from the guy to the girl friend? Disregard any adjustment for the height of the two humans.

Suppose the linear regression line = 4.009x - 77.531 predicts a pizza parlor's profits based on the number of pizzas sold. If x represents the number of pizzas sold, and ŷ represents the pizza parlor's profits in dollars, about how much can the pizza parlor expect in profits if it sells 325 pizzas? A. $1375 B. $1300 C. $1225 D. $1150

Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a=13, b= 13, c=10 A. A=67°, B=67°, C = 46° B. A=46°, B=67°, C=67° C. A=68°, B=68°, C = 44° D. A=67°, B = 46°, C=67°

Find a formula for f¹(x) if f(x) =[x+1/ x+1]^3 ƒ-¹(x)=0 (ƒ-¹)'(x) = Hint: Undo the operations of f(x) from the outside in. Undo the cubed operation first.

can write trigonometric ratios of a right triangle, using my understanding of the Pythagorean theorem and special right triangles. If tan θ = 12/5 , what does cos θ =? 5/13 12/13 5/12 12/5

Find the mean, median, and mode for the data set below. Explain which measure best describes the data. 3 30 26 27 29 30 The mean is (Type an integer or decimal rounded to the nearest hundredth as needed.) The median is (Type an integer or a decimal.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode is (Use a comma to separate answers as needed.) B. There is no mode.

A cooler contains thirteen bottles of sports drink: seven lemon-lime flavored and six orange flavored. You randomly grab a bottle and give it to your friend. Then, you randomly grab a bottle for yourself. You and your friend both get lemon-lime.

Calculate the given part of a circle for each problem below. Then, order the values from least to greatest. (The smallest value being 1 and the largest value being 4). The radius of a circle whose area is 400(pi) square inches The diameter of a circle whose area is 850 square inches The area of a circle whose radius is 2.5 in The area of a circle whose diameter is 8 in.

I can write trigonometric ratios of a right triangle, using my understanding of the Pythagorean theorem and special right triangles. If sin θ = 5/13, what does cos θ = ? 12/13 13/12 5/13 25/169

Solve the equation below by completing the square and then solving for x. 2x²-28x-2=-50 A. x= 2 or x = -18 B. x = 7 or x = 4 C. x = 2 or x = 12 D. x = -7 or x = 4

In Europe, 88% of all households have a television. 51% of all households have a television and a VCR. What is the probability that a household has a VCR given that it has a television? Enter you answer a decimal rounded to the nearest hundredth.

Solve the triangle shown to the right. A≈ (Simplify your answer.) b≈ (Type an integer or decimal rounded to two decimal places as needed.) C (Type an integer or decimal rounded to two decimal places as needed.)

Suppose that there were a negative correlation between the variables a and b. If bis 60 when a is 8, which of these is most likely to be the value of b when a is 16? A. 75 B. 90 C. 60 D. 30

Given f(x) = 4x - 3x² and m(x) = 4 - 6x: a) Write the equation of the tangent line to f(x) when x = 0. b) Write the equation of the tangent line to f(x) when x = 2. c) At what ordered pair does f(x) have a tangent slope of 16 ?

The gas mileage for Peter's car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car's gas tank has 17 gallons of gas at the beginning of a trip. If Peter's car travels at an average speed of 50 miles per hour, which of the following functions fmodels the number of gallons of gas remaining in the tank thours after the trip begins?

Sonequa has two containers, one in the shape of a cylinder and the other in the shape of a cone. The two containers have equal radii and equal heights. She investigated the relationship between the volumes of the cone and the cylinder by transferring water between the two containers. Which of the following claims is most likely to be supported using the results of Sonequa's investigation? The volume of a cylinder is two times the volume of a cone when the two containers have equal radii and equal heights, because one full cylinder of water completely and exactly filled the cone two times. The volume of a cylinder is three times the volume of a cone when the two containers have equal radil and equal heights, because one full cylinder of water completely and exactly filled the cone three times. The volume of a cylinder is two times the volume of a cone when the two containers have equal radii and equal heights, because two full cylinders of water completely and exactly filled the cone one time. The volume of a cylinder is three times the volume of a cone when the two containers have equal radii and equal heights, because three full cylinders of water completely and exactly filled the cone one time.

Find the equations of both of the tangent lines to the ellipse ² + 4y² = 36 that pass through the point (12,3) List the line with the smaller slope first.

A street light is at the top of a 26 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 7 ft/sec. At what rate is the tip of her shadow moving away from the light (ie away from the top of the pole) when the girl is 36 ft away from the pole? How fast is her shadow lengthening?

What is the correct step for substitution given the following system of equations? * y = 5x - 7 -3x - 2y = -12

Find all critical points of the function f(x) = x² − 2x + 4

Given f(x) =2x+6/ 4x+8 and m(x) = -1/2(x+2)² a) At what ordered pair is the tangent line horizontal? (clue: a horizontal line has a slope of zero) b) At what ordered pairs does the normal line have a slope of 32 ? c) What is the slope of the normal line when y=0?

A bag contains 4 blue marbles, 6 red marbles, and 8 green marbles. What is the probability that a marble drawn randomly is not blue?

If h is an explanatory variable and k is the corresponding response variable, which of these would be represented by the horizontal axis on a scatterplot? A. Both hand k B. h C. Neither h nor k D. k

Given the following functions: f(u) = u7/2 and g(z) = x8 +1. Find: f(g(x)) = f'(u) = f'(g(x)) = g'(x) = (ƒog)'(x) =

Unit 09 Learning Target #1: I can describe subsets of a sample space in terms of outcomes, unions, intersections, and complements. Given the following sets C={1, 4, 7, 9} D={3, 4, 5, 7, 8} Determine if the following are true or false CCD [Select] DCC [Select] Cn D=Ø [Select]

Consider the function f(x) = e, -2 ≤ ≤ 2. (a) Estimate the area under the graph of fusing four approximating rectangles and taking the sample points to be right endpoints. Include at least six decimal places in your answers (b) Repeat part (a), with midpoints as the sample points, Include at least six decimal places in your answers (c) Now estimate the area under the graph of f using eight approximating rectangles and taking the sample points to be right endpoints. Include at least six decimal places in your answers (d) Repeat part (c), with midpoints as the sample points. Include at least six decimal places in your answers

Gravel is being dumped from a conveyor belt at a rate of 20 ft³/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same How fast is the height of the pile increasing when the pile is 21 ft high? The height is increasing at t/min

In the United States, 56% of all children get an allowance and 41% of all children get an allowance and do household chores. What is the probability that a child does household chores given that the child gets an allowance?

The interior angle of a regular polygon is 144 degrees Name the figure. Regular heptagon Regular nonagon Regular octogan Regular hexagon Regular decagon regular pentagon regular 11-gon regular dodecagon

The first quartile of a data set is 23, the median is 30, the third quartile is 33, and an outlier is 6. Which of these data values would be represented by a point in a modified box plot? A. 30 B. 6 C. 23 D. 33

A helicopter is flying at an elevation of 320 feet. It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 14°. Find the distance between a point on the ground directly below the helicopter and the landing pad. Round your answer to the nearest foot. Note that for this problem, we are using degrees to measure angles. Make sure your calculator is set to degrees instead of radians.

Learning Target #1: I can describe subsets of a sample space in terms of outcomes, unions, intersections, and complements. Given the following sets A-(1, 5, 7, 8) B-(1, 5, 7, 9) Find AUB [Select] Find A B [Select] Find A [Select ]