Math Questions

A rocket is fired from a building 240 ft tall. The height of the rocket with respect to time (in seconds) is modeled by f(t) = -16r² +32 +240. How long before the rocket hits the ground? 1 second 5 seconds 3 seconds 4 seconds

7x (x+2)(x-6).' For the function h(x) = - A. The solution is B. The solution is solve the following inequality. h(x) ≥0 Select the correct choice below and fill in the answer box within your choice. (Type your answer in interval notation.) . (Use a comma to separate answers as needed.)

A rocket is fired from a building 240 ft tall. The height of the rocket with respect to time (in seconds) is modeled by f (t) = -161² +32t + 240. What is the maximum height? 32 ft 240 ft 256 ft 120 ft

Use the power property to rewrite each expression. Assume all variables are positive. log, (a-4)= The answer format in lowercase characters is: log_base (number) Spaces in the answer are optional.

You decide to build a box with a square base and with a height equal to half the length of a bottom side. The material you choose for the top of the box costs $6 per square foot. Since everyone will see the top of the box, that material is more expensive than what you choose for the sides of the box and the base: $4 per square foot. What equation expresses the cost of your box in terms of the height of the box? Be sure to show a labeled picture of the box.

A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It is determined that the height of the frog as a function of time can by modeled by h (t) = -16t² + 64r + 3. What is the maximum height? 131 ft 99 ft 67 ft 195 ft

Perform the indicated operations. Write the answer in standard form, a+bi. 5-6i/4-2i Multiply the numerator and denominator by the conjugate of the denominator. 5-6i-()/ 4- 2i.() i

Find the radius of a circle on which a central angle measuring 2 radians intercepts an arc on the circle with a length of 35% kilometers. A. 32.0 km B. 20.0 km C. 30.5 km D. 52.5 km

Quarters are currently minted with weights normally distributed and having a standard deviation of 0.062. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 20 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.048. Use a 0.025 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.062. Does the new equipment appear to be effective in reducing the variation of weights? (a) Write the claim mathematically and identify Ho and Ha- A. Ho: 20.062; Ha: o<0.062 (Claim) B. Ho: 20.062 (Claim); Ha: 0 <0.062 C.Ho: o≤ 0.062; Ha: o> 0.062 (Claim) D. Ho: o≤ 0.062 (Claim); Ha: o> 0.062

Samantha invests $555 in an account that earns 14% interest compounded continuously. When will the value of the investment reach $1400? Graph the function on a graphing calculator or a desmos.com and use the graph to make the prediction.

Which figure always has exactly one line of symmetry? A. circle B. rectangle C. trapezoid D. isosceles right triangle

A map using a scale of 1 inch : 5 miles shows a section of land with an area of 3.2 square inches. What is the actual area of the section of land? _________________square miles

5x+2y=8 x+y=4 If you want to solve the system of equations by addition, which of the following could you do? Multiply the second equation by 2 and add Multiply the second equation by 2 and acid Mumply the second equation by 5 and add

Which of the following represents the graph of the inequality? -20x - 15 ≥ -30x - 45 Open circle and shaded to the left Open circle and shaded to the right Closed circle and shaded to the left Closed circle and shaded to the right

Factor. Remove the largest possible common factor. Check your answer by multiplication. 25x8+10x7 +20x4 25x8+10x7 +20x =

For the real-valued functions f(x)=x-2/x+1 and g(x)=4x-5, find the composition fog and specify its domain using interval notation. (fog)(x)'= Domain of fog :

Carmen tutors math. For each hour that she tutors, she earns 40 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use this equation to find Carmen's earnings after tutoring for 13 hours.

Find an equation of the line parallel to 10x-y=9 and passing through (3,8), Express the equation in standard form. Which of the following is the equation of a line parallel to 10x-y=9 and passing through (3,8)? A. x+10y=24 B. 10x-y=24 C. 10x-y=36 D. x+10y=36

A ladder leaning against a wall makes an angle of 68 degrees with level ground. The foot of the ladder is 3 ft away from the wall. How far up the wall does the ladder reach?

Find the solution of the exponential equation e²x+1= 32 in terms of logarithms, or correct to four decimal places. x=

The lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. Find the probability that a randomly selected crocodile is more than 12 feet long. 0.51 0.53 0.59 0.57

2 Which of the following sets of ordered pairs represents a relation that is not a function? A.{(1, 1), (2,3), (6, 11), (10, 19), (50,99)} B.{(-5, -2), (-4,-1), (1,4), (2,5), (3,4)} C.{(1,3), (3, 9), (5, 15), (7, 21), (11,33)} D. {(2,4), (8, 10), (8, 16), (11, 13), (15, 17)}

Find the length of BOTH bases of the trapezoid with the given information. The area of the parallelogram is 95 m². The height is 10 meters. One base is 3 meters longer than the other. Shorter Base = Longer Base=

In a pizza takeout restaurant, the following probability distribution was obtained. The random variable x represents the number of toppings for a large pizza. Find the probability that more than one toppings is ordered. 0.40 0.70 0.20 0.30

Select the correct values of the five-number summary for the data set: 15, 17, 23, 21, 19, 20, 14, 25, 15, 24 Minimum: 14 Minimum: 15 Minimum: 13 1st quartile: 23 1st quartile: 14 1st quartile: 15 Median: 20 Median: 19 Median: 19.5 3rd quartile: 23 3rd quartile: 15 3rd quartile: 25 Maximum: 23 Maximum: 25 Maximum: 24

Directions Answer the questions. All problems are with replacement. 1. How many 3-digit area codes can be made with the digits 0 through 9? 2. If area codes were changed from 3-digit to 4-digit numbers, how many more area codes would be made available? 3. How many 5-character PIN numbers can be made that contain 2 letters followed by 3 digits? 4. In a certain city, all phone numbers begin with one of 5 different 3-digit exchanges. How many different telephone numbers are possible for this area? 5. In the city in problem 4, how many new 3-digit exchanges would need to be added to allow for a total of 120,000 phone numbers?

The dimensions x and y of an object are related to its volume V by the formula V = 8x²y. a. How is dV/dt related to dy/dt if x is constant? b. How is dV/dt related to dx/dt if y is constant? c. How is dV/dt related to dx/dt and dy/dt if neither x nor y is constant?

A sample of students is selected and it is found that 25% own a computer. Choose the correct statement below. Parameter because the value is a numerical measurement describing a characteristic of a population. Parameter because the value is a numerical measurement describing a characteristic of a sample. Statistic because the value is a numerical measurement describing a characteristic of a population. Statistic because the value is a numerical measurement describing a characteristic of a sample.

Find the exact and approximate area of a circle with the given radius r or diameter d. Use pi for π with no spaces in your exact answer. Round approximate answer to the nearest tenth. d = 16 ft A =

Is it possible for a solid to have a cross section that is a single point? If so, give an example. If not, explain why not. None of the other answers are correct No, it is not possible. You cannot have a cross section of a single point. There needs to at least be 2 dimensions in the cross section. Yes; a plane that intersects a solid figure at one of its vertices produces a cross section that is a single point.

The doubling time of a population of flies is 5 hours. By what factor does the population increase in 31 hours? By what factor does the population increase in 1 week? By what factor does the population increase in 31 hours?

Simplify. Assume that all variables are nonnegative real numbers. 3√128x³y^5 3√128x³y^5 = (Type an exact answer, using radicals as needed.)

bicycle riders start a race at the same time. The functions f(x) and g(x) give the distance in miles that each rider has traveled after x hours of riding. What does f(2)- g(2) = 5 mean in this context? A The riders are 2 miles apart 5 hours after the race starts. B The riders are 5 miles apart 2 hours after the race starts. C Both riders travel 2 miles in the first 5 hours of the race. D Both riders travel 5 miles in the first 2 hours of the race.

Let V be a vector space with dimension n. Consider the following statements. (i) Every independent set in V is a basis for V (ii) Every set in V that spans V must be independent (iii) Every set in V with less than n vectors must be independent. Which of the above statements is always true? (a) (ii) and (iii) only (b) (iii) only (c) (ii) only (d) none of them (e) (i) only

A child flies a kite at a height of 50 ft, the wind carrying the kite horizontally away from the child at a rate of 26 ft/sec. How fast must the child let out the string when the kite is 130 ft away from the child? The child must let out the string at a rate of___ft/sec when the kite is 130 ft away from the child. (Simplify your answer.)

Suppose you arrive into a building and are about to take an elevator to the your floor. Once you call the elevator, it will take between 2 and 40 seconds to arrive to you. We will assume that the elevator arrives uniformly between 2 and 40 seconds after you press the button. Find µ. 22 21 11 19

Given the function f(x) =1/x^2 a. Find the average rate of change between x=__and x= (choose two consecutive negative Integers) b. Find the instantaneous rate of change at x=_______ (choose a negative integer value for x) c. Find the equation of the tangent line at your chosen point d. Prove that f(x) is continuous at your chosen point

The coins are placed in a cylindrical storage container that has a radius of 2 in and a height of 5 in. How much empty space is in the cylinder after all 225 coins are placed in? a. Volume of the container is 72.8 in³; Empty space 28.64 in³ b. Volume of the container is 52.5 in³; Empty space 21.64 in³ c. Volume of the container is 62.8 in³; Empty space 18.64 in³ d. Volume of the container is 102.1 in³; Empty space 58.64 in³

The sum of 5 times one number, x, and 6 times a second number, y, is 179. If the sum of the two numbers is 31, find the two numbers. Enter a system of equations to represent the situation, then solve the system. The system of equations is The first number is__and the second number is___

Find the area and perimeter of a rectangle with sides 5 and 7.9 mi None of the other answers are correct area is 12√6 mi² perimeter is 17.9 mi area is 58.5 mi² perimeter is 35 mi area is 39.5 mi² perimeter is 25.8 mi area is 36.24 mi² permeter is 12.9 mi

Consider the Quadratic function f(x) = x² – 3x - 18. Its vertex is Its largest x-intercept is x = Its y-intercept is y =

The following list gives the home run totals for Barry Bonds from 1986 through 2007 (his total career). 16 25 24 19 33 25 34 46 37 34 49 73 46 45 45 5 26 28 Construct a stem-and-leaf plot for the data. Enter the leaves in ascending order, without spaces betweenb them. If a stem has no corresponding leaves, leave that space blank.

Given f(x)= x³-12x+5, find all local maxima and local minima. B) local max:21, local min: - 11 A) local max: - 11, local min: - 21 D) local max: 11, local min:21 C) local max: -21, local min:11

Find T, N, and K for the plane curves in Exercises 1-4. 1. r(t) = ti + (In cos t)j,-π/2 < t< π/2 2. r(t) = (In sect)i + tj,-π/2 < t< π/2 3. r(t) = (2t+ 3)i + (5 −t²)j 4. r(t) = (cost + t sin t)i + (sin 1 - 1 cost)j, t> 0

Adam is also confused. He wonders why, if you take a rectangle and multiply the length of each side by 1.5. the area of the new rectangle isn't 1.5 times as big as the area of the old rectangle. How would you explain this to him?

The polynomial of degree 4, P(x) has leading coefficient 1, has a zero of multiplicity 2 at x = 4, a zero of multiplicity 1 at a x=0, and a zero of multiplicity 1 at x = - 4 Find a possible formula for P(x).

Graph the following function: y=5/2sec(π/4x-3π)

Find all EXACT solutions of the equation given below in the interval [0,π). cos(3x)=-1/√2 If there is more than one answer, enter them in a list separated by commas. Enter an exact expression; decimal approximations or symbolic trigonometric expressions such as arctan (5) will be marked incorrect.

Solve the equation and write the solution set. Write the solutions in order from smallest to largest. Use / to write fractions. Do not enter any spaces in the answer. (9x - 3)²=49 The solution set is

Describe the function f(x) = 5(1/3)^x. O It is an exponential decay function with a base of 1/3 and a y-intercept at y=5. O It is an exponential growth function with a base of 5 and a y-intercept at y=1/3