Math Questions

The city councilman asks the ice hockey team if they would prefer a new skate park or a new ice rink to be built as the new building to be funded by the city. Is the sample Biased or Unbiased? Unbiased Biased

A rocket is launched at the top of a building. The height of the rocket (in meters) written in terms of time (seconds) can be modeled by h (t) = -4.91² + 19.61 + 102.9. At what time does the rocket reach the maximum height? 3 seconds 7 seconds 5.5 seconds 2 seconds

Hattie had $5500 to invest and wants to earn $600 in interest this year. She will put some of the money into an account that earns 9% per year and the rest into an account that pays 12% per year. How much money should she put into each account? Amount in 9% account: $ help (numbers) Amount in 12% account: $ help (numbers)

A builder of tract homes reduced the price of a model by 20%. If the new price is $400,000, what was its original price? How much can be saved by purchasing the model? The original price of the model was $ can be saved by purchasing the model.

he area of a triangular flag is 56 square centimeters. Its altitude is 2 centimeters longer than twice its base. Find the lengths of the altitude and the base. he length of the base is cm.

The Perot Museum of Nature and Science in Dallas, Texas, offers a number of different membership levels for visitors. The Premium Membership is the most popular and costs $25 for each member for 1 month. Last month, 100 people purchased the Premium Membership. This month, 40 new people bought a membership and 15 people canceled. How much money will the Perot Museum earn this month from Premium Memberships?

Three coins are tossed. What is the probability that all three will land tails up? Enter the number that belongs in the green box.

Solve the equation for exact solutions in the interval [0°,360°). Use an algebraic method. 6 sec ²θ tan θ = 8 tan θ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Do not include the degree symbol in your answer.) OB. The solution is the empty set.

Captain Argos is impressed by his flying speed over the ocean. In miles per hour, he's calculated his speed to be the same as T. Is this speed a rational or irrational number? Explain.

Use mathematical induction to prove the statement for all positive integers n. 2+14+26+...+(12n-10) = n(6n-4) What is the first step in a mathematical induction proof? A. Show that S₁ is true. B. Show that So is true. C. Show that Sk is true. D. Show that Sk + 1 is true. Show that 2+14+26++ (12n-10) = n(6n-4) for n = 1. Write the statement S₁. 2= (Do not simplify.) Simplify S₁ on the right. 2= Is S₁ a true statement?

A building casts a shadow 25 m long. At the same time, the shadow cast by a 44-cm tall pole is 59 cm long. Find the height of the building. A. 17.1 m B. 33.5 m C. 18.6 m D. 32.0 m

Determine the symmetries (if any) of the graph of the given relation. 4y³ = 6x³ +3 Choose the correct symmetry of the graph. A. It is symmetric with respect to the x-axis. B. It is symmetric with respect to the y-axis. C. It is symmetric with respect to the origin. D. It is not symmetric with respect to the x-axis, y-axis, or origin.

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