Basic Math Questions and Answers

The radioactive substance uranium-240 has a half-life of 14 hours. The amount A (t) of a sample of uranium-240 remaining (in grams) after / hours is given by the following exponential function. A(t)=4300(1/2)^t/14 Find the amount of the sample remaining after 13 hours and after 50 hours. Round your answers to the nearest gram as necessary.

Consider two fire towers in the Canadian wilderness. Tower B is 40 miles due East of tower A. The guards notice a fire that appears at a bearing of 70 degrees from Tower A, and a bearing of 310 degrees miles from the tower B (the closer of from Tower B. The fire is at a distance the two towers). Hint: Draw a picture.

An object is dropped from a tower, 784 ft above the ground. The object's height above ground x seconds after the fall is s(x) = 784-16x². About how long does it take the object to hit the ground? What is the object's velocity at the moment of impact?

If this animal is a dog, then it has four legs. Choose the equivalent statement. A. If this animal is not a dog, then it doesn't have four legs. B. If this animal has four legs, then it's a dog. C. If this animal does not have four legs, then it is not a dog.

Identify each of the following equations as linear, exponential or quadratic y = 4 + 3x + ² y = 3x y = 3x +4

7. On a group trip to a certain city, 20 people who were 25 years old, 20 people who were 30 years old, and 20 people who were 35 years old purchased tickets for a bus tour of the city. No one else purchased tickets for the bus tour. A 30-year old who had purchased a ticket became ill and did not go on the bus tour, and everyone else who purchased a ticket went on the bus tour. Which of the following statements is true? (A) The standard deviation of the ages of the people who went on the bus tour is greater than the standard deviation of the ages of the people who purchased tickets . (B) The standard deviation of the ages of the people who went on the bus tour is less than the standard deviation of the ages of the people who purchased tickets. (C) The standard deviation of the ages of the people who went on the bus tour is equal to the standard deviation of the ages of the people who purchased tickets. (D) There is not enough information to determine which standard deviation is greater.

Laura wants to determine the miles-per-gallon rating of her car. She filled the tank when the odometer read 14,959 miles. She then drove her car on a trip. At the end of the trip, the odometer read 15,351 miles, and it took 14 gallons to refill the tank. How many miles per gallon does her car deliver?

Solve for x and graph the solution on the number line below. -4x - 6≤ -18 and -4x - 6≥ -30

Use finite approximation to estimate the area under the graph of f(x)=4x² and above the graph of f(x)=0 from xo=0 to x₁=2 using i) a lower sum with two rectangles of equal width. ii) a lower sum with four rectangles of equal width. iii) an upper sum with two rectangles of equal width. iv) an upper sum with four rectangles of equal width.

Find all zeros of the function f(x) = 6x³ + 7x² - 8x - 5. Enter the zeros separated by commas.

A person starts a fire in a field. The fire is expanding outward in all directions forming a larger and larger circle. The radius of the circular fire is increasing at 3 feet/minute. How many minutes will it take until the area of the circular fire is 17620 square feet? Type your answer to the nearest hundredth (2 decimal places).

Find the slope of the line passing through the points (-8, -3) and (-3, 4).

5. Rectangle A is dilated to form rectangle B. A 6 20 B 30 What scale factor was used? Enter the answer and also provide a 1 sentence explanation that describes how you determined your answer. Review the will be evaluated.

Abigail's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y 6.2x + 69, where y represents the expected quiz score and a represents hours spent on homework that week. What is the meaning of the x-value when y = 91? How many hours a student spends studying all year. A student's expected quiz score if they spent 1 hour on their homework. The number of hours a student should spend on their homework to expect a score of 91 on the quiz. A student's expected quiz score if they spent 91 hours on their homework.

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. 1 y²-x-4 2 y≤x-2

Find all zeros of f(x) = x³ - 5x²+x-5. Enter the zeros separated by commas.

Suppose $5000 is invested at 8% interest compounded continuously. How long will it take for the investment to grow to $10000? Use the model A(t) = Pet and round your answer to the nearest hundredth of a year. years for the investment to reach $10000. It will take

What is the diagonal of a rectangular room which measures 14 feet by 6 feet?

Consider the following polynomial function. f(x) = (x + 2)²(x-4)³(x − 3) Step 1 of 3: Find the degree and the y-intercept. Express the intercept as an ordered pair.

This equation shows how the distance Darren has cycled depends on the number of trips he has taken to work. d = 2t The variable t represents the number of trips he has made, and the variable d represents the total distance cycled in kilometers. After 3 trips to work, how many kilometers will Darren have cycled in total? kilometers

problem. 28x-*=20-8 The function f(x) = 500(0.5)x/100 models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.

A person x inches tall has a pulse rate of y beats per minute, as given approximately by y = 584x -1/2 for 30≤x≤ 75. What is the instantaneous rate of change of pulse rate for the following heights? (A) 48-inches (B) 70-inches What is the instantaneous rate of change of pulse rate for a 48 inch tall person? beats per minute per inch (Round to the nearest hundredth as needed.) What is the instantaneous rate of change of pulse rate for a 70 inch tall person? beats per minute per inch (Round to the nearest hundredth as needed.)

Isaiah had 6 inches of snow on his lawn. It then began to snow at a rate of 2 inches per hour. Assume no snow melted. Answer the questions below regarding the relationship between the number of hours since snow began falling and the total amount of snow on Isaiah's lawn.

The manufacturer of color televisions can sell 1000 sets to his dealers at $376 each. If the price is $280, he can sell 2200 sets. The total cost of producing x television sets is C(x) = 2800+180x -0.02x2. Assuming the demand function is linear, find the price per set that will maximize profit. Round your answer to the nearest cent, if necessary.

For events A, D and G, we know that p(A)=0.4, p(D∩G|A)=0.7 and p(D∩G|-A)=0.8. Determine p(~A|D∩G).

Leanne works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant?

You are hiking along the edge of the Green River (which is running straight in the area of interest). Straight across from you on the opposite shore there is a particularly noticeable boulder at the edge of the river. You walk 120 feet along the shore of the river, and now the line from you to the boulder makes an angle of 35° with the edge of the river. You whip out your trusty scientific calculator and deduce that the width of the river at this point is feet. Hint: Draw a picture. "Straight across" means that the line from you to the boulder forms a right angle with the shore of the river.

Find the value or values of c that satisfy the equation f(b)-f(a) / b-a = f'(c) in the conclusion of the mean value theorem for the given function and interval. f(x)=√x-5, [5,10]

A pendulum is a weight suspended from a fixed point that swings back and forth under the influence of gravity. The time that it takes for the pendulum to complete one back-and-forth motion is known as the period of the pendulum. It is known that the function T(L) = 2.01√I models the period of the pendulum, in seconds, if the pendulum has length L meters. Suppose Garrett wanted to construct a pendulum that has a period of 2.5 seconds. How long would the pendulum be? a) Write an equation that models this situation. Equation: b) Solve the equation to answer the question. Complete the sentence with a number in the first box and an appropriate unit in the second box. You may round your numerical response to two decimal places. Sentence: Garrett would need to build a pendulum that is Select an answer long.

For the dinner special at a restaurant, the customer must choose a salad, an entree, a side dish, and a dessert. Here are the items to choose from. Choice Salad Entree Side dish Dessert Possible items Southwest, Garden Roast turkey, Pot roast, T-bone steak, Salmon, Lamb Mixed vegetables, French fries, Baked potato, Pinto beans Chocolate cake, Ice cream, Brownies How many dinner specials are possible?

A shirt is on sale for 25% off. Sandy paid $7.50 for the shirt. What was the shirt's regular price? A) $10.00 B $2.50 C) $8.00 D $9.38

It can be shown that if (x,x + 1,y) is a Pythagorean triple, then so is (3x + 2y + 1,3x + 2y + 2,4x + 3y + 2). Use this idea to find three more Pythagorean triples, starting with (3,4,5). Choose the correct answer below. A. (20,21,29); (119,120,169); (696,697,985) B. (20,21,29); (30,40,50); (696,697,985)

Suppose the demand for a certain brand of a product is given by D(p) =-P2/189 +250, where p is the price in dollars. If the price, in terms of the cost c, is expressed as p(c)=3c-27, find the demand function in terms of the cost.

Find the critical value z a/2 that corresponds to a 91% confidence level. 1.70 1.75 1.645 1.34

Given the vector u = (1,-6), find the magnitude and angle in which the vector points (measured counterclockwise from the positive x-axis, 0≤ θ < 2π)

Event A and B are conditional independent events given D with p(A|D)=0.6, p(B/D)=0.8. Determine p(~A∩~B|D).

Suppose that an airline uses a seat width of 16.6 in. Assume men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.1 in. Complete parts (a) through (c) below. (a) Find the probability that if an individual man is randomly selected, his hip breadth will be greater than 16.6 in. The probability is (Round to four decimal places as needed.) (b) If a plane is filled with 127 randomly selected men, find the probability that these men have a mean hip breadth greater than 16.6 in. The probability is (Round to four decimal places as needed.) (c) Which result should be considered for any changes in seat design: the result from part (a) or part (b)? The result from should be considered because

The first derivative of the continuous function y = f(x) is given below. Find y'' and then use the critical points of f, the behavior at the critical points, and any intervals in which the curve is increasing or decreasing to sketch the general shape of the graph of f. y' = 3sec^2, π/2 < x < π/2

Given events A, B, C with p(A)=0.4, p(B∩C|A)=0.8, p(B∩C|~A)=0.2, find p(B∩C).

Evaluate tan(90°). undefined

Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find the probability that (a) E will speak first (b) that C will speak fifth and B will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will speak first.

Find the value or values of c that satisfy the equation f(b) - f(a) / b-a = f'(c) in the conclusion of the Mean Value Theorem for the given function on the given interval. f (x) = x^7/5 ; [0, 1]

Solve the system by using the addition method. 5x² + y² = 14 6x²-7y²2² =-57 There are infinitely many solutions. The solution set is the empty set, {}. The solution set is a finite set. The solution set is

The surface area of an open-top box with length L, width W, and height H can be found using the formula: A = 2LH+2WH + LW Find the surface area of an open-top box with length 7 cm, width 6 cm, and height 9 cm. 2 cm²

For a school band trip, Marcia decides to order T-shirts for all of the participants. It will cost $4 per shirt for the medium size, and $5 per shirt for the large size. Marcia orders a total of 70 T-shirts and spends $320. How many are medium shirts?

Use the long division method to find the result when 3x + 13x³ - 29x² +28x -22 is divided by x² + 5x - 7. If there is a remainder, express the result in the form q(x) + r(x)/b(x)

Change the following quadratic from standard form into vertex form by completing the square. y=-x²+14x-43 y=-(x-7)² +6 y = (x+7)² +6 y=(x-7)2-43 y = -(x +72-6 y=(x-7)²+6

You have $2,000 on a credit card that charges a 13% interest rate. If you want to pay off the credit card in 3 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

Answer the questions below about the function whose derivative is f'(x) = 1 -- a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? A. X= (Use comma to separate answers as needed) B. The function f has no critical points. a. What are the critical points of f? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A population has a mean µ = 88 and a standard deviation σ=30. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 239.