Basic Math Questions and Answers

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.

The angle of elevation to the top of the Empire State Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the Empire State Building.

Mrs. Torres is mailing a package that weighs 12.5 pounds. The post office charges by the ounce to mail a package. How much does the package weigh in ounces? 187 ounces 200 ounces 192.5 ounces 100 ounces

Convert the following angle measure from degrees to radians. 315⁰

A ramp is set up from a truck's trunk to the ground. The ramp's end at the edge of the trunk is 3.7 ft high. If the angle between the ramp and the ground is 14 degrees, find the length of the ramp. Round your answer to two decimal places if needed. The length of the ramp is

Scientists are studying the temperature on a distant planet. Let y represent the temperature (in degrees Celsius). Let x represent the height above the surface (in kilometers). Suppose that x and y are related by the equation y=47-5x. Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.

Use the long division method to find the result when 12x³ + 23x² + 30x + 25 is divided by 4x +5.

Solve for a and graph the solution on the number line below. Number Line: Inequality Notation: -12 -10 -8 -4x+9 > 1 or -39-4x +9 -6 or -4 -2 0 2 4 Click and drag to plot line. 6 8 I 10 12

Shane is following an English recipe for scones. The recipe calls for 1.2 kilograms of flour. How many pounds of flour, to the nearest tenth of a pound, does he need? Enter the correct answer in the box.

What is the purpose of the QUADRATIC FORMULA? A Determine the distance between two points B Calculate the axis of symmetry of a quadratic function Determine the zeros of a quadratic function D Calculate the y-coordinate of the vertex of a parabola

If the hypotenuse of a right triangle is 1 m more than the longer leg and the shorter leg is 11 m long, find the length of the longer leg. The length of the longer leg is

One eight-ounce glass of apple juice and one eight-ounce glass of orange juice contain a total of 180.2 milligrams of vitamin C. Two eight-ounce glasses of apple juice and three eight-ounce glasses of orange juice contain a total of 443.3 milligrams of vitamin C. How much vitamin C is in an eight-ounce glass of each type of juice? apple juice mg orange juice mg

For any integer n greater than 1, (2n,n²-1,n² + 1) is a Pythagorean triple. Use this pattern to find the Pythagorean triple generated when n= 9. The Pythagorean triple is (Simplify your answer. Use ascending order.)

Solve each equation. Write the properties that justify each step of your solution. 3x-8--7x+18 -2(4-x) 12x-3

An object is thrown upward at a speed of 67 feet per second by a machine from a height of 13 feet off the ground. The height of the object after seconds can be found using the equation - 161² +67t + 13 When will the height be 36 feet? feet When will the object reach the ground? seconds

A person starts walking from home and walks: 4 miles East 6 miles Southeast 4 miles South 3 miles Southwest 2 miles East This person has walked a total of Find the total displacement vector for this walk: If this person walked straight home, they'd have to walk

If AC is a perpendicular bisector, Select ALL that apply (Select all that apply.) The measure of Angle ACB is 90° Point C is the midpoint of BD Measure of angle BAC is congruent to the measure of angle DAC Then BC=CD

Sanjay has borrowed $390 on his father's watch from a pawn shop. He has agreed to pay off the loan with $420 one month later. What is the annual interest rate that he is being charged? Assume that the interest on the loan is computed using simple interest. The annual interest rate is%. (Round to two decimal places as needed.)

Convert 70 in.³ to cubic centimeters. Round your answer to the nearest thousandth, if necessary.

Use your calculator to find 6.3 x 10¹5/7.8 x 10¹2 rounded to one decimal place. Give your answer in scientific notation, with the mantissa

A teacher and 8 students are to be seated along a bench in the bleachers at a basketball game. In how many ways can this be done if the teacher must be seated in the middle and a difficult student must sit to the teacher's immediate left? A) 16 B) 5040 C) 40,320 D) 720

Multiply (8 × 108) (3 × 10-9). Write your answer in scientific notation. For example, you'd enter 2.3*10^4 for 2.3 - 10¹