Basic Math Questions and Answers

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

The radioactive substance cesium-137 has a half-life of 30 years. The amount A (r) (in grams) of a sample of cesium-137 remaining after years is given by the following exponential function. A (t)=381 Find the initial amount in the sample and the amount remaining after 50 years. Round your answers to the nearest gram as necessary. Kimb 30

A laptop computer is purchased for $2350. After each year, the resale value decreases by 30%. What will the resale value be after 4 years? Use the calculator provided and round your answer to the nearest dollar.

4. Susan and Dan went to the roof of their 30-foot tall high school to throw their math books off the edge. The initial velocity of Susan's book was 42 feet per second while the initial velocity of Dan's book was 68 feet per second. A)Complete the equation h(t) = -16 + vt + s for both Susan and Dan where it can be used to represent the situation where h is the height of the textbook at time t seconds, v is the initial upward velocity, and s is the starting point. [1pt]

A casino hotel manager has approximated demand for two-room suites to be p = 9000 q² where p is the price (in dollars) and q is the quantity demanded. Use 18 implicit differentiation to find and interpret OA. dq dp Choose the correct answer below and fill in the answer box to complete your answer. OB. dq when q = 3. which means that if the price is increased by $1, the quantity demanded increases by approximately which means that if the price is increased by $1, the quantity demanded decreases by approximately dp suites. suites.

What is the simple interest rate on a $2450 investment paying $951.83 interest in 10.5 years? % (round to the nearest tenth of a percent)

1. For the given function: y = x²(x + 2)²(x + 1) A. What is the degree and leading coefficient? B. Determine the end behavior C. Find the y intercept if any D. Find the zeros of the polynomial E. Identify the multiplicity of these zeros F. Describe the behavior of the graph at these zeros

Compute the total cost per year of the following pair of expenses. Then complete the sentence: On an annual basis, the first set of expenses is second set of expenses. Suzanne's cell phone bill is $70 per month, and she spends $165 per year on student health insurance. On an annual basis, the money spent on her cell phone bill is% of the money spent on student health insurance. (Round to the nearest percent as needed.) % of the

If cos (0) = -1, what values could be ? Select all that apply.

Convert these numbers written in pseudo-scientific notation to scientific notation. a. 472 x 10-4 b. 61 x 10-4 c. 0.03 x 106 d. 0.0051 x 10-7

Use the formula for nºr to solve. A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there? A) 151,200 B) 210 C) 5040 D) 302,400

A vector with magnitude 9 points in a direction 160 degrees counterclockwise from the positive x axis. Write the vector in component form. Give each value accurate to at least 1 decimal place

Julie is considering installing solar photovoltaic panels on the roof of her house. Her monthly electricity bills currently average $80. The cost of installing a photovoltaic system is $19,000; however, she expects a 35% reduction in this cost due to tax credits and local rebates. Assuming all of her electrical needs are met by the new system and neglecting possible revenue when the system puts electricity back into the grid, what is the approximate payback period for the photovoltaic system? The photovoltaic panels will pay for themselves in approximately months. (Round your answer to the nearest whole number as needed.) *****

The reference angle for an angle in standard position on the coordinate plane with measure 170°is: 80° 10° -10° 170°