Basic Math Questions and Answers

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°

Given the equations m(x)=x-2 and n(x)=x-4, find m(x) -n(x). When typing your answers, be sure to use the following format: • Indicate exponents with a "^" For example, write x² as "x^2." o Do not include spaces. o Write in descending order of exponents, from largest to smallest. Example: 9x² - 11x-7 would be typed in as 9x^2-11x-7 I

The expenses and income of an individual are given in table form to the right. Find the net monthly cash flow (it could be positive or negative). Assume salaries and wages are after taxes. When you need to convert between weeks and months, assume that 1 month = 4 weeks. The net monthly cash flow is $ Income Part-time job: $800/month College fund from grandparents: $500/month Scholarship: $3600/year Expenses Rent: $400/month Groceries: $50/week Tuition and fees: $3000 twice a year Incidentals: $90/week

Suppose that a box contains 8 cameras and that 5 of them are defective. A sample 2 cameras is selected at random. Define the random variable X as the number of defective cameras in the sample. Write the probability distribution for X.Write your answer in fraction form or round to 3 decimal places. What is the expected value of X?

Study this circle graph and answer the questions that follow. School Expenditures Lab fee 6% Materials fee 10% Books and lab manuals 16% Tuition 40% Tools 28% a. Which category represents the largest expenditure? b. Which category represents the smallest expenditure? c. If a student spent a total of $2500, how much of this went toward tools and lab fees combined? d. If a student spent $300 in material fees, how much would she spend on books and lab manuals? a. Which category represents the largest expenditure? Choose the correct answer below. O O O O O Materials fee Tuition Books and lab manuals Tools Lab fee b. Which category represents the smallest expenditure? Materials fee Lab fee Tuition Books and lab manuals Tools c. The student spent a total of $2500 so the combined amount that went towards tools and lab fees was. d. If a student spent $300 on materials, the amount spent on books and lab manuals was $

Investor Dan has $353,000 to invest in bonds. Bond A yields an average of 7% and the bond B yields 9.8%. Dan requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. How much should you invest in bond A? Round to the nearest cent.

Convert the area of 541 square meters to square feet. Include the acres-hectare conversion factor. Use the conversion factors from the table in Lesson 1.5. Show all needed conversion factors. Some spaces don't require numbers in which case enter 1. Some units will be blank in which case select the second item in the list, which is a blank space. Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional analysis that you learned. If it doesn't, resize the window on your computer, if possible.

What is the amplitude of the given function? What is the period of the given function? Which graph matches the given function? ? v Note: You can earn partial credit on this problem.

A tennis ball is dropped from the top of the building, which is 265 feet tall. The height of the ball, h, at time t seconds can be represented by the equation h(t) = -16 +265. After 3.5 seconds, did ball fall on the ground? Explain your answer mathematically.

A squirrel is 40 feet up in a tree and tosses a nut out of the tree with an initial velocity of 12 feet per second. The nuts height, h, at time t seconds can be represented by the equation h(t) = -16+ 12t+40. How long does it take for a squirrel to catch the nut on the ground?

Evaluate sin(-5π/6)

Simplify the radical. Give the exact answer in simplified radical form. √27

Use the theoretical probability formula to solve the problem. Express the probability as a fraction reduced to lowest terms. A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5,2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}. Find the probability of getting two numbers whose sum is greater than 9. A) 6 B) 1/6 C) 1/12 D)1/4

Suppose that $10,484 is invested at an interest rate of 5.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time?

Find the monthly interest payment in the situation below. Vic bought a new plasma TV for $2400. He made a down payment of $500 and then financed the balance through the store. Unfortunately, he was unable to make the first monthly payment and now pays 4% interest per month on the balance (while he watches his TV). What is Vic's monthly interest payment? $ (Round to the nearest dollar as needed.)

Use the long division method to find the result when 16x4 + 4x³ 30x²+x+10 is divided by 4x2 + 2x - 5. If there is a remainder, express the result in the form q(x) +r(x)/b(x).

You are dealt one card from a 52 card deck. Then the card is replaced in the deck, the deck is shuffled, and you draw again. Find the probability of getting a picture card the first time and a club the second time. A)1/13 B) 3/52 C) 1/4 D) 3/13