Basic Math Questions and Answers

For y = 2 cos(6x-π/4), its amplitude is its period is its shift along the x axis is

If 5 dollars can be exchanged for 300 Russian rubles, how many Russian rubles can be obtained for 1200 dollars? One can obtain Russian rubles for 1200 dollars. (Round to the nearest hundredth as needed.)

A company manufactures dog leashes that sell for $20.96, including shipping and handling. The monthly fixed costs (advertising, rent, etc.) are $24,821 and the variable costs (materials, shipping, etc.) are $8.74 per leash. How many leashes must be produced and sold each month for the company to break even?

In a recent year, 19.4% of all registered doctors were female. If there were 55,300 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number.

Solve the following inequality. x²-10x+21 > 0

The half-life of Polonium-209 is 102 years. If 5 kilograms of Polonium-209 remain in a specimen after 200 years, how much of the substance was originally present? A) 13.960 kilograms B) 19.464 kilograms C) 15.874 kilograms D) 8.035 kilograms

A police officer estimated the distance from one side of a street to the other to be 14 m. The actual distance was 13.8 m. Find the absolute error and the percent error of the police officer's estimate. If necessary, round your answers to the nearest tenth.

Bria wants to make the best choice for her retirement plan. She has two options. Bria can withdraw money either monthly or quarterly. She needs compare both options and see if there is a difference in both cases. a) Bria has $850,000 saved for retirement in an account earning 4.5% interest. She has two options either to compounded money monthly or quarterly. How much will she be able to withdraw each month if she wants to take withdrawals for 25 years? Round your answer to the nearest cent. b) How much will she be able to withdraw quarterly if she wants to take withdrawals for 25 years? Round your answer to the nearest cent. c) How much total money will she pull out of the account in both cases? d) How much of that money is interest? Consider both cases. e) Which option is more beneficial for Bria?

A grocery store owner noticed that when the milk price had a $0.25 increase, only 100 bottles of milk sold. If the milk price increased by a total of $0.50, how many bottles of milk would be sold? Hint: Convert all dollar signs to cents.

Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = 3 x intercepts at x = 5 and x = -2 Horizontal asymptote at y = 6 y =

You graph the function f(x) = 300(1.015)*, which gives the total amount in your account after x years of interest that is compounded annually. The function g(x) gives the amount in your account if you make the same initial investment, but at a rate of interest of 2.3% compounded annually. How would the graph of g(x) compare to the graph of f(x)? It would have a greater y-intercept and rise more quickly over time. It would have the same y-intercept, but rise less quickly over time. It would have a greater y-intercept and rise less quickly over time. It would have the same y-intercept, but rise more quickly over time.

Find the points at which the graph of the equation has a vertical or horizontal tangent line. 64x2 + 16y2 + 512x - 256y + 1024 = 0

An account paying 5.25% interest compounded continuously, which originally held $4,000, is now worth $5,000. How many years ago was the account started? (A) 4.250 years (B) 4.309 years (C) 4.361 years (D) 4.476 years

A glass of milk is moved from a refrigerator with a temperature of 3°C to a room with a temperature of 15°C. One minute later the milk has warmed to a temperature of 5°C. Determine the temperature of the milk at time t. After how many minutes does the milk have a temperature that is 80% of the ambient temperature?

Train A has a speed 30 miles per hour greater than that of train B. If train A travels 320 miles in the same times train B travels 260 miles, what are the speeds of the two trains? .

Austin works as a tutor for $9 an hour and as a waiter for $13 an hour. This month, he worked a combined total of 95 hours at his two jobs. Let t be the number of hours Austin worked as a tutor this month. Write an expression for the combined total dollar amount he earned this month.

A homebuyer purchases a home for $475,000 and makes a 20% down payment. If the mortgage is a 30-year fixed-rate mortgage at 5%, find (a) the down payment, (b) the mortgage amount, (c) the monthly payment.

Which expression is equivalent to 6√ g5 , if g> 0?

When using the properties of exponents we either add exponents, subtract exponents, multiply exponents, raise factors to a power, or raise the numerator or denominator to a power. Choose the expression with the correct arithmetic operation needed to simplify the following expression. (pf)8

A high school choir is holding a fundraiser for its spring contest trip. The amount each student needs to raise varies as the number of students who participate in the fundraiser. If 50 students participate in the fundraiser, each student needs to raise $275. Use this information to complete the statements. This proportional situation represents The constant of variation, k. is equal to If all 100 students in choir participate in the fundraiser, each will need to raise variation.

Mardi received an inheritance of $50,000. She invested part of it at 12% and the rest at 11%. Her total annual income from the investments was $5900. Find the amount invested at 12%.

Watch the video that describes Unifying Quadratic Functions. If a is positive, the graph of f(x) = ax² + bx+c is which of the following? Choose the correct answer below. A. An-shape B. A line rising from left to right C. A horizontal line D. A U-shape

The sum of the reciprocals of 2 consecutive integers is 5/6 Find the numbers.

Consider this rational equation. 1/x + 1/x-2 = 1/4 Use the least common denominator to simplify the rational equation into a standard form quadratic equation.

Solve the following proportion for y. y/4 = 8/17 Round your answer to the nearest tenth.

Which of the e-values satisfy the following inequality? 3e ≤ 6 Choose all answers that apply: A.e = 1 B.e = 2 C.e = 3

To find the number of units that gives break-even for the product, solve the equation R = C. Round your answer to the nearest whole unit. 21) A manufacturer has total revenue given by the function R = 70x and has total cost given by C = 50x + 145,000, where x is the number of units produced and sold.

Identify the y-intercept of the graph of R(x)= 12(x-1)/(x+1)(x+6) Choose the correct y-intercept below. 1 -2 6 -1

Analyze the polynomial function f(x) = -4(x+4)(x-3)³ using parts (a) through (h) below_ (a) Determine the end behavior of the graph of the function. (b) Find the x- and y-intercepts of the graph of the function.

A bacteria culture contains 1200 bacteria initially and doubles every hour. (a) Find a function / that models the number of bacteria after t hours. N(t) = (b) Find the number of bacteria after 24 hours.

A Norman Window is a window that has the shape of a semicircle on top of a rectangle. Let's say that we have a Norman window with height of the rectangle y feet tall and a semicircle with radius x feet. The contractor building the window knows that there is going to be exactly 14 feet of trim around the outside of the window (three sides of the rectangle plus the semicircle). Now would be a great time to draw a picture for this problem. Go ahead, I'll wait. (A) Recalling that the circumference of a circle is C = 2πr, write a formula for the amount of trim and solve your formula for y in terms of x. y(x) = (B) Now recalling that the area of a circle is A = 72, write a formula for the area of the Norman window in terms of x. You will need to replace any instance of y with your answer from part (A). A(x) =

List the potential rational zeros of the polynomial function. Do not attempt to find the zeros. f(x) = 11x4-5x³+x²-x+1 Choose the answer below that lists the potential rational zeros.

Analyze the polynomial function f(x) = -4(x + 4)(x-3)³ using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function. The graph off behaves like y= for large values of x.

For the first 80 miles of her road trip. Lina travels 10 miles/hour slower than she did for the remaining 50 miles of her trip. If s represents Lina's speed during the first part of her trip, which expressions represent the total time of her trip in hours? 130s - 800/s(s-10) 130s +800/s(s+10)

Use logarithmic differentiation to find the derivative of y with respect to the given independent variable. y = (sin x) 4x

Brett, a sales person at Arya Sunshine Tours, sold a vacation package to Chelsea and her partner for $11,000 to travel to the Bahamas for 10 days. If the commission on this sale is 8%, calculate the amount of commission received.

Katie is building a rectangular wall. The wall will be 332 bricks wide and 39 bricks tall. She has 15,000 bricks. Does she have enough bricks to build the wall? Explain. Show your work in the box.

The area of a rectangle is 14 ft², and the length of the rectangle is 3 ft less than twice the width. Find the dimensions of the rectangle.

The time it takes to clean up after an anniversary party varies inversely as the number of people cleaning. If 3 people work together to clean, it will take them 90 minutes. How long will it take if the number of people cleaning is increased to 5? A 54 minutes B. 72 minutes C.150 minutes D. 162 minutes

Find the quotient and remainder using long division. -42³-14x² - 8x + 2/2x + 2 The quotient is The remainder is

Your cousin has a budget plan but unexpected expenses keep coming up. She is trying to understand where she went wrong last month so she took a rainy Saturday morning to compare her budget plan to her actual expenses. Her plan was to spend 1/4 of her budget on housing; 1/5 on car related expenses like gas, insurance, maintenance and lease; 3/10 on food; 1/10 on cell phone & other tech; 1/20 on savings; and 1/10 on entertainment. She is trying not to use her credit card because of fees so she has no credit card payments right now. First, make sure that her math was right and that the fractions add up to one whole. You may want to turn them into decimals first. Write the calculations below.

A child flies a kite at a height of 100 ft, the wind carrying the kite horizontally away from the child at a rate of 52 ft/sec. How fast must the child let out the string when the kite is 260 ft away from the child? Let x represent the horizontal distance through which the kite is blown and let y represent the distance between the child and the kite. Write the equation that relate these rates.

Factor the given polynomial completely into a product of linear factors of the form ax + b where a is a real number and b is a real or complex number. P(x) = 27x³ - 125 (Express numbers in exact form. Use symbolic notation and fractions where needed.) 27x³ - 125 =

The intensity of sound is measured on the decibel scale, dB. The equation dB = 10 log I represents the decibel level, where I is the ratio of the sound to the human hearing threshold. A noise is 150,000 times greater than the human hearing threshold. Which shows a valid step in the process of finding the decibel level of the noise? Select the correct answer below:

Subtract 1/x+9 - 9/x+9 z2 +52 – 36 State the difference in simplest form.

A faucet can fill a bathtub in 6 minutes. The drain can empty the tub in 10 minutes. If both the faucet and the drain are open at the same time. this situation is represented by this expression, where t is the number of minutes it will take to completely fill the bathtub. t/6 - t/10 Which expression can also represent this situation?

A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $81,900 per month. A television ad costs $2000, a radio ad costs $100, and a newspaper ad costs $600. The department wants to run 68 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month? television ads radio ads newspaper ads

A person invests 1000 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 1600 dollars?

Density: A Rectangular Prism has a height of 4cm, a width of 5cm, a length of 1.2 cm, and a mass of 85,000 g. What is it's density? .00000035416 g/cm^3 .00035416 g/cm^3 354.16 g/cm^3 3541.6 g/cm^3

Leila has two coupons for a bicycle. Coupon A: 35% off of a $93 bicycle Coupon B: $36 rebate on a $93 bicycle Choose the coupon that gives the lower price. Then fill in the blank with the correct value. Coupon A gives the lower price. The price with coupon A is $less than the price with coupon B. Coupon B gives the lower price. The price with coupon B is $ less than the price with coupon A.