Basic Math Questions and Answers

Use the graph of the function f to solve the inequality. (a) f(x) < 0 (b) f(x) ≥ 0

2. Determine the constant of proportionality for each proportional relationship. Assume that y represents all of the outputs and x represents all of the inputs. a. 2x = 10y b. (³) y = 8x y 10 C. = 10x d. (12)x=y from all over the world. She is reorganizing her collection into coins from Europ to the conclusion that six

The population of New York City in 2013 was about 8,406,000 people. Which number best approximates the population as a single digit times a power of 10? OA. 9×105 OB. 9×106 OC. 8×106 D. 8 x 10-6

The speed of light in a vacuum is about 300,000,000 meters per second, which can be written as 3 x 100 meters per second. What is n? OA. -8 OB. 8 O C. -9 O D. 9

The Treasury Department auctioned $10 billion in 3-month bills in denominations of $10,000 at a discount rate of 3.000%. What would be the effective rate of interest? (Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent.) Effective rate of interest

Using the notation discussed in lecture, suppose a triangle has the following parts: Angle A = 40 degrees, a = 15, b = 20 There are two possibilities for the measure of Angle B, one being an acute angle and the other an obtuse angle. Find these two measurements, rounded to the nearest degree. Then fill in the blanks with these approximate values: The measure of Angle B that is an acute angle is The measure of Angle B that is an obtuse angle is degrees. (Enter an integer.) degrees. (Enter an integer.)

Yaster Shipping, a competing package delivery service, charges a base price for overnight delivery of packages weighing 2 pounds or less and a surcharge for each additional pound (or fraction thereof). You are billed $25.60 for shipping a 6.3 pound package and $63.79 for shipping a 18.0 pound package. How much does it cost to ship a 49.6 pound package?

If a certain number is added to the numerator and denominator of 7/11 the result is 4/5. Find the number. The number added to both is

A construction crew needs to pave a road that is 208 miles long. The crew paves 8 miles of the road each day. The length, L (in miles), that is left to be paved after d days is given by the following function. L(d)=208-8d Answer the following questions. (a) If 144 miles of the road is left to be paved, how many days has the crew been paving the road? (b) How many miles of the road does the crew have left to pave after 12 days?

Let G be the directed graph whose vertices are the integers (2, 3,... N). A directed edge goes from a to b if b/a is an integer greater than 1. Which is the smallest given N so that some vertex in G has in-degree at least 6? 12 16 30 35 I need to learn this.

A small airplane flies 1120 miles with an average speed of 280 miles per hour. 2 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747?

Ms. Santoro is opening a one-year CD for $16,000. The interest is compounded daily. She is told by the bank representative that the annual percentage rate (APR) is 4.8%. What is the annual percentage yield (APY) for this account?

Given that the degree of the polynomial f(x) is 9, which of the following most accurately describes the number of x- intercepts that f(x) has? Select the correct answer below: f(x) has at most 8 x-intercepts. f(x) has at least 8 x-intercepts. f(x) has at least 10 x-intercepts. f(x) has at most 9 x-intercepts. f(x) has at least 9 x-intercepts. f(x) has at most 10 x-intercepts.

On the graph of f(x) = tan x and the interval [-π, π), for what value of x does f(x)=1? Select all that apply:

Which of the q-values satisfy the following inequality? 6-3q ≤1 Choose all answers that apply: A q=0 B q = 1 C q = 2

Solve the following inequality. (x + 5)²(x-3) >0

Water has been draining out of a tank for 10 minutes and has 18 cubic feet of water left in it. Use inverse variation to determine how much time it will take to have only 3 cubic feet of water left.

You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.214. How confident can you be that your predicted value will be reasonably close to the actual value? A. I can't be confident at all; this is about as close to a random guess as you can get. B. I can be a little confident; it might be close, or it might be way off. C. I can be very confident; it will be close, but it probably won't be exact. D I can be certain that my predicted value will match the value exactly

A hemispherical tank is filled with water and has a diameter of 14 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

The weight of a blue whale is about 200,000 kg, or 2 x 105 kg. The weight of a white rhinoceros is about 2000 kg, or 2 x 10³ kg. About how many times heavier is the blue whale than the rhinoceros? A. 1x 102 times B. 4 times C. 1x 10-2 times D. 198,000 times

Identify a pattern in this list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 1, 4, 9, 16, 25, 36,

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.