Basic Math Questions and Answers

Carl owns a company that washes the windows of office buildings. He recently signed a contract for a large office building and estimates that it would take 2 days for 4 workers to wash the windows. Write an equation to describe the relationship between time (t) and the number of workers (n), which are inversely proportional. A) t = 2/n B) t = 6/n C) t = 16/n D) t = 8/n

The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she guesses that the standard deviation is 7 minutes. How large a sample of workers should she take if she wishes to estimate the mean assembly time to within 20 seconds. Assume the confidence level to be 99%. Sample Size =

A population of bacteria triples every hour. Is this situation linear or exponential? A) Linear, because the function increases B) Linear, because the function increases by a common difference C) Exponential, because the function decreases D) Exponential, because the function grows by a common ratio

A station wagon covered a total distance of 3343 kilometres averaging a speed of 32 km/h in slow-moving traffic and 79 km/h in fast-moving traffic. The journey took 56 hours. How many hours did the station wagon spend in slow-moving traffic? (Hint distance = speed x time)

Beth can travel 203 miles in the same length of time it takes Anna to travel 192 miles. If Beth's speed is 4 mph greater than Anna's, find both rates. Hint: You'll be using the d = r*t formula, but in a different form. For the time column in the table below, you should put in expressions using the formula t= d/r a.Write down the unknown(s) you're being asked to find and assign a variable or expression to represent it (them). b. Organize the information provided in the table below. Rate Time Distance Beth Anna c.Using the information given in the problem and your table, write an equation representing this scenario. Then solve the equation. d. Write a sentence answering the question asked in the exercise using the appropriate units of measure. e.Assess your solution. Write a sentence indicating whether your solution makes sense. If it doesn't make sense, explain why.

toy company recently added some made-to-scale models of racecars to their product line. The length of a certain racecar is 19 ft. Its width is 7 ft. The width of the e-cast replica is 1.75 in. Find the length of the model.

Factor each expression: 125x³ +216 = 8a³-276³=

Use a graphing device to solve the inequality, as in Example 5. Express your answer using interval notation, with the endpoints of the intervals rounded to two decimals. x3-8x2 - 11x + 18 ≥ 0

Suppose you have 60 kg of a radioactive material that decays 50% of its mass every year. How much material will you have left after 4 years? 8.12 kg 32.1 kg 12.14 kg 3.14 kg

Suppose that you begin with 10 grams of magic crystals, and your crystals grow at a continuous rate of 25% every day (that's why they're magic). How many grams of crystals will you have after one week (7 days)? 85.28 g 47.68 g 100 g 57.55 g

According to a country's census, the number of people (in thousands) who are expected to be over 100 years old in year x is approximated by the function f(x)=0.27x² +3.54x+50.78, where x = 0 corresponds to the year 2000 and the formula is valid through 2045. (a) Find a formula giving the rate of change in the number of people over 100 years old. (b) What is the rate of change in the number of people expected to be over 100 years old in the year 2015? (c) Is the number of people expected to be over 100 years old increasing or decreasing in 2015? (a) The formula for the rate of change of the number of people over the age of 100 is f'(x) =

Find the difference. (-67x² +68x+25) - (31x^2 + 49) =

Solve the triangle. a=25.53 km, b=20.81 km, c= 18.57 km Find the measure of angle A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A= (Round to two decimal places as needed.) B. There is no solution.

Divide the following and express your answer in appropriate scientific notation: 6.84 x 10(71)/1.2 × 10(43)

Solve the following inequality. 2x² <-3x+14 Select the correct choice below and, if necessary, fill in the answer box. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no real solution.

A certain car model was expected to get 459 miles (highway) on 24 gallons of gas. What was the mean number of miles per gallon (mpg)? The mean number of miles per gallon (mpg) is (Round to the nearest tenth as needed.)

You want to start saving up for a trip to Europe after you graduate from CSM in two years. Your goal is to save $3000, so you decide to start a savings account that earns 2.5% interest compounded quarterly. How much should you deposit each quarter to meet your goal? $233.38 $600.00 $366.87 $122.03

The number of people y (in millions) who have a driver's license can be estimated by the linear equation y-1.5x+250, where x is the number of years after 2000. a. Use this equation to complete the ordered pair (7.) b. Write a sentence explaining the meaning of the ordered pair in part (a). c. If this trend continues, predict the number of people with driver's licenses in 2019. Part 2 of 3 a. Complete the ordered pair. (Simplify your answer.) b. Choose the sentence which best describes the meaning of this ordered pair. Select the correct choice below and, if necessary, fill in the answer box to complete your choice (Simplify your answers.) A. In million people lost a driver's license. B. In there were million more people with a driver's license than in 2000. C. In million people obtained a driver's license. D. In there were million people with a driver's license.

A restaurant manager has developed time guidelines for his kitchen staff. One such guideline requires a food prep worker to prepare 27 containers of granola in 7 minutes 40 seconds or less. What is the maximum time allowed per container?

f(x) = -3/x^2 Find two points on the graph of this function, other than the origin, that fit within the given [-10, 10] by [-10, 10] grid. Express each coordinate as an Integer or simplified fraction, or round to four decimal places as necessary.

Factor each expression: 27x³+1 = 8a³ - 125b³=

In a circle with a radius of 6 ft, an arc is intercepted by a central angle of 3π/2 radians What is the length of the arc? 2π ft 3π ft 6 π ft 9π ft

Given the two functions, which statement is true? f(x) = log15 x, g(x) = log15 (x+4) g(x) is stretched vertically by a factor of 2 and shifted to the left 4 units compared to f(x). g(x) is shrunk vertically by a factor of 12 and shifted to the left 4 units compared to f(x). g(x) is stretched vertically by a factor of 2 and shifted to the right 4 units compared to f(x). g(x) is shrunk vertically by a factor of 12 and shifted to the right 4 units compared to f(x).

Which of the following polynomials is guaranteed by the Intermediate Value Theorem to have a zero on the interval [3, 4]? Select the correct answer below: f(x) = 2x² + x − 3 g(x) = -4x² + 3x - 4 h(x) = x³ - 2x² - x +4 j(x) = 2x² - 5x -5

According to a researcher's data, about 63% of all of San Diego has taken at least 1 dance class. Suppose that we obtain 300 randomly selected San Diegans. a) Is the sample large enough to use the normal approximation for the binomial? Show it using the conditions.

The monthly demand equation for an electric utility company is estimated to be p= 50- (10)x, where p is measured in dollars and x is measured in thousands of kilowatts-hour. The utility has fixed cost of 8.5 million dollars per month and variable costs of $35 per 1000 kilowatts-hours of electricity generated, so the cost function is C(x) = 8.5(106) + 35x. a. The value of x and the corresponding price for 1000 kilowatts-hour that maximizes the utility's profit is GHC b. The Total cost of producing this kilowatt of electricity is GHC

The hole for a footing needs to be 7 ft deep. If it is currently 1 ft 7 in. deep, how much deeper does it need to be dug? Give the answer in inches. The hole needs to be dug inches deeper.

Lacey is at her house, which is located at (2, 4) on a coordinate grid. She wants to go to a bookstore that is located at (1, 6). Which route could she take? Assume 1 unit = 1 mile. A.1 mile to the right and 6 miles up B.2 miles to the left and 1 mile up C. 6 miles to the right and 1 mile up D.1 mile to the left and 2 miles up

Psychologists use the formula i = 100m/c to measure a person's intelligence. Called the intelligence quotient, or I.Q., i is expressed in terms of m, the person's mental age, and c, his or her chronological age, or number of years he or she has lived. a) Find the I.Q. of someone whose mental age is 18 and whose chronological age is 15. b) Solve the formula for m in terms of i and c. c) Check your answer for part a of this exercise in your formula for part b, letting m= 18 and c = 15. d) Solve the formula that you wrote for part b of this exercise for c in terms of i and m.

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). If a sample of 50 individuals is randomly selected, find the probability that the mean of the sample will be greater than 200 pounds. A 0,7613 B. 0.8815 C 0.0985 D. 0.9015

The perimeter of a square box is 12x + 32. Drag numbers to complete an equivalent expression that shows the perimeter as four times the side length of the box. Numbers may be used once, more than once, or not at all. 1 2 3 4 5 6 7 8

Identify the explicit formula for the sequence given by the following recursive formula: f(n)= [ƒ(1)=-2 f(n)=f(n-1)+4 if n>1 A) f(n) = 2 - 4(n − 1) B) f(n) = −4 + 2(n − 1) C) f(n) = -2 + 4(n − 1) D) f(n) = 4 - 2(n − 1)

Given the function f(x) = 2x - 1, evaluate and simplify the expressions below. See special instructions on how to enter your answers. f(a) = f(a+h) = f(a+h)-f(a)/h =

If we are collecting sample data for a study, the that we choose can greatly influence the validity of our conclusions. For example, we can use sound statistical methods to analyze data in voluntary response samples, but the results are not necessarily valid. If we are collecting sample data for a study, the the validity of our conclusions. For example, we voluntary response samples, but the results are

A line passes through the point (, 2) and has a slope of -2. Write an equation in point-slope form for this line.

The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level, then the pressure P (a) (in mmHg) is approximated by P (a)=760e^-0.13a (a) Find the atmospheric pressure at sea level. (b) Determine the atmospheric pressure at 4.996 km (the altitude of Mount Blackburn). Round to the nearest whole unit. Do not round intermediate calculations.

Solve the following inequality. x2 +5x-6<0

A family buys a studio apartment for $180,000. They pay a down payment of $54,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would an $81,000 down payment be? a. The down payment is% of the purchase price. (Type a whole number.)

Rewrite this number in decimal notation without the use of exponents or scientific notation: 2.858 x 10¹ Enter an integer or decimal number [more..] Answers may be entered with or without commas, but answers must be exact (no rounding at all). Also, do not include any spaces in your answer.

Find the degree, leading coefficients, and the maximum number of real zeros of the polynomial. f(x) = x² + 2 + 5x^8 - 3x^5 Degree = Leading Coefficient = Maximum number of real zeros =

Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.Voltage measurements of batteries: 1.5 V, 3 V, 4.5 V, 6 V, and 7.5 V Choose the correct answer below. Nominal Interval Ratio Ordinal

Graph the rational function. f(x) = 3x+3/x+2 Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.

A small airline has a policy of booking as many as 57 persons on an airplane that can seat only 50. (Past studies have revealed that only 77% of the booked passengers actually arrive for the flight.) Find the probability that if Air-USA books 57 persons, not enough seats will be available.

There are currently 10 frogs in a (large) pond. The frog population grows exponentially, tripling every 9 days. How long will it take (in days) for there to be 270 frogs in the pond? The pond's ecosystem can support 7290 frogs. How long until the situation becomes critical?

Let f(x) = 7/x The slope of the tangent line to the graph of f(x) at the point (-6,-7/6) is The equation of the tangent line to the graph of f(x) at (-6, -7/6) is y=mx+b for m= ___ and b= ___

Petty Marine Co. has a long-term plan to expand to a second location that's actually near some water, so they want to start a monthly annuity to save $100,000 in capital over 4 years. The best rate they can find is 10%. Find the monthly payment. Round to the nearest cent. A monthly payment of $ would be necessary.

A charity organization had to sell a few tickets to their fundraiser just to cover necessary production costs. After selling 10 tickets, they were still at a net loss of $800 (due to the production costs). They sold each ticket for $70. Let y represent the net profit (in dollars) when they have sold a tickets. Complete the equation for the relationship between the net profit and number of tickets sold.

Let (4, -7) be a point on the terminal side of θ. Find the exact values of sinθ, cscθ, and cotθ.

If 11900 dollars is invested at an interest rate of 10 percent per year, compounded semiannually, find the value of the investment after the given number of years, using the following formula: A(t) = 11900(1+0,1/2)2t (a) 5 years: Your answer is (b) 10 years: Your answer is (c) 15 years: Your answer is

A major league baseball team has 20 players on the active roster. How many choices does a manager have for batting order, listing the nine starters from 1 through 9?