Basic Math Questions and Answers

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?

The time that it takes to fold 1,000 origami cranes varies inversely with the number of people folding the cranes. If a class of 25 students work together to fold the 1,000 cranes, it will take 3 hours. Write an equation to show the relationship between time (t) and the number of people (n) folding cranes.

A class survey asked students to indicate if they are MAC or PC users. Of the following graphs, which is most appropriate to display their results? A. Pie chart B. Histogram C. Either a pie chart or a histogram D. None of the above

A grocery store has a discount of 13% off hand soap. At the same time, the hand soap manufacturer has a coupon for $2.00 off. Assuming both promotions can be applied at the same time, how much more would you pay if you applied the coupon first? A) $0.26 B) $0.19 C) $0.22 D) $0.30

Cidnee is weighing combinations of geometric solids. She found that 4 cylinders and 5 prisms weigh 32 ounces and that 1 cylinder and 8 prisms weigh 35 ounces. Write and solve a system of equations to determine the weight of each cylinder and prism. Cylinders weigh Prisms weigh

Is x = 0 a valid potential solution to the equation log(x + 7) + log(x - 3) = 17? A) Yes, logarithms are valid for any integer. B) No, because it isn't possible to take the logarithm of zero: log(0). C) No, because 17 isn't divisible by 7 or 3. D) No, because when x = 0, the second term is log(-3), and it's impossible to take the logarithm of a negative number.

A student is gathering data on the driving experiences of other college students. One of the variables measured is the type of car the student drives. These data are coded using the following method: 1 = subcompact, 2 = compact, 3 = standard size, 4 = full size, 5= premium, 6 = mini van, 7 = SUV, and 8 = truck. The student plans to see if there is a relationship between the number of speeding tickets a student gets in a year and the type of vehicle he or she drives. Identify the response variable in this study. A. College students B. type of car C. number of speeding tickets D. average number of speeding tickets last year

Graph the linear equation. x = -7y

Rewrite the expression x^5/8 in radical form.

In a random sample of 900 Americans, 40% indicated that they have a cat for a pet. Estimate with 99% confidence the proportion of all Americans that have cats as pets. (Give the confidence interval in percentages.) Confidence Interval:

Each order of lasagna or ravioli at Casa Italia weighs 1 lb and consists of meat filling wrapped in pasta. On Tuesday evening, the restaurant served 40 orders of ravioli and 60 orders of lasagna and used 60 lb of meat filling. On Wednesday evening, it sold 60 orders of ravioli and 30 orders of lasagna and used 50 lb of meat filling. a. How much meat filling is used in an order of ravioli? b. How much meat filling is used in an order of lasagna?

Use the following information: In the United States, land is commonly measured in terms of acres. One acre is equal to 43,560 square feet. In the "Old West," a common homestead parcel was 40 acres of land. How many 40-acre parcels are there in 1 square mile?

The following rule describes the relationship between and y. Rule: To find y add 2 to x. Complete the table for the given rule.

The point P(5, 0.8) lies on the curve y. If Q is the point (a, 4), find the slope of the secant line PQ for the following values of a. If a 5.1, the slope of PQ is: and if a 5.01, the slope of PQ is: and if a 4.9, the slope of PQ is: and if a 4.99, the slope of PQ is: Based on the above results, guess the slope of the tangent line to the curve at P(5, 0.8).

A dripping faucet wastes 3 cups of water every 24 hours. How much water is wasted in a week?

Use graphing technology to find the domain of the function f(x) = √(x - 2) - 2.

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function C(x)-0.1x²-56x+24,712. How many machines must be made to minimize the unit cost? Do not round your answer.

A cookie company uses one cup of sugar for every 20 cookies it makes. Let S represent the total number of cups of sugar used, and let N represent the number of cookies made. Write an equation relating S to N, and then graph your equation using the axes below.

In a national survey conducted by the Centers for Disease Control to determine health risk behaviors among college students. Asked "How often do you wear a seat belt when driving a car"? Response frequency I do not drive a car 249 Never 118 Rarely 249 Sometimes 345 Most of the time 716 Always 3093 b) What percentage of respondents answered "Always"?

In a survey people are asked "Which brand of toothpaste do you prefer?" The data gathered from this question would be what type of data? A. categorical B. quantitative C. continuous

How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 20-foot radius?

The point P(1,0) lies on the curve y = sin(107/2). If Q is the point (z, sin(107/2)), find the slope of the secant line PQ (correct to four decimal places) for z = 2, 1.5, 1.4, 1.3, 1.2, 1.1, .5. .6, .7.8.9. (Do the slopes appear to be approaching a limit?)

A group of friends will go on a weekend camping trip and split the cost of gas equally. The cost that each person will pay for gas is inversely proportional to the number of people who go on the trip. If four friends go on the trip, each person pays $23 for gas. Write an equation that describes the relationship between cost (c) that each person pays for gas, and the number of people on the trip (n).

What is the value of the expression below when w =7 and x=6? 5w-x

Suppose the function f(t) = et describes the growth of a colony of bacteria, where t is hours. Find the number of bacteria present at 5 hours. A) 59.598 B) 148.413 C) 79.432 D) 8.155

Lily has an account that pays 3.48% simple interest per year and wants to accumulate $4,000 in interest from it over the next 12 years. How much money should Lily invest in this account to meet her goal?

Choose the measurement closest to 50 liters: 14 gal, 140 gal or 50 gal. Choose the correct answer below. 140 gal 50 gal 14 gal

Choose true or false. Explain your answer. For a dilation, corresponding angles of the image and preimage are congruent. Choose the correct answer below. A. True, because the image and preimage are congruent, so the corresponding angles are congruent. B. False, because the image and preimage are congruent, so the corresponding angles are similar. C. True, because the image and preimage are similar, so the corresponding angles are congruent. D. False, because the image and preimage are similar, so the corresponding angles are similar, not congruent.

Michael is mixing two types of candy for a party. The chocolate pieces cost $0.40 per ounce, and the hard candy costs $0.20 per ounce. How many ounces of each type of candy should he purchase if he wants a mixture that is 50 ounces and costs $0.35 per ounce?

Determine the volume and the surface area of the three-dimensional figure. Use the key on your calculator. The volume is 696.91 cm³. (Simplify your answer. Type an integer or a decimal rounded to the nearest hundredth as needed.) The surface area is (Simplify your answer. Type an integer or a decimal rounded to the nearest hundredth as needed.)

Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(p) = -4p² +12,000p. What unit price should be established for the dryer to maximize revenue? What is the maximum revenue? The unit price that should be established to maximize revenue is $ 1500 (Simplify your answer.)

A local minimum of a function is its A) largest value of the function over its entire domain. B) smallest value of the function over its entire domain. C) smallest value for a given interval. D) largest value for a given interval.

Your factory produces lemon-scented widgets. You know that each unit is cheaper, the more you produce. But you also know that costs will eventually go up if you make too many widgets due to the costs of storage of the overstock. The new head of accounting says that your cost for producing x thousands of units a day can be approximated by the formula C = 0.2x² - 4.02x + 253. Find the daily production level that will minimize your costs.

For the following stirred tank reaction, carry out the following analysis. a. Write an initial value problem for the mass of the substance. b. Solve the initial value problem. A 400-L tank is initially filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 2 L/min. The thoroughly mixed solution is drained from the tank at a rate of 2 L/min.

A principal of $2700 is invested at 5.5% interest, compounded annually. How many years will it take to accumulate $6000 or more in the account? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.

Barry is going to the movies and wants to buy drinks and candy for his friends. Drinks represent x and drinks are $3 each. Candy represents y, and candy is $6 each, Barry has $24 total to spend. Which equation below in Standard Form represents the situation. (Standard Form: Ax+ByC) 3x+2y=6 6x + 3y - 24 24x+6y=3 3x+6y=24