Basic Math Questions and Answers

Estimate the total number of hours Americans spend stuck in traffic each year. If you are unfamiliar with estimation techniques, you may find it difficult to know how to begin solving this problem. This tutorial is designed to introduce you to the art of estimation. Learning to calculate rough estimates has many applications both in the sciences and in other fields. The ability to estimate the order of magnitude of unknown quantities can produce invaluable guides for measurements and planning. When estimating, you are looking for a number that is within an order of magnitude (i.e., a power of ten) of the actual value_ This is a broad range, so it is neither necessary nor desirable to work with precise numbers. You want numbers that are both reasonable and easy to use in calculations. For example, there are 365 days in a year. For the purposes of estimation, 365 is unnecessarily precise; 3 x 10² or 4 x 10² are both reasonable approximations and are more convenient for calculation. There is no definite rule concerning the precision of approximations. How coarse you make your approximations depends on how you plan to use the numbers and how precise you want your estimate to be. When beginning any approximation problem, ask yourself, "What do I need to know in order to solve this?" This particular problem asks about Americans, so the total number A of Americans is a good place to start. In actuality, there are a little over 325 million. Choose a convenient approximation for this value, express it using scientific notation, and enter it below. Do not check your answer yet.

Given the polynomial functions f(a) and g(x), find h(x) = f(x) = g(x). f(x)= 4¹-a³ +3m² +6 g(x)=5a-2a² + 3m - 2 h() = -4¹+4+²+3x+4 h(x) = 4r¹ - 6x³ +5²-32-8 h(a)-4a¹-62³5² +38 h(x) 42-62³ ²3x4

Which of the following is the best version of the underlined portion of sentence 2 (reproduced below)? Elk have been observed, cavorting over patches of snow, jumping and twisting their bodies, even when abundant bare ground is available nearby. (as it is now) observed cavorting over patches of snow, jumping and twisting their bodies, observed, cavorting over patches of snow, jumping, and twisting their bodies observed cavorting, over patches of snow, jumping and twisting their bodies,

The price of a train ticket consists of an initial fee plus a constant fee per stop. The table compares the number of stops and the price of a ticket (in dollars). What is the fee per stop?

A square power-takeoff shaft with 2 1/4-inch sides needs to be covered with a round guard. The guard should have at least 2/5-inch clearance at all points. What should be the inside diameter of the guard? Round to the nearest hundredths place.

Helen purchased 3 books from an online bookstore and received a 20% discount on her total order. Each book cost the same amount. The shipping cost was $10 and was not discounted. Write an expression that can be used to represent the total amount Helen paid for 3 books plus the shipping cost. Simplify the expression, and then identify each term, the constant term, and the factors and coefficients of the terms that contain a variable.

A local Target store bought 98 pizzas at Pizza Hut for its holiday party. Each guest ate 1/9 of a pizza and there was no pizza left over. How many guests did Target have for the party?

Quilters Newsletter Magazine gave instructions on making a quilt. The quilt required 6 yards of white-on-white print, 5 yards blue check, yard blue-and-white stripe, yards blue scraps, yard yellow scraps, and 5 yards lining. How many total yards are needed? 6125 fitin Total yards

A company finds it can produce 30 heaters for $8800, while producing 35 heaters costs $10,150. Express the cost, y, as a linear function of the number of heaters, x.

Which of the following is a characteristic of the authoritarian parenting style? Placing high value on conformity and obedience Giving reasonable demands Expressing warmth and affection Listening to the child's point of view

Michael Wittry has been investing in his Roth IRA retirement account for 24 years. Five years ago, his account was worth $215,670. After losing of its original value, it then gained of its new value back. What is the current value of his Roth IRA? (Do not round intermediate calculations.) Current value

A student earned grades of 92, 83, 77, 84, and 82 on her five regular tests. She earned a grade of 95 on her class project, and her homework grade was 77. The five regular tests count for 60% total of the final grade, and the project counts for 15%, and the homework grade also counts for 15%. If the final exam counts for 10% of the final grade, what minimum grade on the final will ensure that she gets a weighted average of at least 80 (B-) for her final weighted mean grade?

Joy Wigens, who works at Putnam Investments, received a check for $5,935. She deposited 1/5 of the check in her Citibank account. How much money does Joy have left after the deposit?

A police officer uses a radar gun to determine the speed of five vehicles traveling on the highway. The speed of those vehicles are as follows. 65, 63, 67, 57, 68 (a) Calculate the average speed of the five vehicles. (b) Calculate the standard deviation of the speeds given in the data set. (Round your answer to three decimal places.)

As a science experiment, Mo and Jo want to send their model rocket into space. They need 1/6 cup of H₂O (water) and 1/8 cup of a secret component. How much is there of these two components together? There is cup of these components together. (Type a whole number or a simplified fraction.)

Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) f(x) = 8 / x^2 + 4x - 5

Some friends who were playing darts decided to impose a 5-point penalty for each dart that missed the dart board completely. During the evening, a boy had 2 darts in the 20-point section, 3 darts in the triple-15-point section, and 6 darts in the double-10-point section. He missed the dart board completely 5 times. How many points did the boy score?

James invested $20,000 into two accounts. One account pays 6% simple interest, while the other account pays 5% simple interest. If his interest earnings total $1120 after one year, how much did he invest at each rate?

Total replacement insurance coverage against breakage or loss of a new laptop computer is $19.00 per month increasing by 5% per year. What is the cost per month for two years? A- $18.33 B- $19.95 C-$20.95 D- $22.25

The Jetsons are taking a family vacation. Their car gets 30 miles per gallon in gas mileage. They are traveling for seven hours at a rate of 55 miles per hour. Assuming no stops, how much gas will they need to complete their seven hour trip? 20 gallons 12 gallons 13 gallons 4 gallons There is not enough information to answer the question

Sketch the points A, B, C, and D on a set of coordinate axes below. Then, find the distance from A to B and from C to D. a. A(3,1,0) B(-1,2,-5) Distance between A and B: b. C(5,-4,-6) D(8,- 7,4) Distance between C and D:

Last week you went shopping and spent exactly $180 on shirts and jeans. The shirts each cost $15 and the jeans each cost $30. Which of the following are constants in this situation? I. The total amount spent. II. The number of shirts purchased III. The cost per shirt IV. The cost per jean V. The total number of items purchased Choose the most accurate answer. I and V III and IV I and III and IV II and V ll only lonly

The number of hours in 80 minutes is 80/60. Which statements are true? The number of hours in decimal form is 1.3. The amount of time is a full hour and 1/3 hour. The number of hours is a terminating decimal. The number of hours is between 1 and 1.35. Dividing 6 by 8 will give the correct decimal value.

In 1996 the value of a 1957 Ford Mustang was appreciating at 10% per year. Al's father bought one back then for $4000 and he's kept it in immaculate shape. Al is bragging that it must be worth at least $50,000 now. What do you think of Al's claim? If it continues to appreciate at 10% per year, when will the car be worth $50,000?

A handywoman charges $20 to come to your house to give an estimate for a job and then another $35 for every hour she works on the job. Which of the following are constants in this situation? I. The total cost of the job II. The cost of the estimate III. The amount of time the handywoman works on the job IV. The hourly rate the handywoman charges Choose the most accurate answer. I and III II and IV I and IV II and III ll only IV only

Craig earns the same amount of money each month. His telephone bill is 1/20 of his monthly earnings, and he pays a total of $720 each year for his telephone service. How much does Craig earn each month, in dollars?

Suppose that K is the function that computes how many kilograms are in a pounds. Find the algebraic rule for K. (If you do not know how many pounds are in one kilogram, you can look it up on Google.) K(x) Evaluate K (109) and interpret the result. Something that weighs kilograms. = pounds would weigh about

The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club. Each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell. How many pies did the club make?

A band is trying to decide how to price tickets for its next concert. Their market research suggests that, if they price the tickets at $20 per ticket, then they will sell 1000 tickets. For each $2 increase in ticket price, the number of tickets they will sell decreases by 5. Write a formula for N(p), the number of tickets they will sell if they price the tickets at p dollars per ticket.

Researchers counted 8,912 monarch butterflies on one branch of a tree at a site in Mexico. They estimated that the total number of butterflies at the site was 1,000 times as large. About how many butterflies were at the site in all? Explain your thinking, and include a statement of the solution.

The package insert for a medication reads a patient should receive 5 mL of medication for every 50 kg of body weight. If a patient weighs 66 lb, what is the amount of medication, in milliliters, the patient should be administered?

Marni bought two kinds of nuts-cashews and almonds. She spent $42, and for that money she bought 2 pounds of cashews and 3 pounds of almonds. Which of the following are variables in this situation? 1. The cost of cashews ($ per pound) 11. The cost of almonds ($ per pound) III. The total cost ($) IV. The total amount of nuts purchased (pounds) Choose the most accurate answer. I and II and III III and IV I and IV I and II I and II and IV

4. To simplify an expression involving decimals, such as 2x(1.1 +2.9+ 3.8), you should: Either is ok, but adding first is usually easier Never add first Add first Either is ok, but distributing first is usually easier Distribute first

There are at least 12 people on a bus. a. Write and graph an inequality to show the number of people who may be on the bus. b. Three people get on the bus at the next stop and no one gets off. Write an inequality that represents the number of people who may be on the bus now. Explain your thinking.

If f:A → B then A is the If f:A → B then B is the Suppose that S = the set of squirrels in NY's Central Park and let X be the function on S that tells you the weight of the squirrels. In particular, X(a Central Park squirrel) = that squirrel's weight in grams. If we write 400 grams ≤X<≤500 grams this refers to the set of Suppose that S = the set of squirrels in California and let X be the function on S that tells you the weight of the squirrels. In particular, X(a California squirrel) = that squirrel's weight in grams. If we write 400 grams ≤x≤500 grams this refers to the set of

Sam and Carlos are bowling with plastic pins in Sam's living room. Remarkably, Sam knocks down 8 pins on every bowl, and Carlos knocks down 9 pins on every bowl. At the end of the day, Sam and Carlos have knocked down the same total number of pins. What is the least number of total pins that Sam and Carlos could have each knocked down? 36 72 144 56

Given the functions below, find the domain of (f.g)(x). f(x) = -4/-x+4 g(x) = -8/-2x-6 Select the correct answer below: All real numbers except -3 and -7/4 All real numbers except -3 and-3/2 All real numbers except -3 and -2 All real numbers except -3 and -5/4 All real numbers except -3 and 4

Chris is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice to spice ration is 15 : 1. He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, Chris spends 4.50 dollars on rice. How many servings can Chris make with the current amount of spice he has? 10 6 4 8

A skyscraper has an observation deck. There are always 5 employees on the deck. At any time, there must be fewer than 40 people on the deck. a. Write an inequality that represents the number of visitors, v, who can be on the deck at any time. Show your work. b. Graph the inequality you wrote in problem 3a.

Luke and Yoda were picking strawberries. Yoda picked 36 strawberries. He picked 6 times as many strawberries as Luke picked. Which equation will help us find how many strawberries (L Luke picked? LX 36 = 6 6XL = 36 36 x 6 = L

Write the indicated amounts using Arabic numbers and proper abbreviations. Use decimals instead of fractions and include a space between the number and the abbreviation.

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.19 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.59 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info). How much chicken will you be buying? 3 pounds How much far are the two stores? My neighborhood store is 2.4 miles away, and takes about 7 minutes. The store across town is 8.5 miles away, and takes about 26 minutes. How kind of mileage does your car get? It averages about 19 miles per gallon in the city. How many gallons does your car hold? About 14 gallons How much is gas? About $3.77/gallon right now. Going to the close store is cheaper Going to the further store is cheaper The cheaper option saves you $ Give your answer to the nearest cent.

Given each pair of points, identify the slope. Next, identify which slope (-12, 13), (-15, 8) Slope: (8,3), (-10, 9) Slope: (-3, 4), (13,- 15) Slope: (-7, 7), (-14, 10) Slope: Which slope is the steepest?:

Divide: 6x³+2x²+22x / 2x² + 5 3x +1+ (7x - 5 / 2x²+5) 3x + 1 3x +1+ (7x + 5 / 2x²+5) 3x - 1+ (7x-5 / 2x²+5)

A patient suffering from a cold is given a prescription for 2 teaspoons of cough suppressant every 6 h for 8 days. The patient will be using a teaspoon to measure the dose of medication. If the medication is supplied in pint bottles, how many bottles will the patient need during the 8 days?

Over the last three evenings, Keiko received a total of 128 phone calls at the call center. The second evening, she received 4 times as many calls as the third evening. The first evening, she received 8 more calls than the third evening. How many phone calls did she receive each evening? Number of phone calls the first evening: Number of phone calls the second evening: Number of phone calls the third evening:

Andrew started biking to the internet cafe traveling 14 mph, after some time the bike got a flat so Andrew walked the rest of the way, traveling 6 mph. If the total trip to the internet cafe took 10 hours and it was 92 miles away, how long did Andrew travel at each speed?

Find the set A ∩ B. U=(1, 2, 3, 4, 5, 6, 7) A = (1, 2, 3, 4) B=(1, 2, 5) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A∩B (Use a comma to separate answers as needed.) B. A∩B is the empty set.

Divide: 4x³-43x+21 / (x - 3) 4x² + 12x - 7 4x² - 31x + (-72 / x - 3) 4x² - 12x - 7 4x² + 31x + (-72 / x - 3)

Jerry made 8,700 mL of tomato soup. He packed 1.6 L of the soup for his kids' lunches. He then froze half of the remaining soup. How many milliliters of soup did Jerry freeze? Jerry froze mL of soup