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mathematics
survey of mathematics
Questions and Answers of
Survey of Mathematics
Estimate the maximum number of smaller figures (at left) that can be placed in the larger figure (at right) without the small figures overlapping.
Estimate the maximum number of smaller figures (at left) that can be placed in the larger figure (at right) without the small figures overlapping.
The chart on page 17 shows the calories burned per hour for an average person who weighs 150 lb.(a) Estimate the number of calories Phyllis, who weighs 150 lb, burns in a week if she lifts weight for
The federal government owns a great deal of land in the United States. The graph below shows the percent of land owned by the federal government in the 12 states in which the federal government owns
The graph below shows that as a society we tend to get heavier as we grow older. Also, with age, the amount of muscle tends to drop, and fat accounts for a greater percentage of weight.(a) Estimate
The bar graph below shows population figures for 1900 and 2000 and estimated population figures for 2050.(a) Estimate the number of people 65 and older in 1900.5 million.(b) Estimate the number
The circle graph below shows the biggest obstacles to sticking to an exercise program, as reported by 2987 employees at the CDA Corporation.(a) Estimate the number of adults surveyed who
The circle graph below shows the number of cups of coffee consumed per week by people in the United States. Assume 700 people were surveyed.(a) Estimate the number of people surveyed who consume
Following is a map of the Olympic Peninsula in the state of Washington. Using the scale on the map, estimate the distance of the route shown in red, starting at Forks and ending at Sequim, passing
Below is a map of Californias scenic Pacific Coast Highway. Using the scale on the map, estimate the distance between Carmel-by-the-Sea and Hearst Castle. Monterey Carmel-by-the-Sea Point
The Kleins are planning a vacation in the Great Smoky Mountains National Park. Their round-trip airfare from Houston, Texas, to Knoxville, Tennessee, totals $973. Car rental is $61 per day and
Estimate the difference in the value of 50 U.S. dollars and 100 Mexican pesos. Assume that one Mexican peso is about 0.068 U.S. dollar.
Donna is a long-distance runner whose average time per mile in marathons is 9 minutes, 55 seconds. Estimate the time it will take her to complete a 26-mile, 385-yard (or ≈ 26.2-mile) marathon.
Chuck hires 11 people to pick straw-berries from his field. He agrees to pay them $1.50 for each quart they pick. Estimate the total amount of money he will have to pay if each person picks 8 quarts.
In a tug of war, the weight of the members of the two three-person teams is given below. Estimate the difference in the weights of the teams.Team A...........Team
Estimate the answer. There is no one correct estimate.26.9 + 67.3 + 219 + 143.3
Select the correct option for the following sequence. is to is to as b) d) e)
Find the next three numbers in the sequence.1, 8, 11, 88, 101, 111, 181, 808, 818, 888, 1001, 1111,. . .
Complete the following square of numbers. Explain how you determined your answer. 2 5 10 17 3 10 25 52 4 17 52 ? 4)
You have purchased one lottery ticket each week for many months and have not won more than $5.00. You decide, based on your past experience, that you are not going to win the grand prize and so you
While logging on to your computer, you type in your user-name followed by what you believe is your password. The computer indicates that a mistake has been made and asks you to try again. You retype
(a) Construct a quadrilateral (a four-sided figure) and measure the four interior angles with a protractor. What is the sum of the measures?(b) Construct three other quadrilaterals, measure the
(a) Construct a triangle and measure the three interior angles with a protractor. What is the sum of the measures?(b) Construct three other triangles, measure the angles, and record the sums. Are
The sum of any two odd numbers is divisible by 4.Find a counterexample to show that each statement is incorrect.
The difference of any two counting numbers will be a counting number.Find a counterexample to show that each statement is incorrect.
The product of any two three-digit numbers is a five-digit number.Find a counterexample to show that each statement is incorrect.
When a counting number is added to 3 and the sum is divided by 2, the quotient will be an even number.Find a counterexample to show that each statement is incorrect.
The sum of any three two-digit numbers is a three-digit number.Find a counterexample to show that each statement is incorrect.
The product of any two counting numbers is divisible by 2.Find a counterexample to show that each statement is incorrect.
Pick any number and add 10 to the number. Divide the sum by 5. Multiply the quotient by 5. Subtract 10 from the product. Then subtract your original number.(a) What is the result?(b) Arbitrarily
Pick any number and add 1 to it. Find the sum of the new number and the original number. Add 9 to the sum. Divide the new sum by 2 and subtract the original number from the quotient.(a) What is the
Pick any number and multiply the number by 4. Add 6 to the product. Divide the sum by 2 and subtract 3 from the quotient.(a) What is the relationship between the number you started with and the final
Pick any number, multiply the number by 3, add 6 to the product, divide the sum by 3, and subtract 2 from the quotient.(a) What is the relationship between the number you started with and the final
Draw the next diagram in the pattern (or sequence).
Draw the next diagram in the pattern (or sequence).
The graph below shows the average ticket price for a show on Broadway for each season from 2009 through 2014.(a) Assuming this trend continues, use the graph to predict the average ticket price for a
The graph below shows the amount of money spent in the United States on video games played on mobile devices in 2013 and the projected amount for the years 20142018.(a) Assuming
Four rows of a triangular figure are shown.(a) If you added six additional rows to the bottom of this triangle, using the same pattern displayed, how many triangles would appear in the 10th row?(b)
The pattern shown is taken from a quilt design known as a triple Irish chain. Complete the color pattern by indicating the color assigned to each square. 12|3 4 |5 67 89 10 11 12
The ancient Greeks labeled certain numbers as triangular numbers. The numbers 1, 3, 6, 10,15, 21, and so on are triangular numbers.(a) Can you determine the next two triangular numbers?(b) Describe a
The ancient Greeks labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers.(a) Determine the next three square numbers.(b) Describe a procedure to
(a) Find the sum of the digits in each of your products in part (a). If the sum is not a one-digit number, find the sum of the digits of the resulting sum again until you obtain a one-digit
Find the letter that is the 118th entry in the following sequence. Explain how you determined your answer.Y, R, R, Y, R, R, Y, R, R, Y, R, R, Y, R, R,. . .
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).2, -8/3, 32/9, -128/27,…
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).1, 1, 2, 3, 5, 8, 13, 21,. . .
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).0, 1, 3, 6, 10, 15, . . .
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).1, 4, 9, 16, 25,. . .
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).5, -25, 125, -625, . . .
Use inductive reasoning to predict the next three numbers in the pattern (or sequence).1, 1/2, 1/3, 1/4, . . . .
use inductive reasoning to predict the next three numbers in the pattern (or sequence).7, 5, 3, 1, . . .
use inductive reasoning to predict the next three numbers in the pattern (or sequence).5, -5, 5, -5,. . .
use inductive reasoning to predict the next three numbers in the pattern (or sequence).4, 7, 10, 13, …
use inductive reasoning to predict the next three numbers in the pattern (or sequence).1, 3, 5, 7, …
Draw the next figure in the pattern (or sequence).
Draw the next figure in the pattern (or sequence).
Draw the next figure in the pattern (or sequence)
Draw the next figure in the pattern (or sequence). A.D
Use inductive reasoning to predict the next line in the pattern. 10 = 101 100 = 102 1000 = 10310,000 = 104
Use inductive reasoning to predict the next line in the pattern. 1 133 1 146 41
Use inductive reasoning to predict the next line in the pattern.15 x 10 = 15016 x 10 = 16017 x 10 = 17018 x 10 = 180
Use inductive reasoning to predict the next line in the pattern.1 x 3 = 32 x 3 = 63 x 3 = 94 x 3 = 12
The type of reasoning generally used to arrive at a conjecture is called ___________ reasoningFill in the blank with an appropriate word, phrase, or symbol(s).
The type of reasoning used to prove a conjecture is called __________________ reasoningFill in the blank with an appropriate word, phrase, or symbol(s).
The process of reasoning to a specific conclusion from a general statement is called _____________ reasoningFill in the blank with an appropriate word, phrase, or symbol(s).
The process of reasoning to a general conclusion through observation of specific cases is called _____________ reasoning.Fill in the blank with an appropriate word, phrase, or symbol(s).
A belief based on specific observations that has not been proven or disproven is called a conjecture or_________Fill in the blank with an appropriate word, phrase, or symbol(s).
A specific case that satisfies the conditions of a conjecture but shows the conjecture is false is called.Fill in the blank with an appropriate word, phrase, or symbol(s).
If a/b has a remainder of 0, then a is by b.Fill in the blank with an appropriate word, phrase, or symbol(s).
A pole is in the middle of a small lake. One half of the pole is in the ground. One third of the pole is covered by water. Eleven feet, or one sixth, of the pole are out of water. What is the length
If the length, width, and height of a cube all double, what happens to the volume of the cube?
A 20 ft by 20 ft carpet is partitioned into 5 ft by 5 ft squares. How many squares will there be?
If the length and width of a rectangle each double, what happens to the area of the rectangle?
How many cubic inches fit in 1 cubic foot?
How many square inches, 1 in. by 1 in., fit in an area of 1 square foot, 1 ft by 1 ft?
Steve and Mark ran a 100-yard race. Mark won by 5 yards, which means Steve had run only 95 yards when Mark crossed the finish line. They decided to race again, with Mark starting 5 yards behind the
The manager of the video department at Target plans to purchase a large number of DVDs of The Lego Movie. One supplier is selling boxes of 20 DVD movies for $240, and a second supplier is selling
Following are the amounts of ingredients recommended to make various servings of Uncle Bens Original Converted Rice. Note: 1 tbsp=3 tsp.Determine the amount of each ingredient needed to
The following amounts of ingredients are recommended to make various servings of Nabisco Instant Cream of Wheat. Note: 16 tbsp=1 cup.Determine the amount of each ingredient needed to make 3 servings
Four partners decide to share the cost of a boat equally. By bringing in an additional partner, they can reduce the cost to each of the five partners by $3000. What is the total cost of the boat?
With a certain medical insurance policy, the customer must first pay an annual $100 deductible, and then the policy covers 80% of the cost of x-rays. The first insurance claims for a specific year
You place $1000 in a mutual fund. The first year, the value of the fund increases by 10%. The second year, the value of the fund decreases by 10%. Determine the value of the fund at the end of the
Assume that the rate of inflation is 2% per year for the next 2 years. What will the price of a sofa be 2 years from now if the sofa costs $999 today?
The following table illustrates the 10 countries that spent the most money, per person, on fast food in 2012. The table also shows the total amount of money spent on fast food for each country.(a) By
When a car’s tire pressure is 30 pounds per square inch (psi), it averages 20.8 mpg of gasoline. If the tire pressure is increased to 35 psi, the car averages 21.6 mpg of gasoline. (a) If Mr.
The chart below shows parking rates at John F. Kennedy (JFK) Airport in New York, New York, as of July 8, 2014.
A faucet leaks 1 oz of water per minute.(a) How many gallons of water are wasted in a year? (A gallon contains 128 oz.) (b) If water costs $11.20 per 1000 gal, how much additional money is being
A faucet is leaking at a rate of one drop of water per second. Assume that the volume of one drop of water is 0.1 cubic centimeter (10.1 cm3)(a) Determine the volume of water in cubic centimeters
The federal income tax rate schedule for a joint return in 2014 is illustrated in the table below. If the Marquez family paid $12,715 in federal taxes, determine the familys adjusted
The following chart shows retail stores’ average percent profit margin on certain items.Product Category........................Average Profit Margin (%)Video equipment
A plane is flying at an altitude of 15,000 ft, where the temperature is -6°F. The nearby airport, at an altitude of 3000 ft, is reporting precipitation. If the temperature increases 2.4°F for every
Shawn, a furnace technician, charges a $50 flat rate plus $40 per hour to repair furnaces. During one month, his total income from repairing 15 furnaces was $1750. How many hours did he spend
Fatima purchased 4 tires by mail order. She paid $52.80 per tire plus $5.60 per tire for ship-ping and handling. There is no sales tax on this purchase because the tires were purchased out of state.
Fernando works 40 hours per week and makes $8.50 per hour.(a) How much money can he expect to earn in 1 year (52 weeks)?(b) If he saves all the money he earns, how long will he have to work to save
Wendy fills her gas tank completely and makes a note that the odometer reads 38,451.4 miles. The next time she put gas in her car, filling the tank took 12.6 gal and the odometer read 38,687.0 miles.
The table below gives the approximate energy values of some foods, in kilo-joules (kJ), and the energy requirements of some activities. (a) How soon would you use up the energy from a fried egg
In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery com-mission, you win.(a) How many different
On four exams, Wallace’s grades were 79, 93, 91, and 68. What grade must he obtain on his fifth exam to have an 80 average?
The Browns want to purchase a house that costs $150,000. They plan to take out a $120,000 mortgage on the house and put $30,000 as a down payment. The bank informs them that with a 15-year mortgage
The balance in Gabriela’s checking account is $349.72. She purchased four video games at $32.39 each, including tax. If she pays by check, what is the new balance in her checking account?
Jackson wants to purchase a home theater system that sells for $2500. Either he can pay the total amount at the time of purchase or he can agree to pay $250 down and $130 a month for 18 months. How
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