Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 7, 5, 3, 1, …
> When a counting number is added to 3 and the sum is divided by 2, the quotient will be an even number.
> In Exercises 43 and 44, estimate the percent of area that is shaded in the following figures.
> The sum of any three two-digit numbers is a three-digit number.
> The product of any two counting numbers is divisible by 2.
> 86 + 47.2 + 289.8 + 532.4 + 12.8
> In Exercises 41 and 42, estimate, in degrees, the measure of the angles depicted. For comparison purposes a right angle, /, measures 90°.
> Estimate the number of grapes shown in the photo.
> 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 select some different numbers and repeat the process, rec
> Estimate the number of bananas shown in the photo.
> 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 final number? (b) Arbitrarily select some different num
> 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 answer? (b) Arbitrarily select some different numbers
> Pick any number, multiply the number by 3, add 6 to the product, divide the sum by 3, and subtract 2 from the quotient. See Example 5. (a) What is the relationship between the number you started with and the final number? (b) Arbitrarily select some diff
> In Exercises 37 and 38, 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 2 hours each week and jogs at 5 miles per hour for 4
> Land Ownership by the Federal Government 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 greatest p
> A belief based on specific observations that has not been proven or disproven is called a conjecture or _________________.
> In Exercises 35 and 36, draw the next diagram in the pattern (or sequence).
> Gaining Weight 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 average percent of body fat for a wo
> Broadway Tickets 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 show on Broadway for the 2015 seaso
> An Aging Population 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. (b) Estimate the number of people 65 and older in 2050. (c) Estimate the
> Video Games 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 2014–2018. (a) Assuming this trend continues, use the graph to predi
> Exercising 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 don’t have the energy to exercise. (b
> Triangles in a Triangle 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) If the triangles in all 10 row
> Coffee Consumption 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 5–7 cups of coffee pe
> Quilt Design 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.
> The Olympic Peninsula 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 through Port Angeles.
> 26.9 + 67.3 + 219 + 143.3
> A Triangular Pattern 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 procedure to determine the nex
> The Pacific Coast Highway Below is a map of California’s scenic Pacific Coast Highway. Using the scale on the map, estimate the distance between Carmel- by-the-Sea and Hearst Castle.
> A Square Pattern 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 determine the next five square numbers with
> The Cost of a Vacation 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 lodging is a total of $97 per day, and
> (a) Select a variety of one- and two-digit numbers between 1 and 99 and multiply each by 9. Record your results. (b) 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 t
> Currency 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.
> 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, ….
> Estimating Time 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
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
> Picking Strawberries Chuck hires 11 people to pick strawberries 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.
> A specific case that satisfies the conditions of a conjecture but shows the conjecture is false is called a _____________.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 1, 1, 2, 3, 5, 8, 13, 21, …..
> Estimating Weights 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.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 0, 1, 3, 6, 10, 15, …..
> Monthly Expenses Li’s total monthly expenses consist of room and board: $595; car payment: $289; gas: $120; insurance: $110; and miscellaneous expenses: $230. Estimate Li’s total monthly expenses.
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 1, 4, 9, 16, 25, …..
> The number of months needed to save $400 if you save $23 each month
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 5, −25, 125, −625, ….
> A 15% tip on a meal that costs $26.32
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence).
> The weight of one pork chop in a package of six pork chops if the weight of the package is 3.25 lb
> The symbol ≈ means is approximately ________________ to.
> The total weight of three people on an elevator if their weights are 95 lb, 127 lb, and 210 lb
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 5, −5, 5, −5, …..
> The cost of 5 items purchased at a hardware store if the items cost $1.29, $6.86, $12.43, $25.62, and $8.99
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 4, 7, 10, 13, …
> The cost of 5 items at a grocery store if the items cost $7.99, $4.23, $16.82, $3.51, and $20.12
> Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 1, 3, 5, 7, …
> The cost of 12 gallons of gas if one gallon costs $3.75
> Draw the next figure in the pattern (or sequence).
> The amount of money Issac spends on fast food in a year if the average amount he spends per month is $47
> If a ÷ b has a remainder of 0, then a is by ___________ b.
> Draw the next figure in the pattern (or sequence).
> The cost of dinner per person if dinner for 8 people costs $210 and they split the bill evenly
> Draw the next figure in the pattern (or sequence).
> The cost of one tire if a set of 4 tires costs $410
> Draw the next figure in the pattern (or sequence).
> 296.3 ÷ 0.0096
> Use inductive reasoning to predict the next line in the pattern. 10 = 101 100 = 102 1000 = 103 10,000 = 104
> 22% of 9116
> Use inductive reasoning to predict the next line in the pattern.
> 11% of 8221
> The process of arriving at an approximate answer to a question is called____________.
> Use inductive reasoning to predict the next line in the pattern. 15 × 10 =150 16 × 10 =160 17 × 10 =170 18 × 10 =180
> 51, 608 × 6981
> Use inductive reasoning to predict the next line in the pattern. 1 × 3 = 3 2 × 3 = 6 3 × 3 = 9 4 × 3 = 12
> 0.63 × 1523
> The type of reasoning generally used to arrive at a conjecture is called __________ reasoning.
> 405/0.049
> The type of reasoning used to prove a conjecture is called ______________ reasoning.
> 1776 × 0.0098
> The process of reasoning to a specific conclusion from a general statement is called _____________ reasoning.
> 197,500 ÷ 4.063
> Another name for the counting numbers is the ______________ numbers.
> Not getting a correct answer when making a random guess of an answer to a particular multiple-choice question on an SAT test with possible answers of a, b, c, d, e, one of which is correct.
> Not drawing a heart from a standard deck of 52 playing cards (see Figure 6.6). Figure 6.6 Playing cards in a standard 52-card deck.
> Not drawing a queen from a standard deck of 52 playing cards (see Figure 6.6). Figure 6.6 Playing cards in a standard 52-card deck.
> What is the probability of randomly selecting a day of the week whose name includes the letter “d”?
> What is the probability of randomly selecting a day of the week whose name doesn’t include the letter “y”?
> Rolling a single six-sided die and getting a result that is less than 10.
> Finding that the next baby born to a couple is a girl, given that the couple already has two children and they are both boys.
> Finding that when tossing a coin, it turns up heads, given that it has turned up heads in the previous five tosses.
> Finding that the next person you meet has the same birthday as yours (ignoring leap years).
> Finding that the next President of the United States was born on a Saturday.
> Find the probability of randomly selecting one of the test subjects and getting someone who is in Group A and passed the exam.
> Drawing an ace from a standard deck of 52 playing cards (see Figure 6.6) Figure 6.6 Playing cards in a standard 52-card deck.
> Making a correct random guess as an answer to a particular multiple-choice question on an SAT test with possible answers of a, b, c, d, e, one of which is correct.
> Randomly selecting one of the 365 days of the year and getting a day in September.
> Rolling a single six-sided die and getting an odd number (1, 3, or 5).
> Tossing two coins and getting either one head or two heads.
> How many different four-child families are possible if birth order is taken into account? What is the probability of a four-child family that has two girls and two boys?
> How many different three-child families are possible if birth order is taken into account? What is the probability of a three-child family with three girls?
> Because either there is life on Mars or there is not, the probability of life on Mars is 0.5.
