Question: Dense Set of Numbers A set of

> Determine the indicated term for the geometric sequence with the first term, a1, and common ratio, r. Determine a8 when a1 = 3, r = 4

> Reduce each fraction to lowest terms.

> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r. a1 = -6, r = -2

> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r.

> Write the first five terms of the geometric sequence with the first term, a1, and common ratio, r. a1 = 2, r = 3

> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. -4, -11, -18, -25, ……. , -193; n = 28

> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. 5, 9, 13, 17, ……. , 101; n = 25

> Determine the sum of the terms of the arithmetic sequence. The number of terms, n, is given. 2, 4, 6, 8, ….. , 100; n = 50

> Write an expression for the general or nth term, an, of the arithmetic sequence. -7, -2, 3, 8, ……

> Write an expression for the general or nth term, an, of the arithmetic sequence. 3, 9, 15, 21, 27,…..

> Write an expression for the general or nth term, an, of the arithmetic sequence. 2,4,6,8,…

> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d.

> Evaluate the expression. Assume x ≠ 0. (a)(-6)0 (b)-(-6)0

> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d. Determine a12 when a1 = 7, d = -3.

> Determine the indicated term for the arithmetic sequence with the first term, a1, and common difference, d. Determine a10 when a1 = 9, d = -3.

> Determine whether the integers are closed under the given operation. Addition

> Determine whether the natural numbers are closed under the given operation. Division

> Describe three other activities that can be used to illustrate the associative property (see Exercises 69–74).

> Determine whether the activity can be used to illustrate the associative property. For the property to hold, doing the first two actions followed by the third would produce the same end result as doing the second and third actions followed by the first.

> Mowing the lawn, trimming the bushes, and removing dead limbs from trees

> Determine whether the activity can be used to illustrate the associative property. For the property to hold, doing the first two actions followed by the third would produce the same end result as doing the second and third actions followed by the first.

> Turning on a computer and sending an email on the computer

> Putting your wallet in your back pocket and putting your keys in your front pocket

> Use the sieve of Eratosthenes to find the prime numbers less than or equal to the given number. 150

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression.

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. -4(3x – 5)

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. 8(3d – 5)

> Use the distributive property to multiply. Then, if possible, simplify the resulting expression. 8(b + 7)

> State the name of the property illustrated. g • (h + i) = (h + i) • g

> State the name of the property illustrated. (r + s) • t = (r • t) + (s • t)

> State the name of the property illustrated.

> State the name of the property illustrated. 4 • (11 • x) = (4 • 11) • x

> Determine whether the number is rational or irrational. π

> State the name of the property illustrated. c + d = d + c

> State the name of the property illustrated. 13 + 5 = 5 + 13

> Does a + (b • c) = (a + b) • (a + c)? Give an example to support your answer.

> Does the associative property hold for the integers under the operation of subtraction? Give an example to support your answer.

> Halfway between Two Numbers to find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair.

> Give an example to show that the associative property of multiplication may be true for the negative integers.

> Halfway between Two Numbers to find a rational number halfway between any two rational numbers given in fraction form, add the two numbers together and divide their sum by 2. Find a rational number halfway between the two fractions in each pair.

> Give an example to show that the commutative property of multiplication may be true for the negative integers.

> Income Tax Some states allow a husband and wife to file individual tax returns (on a single form) even though they have filed a joint federal tax return. It is usually to the taxpayers’ advantage to do so when both husband and wife work. The smallest am

> Dense Set of Numbers A set of numbers is said to be a dense set if between any two distinct members of the set there exists a third distinct member of the set. The set of integers is not Dense, since between any two consecutive integers there is not ano

> Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d. a1 = -11, d = 5

> Use proportions to solve the problem. 15 units of insulin from a vial marked U40

> Does the commutative property hold for the rational numbers under the operation of division? Give an example to support your answer.

> Use proportions to solve the problem. Speed Limit When Jacob crossed over from Niagara Falls, New York, to Niagara Falls, Canada, he saw a sign that said 50 miles per hour (mph) is equal to 80 kilometers per hour (kph). a) How many kilometers per hour ar

> Use proportions to solve the problem. Lasagna A recipe for 6 servings of lasagna uses 16 ounces of Italian sausage. (a) If the recipe were to be made for 15 servings, how many ounces of Italian sausage would be needed? (b) How many servings of lasagna ca

> Does (x + 5) + 6 = x + (5 + 6) illustrate the commutative property or the associative property? Explain your answer.

> Use proportions to solve the problem. Paint A gallon of paint covers 825 ft2 . Assuming paint can only be purchased in whole gallons, how many gallons are needed to paint a house with a surface area of 6600 ft2?

> Cooking Oatmeal Following are the instructions given on a box of oatmeal. Determine the amount of water (or milk) and oats needed to make / servings by: a) Adding the amount of each ingredient needed for 1 serving to the amount needed for 2 servings

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Golf Membership Malcolm has two options for membership to a golf club. Option A has an annual cost of $3300 for unlimited golf. Opti

> Determine whether the real numbers are closed under the given operation. Division

> Evaluate the expression. Assume x ≠ 0.

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Enclosing Two Pens Chuck has 140 ft of fencing in which he wants to fence in two connecting, adjacent square pens

> Dimensions of a Room A rectangular room measures 8 ft 3 in. by 10 ft 8 in. by 9 ft 2 in. high. a) Determine the perimeter of the room in feet. Write your answer as a mixed number. b) Calculate the area of the floor of the room in square feet. c) Calc

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Scholarship Donation Each year, Andrea donates a total of $1000 for scholarships at Nassau Community College. This year, she wants t

> Determine whether the real numbers are closed under the given operation. Multiplication

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Laundry Cost The cost of doing the family laundry for a month at a local laundromat is $80. A new washer and dryer cost a total of $

> Write an expression that will solve the problem and then evaluate the expression. Traveling across Texas While on vacation, Omar traveled the entire length of Interstate Highway 10 in Texas (see the map that follows). Omar recorded the following travel t

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Furniture Pier 1 Imports has a sale offering 10% off of all furniture. If Amanda spent $378.99 on furniture before tax, what was the

> Determine whether the irrational numbers are closed under the given operation. Subtraction

> Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value(s). MODELING—Jet Skiing At Action Water Sports of Ocean City, Maryland, the cost of renting a Jet Ski is $42 per half hour, whi

> Write an expression that will solve the problem and then evaluate the expression. Width of a Picture The width of a picture is in., as shown in the diagram. Find x, the distance from the edge of the frame to the center.

> Determine whether the natural numbers are closed under the given operation. Multiplication

> A statement of equality between two ratios is called a(n)___________ .

> Write an equation and solve. Three times the difference of a number and 4 is 6 more than the number.

> Determine whether the irrational numbers are closed under the given operation. Addition

> Write an equation and solve. A number divided by 4 is 12 less than the number.

> Write an expression that will solve the problem and then evaluate the expression. Art Supplies Denise teaches kindergarten and is buying supplies for her class to make papier-mâché piggy banks. Each piggy bank to be made require

> Write an equation and solve. Eight less than 3 times a number is 6 times the number, increased by 10.

> Determine whether the rational numbers are closed under the given operation. Division

> Write an equation and solve. Fourteen increased by 6 times a number is 32.

> Write an expression that will solve the problem and then evaluate the expression. Crop Storage Todd has a silo on his farm in which he stores silage made from various crops. His silo is currently 1/4 full of corn silage, 2/5 full of hay silage, and 1/3 f

> One way to find a rational number between two distinct rational numbers is to add the two distinct rational numbers and divide by 2. Do you think that this method will always work for finding an irrational number between two distinct irrational numbers?

> Determine whether the rational numbers are closed under the given operation. Multiplication

> Determine whether the number is rational or irrational. 5/8

> Write an equation and solve. A number divided by 4 is 6.

> Write an expression that will solve the problem and then evaluate the expression. Alphabet Soup Margaret’s recipe for alphabet soup calls for (among other items) ¼ cup snipped parsley, 1/8 teaspoon pepper, and Â&frac

> Give an example to show that for b? 0,

> Determine whether the integers are closed under the given operation. Subtraction

> Write an equation and solve. A number increased by 8 is 12.

> Write an expression that will solve the problem and then evaluate the expression. Thistles Rachel has four different varieties of thistles invading her pasture. She estimates that of these thistles, 1/2, are Canada thistles 1/4, are bull thistles, 1/6 ar

> Give an example to show that (a ≠ b? (a + (b.

> Evaluate each expression using the order of operations.

> Write the phrase as a mathematical expression. The quotient of 8 and y, decreased by 3 times x

> Divisibility by Seven the following describes a procedure to determine whether a number is divisible by 7. We will demonstrate the procedure with the number 203. (i) Remove the units digit from the number, double the units digit, and subtract it from the

> Determine whether the sequence is a Fibonacci type sequence (each term is the sum of the two preceding terms). If it is, determine the next two terms of the sequence 3, 5, 8, 13, 21, 34, ……

> Without doing any calculations, determine whether (17 = 4.123.

> Evaluate each expression using the order of operations.

> Write the phrase as a mathematical expression. The sum of 8 and t, divided by 2

> Show that 2n - 1 is a (Mersenne) prime for n = 2, 3, 5, and 7 but composite for n = 11.

> Give an example to show that the stated case can occur. The product of two irrational numbers may be a rational number.

> Evaluate each expression using the order of operations.

> Write the phrase as a mathematical expression. 8, increased by 5 times x

> A number in which each digit except 0 appears exactly three times is divisible by 3. For example, 888,444,555 and 714,714,714 are both divisible by 3. Explain why this outcome must be true.

> Give an example to show that the stated case can occur. The sum of two irrational numbers may be a rational number.

> Evaluate each expression using the order of operations.