Write the phrase as a mathematical expression. The quotient of 8 and y, decreased by 3 times x
> 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
> 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
> 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.
> 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.
> Write the phrase as a mathematical expression. 8 less than y
> Write the phrase as a mathematical expression. 5 less than twice a number
> Recall that if a number is divisible by both 2 and 3, then the number is divisible by 6. If a number is divisible by both 2 and 4, is the number necessarily divisible by 8? Explain your answer.
> Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement can be modified in more than one way to be made a true statement. The product of any two irrational numbers is always an irratio
> Evaluate each expression using the order of operations.
> Write the phrase as a mathematical expression. 7 times x, increased by 4
> Use the Euclidean algorithm to find the GCD. 496
> Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement can be modified in more than one way to be made a true statement. The product of any two rational numbers is always a rational n
> Alternative methods for adding and subtracting two fractions are shown below. These methods may not result in a solution in its lowest terms. Use the appropriate formula above to evaluate the expression.
> Speed of Light (a)Light travels at a speed of 1.86 × 105 mi/sec. A lightyear is the distance that light travels in 1 year. Determine the number of miles in a light-year. (b) Earth is approximately 93,000,000 mi from the sun.How long does i
> Use the Euclidean algorithm to find the GCD. 36
> Write the first five terms of the arithmetic sequence with the first term, a1, and common difference, d. a1 = 9, d = 7
> Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement can be modified in more than one way to be made a true statement. (p is a rational number for any prime number p.
> Alternative methods for adding and subtracting two fractions are shown below. These methods may not result in a solution in its lowest terms. Use the appropriate formula above to evaluate the expression.
> Use a scientific calculator to perform the necessary operations. Smartphone Usage In 2014, there were approximately 1.75×109 smartphone users worldwide. If the world’s population in 2014 was about 7.19 × 109, determine the approximate percentage of the w
> Use the Euclidean algorithm to find the GCD. 210, 560
> Dropping an Object The formula can be used to estimate the time, t, in seconds it takes for an object dropped to travel d feet. (a)Estimate the time it takes for an object to drop 100 ft. (b)Estimate the time it takes for an object to drop 400 ft. (c)Es
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. Milligrams and Kilograms In the metric system, 1 gram = 103 milligrams and 1 gram = 10-3 kilogram. What is the relationship between milligrams and kilograms?
> Use the Euclidean algorithm to find the GCD. 78, 104
> A Swinging Pendulum the time T required for a pendulum to swing back and forth may be found by the formula Where l is the length of the pendulum and g is the acceleration of gravity. Determine the time in seconds fo the pendulum to swing back and forth i
> Perform the indicated operation and reduce your answer to lowest terms.
> Evaluate the expression. Assume x ≠ 0. (a)23 – 2 (b) (-2)3 # (-2)
> Use a scientific calculator to perform the necessary operations. Radioactive Isotopes The half-life of a radioactive isotope is the time required for half the quantity of the isotope to decompose. The half-life of uranium-238 is 4.5 × 109 years, and the
> Use the Euclidean algorithm to find the GCD. 36, 60
> Without using a calculator, indicate between which two adjacent ruler marks each of the following irrational numbers will fall. Support your answer by obtaining an approximation with a calculator.
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. Bucket Full of Molecules A drop of water contains about 40 billion molecules. If a bucket has half a million drops of water in it, how many molecules of water are in the bucket? Write your
> State a procedure that defines a divisibility test for 22.Euclidean Algorithm Another method that can be used tofind the greatest common divisor is known as the Euclidean algorithm. We illustrate this procedure by finding the GCD of 60 and 220. First div
> Without using a calculator, indicate between which two adjacent ruler marks each of the following irrational numbers will fall. Support your answer by obtaining an approximation with a calculator.
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. Computer Speed As of September 25, 2014, the fastest computer in the world was the Tianhe-2 (Milky Way-2) computer located at Sun Yat-Sen University in Guangzhou, China. This computer is ca
> Show that Goldbach’s conjecture is true for the even numbers 4 through 20.
> F = ma; determine m when F = 40 and a = 5(physics).
> Without using a calculator, indicate between which two adjacent ruler marks each of the following irrational numbers will fall. Support your answer by obtaining an approximation with a calculator.
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. Traveling to Proxima Centauri The star closest in distance to our own sun is Proxima Centauri. The distance from Earth to Proxima Centauri is approximately 2.5 * 1013 miles. If a spacecraft
> Determine the first five Mersenne prime numbers.
> Rationalize the denominator.
