Evaluate the expression. Assume x ≠ 0. (a)23 – 2 (b) (-2)3 # (-2)
> 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.
> 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.
> 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.
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. China’s GDP In 2013, the GDP (see Exercise 65) of China was about $9.24 trillion, and the population of China was about 1.396 billion people. Determine China’s GDP per person by dividing th
> The primes 2 and 3 are consecutive natural numbers. Is there another pair of consecut
> Rationalize the denominator.
> Perform the indicated operation and reduce your answer to lowest terms.
> Write the mathematical expression as a phrase. (There are several acceptable answers.) 3x + 5
> China’s Population. In September 2014, the population of China was about 1.396 billion people, and the population of the world was about 7.194 billion people. Determine the ratio of China’s population to the world’s population by dividing China’s populat
> Landscape Trimming Bianca trims her palm trees every 45 days and her viburnum shrubs every 25 days. If Bianca trims both her palm trees and her viburnum shrubs on the same day, how many days will it be until they are both trimmed on the same day again?
> Rationalize the denominator.
> Perform the indicated operation and reduce your answer to lowest terms.
> Use a scientific calculator to perform the necessary operations. Spain’s Debt per Person In 2014, the Spanish national debt was about 849 billion euros (the euro is the unit of currency in Spain). Spain’s population in 2014 was about 46.7 million people.
> Car Maintenance For many sport utility vehicles, it is recommended that the oil be changed every 3500 miles and that the tires be rotated every 6000 miles. If Carmella just had the oil changed and tires rotated on her SUV during the same visit to her mec
> Rationalize the denominator.
> Perform the indicated operation and reduce your answer to lowest terms.
> List the numbers from smallest to largest. 267,000,000; 3.14 * 107; 1,962,000; 4.79 * 106
> Stacking Trading Cards Desmond collects trading cards. He has 432 baseball cards and 360 football cards. He wants to make stacks of cards on a table so that each stack contains the same number of cards and each card belongs to one stack. If the baseball
> A = lw; determine A when l = 9 and w = 4.(geometry)
> Perform the indicated operation. Simplify the answer when possible.
> Perform the indicated operation and reduce your answer to lowest terms.
> List the numbers from smallest to largest. 8.5 × 10-5; 8.2 × 103 ; 1.3 × 10-1 ; 6.2 × 104
> Barbie and Ken Mary collects Barbie dolls and Ken dolls. She has 390 Barbie dolls and 468 Ken dolls. Mary wishes to display the dolls in groups so that the same number of dolls are in each group and that each doll belongs to one group. If each group is t
> Perform the indicated operation. Simplify the answer when possible.
> Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.
> Perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in dec
> U.S. Senate Committees The U.S. Senate consists of 100 members. Senate committees are to be formed so that each of the committees contains the same number of senators and each senator is a member of exactly one committee. The committees are to have more
> Perform the indicated operation. Simplify the answer when possible.
> Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.
> Write the mathematical expression as a phrase. (There are several acceptable answers.) x – 2
> Perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in dec
> Find (a) the greatest common divisor (GCD) and (b) the least common multiple (LCM). 18, 78, and 198
> Perform the indicated operation. Simplify the answer when possible.
> Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.
> Perform the indicated operation without the use of a calculator and express each answer in scientific notation. (b) Confirm your answer from part (a) by using a scientific calculator to perform the operations. If the calculator displays the answer in dec
> Find (a) the greatest common divisor (GCD) and (b) the least common multiple (LCM). 240 and 285
> Perform the indicated operation.
