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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Jaime is chair of the humanities department at Santa Fe College. Jaime has a budget in which 1/2 of the money is for photocopying, 5/2 of the money is for computer-related expenses, and the rest of
In the Recreational Mathematics, we introduced some of the basic rules of the game Four 4’s. We now expand our operations to include square roots. For example, one way to represent the whole number
Fill in the blank with an appropriate word, phrase, or symbol(s).A letter of the alphabet used to represent numbers is called a(n) ___________.
Write the first 10 terms of the Fibonacci sequence.
Rationalize the denominator √2/√7
Simplify √75 + √48.
Express 6.45 as a quotient of two integers.
Write 13/40 as a terminating or repeating decimal.
Determine whether the sequence is a Fibonacci–type sequence. If so, determine the next two terms.0, 1, 1, 2, 2, 3, 3, 4, 4, . . .
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
Write down the first 15 terms of the Fibonacci sequence.
While on vacation, Janet traveled the full length of Interstate Highway 5 from the U.S.- Canadian border to the U.S.€“ Mexican border (see the map below). She recorded the following travel
A number whose proper factors(factors other than the number itself) add up to the number is called a perfect number. For example, 6 is a perfect number because its proper factors are 1, 2, and 3, and
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
Use the Euclidean algorithm to find the GCD.78, 60
In the metric system, 1 gram=103 milligrams and 1 gram=10-3 kilogram. What is the relationship between milligrams and kilograms?Use a scientific calculator to perform the necessary operations.
Describe three other activities that can be used to illustrate the associative property.
Use the appropriate formula above to evaluate the expression.5/8 + 1/3
Use the Euclidean algorithm to find the GCD.150, 180
In 2013, Iceland was the country with the largest percentage of its population using the Internet. If 96% of Iceland’s population of about 3.26 x 105 people used the Internet, how many people in
Does 0 ÷ a = a ÷ 0 (assume a ≠ 0)? Explain.
Explain why the quotient of a nonzero number divided by 0 is undefined.
The formula t = √d/4 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
Use the appropriate formula above to evaluate the expression.4/7 + 2/5
Use the Euclidean algorithm to find the GCD.210, 560
Perform the indicated operation and write your answer in scientific notation.(1.5 x 10-3)/(5 x 10-4)
In 2014, there were approximately 1.75 x 109 smartphone users worldwide. If the world’s population in 2014 was about 7.19 x 109,determine the approximate percentage of the worldwide population that
Explain why a/b = -a/-b
Refer to the Recreational Mathematics. Complete the following KenKen puzzle. 24X 3- 3- 7+ 1- 5+ 2.
Use the appropriate formula above to evaluate the expression.5/6 - 7/8
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.√c is
Many people have no idea of the difference in size between a million (1,000,000), a billion (1,000,000,000), and a trillion (1,000,000,000,000). (a) Write a million, a billion, and a trillion in
A number whose proper factors(factors other than the number itself) add up to the number is called a perfect number. For example, 6 is a perfect number because its proper factors are 1, 2, and 3, and
Perform the indicated calculation by first converting each number to scientific notation. Write your answer in decimal notation.(550,000)(2,000,000)
Find the quotient:(-1 + 2 - 3 + 4 - 5 + . . . . - 99 +100)/(1 - 2 + 3 - 4 + 5 - . . . . + 99 - 100)
(a) Consider the three words man eating tiger.Does (man eating) tiger mean the same as man(eating tiger)?(b) Does (horse riding) monkey mean the same as horse (riding monkey)?
(a) Light travels at a speed of 1.86 x 105 mi/sec.A light-year is the distance that light travels in 1 year. Deter-mine the number of miles in a light-year. (b) Earth is approximately 93,000,000
Use the appropriate formula above to evaluate the expression.7/3 - 5/12
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
The exponential function E(t) = 210€¢ 2tapproximates the number of bacteria in a certain culture after t hours.(a) The initial number of bacteria is determined when t =0. What is the
Evaluate each expression using the order of operations.1/4 + 1/3 • 6/7
The sum of any two rational numbers is always a rational number.Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement can be
A number whose proper factors(factors other than the number itself) add up to the number is called a perfect number. For example, 6 is a perfect number because its proper factors are 1, 2, and 3, and
Perform the indicated calculation by first converting each number to scientific notation. Write your answer in decimal notation.0.000002/0.0000004
The distance from Earth to the sun is about 1.49 x 1011 meters.The distance from Earth to the moon is about 3.84 x 108 meters.The distance from Earth to the sun is how many times larger than the
Evaluate each expression using the order of operations.(4/9 + 5/6)/(2/3)
The product of any two rational numbers is always a rational number.Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement can
A number whose proper factors(factors other than the number itself) add up to the number is called a perfect number. For example, 6 is a perfect number because its proper factors are 1, 2, and 3, and
(a) Use the rules given to represent the following whole numbers: 12, 15, 16, 17, 20.(b) We will now change our rules to allow the number 44 to count as two of the four 4’s.. Use the number 44 and
As a result of a recent water and sewer system improvement, the city of Galena, Illinois, has an outstanding debt of $20,000,000. If the population of Galena is 3600 people, how much would each
Evaluate each expression using the order of operations.(7/8 - 3/4)/(5/6)
The product of an irrational and a rational number is always an irrational number.Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false
The following procedure can be used to determine the number of factors (or divisors) of a composite number. Write the number in prime factorization form. Examine the exponents on the prime numbers in
Determine whether the sequence is arithmetic or geometric. Then determine the next two terms of the sequence.
Evaluate each expression using the order of operations.13/15 - 9/10 • 5/6
The product of any two irrational numbers is always an irrational number.Determine whether the statement is true or false. Rewrite each false statement to make it a true statement. A false statement
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 sequence is arithmetic or geometric. Then determine the next two terms of the sequence.
Evaluate each expression using the order of operations.(7/8)/(3/4) • 10/11
The sum of two irrational numbers may be an irrational number.Give an example to show that the stated case can occur.
The product of any three consecutive natural numbers is divisible by 6. Explain why.
Determine the indicated term of the sequence with the given first term, a1, and common difference, d, or common ratio, r.Determine a9 when a1 = -6, d = 2.
Evaluate each expression using the order of operations.(-8/15)/(2/3) • 7/9
The sum of two irrational numbers may be a rational number.Give an example to show that the stated case can occur.
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.
Use the fact that if a|b and a|c,then a|(b + c) to determine whether 54,036 is divisible by 18. Write 54,036 as 54,000 + 36.
Determine the indicated term of the sequence with the given first term, a1, and common difference, d, or common ratio, r.Determine a10 when a1 = -20, d = 5.
Evaluate each expression using the order of operations.1/3 • 3/7 + 3/5 • 10/11
The product of two irrational numbers may be an irrational number.Give an example to show that the stated case can occur.
Show that 2n -1 is a (Mersenne) prime for n = 2, 3, 5, and 7 but composite for n = 11.
Determine the indicated term of the sequence with the given first term, a1, and common difference, d, or common ratio, r.Determine a5 when a1 = 3, r = 2.
Evaluate each expression using the order of operations.3/5 • 10/21 + 6/11 • 33/32
The product of two irrational numbers may be a rational number.Give an example to show that the stated case can occur.
Goldbach also conjectured in his letter to Euler that every integer greater than 5 is the sum of three prime numbers. For example, 6 = 2 + 2 + 2 and 7 = 2 + 2 + 3. Show that this conjecture is true
Determine the indicated term of the sequence with the given first term, a1, and common difference, d, or common ratio, r.Determine a10 when a1 = -1, r = 3.
Evaluate each expression using the order of operations.(3/4 + 1/6)/(2 - 7/6)
Without doing any calculations, determine whether √2 = 1.414.
Determine the sum of the arithmetic sequence. The number of terms, n, is given.3, 6, 9, 12,. . ., 150; n=50
Evaluate each expression using the order of operations.(3 - 4/9)/(4 + 2/3)
Without doing any calculations, determine whether √17 = 4.123.
Consider the first eight prime numbers greater than 3. The numbers are 5, 7, 11, 13, 17, 19, 23, and 29.(a) Determine which of these prime numbers differs by 1 from a multiple of the number
Determine the sum of the arithmetic sequence. The number of terms, n, is given.0.5, 0.75, 1.00, 1.25, . . ., 5.25; n=20
The number π is an irrational number. Often the values 3.14 or 22/7 are used for π. Does π equal either 3.14 or 22/7.
When David finished his first year of high school, his height wasinches. When he returned to school after the summer, David€™s height was inches. How much did David€™s height
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 are plumeless thistles, and the rest
Determine the sum of the first n terms of the geometric sequence for the values of a1 and r.n = 4, a1 = 3, r = 2
A stairway consists of 14 stairs, each inches high. What is the vertical height of the stairway?Write an expression that will solve the problem and then evaluate the expression. ploo
Determine the sum of the first n terms of the geometric sequence for the values of a1 and r.n = 6, a1 = 1, r = -2
Give an example to show that √(a • b) = √a • √b
Margaret€™s recipe for alphabet soup calls for (among other items) 1/4 cup snipped parsley,1/8 teaspoon pepper, and 1/2 cup sliced carrots. Margaret is expecting company and needs to
First determine whether the sequence is arithmetic or geometric; then write an expression for the general or nth term, an.1, 4, 7, 10, . . .
Give an example to show that √(a / b) = √a/√b
To repair his sprinkler system, Tony needs a total of inches of PVC pipe. He has on hand pieces that measure inches,inches, and inches in length. If he can combine these pieces and
First determine whether the sequence is arithmetic or geometric; then write an expression for the general or nth term, an.2, -2, 2, -2, . . .
(a) Is √0.04 rational or irrational? Explain.(b) Is √0.7 rational or irrational? Explain.
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 full of oats silage. What fraction of
Determine the prime factorization of 825.
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.Write an expression that will solve the problem and then evaluate the
The back of a framed picture that is to be hung is shown at the top of the next page. A nail is to be hammered into the wall, and the picture will be hung by the wire on the nail.a) If the center of
While on vacation, Omar traveled the entire length of Interstate Highway 10 in Texas (see the map that follows). Omar recorded the following travel times between cities on his trip. Anthony to El

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