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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Simplify the expression. Rationalize the denominator when necessary.4/√3
State the name of the property illustrated.(r + s) + t = t + (r + s)
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).96 and 212
Perform the indicated operation.5√3 + 7√12 - 3√75
Evaluate the expression using the order of operations.− 15 + 25 ÷ 5
State the name of the property illustrated.g • (h + i) = (h + i) • g
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).240 and 285
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.0.̅2̅3̅
Perform the indicated operation.√63 + 13√98 - 5√112
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.0.1̅3̅5̅
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).18, 78, and 198
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.8(b + 7)
Evaluate the expression using the order of operations.(25 + 20 ÷ 5) − (3 + 7 • 2)
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.1.̅3̅6̅
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).24, 48, and 128
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.5(a + 2)
Evaluate the expression using the order of operations.(−17 + 21)2 • 3 ÷ (13 − 19)
(a) perform the indicated operation without the use of a calculator and express each answer in scientific notation.0.00004/200
State the name of the property illustrated.7 + 9 = 9 + 7
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.9(2c - 3)
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.2.05̅
Brenda cuts her grass every six days and trims her shrubs every 16 days. If Brenda cut her grass and trimmed her shrubs on June 1, how many days will it be before she cuts her grass and trims her
Evaluate the expression using the order of operations.(13 − 17)2 • 5 ÷ [23 − (− 17)]
Perform the indicated operation without the use of a calculator and express each answer in scientific notation.0.0012/0.000006
State the name of the property illustrated.5 • m = m • 5
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.8(3d - 5)
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.2.49̅
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.
Jerrett is setting up chairs for his school band concert. He needs to put 120 chairs on the gymnasium floor in rows of equal size, and there must be at least 2 chairs in each row. List the number of
Evaluate the expression using the order of operations.-3 [ (-52 + 53) ÷ (- 22 + 23)]
State the name of the property illustrated.(1 + 2) + 3 = 1 + 2(2 + 3)
List the numbers from smallest to largest.1.03 x 104 ; 1.7; 3.6 x 10-3; 9.8 x 102
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.-3(2x - 1)
Evaluate the expression using the order of operations.-5 [ (-23 - 22) • 24 ÷ 42]
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
Determine the sum of the first 50 multiples of 3.
List the numbers from smallest to largest.8.5 x 10-5; 8.2 x 103; 1.3 x 10-1; 6.2 x 104
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.-4(3x - 5)
Martha collects Matchbox and HotWheels toy cars. She has 70 red cars and 175 blue cars. She wants to line up her cars in groups so that each group has the same number of cars and each group contains
State the name of the property illustrated.(3 • a) • b = 3 • (a • b)
List the numbers from smallest to largest.40,000; 4.1 x 103 ; 0.00079; 8.3 x 10-5
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.32((1/16)x - 1/32)
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
Determine whether the set of numbers is closed under the given operation.Natural numbers, subtraction.
List the numbers from smallest to largest.267,000,000; 3.14 x 107; 1,962,000; 4.79 x 106
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.15((2/3)x - 4/5)
Elizabeth is the manager at Queen Palm Nursery and is in charge of displaying potted trees in rows. Elizabeth has 150 citrus trees and 180 palm trees. She wants to make rows of trees so that each row
Determine whether the set of numbers is closed under the given operation.Whole numbers, multiplication.
The USS Virginia submarine is at an underwater depth of 600 feet. It then rises 200 feet, dives 400 feet, and finally dives another 300 feet. What is the USS Virginia’s final depth?
Each swing of a pendulum (from far left to far right) is 3 in. shorter than the preceding swing. The first swing is 8 ft.(a) Find the length of the twelfth swing.(b) Determine the total distance
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.√2(√8 - √2)
It was found that the U.S. national debt in 2014 was about $55,642.63 per person. In 2010, the U.S. national debt was about $13.08 trillion, and the U.S. population was about 309.5 million
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
Determine whether the set of numbers is closed under the given operation.Integers, division.
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.(-3) (2 - √3)
Rita is given a starting salary of $35,000 and promised a $1400 raise per year after each of the next 8 years.(a) Determine her salary during her eighth year of work.(b) Determine the total salary
Sara and Harry both work the same night shift. Sara has every fifth night off and Harry has every sixth night off. If they both have tonight off, how many days will pass before they have the same
Determine whether the set of numbers is closed under the given operation.Real numbers, subtraction.
Mount Whitney, in the Sierra Nevada mountains of California, is the highest point in the contiguous United States. It is 14,495 ft above sea level. Death Valley, in California and Nevada, is the
Use the distributive property to multiply. Then, if possible, simplify the resulting expression.5(√2 + √3)
The current enrollment at Loras College is 8000 students. If the enrollment increases by 8% per year, determine the enrollment 10 years later.
In September 2014, the population of the United States was about 319 million people, and the population of the world was about 7.194 billion people. Determine the ratio of the U.S. population to the
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
Determine whether the set of numbers is closed under the given operation.Irrational numbers, multiplication.
While making a traditional Japanese samurai sword, the master sword maker prepares the blade by heating a bar of iron until it is white hot. He then folds it over and pounds it smooth. Therefore,
Two numbers with a greatest common divisor of 1 are said to be relatively prime. For example, the numbers 9 and 14 are relatively prime, since their GCD is 1. Determine whether the following pairs of
Evaluate each expression.23 • 24
Part of a World Standard Time Zones chart used by airlines and the United States Navy is shown. The scale along the bottom is just like a number line with the integers -12, -11,. . . , 11, 12 on
Feeding your cats and giving your cats water.Determine whether the activity can be used to illustrate the commutative property. For the property to hold, the end result must be identical, regardless
The gross domestic product (GDP) of a country is the total output of goods and services produced within that country. In 2013, the GDP of the United States was about $16.8 trillion, and the U.S.
If your salary were to increase at a rate of 6% per year, find your salary during your 15th year if your original salary is $31,000.
The primes 2 and 3 are consecutive natural numbers. Is there another pair of consecutive natural numbers both of which are prime? Explain.
Evaluate each expression.75/72
A city bus currently has 23 people on it. At the next stop, 10 people get off the bus, and 8 people get on the bus. At the next stop, 15 people get off the bus, and 6 people get on the bus. At the
Putting your wallet in your back pocket and putting your keys in your front pocket.Determine whether the activity can be used to illustrate the commutative property. For the property to hold, the end
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 the GDP by the
When dropped, a ball rebounds to four-fifths of its original height. How high will the ball reboundafter the fourth bounce if it is dropped from a height of 30 ft?
Determine the next two sets of twin primes that follow the set 11, 13.
Evaluate each expression.90
Perform the indicated operation and reduce your answer to lowest terms.2/5 + 1/3
Washing clothes and drying clothes.Determine whether the activity can be used to illustrate the commutative property. For the property to hold, the end result must be identical, regardless of the
The distance from Earth to the moon is approximately 239,000 mi. If a spacecraft travels at a speed of 20,000 mph, how many hours would the spacecraft need to travel from Earth to the moon? Use
Determine the first five Mersenne prime numbers.
Evaluate each expression.5-3
Perform the indicated operation and reduce your answer to lowest terms.5/6 - 3/4
Determine whether the statement is true or false. Modify each false statement to make it a true statement.Every integer is a whole number.
Turning on a computer and sending an email on the computer.Determine whether the activity can be used to illustrate the commutative property. For the property to hold, the end result must be
The star closest in distance to our own sun is Proxima Centauri. The distance from Earth to Proxima Centauri is approximately 2.5 x 1013 miles. If a spacecraft travels at a speed of 20,000 mph,
In 2014 India’s population was about 1.3 billion people. If India’s population is growing by about 1.2% per year, estimate India’s population in the year 2030. Round your answer to the nearest
Determine the first three Fermat numbers and determine whether they are prime or composite.
Without using a calculator, indicate be-tween which two adjacent ruler marks each of the following irrational numbers will fall. Support your answer by obtaining an approximation with a
Evaluate each expression.(23)4
Perform the indicated operation and reduce your answer to lowest terms.2/11 + 5/22
Determine whether the statement is true or false. Modify each false statement to make it a true statement.The difference of any two negative integers is a negative integer.
Putting batteries in your calculator, pressing the ON key, and pressing the 7 keyDetermine whether the activity can be used to illustrate the associative property. For the property to hold,
The 1950 Niagara Treaty be-tween the United States and Canada requires that during the tourist season a minimum of 100,000 cubic feet of water per second 1 ft3/sec2 flow over Niagara Falls (an-other
Without using a calculator, indicate be-tween which two adjacent ruler marks each of the following irrational numbers will fall. Support your answer by obtaining an approximation with a
Evaluate each expression.80
Perform the indicated operation and reduce your answer to lowest terms.8/9 - 5/6
Determine whether the statement is true or false. Modify each false statement to make it a true statement.The sum of any two negative integers is a negative integer.

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