Nature of Mathematics 13e Karl Smith - Test Bank Instant Download - Complete Test Bank With Answers Sample Questions Are Posted Below 1. Use the definition of multiplication to show what the expression means. a. , (7 terms) b. , (140 terms) c. , (6 terms) …
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Nature of Mathematics 13e Karl Smith – Test Bank
Instant Download – Complete Test Bank With Answers
Sample Questions Are Posted Below
| 1. Use the definition of multiplication to show what the expression means.
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| 2. Classify as an example of the commutative property, the associative property, or both.
2 + (3 + 5) = (2 + 5) + 3
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| 3. Consider the set with an operation defined by the table.
means find the entry in row and column ; for example, (the entry in row 7 and column 9). Find .
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| 4. Consider the set of natural numbers and an operation which means select the first of the two. That is, ; ; ; .
Is associative for ?
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| 5. Consider the operation defined by the table.
Find and.
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| 6. Do the problem mentally using the distributive property.
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| 7. Is the set of odd natural numbers closed for the operation of multiplication?
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| 8. Let . Define an operation as . Check the commutative and associative properties.
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| 9. Consider a soldier facing in a given direction (say north). Let us denote “left face” by l, “right face” by r, “about face” by a, and “stand fast” by f. (The element f means “don’t move from your present position.” It does not mean “return to your original position.”) Then we define and an operation meaning “followed by.” Thus, means “left face” followed by “left face” and is the same as the single command “about face.” Does the set H and operation satisfy the associative property?
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10. Consider a soldier facing in a given direction (say north). Let us denote “left face” by l, “right face” by r, “about face” by a, and “stand fast” by f. (The element f means “don’t move from your present position.” It does not mean “return to your original position.”) Then we define and an operation meaning “followed by.” Thus, means “left face” followed by “left face” and is the same as the single command “about face.” Complete the following table.
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| 11. Classify the equality as an example of the commutative property, the associative property, or both.
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| 12. Consider the set with an operation defined by the table.
means find the entry in row a and column b; for example, (the entry in row 7 and column 9). Find .
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| 13. Do the problem mentally using the distributive property.
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| 14. Let . Define an operation as . Check the commutative and associative properties.
It is __________ (commutative but not associative, associative but not commutative, neither commutative nor associative, associative and commutative).
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| 15. Classify the equality as an example of the commutative property, the associative property, or both.
This is an example of __________ (commutative property, associative property, both properties).
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| 16. Use the definition of multiplication to show what the expression means.
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17. Consider a soldier facing in a given direction (say north). Let us denote “left face” by l, “right face” by r, “about face” by a, and “stand fast” by f. (The element f means “don’t move from your present position”. It does not mean “return to your original position”). Then we define and an operation meaning “followed by”. Thus, means “left face” followed by “left face” and is the same as the single command “about face”. Complete the following table.
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| 18. Classify the following as an example of the commutative property, the associative property, or both.
2 + (3 + 5) = (2 + 5) + 3
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| 19. Consider the set of natural numbers and an operation which means select the first of the two. That is,
Is associative for ? Answer yes or no.
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| 20. Consider the operation defined by the table.
Find and.
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| 21. Is the set of even natural numbers closed for the operation of multiplication?
Answer yes or no.
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| 22. Consider a soldier facing in a given direction (say north). Let us denote “left face” by l, “right face” by r, “about face” by a, and “stand fast” by f. (The element f means “don’t move from your present position.” It does not mean “return to your original position.”) Then we define and an operation meaning “followed by”. Thus, means “left face” followed by “left face” and is the same as the single “about face”. Does the set H and operation satisfy the commutative property?
Answer yes or no.
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| 1. What is a prime number?
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| 2. What does g.c.f. mean?
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| 3. Is the number 1,997 prime?
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| 4. Is the statement 5|46 true or false?
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| 5. Write the prime factorization for the number 300.
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| 6. Find the canonical representation for the number 111.
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| 7. Find the g.c.f. and l.c.m. of the sets of numbers {9, 12, 14}.
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| 8. Two movie theaters, UAI and UAII, start their movies at 7:00 P.M. The movie at UAI takes 75 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time?
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| 9. In 1742 the mathematician Christian Goldbach observed that every even number (except 2) seemed representable as the sum of two primes. Goldbach could not prove this result, known today as Goldbach’s conjecture, so he wrote to his friend, the world-famous mathematician Leonhard Euler. Euler was unable to prove or disprove this conjecture, and it remains unsolved to this day. Write the numbers 16, 18, 20 as the sum of two primes.
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| 10. Some primes are 1 more than a square. For example, 5 = 2 2 + 1. Can you find any other primes p so that p = n 2 + 1?
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| 11. What is a prime number?
The natural number that has __________ (exactly two divisors, more than two divisors).
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12. Write the prime factorization for the number 24.
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| 13. Find the canonical representation for the number 83.
If the number is prime, answer prime.
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| 14. Find the g.c.f. and l.c.m. of the sets of numbers .
The g.c.f. of the sets of numbers is __________. The l.c.m. of the sets of numbers is __________.
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| 15. Two movie theaters, UAI and UAII, start their movies at 7:00 P.M. The movie at UAI takes 60 minutes and the movie at UAII takes 90 minutes. If the shows run continuously, when will they again start at the same time?
Be sure to include A.M. or P.M. in your answer.
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| 16. In 1742 the mathematician Christian Goldbach observed that every even number (except 2) seemed representable as the sum of two primes. Goldbach could not prove this result, known today as Goldbach’s conjecture, so he wrote to his friend, the world-famous mathematician Leonhard Euler. Euler was unable to prove or disprove this conjecture, and it remains unsolved to this day. Write the numbers 4, 6, 8 as the sum of two primes.
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| 17. What does l.c.m mean?
a. The largest number that divides (evenly) into each of the numbers in the given set. b. The smallest number that each of the numbers in the set divides into evenly.
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| 18. Is the number 1 prime?
Answer yes or no.
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19. Is the statement 6|50 true or false?
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| 1. Simplify the expression.
– 14 + 8
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| 2. Simplify the expression.
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| 3. Simplify the expression.
( – 1 ) 4
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| 4. Simplify the expression.
– 30 – ( – 30 )
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| 5. Simplify the expression.
– 9 – ( 10 – 4 )
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| 6. Simplify the expression.
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| 7. Simplify the expression.
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| 8. Simplify the expression.
4 – ( – 6 ) – | 1 – 9 |
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| 9. Give the answer to the question. Let k be a natural number.
Is ( – 5 ) 2k + 1 positive or negative?
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| 10. Simplify the expression.
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| 11. Simplify the expression.
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| 12. Simplify the expression.
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| 13. Simplify the expression.
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| 14. Simplify the expression.
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| 15. Simplify the expression.
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| 16. Simplify the expression.
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| 17. Simplify the expression.
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| 18. Let k be a natural number.
Is positive, negative, or an undefinable number?
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| 1. Perform the following operation.
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| 2. Completely reduce the fraction.
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| 3. Completely reduce the fraction.
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| 4. Perform the following operation.
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| 5. Perform the following operation.
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| 6. Perform the following operation.
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| 7. Perform the following operation.
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| 8. Perform the following operation.
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| 9. Perform the following operation.
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| 10. Perform the following operation.
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| 11. A unit fraction (a fraction with a numerator of 1) is sometimes called an Egyptian fraction. Egyptians expressed their fractions as a sum of distinct (different) unit fractions. How might the Egyptians have written the fraction ?
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| 12. Perform the following operation.
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| 13. Perform the following operation.
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| 14. Completely reduce the fraction.
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| 15. Completely reduce the fraction.
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| 16. Perform the following operation.
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| 17. Perform the following operation.
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| 18. Perform the following operation.
Please express the answer as an improper fraction.
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| 19. Perform the following operation.
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| 20. Perform the following operation.
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| 21. Perform the following operation.
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| 22. A unit fraction (a fraction with a numerator of 1) is sometimes called an Egyptian fraction. Egyptians expressed their fractions as a sum of distinct (different) unit fractions. How might the Egyptians have written the fraction ?
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| 1. Use the definition of square root to find the indicated product.
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| 2. Approximate the irrational number with a rational number correct to the nearest thousandth.
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| 3. Simplify the expression.
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| 4. Simplify the expression.
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| 5. Simplify the expression.
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| 6. How far from the base of a building must a 13-ft ladder be placed so that it reaches 5 ft up the wall?
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| 7. What is the exact length of the hypotenuse if the legs of a right triangle are 2 in. each?
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| 8. An empty lot is 500 ft by 1,200 ft. How many feet would you save by walking diagonally across the lot instead of walking the length and width?
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| 9. Consider a square as shown in the figure. Find the total length of the four segments making up the stairs.
5 in 5 in
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| 10. Find an irrational number between 4 and 8.
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| 11. A man wanted to board a plane with a 5.4-ft-long steel rod, but airline regulations say that the maximum length of any object or parcel checked on board is 4 ft. Without bending or cutting the rod, or altering it in any way, how did the man check it through without violating the rule?
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| 12. Use the definition of square root to find the indicated product.
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| 13. Approximate the irrational number with a rational number correct to the nearest thousandth.
__________
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| 14. How far from the base of a building must a 26-ft ladder be placed so that it reaches 10 ft up the wall?
__________ ft
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| 15. An empty lot is 1,500 ft by 11,200 ft. How many feet would you save by walking diagonally across the lot instead of walking the length and width?
__________ ft
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| 16. Consider a square as shown in the figure. Find the total length of the four segments making up the stairs.
7 in. 7 in. __________ in.
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| 17. Simplify the expression. Assume that the variables are positive.
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| 18. Simplify the expression
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| 19. Simplify the expression
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20. What is the exact length of the hypotenuse if the legs of a right triangle are 10 in. each?
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21. A man wanted to board a plane with a 4.3-ft-long steel rod, but airline regulations say that the maximum length of any object or parcel checked on board is 4 ft. Without bending or cutting the rod, or altering it in any way, how did the man check it through without violating the rule?
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22. Find an irrational number between 1 and 2.
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| 1. Express the number as a decimal.
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| 2. Express the number as a decimal.
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| 3. Change the terminating decimal to fractional form.
6.98
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| 4. Carry out the operations with decimal forms.
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| 5. Carry out the operations with decimal forms.
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| 6. Identify the illustrated property.
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| 7. Check whether this set and operation form a group.
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| 8. Find a rational number and an irrational number between the given pair of numbers.
4.5 and 4.6
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| 9. Let be an arbitrary operation. Describe the operation for the problem.
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| 10. Let be an arbitrary operation. Describe the operation for the problem.
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| 11. Check whether the set and the operation form a group.
Ω for ×
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| 12. Express the number as a decimal. Give your answer to two decimal places, if required.
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| 13. Carry out the operations with decimal forms. Give your answer to three decimal places.
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| 14. Carry out the operations with decimal forms. Give your answer to one decimal place, if required.
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| 15. Express the number as a decimal.
Use an overbar to indicate the numerals that repeat, if needed.
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| 16. Change the terminating decimal to fractional form.
0.63
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| 17. Let be an arbitrary operation.
Describe the operation .
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| 18. Let be an arbitrary operation.
Describe the operation .
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| 19. Identify the illustrated property as commutative, associative, distributive, or inverse.
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| 20. Check whether this set and operation form a group. Answer yes, no, or in definably.
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| 21. Check whether the set and the operation form a group. Answer yes or no.
Ω for +
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| 22. Find a rational number and an irrational number between the given pair of numbers.
4.5 and 4.6
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| 1. Perform the operation using arithmetic for a 12-hour clock.
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| 2. Perform the operation using arithmetic for a 12-hour clock.
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| 3. Is the statement true?
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| 4. Perform the operation.
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| 5. Solve the equation for x.
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| 6. Solve the equation for x.
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| 7. Assume that today is Monday (day 2). Determine the day of the week it will be at the end of the period at 2 years. (Assume no leap years.)
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| 8. Suppose you make six round trips to visit a sick aunt and wish to record your mileage to the nearest mile. You forget the original odometer reading, but you do remember that the units digit has increased by 8 miles. If you know that your aunt lives somewhere between 26 and 31 miles from your house, how far exactly is her house?
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| 9. Is the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} a group for multiplication modulo 11?
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| 10. An International Standard Book Number (ISBN) is used to identify books. The ISBN number for some book is 0-534-36890-5. The first digit, 0, indicates the book is published in an English-speaking country. The next three digits, 534, identify the publisher (Brooks/Cole) and the next five digits identify the particular book. The last digit is a check digit, which is used as follows. Multiply the first digit by 10, the next digit by 9, and so on:
10(0) + 9(5) + 8(3) + 7(4) + 6(3) + 5(6) + 4(8) + 3(9) + 2(0) + 1(5) = 209 This number is congruent to 0, (mod 11). This is not by chance. The check digit, 5, is chosen so that this sum is 0, (mod 11). In other words, the check digit x for the book with ISBN number 0-534-34015-x is found by considering: 10(0) + 9(5) + 8(3) + 7(4) + 6(3) + 5(4) + 4(0) + 3(1) + 2(5) = 148 ≡ 5 This means that for check digit x, 5 + x ≡ 0, (mod 11). The one-digit solution to this equation is x = 6, so the check digit is 6. What is the check digit for the book with ISBN 0-8028-1430-x?
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| 11. Perform the indicated operation.
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12. Perform the operation using arithmetic for a 12-hour clock.
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13. Perform the operation using arithmetic for a 12-hour clock.
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| 14. Perform the operation.
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| 15. Suppose you make six round trips to visit a sick aunt and wish to record your mileage to the nearest mile. You forget the original odometer reading, but you do remember that the units digit has increased by 8 miles. If you know that your aunt lives somewhere between 2 and 5 miles from your house, how far exactly is her house?
__________ miles
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| 16. An International Standard Book Number (ISBN) is used to identify books. The ISBN number for some book is . The first digit, 0, indicates the book is published in an English-speaking country. The next three digits, 534, identify the publisher (Brooks/Cole) and the next five digits identify the particular book. The last digit is a check digit, which is used as follows. Multiply the first digit by 10, the next digit by 9, and so on:
This number is congruent to 0, (mod 11). This is not by chance. The check digit, 5, is chosen so that this sum is 0, (mod 11). In other words, the check digit x for the book with ISBN number is found by considering: This means that for check digit x, . The one-digit solution to this equation is , so the check digit is 6. What is the check digit for the book with ISBN ? x = __________
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| 17. Solve the equation for x.
Assume that . If there is no solution, answer none. If you get several answers, enter one of them.
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| 18. Perform the indicated operations.
__________ __________
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19. Is the statement true or false?
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20. Assume that today is Monday (day 2). Determine the day of the week it will be at the end of the period at 155 days. (Assume no leap years.)
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21. Is the set {0, 1, 2, 3, 4, 5, 6} a group for addition modulo 7? Answer yes or no.
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Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
Original price was: $30.00.$20.00Current price is: $20.00.
