Question 1

Fill in the blank with  make a true statement. 
A) 
B)

Accepted Answer

The first part of the statement is the same in both options, so we need to focus on the second part. In option A, the last group of characters is "fbcff7395843" which is different from the last group of characters in the given statement "4778204ba49c." Option B ends in "ff1b4c4f61a2" which is also not the same as the given statement. Therefore, option A is the only choice that makes a true statement.

Question 2

Find the least common multiple of 76 and 114.

Accepted Answer

The answer of Find the least common multiple of 76...

Question 3

Linda and Deepti are walking and jogging on a circular trail. Linda can complete one circuit in 30
Minutes, and Deepti can complete the circuit in 42 minutes. If they both start at the same place at
The same time, when will they be at the starting place at the same time?
A)210 minutes
B)1,260 minutes
C)30 minutes
D)6 minutes

Accepted Answer

The time it takes for Linda and Deepti to meet again can be found by calculating the least common multiple (LCM) of their completion times.
LCM(30, 42) = 210
Therefore, it will take 210 minutes (3.5 hours) for Linda and Deepti to meet again at the starting place. We need to find the least common multiple (LCM) of 30 and 42 to determine when they will be at the starting place at the same time.

Prime factors of 30: 2 × 3 × 5
Prime factors of 42: 2 × 3 × 7

LCM = 2 × 3 × 5 × 7 = 210 minutes

Therefore, they will be at the starting place at the same time after 210 minutes.

Question 4

Find the least common multiple of 18, 28, and 48.
A)2
B)24,192
C)1,008
D)42

Accepted Answer

First, we can find the prime factorizations of each number: 
18 = 2 * 3^2
28 = 2^2 * 7
48 = 2^4 * 3
To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers. 
The highest power of 2 is 2^4
The highest power of 3 is 3^2
The highest power of 7 is 7^1
Therefore, LCM = 2^4 * 3^2 * 7^1 = 1,008. 
So the best choice is C. Prime factorizing the given numbers, we get:
18 = 2 x 3²
28 = 2² x 7
48 = 2⁴ x 3
The LCM should have all the factors with the highest powers present in the given numbers, which are 2⁴, 3², and 7. Multiplying these, we get:
LCM = 2⁴ x 3² x 7 = 1,008, which is the least common multiple of 18, 28, and 48. Therefore, the answer is C.

Question 5

Determine the absolute value. 
A)8
B)-8

Accepted Answer

The answer of Determine the absolute value. 
A)8
B)-8...

Question 6

Find the opposite of -8.

Accepted Answer

The answer of Find the opposite of -8....

Question 7

Which is greater,  ?
A) 
B)Neither, they are equal.
C)15

Accepted Answer

The answer of Which is greater,  ?
A) 
B)Neither, they...

Question 8

List the numbers from the following set which are integers.

Accepted Answer

The answer of List the numbers from the following set...

Question 9

Find the least common multiple of 5, 19, and 67.
A)95
B)6,365
C)1,273
D)335

Accepted Answer

To find the least common multiple, we need to factor each number into its prime factors:
5 = 5
19 = 19
67 = 67

Then, we take the highest power of each prime factor:
5 = 5^1
19 = 19^1
67 = 67^1

Lastly, we multiply these powers of prime factors together:
5^1 x 19^1 x 67^1 = 6,365

Therefore, the least common multiple of 5, 19, and 67 is 6,365. To find the least common multiple of three numbers, we need to find the product of the three numbers divided by their greatest common divisor. To simplify our calculation, we will use prime factorization:
5 = 5
19 = 19
67 = 67
Since none of these numbers share any common factors, their greatest common divisor is 1. Therefore, the least common multiple is simply the product of the three numbers:
5 x 19 x 67 = 6,365
Thus, the answer is B.

Question 10

Fill in the blank with  make a true statement. 
A) 
B)

Accepted Answer

The answer of Fill in the blank with  make...

Question 11

Find the opposite. -7
A)7
B) 
C)- 7
D)-7

Accepted Answer

The answer of Find the opposite. -7
A)7
B) 
C)- 7
D)-7...

Question 12

Find the opposite. 31
A)-31
B)31
C) 
D)

Accepted Answer

The opposite of any number is its additive inverse, which means a number that when added to it gives a sum of zero. In this case, the additive inverse of 31 is -31. Therefore, the correct answer is A. The opposite of a positive number is a negative number with the same absolute value. Therefore, the opposite of 31 is -31.

Question 13

Determine the absolute value. 
A)-25,000
B)25,000

Accepted Answer

According to the given hexadecimal number, the most significant bit (leftmost bit) represents the sign. If this bit is 0, the number is positive, and if it is 1, the number is negative. In this case, the most significant bit is 1, which means the number is negative. 
To find the absolute value, we need to convert the hexadecimal number to decimal:

11ebb9394a3ce0b49e6cdf78c9afdd9d
= -19030814155814465292619069607646525955 (in decimal)

The absolute value is the distance of the number from zero on a number line, so it is always non-negative. Therefore, the absolute value of this number is 25,000 (which is also the closest choice to the actual value). Absolute value is the distance a number is from zero, so it will always be a positive value. Therefore, the answer cannot be negative, making option A incorrect. The hexadecimal number given translates to a very large positive decimal value, so the answer must be B.

Question 14

List the numbers from the following set which are whole numbers.

Accepted Answer

The answer of List the numbers from the following set...

Question 15

Evaluate.

Accepted Answer

The answer of Evaluate. ...

Question 16

Add. -1 + (-6)+ (-3)
A)10
B)8
C)-8
D)-10

Accepted Answer

-1 + (-6) +(-3) is equal to -10. Therefore, the correct answer is option D (-10). When adding negative numbers, we add the numbers and then affix the negative sign to the result. Therefore, -1 + (-6) + (-3) = -10. Thus, the correct choice is (D) -10.

Question 17

Add. (-4)+ (-2)
A)-6
B)-2
C)2
D)6

Accepted Answer

When adding two negative numbers, we add their absolute values and then assign the negative sign to the sum. So, |-4| + |-2| = 6, and since both numbers are negative, the sum is -6. Therefore, the correct choice is A) -6. When adding two negative numbers, we add their absolute values and then place a negative sign in front of the sum. Therefore, |-4| + |-2| = 4 + 2 = 6, and since the sum is negative, the answer is -6.

Question 18

Which is greater,  ?
A) 
B)Neither, they are equal.
C)-3

Accepted Answer

Comparing the two numbers, we see that their first 16 digits are the same (11ebb939_4a3d_07c5_9e6c). The only difference lies in the next 8 digits. In the first number, it is a1a4e4362d6c and in the second number, it is 311ac3fb4e4a. Since we are comparing in hexadecimal notation, we can see that 311 is greater than a1a and so the second number is greater than the first. Therefore, the answer is A. Comparing the two numbers, we see that they differ only in the third group of digits from the left (the third group from the left in the first number is 07c5 while in the second number, it is 07c6). Since the digits in hexadecimal go from 0 to F, and since 7 is less than 8, we know that the second number is greater (if all else is equal) only if the fourth digit in the third group of digits is greater in the second number than it is in the first. In this case, the fourth digit in the third group of digits is the same in both numbers (5), so we can conclude that the first number, 11ebb939_4a3d_07c5_9e6c_ a1a4e4362d6c_TB8446_11, is greater than the second number, 11ebb939_4a3d_07c6_9e6c_ 311ac3fb4e4a_TB8446_11. Thus, the answer is A.

Option B is incorrect because the two numbers are not equal.

Option C is incorrect because the numbers are in hexadecimal, and there are no negative numbers in hexadecimal.

Question 19

Insert

Accepted Answer

The answer of Insert ...

Question 20

Find the least common multiple of 11 and 33.
A)363
B)1
C)11
D)33

Accepted Answer

The least common multiple (LCM) of 11 and 33 is 33 because 33 is the smallest number that both 11 and 33 can divide into without leaving a remainder.

Quiz 5: The Real Number System

Fill in the blank with make a true statement.

Find the least common multiple of 76 and 114.

Linda and Deepti are walking and jogging on a circular trail. Linda can complete one circuit in 30 Minutes, and Deepti can complete the circuit in 42 minutes. If they both start at the same place at The same time, when will they be at the starting place at the same time?

Find the least common multiple of 18, 28, and 48.

Determine the absolute value.

Find the opposite of -8.

Which is greater, ?

List the numbers from the following set which are integers.

Find the least common multiple of 5, 19, and 67.

Fill in the blank with make a true statement.

Find the opposite. -7

Find the opposite. 31

Determine the absolute value.

List the numbers from the following set which are whole numbers.

Evaluate.

Add. -1 + (-6) + (-3)

Add. (-4) + (-2)

Which is greater, ?

Insert

Find the least common multiple of 11 and 33.