A student is experimenting with lighting rods and places one into the ground she find that the approximate length of rod above ground is 5/7 of a yard and the approximate length below ground 1/3 of a yard how many times farther above the ground is the lighting rod than below the ground

Answer 1

To find how many times farther above the ground the lightning rod is compared to below the ground, we need to compare the two lengths.

The length of the rod above ground is \( \frac{5}{7} \) yard, and the length below the ground is \( \frac{1}{3} \) yard.

To solve for how many times farther the rod is above the ground than below, we can divide the length above ground by the length below ground:

\[ \text{Ratio} = \frac{\text{Length above ground}}{\text{Length below ground}} = \frac{\frac{5}{7}}{\frac{1}{3}} \]

To divide fractions, we multiply by the reciprocal:

\[ \text{Ratio} = \frac{5}{7} \times \frac{3}{1} = \frac{5 \times 3}{7 \times 1} = \frac{15}{7} \]

Thus, the length of the lightning rod above the ground is \( \frac{15}{7} \) times farther than the length below the ground.

To express this as a mixed number:

\[ \frac{15}{7} = 2 \frac{1}{7} \]

Therefore, the lightning rod is approximately \( 2 \frac{1}{7} \) times farther above the ground than below the ground.

Answer 2

why is the number 19/100 a rational number

Answer 3

A rational number is defined as any number that can be expressed as the quotient (or fraction) of two integers, where the numerator is an integer and the denominator is a non-zero integer.

In the case of the number \( \frac{19}{100} \):

• The numerator is \( 19 \), which is an integer.
• The denominator is \( 100 \), which is also an integer and is not zero.

Since both conditions of being a rational number are satisfied (the presence of an integer numerator and a non-zero integer denominator), \( \frac{19}{100} \) is indeed a rational number.

Additionally, rational numbers can be represented in decimal form, and \( \frac{19}{100} \) is equal to \( 0.19 \), which is also a terminating decimal, further confirming that it is a rational number.

Answer 4

A. is it quotient of 9 divided by 10
B. is it quotient of 19 divided by 100
C. is it quotient of 100 divided by 19
D. is it quotient of 10 divided by 9

Answer 5

To determine which of the options is a rational number, we can evaluate each one:

A. Quotient of 9 divided by 10:
\[ \frac{9}{10} \]
This is a rational number because both 9 and 10 are integers, and the denominator is non-zero.

B. Quotient of 19 divided by 100:
\[ \frac{19}{100} \]
This is also a rational number for the same reasons: 19 and 100 are both integers, and the denominator is non-zero.

C. Quotient of 100 divided by 19:
\[ \frac{100}{19} \]
This is a rational number as well, since both 100 and 19 are integers, and the denominator is non-zero.

D. Quotient of 10 divided by 9:
\[ \frac{10}{9} \]
This is also a rational number, as both 10 and 9 are integers, and the denominator is non-zero.

Conclusion:

All four options (A, B, C, and D) represent rational numbers.

Answer 6

Sorry but you can only pick one so which is most likely

Answer 7

If we are to pick one option that is most likely to be a rational number among the ones provided, it would be best to consider the original example given in your previous inquiry about the number \( \frac{19}{100} \).

Thus, if we are to select one option as "most likely," I would choose:

B. is it quotient of 19 divided by 100

This option directly refers to the specific rational number that you had mentioned earlier. However, to reiterate, all provided options (A, B, C, and D) are indeed rational numbers.

Answer 8

Which of the following describes the quotient of 5 and -45

A. The quotient is a rational number
B. The quotient is an integer
C. The quotient is a undefined
D. The quotient is an irrational number

Answer 9

To find the quotient of 5 and -45, we can represent it as:

\[ \frac{5}{-45} = -\frac{1}{9} \]

Now we can evaluate the options based on this result:

A. The quotient is a rational number:
This statement is true because \(-\frac{1}{9}\) can be expressed as a fraction of two integers, making it a rational number.

B. The quotient is an integer:
This statement is false because \(-\frac{1}{9}\) is not an integer; it is a fractional number.

C. The quotient is undefined:
This statement is false because division by -45 is valid and does not lead to an undefined situation (undefined occurs only when dividing by zero).

D. The quotient is an irrational number:
This statement is false because \(-\frac{1}{9}\) is a rational number, not an irrational one.

Conclusion:

The correct answer is A. The quotient is a rational number.

Answer 10

Which of the following is true about the quotient below -4/0

A. The quotient is to -4
B. The quotient is undefined because the denominator is zero
C. The quotient is undefined because the numerator is negative
D. The quotient is equal to 0

Answer 11

To analyze the expression \(-\frac{4}{0}\):

• Dividing any number by zero is undefined in mathematics.

Now, let's evaluate the options:

A. The quotient is -4:
This statement is false because division by zero is not defined; therefore, the quotient cannot equal \(-4\).

B. The quotient is undefined because the denominator is zero:
This statement is true. The division by zero makes the quotient undefined.

C. The quotient is undefined because the numerator is negative:
This statement is false. The negativity of the numerator does not affect the undefined status of division by zero.

D. The quotient is equal to 0:
This statement is false. The division by zero does not result in zero; it remains undefined.

Conclusion:

The correct answer is B. The quotient is undefined because the denominator is zero.