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3 years ago

Which of the following represents the additive inverse of 125? A. -(-125) B. 125 C. -125 D. 1/25

Mathematics

2 answers:

Elden [556K]3 years ago

7 0

Additive inverse of 125 is – 125, option C is correct.

Solution:

Given that , a number is 125

We have to find the additive inverse for the above given number from the above given set of options.

Now, we know that, sum of a number and its additive inverse equals to 0.

So, let us check option by option.

Option A:

Given number is -(-125)

-(-125) ⇒ 125 + ( - ( - 125 ) )

⇒ 125 + 125

⇒ 250 ⇒ wrong option

Option B:

Given number is 125

⇒ 125 + 125 ⇒ 250 ⇒ wrong option

Option C:

Given number is -125

125 + ( - 125 ) ⇒ 125 – 125 ⇒ 0 ⇒ correct option

Hence, additive inverse of 125 is – 125, option C is correct

Scrat [10]3 years ago

5 0

Answer:

Step-by-step explanation:

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Part A

Answers:
Mean = 5.7
Standard Deviation = 0.046

-----------------------

The mean is given to us, which was 5.7, so there's no need to do any work there.

To get the standard deviation of the sample distribution, we divide the given standard deviation s = 0.26 by the square root of the sample size n = 32
So, we get s/sqrt(n) = 0.26/sqrt(32) = 0.0459619 which rounds to 0.046

================================================

Part B

The 95% confidence interval is roughly (3.73, 7.67)
The margin of error expression is z*s/sqrt(n)
The interpretation is that if we generated 100 confidence intervals, then roughly 95% of them will have the mean between 3.73 and 7.67

-----------------------

At 95% confidence, the critical value is z = 1.96 approximately

ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*5.7/sqrt(32)
ME = 1.974949
The margin of error is roughly 1.974949

The lower and upper boundaries (L and U respectively) are:
L = xbar-ME
L = 5.7-1.974949
L = 3.725051
L = 3.73
and
U = xbar+ME
U = 5.7+1.974949
U = 7.674949
U = 7.67

================================================

Part C

Confidence interval is (5.99, 6.21)
Margin of Error expression is z*s/sqrt(n)
If we generate 100 intervals, then roughly 95 of them will have the mean between 5.99 and 6.21. We are 95% confident that the mean is between those values.

-----------------------

At 95% confidence, the critical value is z = 1.96 approximately

ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*0.34/sqrt(34)
ME = 0.114286657
The margin of error is roughly 0.114286657

L = lower limit
L = xbar-ME
L = 6.1-0.114286657
L = 5.985713343
L = 5.99

U = upper limit
U = xbar+ME
U = 6.1+0.114286657
U = 6.214286657
U = 6.21

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