Answer:
The value of ROE that will be exceeded by 78% of the firms is -1.77%.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean 
and standard deviation 
the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
The mean ROE for the firms studied was 14.93% and the standard deviation was 21.74%. This means that 
What value of ROE will be exceeded by 78% of the firms?
This is the value of X when Z has a pvalue of 1-0.78 = 0.22.
This is 
So:
The value of ROE that will be exceeded by 78% of the firms is -1.77%.
Point - slope form = y - y1 = m(x - x1)
y - 4 = 2(x-1)
Answer:
257 is prime.
Step-by-step explanation:
To evaluate if a number is prime, we just need to evaluate it for the prime numbers that are equal or lesser than the said number's square root.
In this case, √257 = 16.03 so we just need to see if 257 is divisible by <u>2, 3, 5, 7, 11 and 13</u> (the prime numbers that come before 16)
- 257 is odd, so it is not divisible by 2.
- The sum of its digits is 14, therefore, it is not divisible by 3.
- 257 ends in 7, therefore it's not divisible by 5.
- 257/ 7 = 36.71 so it's not divisible by 7.
- 257/ 11 = 23.36 so it's not divisible by 11
- Finally 257 / 13= 19.76 so it's not divisible by 13.
Therefore, 257 is prime.
Answer:
$25.03725
Step-by-step explanation:
<u>Step 1: Multiply both sides by %5 to get the raise</u>
26.355 * %5 is same as 26.355 * 0.05
$1.31775 is the raise
<u>Step 2: Subtract the raise from the new salary</u>
26.355 - 1.31775
25.03725
Answer: $25.03725
