Given:
In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.
To find:
The length of the missing side.
Solution:
In a right angle triangle,
Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.
Substituting Perpendicular = 8 inches and Base = 12 inches, we get
Taking square root on both sides, we get
The length of the missing side is 14.4 inches. Therefore, the correct option is D.
Answer:
Jessie scored higher than Reagan.
Step-by-step explanation:
We are given that Reagan scored 1140 on the SAT. The distribution of SAT scores in a reference population is normally distributed with mean 1000 and standard deviation 100.
Jessie scored 30 on the ACT. The distribution of ACT scores in a reference population is normally distributed with mean 17 and standard deviation 5.
For finding who performed better on the standardized exams, we have to calculate the z-scores for both people.
1. <u>Finding z-score for Reagan;</u>
Let X = distribution of SAT scores
SO, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 1000
= standard deviation = 100
Now, Reagan scored 1140 on the SAT, that is;
z-score = = 1.4
2. <u>Finding z-score for Jessie;</u>
Let X = distribution of ACT scores
SO, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean = 17
= standard deviation = 5
Now, Jessie scored 30 on the ACT, that is;
z-score = = 2.6
This means that Jessie scored higher than Reagan because Jessie's standardized score was 2.6, which is 2.6 standard deviations above the mean and Reagan's standardized score was 1.4, which is 1.4 standard deviations above the mean.