Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
The proportion of students between 400 and 590 is the <u>p-value of Z when X = 590 subtracted by the p-value of Z when X = 400</u>, hence:
X = 590:
Z = 0.76
Z = 0.76 has a p-value of 0.7764.
X = 400:
Z = -0.89
Z = -0.89 has a p-value of 0.1867.
0.7764 - 0.1867 = 0.5897 = 58.97%.
58.97% of students would be expected to score between 400 and 590.
More can be learned about the normal distribution at brainly.com/question/27643290
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Answer:
The answer is 2,484.
Step-by-step explanation:
First you would have to multiply 42 times 36 then subtract 1,512 from 3,996 you will get 2,484
Refer to the edited figure.
Triangles ABC and A'B'C' are similar because of AAA.
Also,
Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.
Answer:
c
Step-by-step explanation:
One way to do it is with calculus. The distance between any point
on the line to the origin is given by
Now, both
and
attain their respective extrema at the same critical points, so we can work with the latter and apply the derivative test to that.
Solving for
, you find a critical point of
.
Next, check the concavity of the squared distance to verify that a minimum occurs at this value. If the second derivative is positive, then the critical point is the site of a minimum.
You have
so indeed, a minimum occurs at
.
The minimum distance is then
