- The ratio of the heights of the pyramid given at the end of the answer is of: 1:3.
- The ratio of the surface areas of the pyramid given at the end of the answer is of: 1:9.
- The ratio of the volumes of the pyramid given at the end of the answer is of: 1:27.
<h3>How to obtain the ratios?</h3>
The first step in obtaining the ratios is finding the ratio of the heights, which is given as follows:
5:15 = 1:3.
The heights are measured in units, while the surface area is measured in units squared, hence the ratio is squared, as follows:
(1:3)² = 1:9.
The volume is measured in cubic units, hence the ratio is cubed, as follows:
(1:3)³ = 1:27.
<h3>Missing Information</h3>
The pyramid is given at the end of the answer.
For different dimensions, the procedure of taking the ratio of the heights, then the surface area is squared and the volume is cubed remains.
More can be learned about ratios of area and volume at brainly.com/question/15990299
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C. 6 + 7 = 13
<span>This is because 33, 21, and 15 are composite numbers, and 13 is not.</span>
Using the normal distribution, it is found that:
a) 68.2% of standardized test scores are between 406 and 644.
b) 31.8% of standardized test scores are less than 406 or greater than 644.
c) 2.3% of standardized test scores are greater than 763.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
- It 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, which is the percentile of X.
In this problem:
- The mean is of 525, hence .
- The standard deviation is of 119, hence .
Item a:
The proportion is the <u>p-value of Z when X = 644 subtracted by the p-value of Z when X = 406</u>, hence:
X = 644:
has a p-value of 0.841.
X = 406:
has a p-value of 0.159.
0.841 - 0.159 = 0.682.
0.682 = 68.2% of standardized test scores are between 406 and 644.
Item b:
Complementary event to the one found in item A, hence:
1 - 0.682 = 0.318.
0.318 = 31.8% of standardized test scores are less than 406 or greater than 644.
Item c:
The proportion is <u>1 subtracted by the p-value of Z when X = 763</u>, hence:
has a p-value of 0.977.
1 - 0.977 = 0.023
0.023 = 2.3% of standardized test scores are greater than 763.
You can learn more about the normal distribution at brainly.com/question/24663213
Answer:
It is a combination answer
495 ways
Step-by-step explanation:
In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.
Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.
Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.
Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!
In this case however, we are simply selecting 4 out of 12
Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways
Step-by-step explanation:
2(9n-1)+7(n+6)=-60
18n - 9 + 7n + 42 = -60
25n + 33 = -60
25n = -93
n = -3.72
11(4-6y)+5(13y+1)=9
44 - 66y + 65y + 5 = 9
-y + 49 = 9
-y = -40
y = 40