Which algebraic expression is equivalent to the expression below? 8(4x + 6) + 19
1 answer:
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Answer:
The volume of pyramid B is 81 cubic units
Step-by-step explanation:
Given
<u>Pyramid A</u>
-- base sides
-- Volume
<u>Pyramid B</u>
--- base sides
Required
Determine the volume of pyramid B <em>[Missing from the question]</em>
From the question, we understand that both pyramids are equilateral triangular pyramids.
The volume is calculated as:
Where B represents the area of the base equilateral triangle, and it is calculated as:
Where s represents the side lengths
First, we calculate the height of pyramid A
For Pyramid A, the base area is:
The height is calculated from:
This gives:
Make h the subject
To calculate the volume of pyramid B, we make use of:
Since the heights of both pyramids are the same, we can make use of:
The base area B, is then calculated as:
Where
So:
So:
Where
and
Answer:
a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}
b) {0,1,2,3}
c)
d)
Step-by-step explanation:
We are given the following in the question:
Suppose a couple planned to have three children. Let X be the number of girls the couple has.
a) possible arrangements of girls and boys
Sample space:
{GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}
b) sample space for X
X is the number of girls couple has. Thus, X can take the values 0, 1, 2 and 3 that is 0 girls, 1 girl, 2 girls and three girls from three children.
Sample space: {0,1,2,3}
c) probability that X=2
P(X=2)
That is we have to compute the probability that couple has exactly two girls.
Favorable outcome: {GGB, GBG, BGG}
d) probability that the couple have three boys.
Favorable outcome: {BBB}