Step-by-step explanation:
The volume of a cube is
where a is the side length,
Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally
The area of a square with side length a, is
If we multiply that by the height of the cube, which is a.
That is the easy way to derive the formula of the volume of a cube.
Back on track, we know the volume so we must solve for a.
1.
Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.
To do this, we take the cube root of both sides
![\sqrt[3]{125} = \sqrt[3]{a {}^{3} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B125%7D%20%20%3D%20%20%5Csqrt%5B3%5D%7Ba%20%7B%7D%5E%7B3%7D%20%7D%20)
The cube root of 125 is 5 so
5 cm
2.
![\sqrt[3]{8} = \sqrt[3]{ {a}^{3} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B8%7D%20%20%3D%20%20%5Csqrt%5B3%5D%7B%20%7Ba%7D%5E%7B3%7D%20%7D%20)
2 ft
3.
7 yd
4.
10 mm
5.
12 in. or 1 ft
6.
1 m
Answer:
37.5
Step-by-step explanation:
Formula for surface area of a triangular prism: bh+2ls+lb
(7*4)+2(8*5)+(8*7)
28+80+56
=164 cm^2
Answer:
2.5% probability that a randomly selected book has fewer than 133 pages.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 189 pages
Standard deviation = 28 pages
What is the probability that a randomly selected book has fewer than 133 pages?
133 = 189 - 2*28
So 133 is two standard deviations below the mean.
The Empirical Rule states that 95% of the measures are within 2 standard deviations of the mean. The other 5% is more than two standard deviations distant from the mean. The normal distribution is symmetric, which means that of those 5%, 2.5% are more than 2 standard deviations below the mean and 2.5% are more than 2 standard deviations above the mean.
This means that there is a 2.5% probability that a randomly selected book has fewer than 133 pages.
Answer:
B
Step-by-step explanation:
The diagram shows four points through which the line of proportional relationship should pass. One of these points has coordinates (8,28).
The line representing proportional relationship is always straight line passing through the origin and has the equation
where k is the coefficient of proportionality.
Substitute coordinates of known point into the equation:
so the coefficient of proportionality is equal to 
