Answer:
4
Step-by-step explanation:
The volume of a cube can be represented as s^3 = v, where s = side and v = volume. In this case, we're given the volume as 64, so s^3 = 64. To solve this problem, we first have to know what a cube root is.
What's a cube root?
- The cube root of a number is the number you multiply by itself 3 times to get another number.
- One common cube is 27, and the cube root of it is 3 because 3 x 3 x 3 = 27.
Given the information above, let's go in order with the list of cube roots to see which one has a cube of 64.
- 1: 1 x 1 x 1 = 1.
- 2: 2 x 2 x 2 = 8.
- 3: 3 x 3 x 3 = 27.
- 4: 4 x 4 x 4 = 64. (This is the cube root!)
We found the cube root of 64, or the side of the cube with a volume of 64. The side of the cube, therefore, is 4.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
B and E
Step-by-step explanation:
The 2 in front of the x^3 stretches it vertically and the +8 shifts it up.
a. In order for to be a PDF, needs to be non-negative (it is) and the integral over its support must evaluate to 1. is symmetric about , i.e. even, so
and so is indeed a PDF.
b. Let be a random variable with as its PDF. Then
The integrand is odd, so the integral vanishes and the mean is .
The variance of is
The second moment is
This integrand is even, so
Integrate by parts, taking
so that
Integrate by parts again, this time with
and so the variance is .
<span>=<span><span>(<span><span>4x</span>+<span>−5</span></span>)</span><span>(<span><span>3x</span>+2</span>)</span></span></span><span>=<span><span><span><span><span>(<span>4x</span>)</span><span>(<span>3x</span>)</span></span>+<span><span>(<span>4x</span>)</span><span>(2)</span></span></span>+<span><span>(<span>−5</span>)</span><span>(<span>3x</span>)</span></span></span>+<span><span>(<span>−5</span>)</span><span>(2)</span></span></span></span><span>=<span><span><span><span>12<span>x2</span></span>+<span>8x</span></span>−<span>15x</span></span>−10</span></span><span>=<span><span><span>12<span>x2</span></span>−<span>7x</span></span>−<span>10</span></span></span>
She was unable to salvage 4.8% of the total number of samples. If she was able to salvage 12 of the 24 improperly stored samples, then she was unable to salvage 12 of them. Divide the number that was not salvaged (12) by the total number of samples (250), then multiply by 100 to get the percentage.