Answer:
She has 42 pieces of wood each of 1 inch of length.
Step-by-step explanation:
Amy has 42 inches piece of wood.
She has to cut an inch.
After cutting pieces of inch each she counts the pieces to be 42.
Mathematically
Total length / unit lenght = Number of pieces
42 inches/ 1 inch= 42 pieces.
She has 42 pieces of wood each of 1 inch of length.
Answer:
answer????
Step-by-step explanation:
Answer:
The lower bound is,
and the upper bound is
.
Step-by-step explanation:
Let the random variable <em>X</em> follows a normal distribution with mean <em>μ </em>and standard deviation <em>σ</em>.
The the random variable <em>Z, </em>defined as
is standardized random variable also known as a standard normal random variable. The random variable
.
The standard normal random variable has a symmetric distribution.
It is provided that
.
Determine the upper and lower bound as follows:
![P(-z\leq Z\leq z)=0.51\\P(Z\leq z)-P(Z\leq -z)=0.51\\P(Z\leq z)-[1-P(Z\leq z)]=0.51\\2P(Z\leq z)-1=0.51\\2P(Z\leq z)=1.51\\P(Z\leq z)=0.755](https://tex.z-dn.net/?f=P%28-z%5Cleq%20Z%5Cleq%20z%29%3D0.51%5C%5CP%28Z%5Cleq%20z%29-P%28Z%5Cleq%20-z%29%3D0.51%5C%5CP%28Z%5Cleq%20z%29-%5B1-P%28Z%5Cleq%20z%29%5D%3D0.51%5C%5C2P%28Z%5Cleq%20z%29-1%3D0.51%5C%5C2P%28Z%5Cleq%20z%29%3D1.51%5C%5CP%28Z%5Cleq%20z%29%3D0.755)
Use a standard normal table to determine the value of <em>z.</em>
The value of <em>z</em> such that P (Z ≤ z) = 0.755 is 0.69.
The lower bound is,
and the upper bound is
.
Answer:
X >= 7
Step-by-step explanation:
7x + 8 >= 57
7x >= 57-8
7x >= 49
x >= 49/7
x >= 7
Assuming the area below the line y=0 (i.e. x>1) does NOT count, the area to be rotated is shown in the graph attached.
A. Again, using Pappus's theorem,
Area, A = (2/3)*1*(1-(-1))=4/3 (2/3 of the enclosing rectangle, or you can integrate)
Distance of centroid from axis of rotation, R = (2-0) = 2
Volume = 2 π RA = 2 π 2 * 4/3 = 16 π / 3 (approximately = 16.76 units)
B. By integration, using the washer method
Volume =


![=2\pi[x^4/4-2x^3/3-x^2/2+2x]_{-1}^{1}](https://tex.z-dn.net/?f=%3D2%5Cpi%5Bx%5E4%2F4-2x%5E3%2F3-x%5E2%2F2%2B2x%5D_%7B-1%7D%5E%7B1%7D)
![=2\pi([1/4-2/3-1/2+2]-[1/4+2/3-1/2-2])](https://tex.z-dn.net/?f=%3D2%5Cpi%28%5B1%2F4-2%2F3-1%2F2%2B2%5D-%5B1%2F4%2B2%2F3-1%2F2-2%5D%29)

= 16 π /3 as before