Check the picture below.
keep in mind that the yellow shaded area is the "true" region, namely where f(x) ⩾ 0, and the values "x" takes on are pretty much all real values.
Answer:
Sample number 3
Step-by-step explanation:
From the given information:
Sample Service life(hours) Total Mean(X)
1 2 3 4
1 495 500 505 500 2000 500
2 525 515 505 515 2060 515
3 470 480 460 470 1880 470
Total = ![\text{addition \ of \ numbers \ of \ observations}](https://tex.z-dn.net/?f=%5Ctext%7Baddition%20%20%5C%20of%20%5C%20numbers%20%5C%20of%20%5C%20observations%7D)
Mean = ![\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7Baddition%20%20%5C%20of%20%5C%20numbers%20%5C%20of%20%5C%20observations%7D%7D%7B4%7D)
Thus;
![UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480](https://tex.z-dn.net/?f=UCL%20%3D%20%5Cmu%2Bx%20%3D%20500%20%2B%2020%20%3D%20520%5C%5C%20%5C%5C%20%20LCL%3D%20%5Cmu%20-x%20%3D%20500%20-20%20%3D480)
To plot on an X_Bar chart, we have:
Sample Mean (X) UCL LCL
1 500 520 480
5 515 520 480
6 470 520 480
The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.
Answer: The answer is 2,713 in³
The volume (V) of the prop is the sum of the volume of cone (V1) and half of the volume of the sphere (V2): V = V1 + 1/2 * V2
Volume of the cone is:
V1 = π r² h / 3
According to the image,
h = 14 in
r = 9 in
and
π = 3.14
V1 = 3.14 * 9² * 14 / 3 = 1,186.92 in³
The volume of the sphere is:
V2 = π r³ * 4/3
According to the image,
r = 9 in
and
π = 3.14
V2 = 3.14 * 9³ * 4/3 = 3,052.08 in³
The volume of the prop is:
V = V1 + 1/2 * V2
V = 1,186.92 in³ + 1/2 * 3,052.08 in³
V = 1,186.92 in³ + 1,526.04 in³
V = 2,712.96 in³ ≈ 2,713 in³
Show that the angles A and B are congruent
Answer:
![\angle A =\angle B =90^\circ](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%5Cangle%20B%20%3D90%5E%5Ccirc)
Step-by-step explanation:
The diagram of the sled kite is attached below.
The central part of the kite is square.
We know by the property of a square that all its angles are congruent and equal to 90 degrees.
Therefore:
![\angle A =\angle B =90^\circ](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%5Cangle%20B%20%3D90%5E%5Ccirc)
Angles A and B are congruent.