Answer:
upper control limit = 6.058
lower control limit = 0.442
Step-by-step explanation:
Given that:
The numbers of sample n Mogul executives took = 8 Eagletrons at a time.
They find out that the average sample mean is 88.50 mph and;
the average range
is 3.25 mph.
From the tables:
![\text {Table values for n = 8 } \left \{ {{D_4=1.864} \atop {D_3=0.136}} \right.](https://tex.z-dn.net/?f=%5Ctext%20%7BTable%20values%20for%20n%20%3D%208%20%7D%20%5Cleft%20%5C%7B%20%7B%7BD_4%3D1.864%7D%20%5Catop%20%7BD_3%3D0.136%7D%7D%20%5Cright.)
Control Limit =
= 3.25
Therefore; the upper control limit and the lower control limit can be computed as follows:
upper control limit = ![D_4 \overline r](https://tex.z-dn.net/?f=D_4%20%5Coverline%20r)
upper control limit = 1.864(3.25)
upper control limit = 6.058
lower control limit = ![D_3 \overline r](https://tex.z-dn.net/?f=D_3%20%5Coverline%20r)
lower control limit = 0.136(3.25)
lower control limit = 0.442
Answer:
<u>Option A. 11.15 in³ </u>
Step-by-step explanation:
The question is as following:
A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom. The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
A.) 11.15 in³
B.) 11.22 in³
C.) 0.07 in³
D.) 33.67 in³
=========================================
<u>Solution:</u>
Volume of the cone = π r² h/3
Vcone = 3.14 * (1.75in)² * 3.5in/3
Vcone = 3.14 * 3.0625 in² * 1.167
Vcone = 11.22 in³
Volume of the gum ball = 4/3 * π * r³
Vball = 4/3 * 3.14 * (0.5in/2)³
Vball = 4/3 * 3.14 * (0.25in)³
Vball = 4/3 * 3.14 * 0.015625 in³
Vball = 0.065 in³
11.22 in³ - 0.065 in³ = 11.155 in³
<u>The answer is option A. 11.15 in³ </u>
Answer:
1140
Step-by-step explanation:
3x(x + 2) - 3x
x = 19
3 * 19( 19 + 2) - 3 * 19
3 * 19(21) - 3 * 19
3 * 19 = 57
57(21) - 3 * 19
57 * 21 = 1197
1197 - 57
1140
Hope this helped!
Answer:
There is no greatest perfect square of 1290
Step-by-step explanation:
Using the combination formula, it is found that:
a) 180 different starting lineups can be created.
b) The probability that mary and alice will get on the lineup is
.
The order in which the players are chosen is not important, hence the <em>combination formula </em>is used to solve this question.
<h3>What is the combination formula?</h3>
is the number of different combinations of x objects from a set of n elements, given by:
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
Item a:
The lineup is composed by:
- 2 guards from a set of 5.
- 2 forwards from a set of 4.
- 1 center from a set of 3.
Hence the number of lineups is given by:
![N = C_{5,2}C_{4,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{4!}{2!2!} \times \frac{3!}{1!2!} = 180](https://tex.z-dn.net/?f=N%20%3D%20C_%7B5%2C2%7DC_%7B4%2C2%7DC_%7B3%2C1%7D%20%3D%20%5Cfrac%7B5%21%7D%7B2%213%21%7D%20%5Ctimes%20%5Cfrac%7B4%21%7D%7B2%212%21%7D%20%5Ctimes%20%5Cfrac%7B3%21%7D%7B1%212%21%7D%20%20%3D%20180)
Item b:
The number of lineups with Mary and Alice are given as follows:
- 2 guards from a set of 5.
- Mary and 1 other forward from a set of 3.
Hence:
![n = C_{5,2}C_{3,1} = \frac{5!}{2!3!} \times \frac{3!}{1!2!} = 30](https://tex.z-dn.net/?f=n%20%3D%20C_%7B5%2C2%7DC_%7B3%2C1%7D%20%3D%20%5Cfrac%7B5%21%7D%7B2%213%21%7D%20%5Ctimes%20%5Cfrac%7B3%21%7D%7B1%212%21%7D%20%3D%2030)
Hence the probability is given by:
![p = \frac{30}{180} = \frac{1}{6}](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B30%7D%7B180%7D%20%3D%20%5Cfrac%7B1%7D%7B6%7D)
The probability that mary and alice will get on the lineup is
.
More can be learned about the combination formula at brainly.com/question/25821700
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