Answer:
![\displaystyle m=\frac{2}{25}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B2%7D%7B25%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Slope Formula:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
Point (200, 14)
Point (225, 16)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>
- Substitute in points [SF]:
![\displaystyle m=\frac{16-14}{225-200}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B16-14%7D%7B225-200%7D)
- [Fraction] Subtract:
![\displaystyle m=\frac{2}{25}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B2%7D%7B25%7D)
Answer:
P(6) = 5
Step-by-step explanation:
The dice is cast 30 times (k = 30)
So if the big numbers apply, then you would expect the outcome to be evenly distributed, meaning
5 x 1
5 x 2
5 x 3
5 x 4
5 x 5
5 x 6
____ +
30 casts in total (evenly distributed over all numbers of the dice)
P(6) = 1/6 * 30
P(6) = 5
Answer:
0.38% probability that the sample contains exactly two defective parts.
Step-by-step explanation:
For each part, there are only two possible outcomes. Either it is defective, or it is not. The probabilities for each part being defective are independent from each other. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![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)
And p is the probability of X happening.
In this problem we have that:
![n = 5, p = 0.02](https://tex.z-dn.net/?f=n%20%3D%205%2C%20p%20%3D%200.02)
What is the probability that the sample contains exactly two defective parts?
This is ![P(X = 2)](https://tex.z-dn.net/?f=P%28X%20%3D%202%29)
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 2) = C_{5,2}.(0.02)^{2}.(0.98)^{3} = 0.0038](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20C_%7B5%2C2%7D.%280.02%29%5E%7B2%7D.%280.98%29%5E%7B3%7D%20%3D%200.0038)
0.38% probability that the sample contains exactly two defective parts.
Answer:
38/7
Step-by-step explanation: