Answer: 0.8926
Step-by-step explanation:
Given : A shipment of 50 inexpensive digital watches, including 10 that are defective.
The probability that a digital watch is defective ![: p=\dfrac{10}{50}=0.2](https://tex.z-dn.net/?f=%3A%20p%3D%5Cdfrac%7B10%7D%7B50%7D%3D0.2)
Sample size : n=10
Also, they reject the whole shipment if 1 or more in the sample are found defective.
Using the binomial probability formula :
![P(x)=^nC_xp^x(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28x%29%3D%5EnC_xp%5Ex%281-p%29%5E%7Bn-x%7D)
Let x be the random variable that represents the number of defective watches.
The probability that the shipment will be rejected :-
![P(x\geq1)=1-P(0)\\\\=1-^{10}C_0(0.2)^0(0.8)^{10}\\\\=1-(0.8)^{10}=0.8926258176\approx0.8926](https://tex.z-dn.net/?f=P%28x%5Cgeq1%29%3D1-P%280%29%5C%5C%5C%5C%3D1-%5E%7B10%7DC_0%280.2%29%5E0%280.8%29%5E%7B10%7D%5C%5C%5C%5C%3D1-%280.8%29%5E%7B10%7D%3D0.8926258176%5Capprox0.8926)
Hence, the probability that the shipment will be rejected = 0.8926
Answer:
It is not a right angled troagle
Step-by-step explanation:
Given
Sides: 5m, 7m and 9m
Required
Is it a right angled triangle?
A triangle is right angled if:
![a^2 = b^2 + c^2](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2)
Where a is the longest side and b,c is any of the other.
So, we have:
![9^2 = 5^2 + 7^2](https://tex.z-dn.net/?f=9%5E2%20%3D%205%5E2%20%2B%207%5E2)
![81 = 25 + 49](https://tex.z-dn.net/?f=81%20%3D%2025%20%2B%2049)
![81 \neq 74](https://tex.z-dn.net/?f=81%20%5Cneq%2074)
Since they're not equal then it is not a right angled troagle
Hi your answer is going to be C. I'm great at math
Answer:
![m = -\frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
![y\ intercept = -1](https://tex.z-dn.net/?f=y%5C%20intercept%20%3D%20-1)
![y = -\frac{1}{2}x -1](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20-1)
Step-by-step explanation:
Given
![(x_1,y_1) = (-2,0)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%28-2%2C0%29)
![(x_2,y_2) = (0,-1)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%280%2C-1%29)
Required
Determine the slope and y intercept from graph
To calculate the slope, we have:
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{-1-0}{0 - (-2)}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1-0%7D%7B0%20-%20%28-2%29%7D)
![m = \frac{-1}{0 +2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%7D%7B0%20%2B2%7D)
![m = -\frac{1}{2}](https://tex.z-dn.net/?f=m%20%3D%20-%5Cfrac%7B1%7D%7B2%7D)
The y intercept is when ![x = 0](https://tex.z-dn.net/?f=x%20%3D%200)
So,
![y\ intercept = -1](https://tex.z-dn.net/?f=y%5C%20intercept%20%3D%20-1)
The equation is then calculated using:
![y = m(x - x_1) + y_1](https://tex.z-dn.net/?f=y%20%20%3D%20m%28x%20-%20x_1%29%20%2B%20y_1)
This gives
![y = -\frac{1}{2}(x - (-2)) + 0](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x%20-%20%28-2%29%29%20%2B%200)
![y = -\frac{1}{2}(x - (-2))](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x%20-%20%28-2%29%29)
![y = -\frac{1}{2}(x +2)](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%28x%20%2B2%29)
![y = -\frac{1}{2}x -\frac{1}{2}*2](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20-%5Cfrac%7B1%7D%7B2%7D%2A2)
![y = -\frac{1}{2}x -1](https://tex.z-dn.net/?f=y%20%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx%20-1)
<em>See attachment for graph</em>