Answer:
y = 11
Explanation:
8(y − 5) = 6y − 18
Simplify both sides of the equation
8(y − 5) = 6y − 18
(8)(y) + (8)(−5) = 6y + −18( Distribute)
8y + −40 = 6y + −18
8y − 40 = 6y − 18
Subtract 6y from both sides
8y − 40 − 6y = 6y − 18 − 6y
2y − 40 = −18
Add 40 to both sides
2y − 40 + 40 = −18 + 40
2y = 22
Step 4: Divide both sides by 2
2y / 2 = 22 / 2
y = 11
Let A = {1, 2, 3, 4,}, B = {3, 4, 5, 6, 7}, and C = {2, 3, 5, 7} Find: B∩C
natka813 [3]
The notation
![B \cap C](https://tex.z-dn.net/?f=B%20%5Ccap%20C)
means "B intersect C" telling you to look at the intersecting, or overlapping, region of the Venn Diagram. This is where the common values that are found in BOTH set B and set C.
The values {3, 5, 7} are in both set B and set C.
So that is why
Answer:
![a. \ P(X=0)=5.574\times10^{-7}](https://tex.z-dn.net/?f=a.%20%5C%20P%28X%3D0%29%3D5.574%5Ctimes10%5E%7B-7%7D)
![b. \ \ P(X\leq 1)=8.584\times10^{-6}](https://tex.z-dn.net/?f=b.%20%5C%20%5C%20P%28X%5Cleq%201%29%3D8.584%5Ctimes10%5E%7B-6%7D)
![c.\ \ \ P(X\geq 4)=0.9997](https://tex.z-dn.net/?f=c.%5C%20%5C%20%5C%20P%28X%5Cgeq%204%29%3D0.9997)
Step-by-step explanation:
a. #We notice this is a Poisson probability function expressed as:
![f(x)=\frac{\mu^xe^{-\mu}}{x!}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D)
x-number of occurrences in a given interval.
-mean occurrences of the event
-The mean is calculated as:
![\mu=\frac{14.4}{4}=3.6](https://tex.z-dn.net/?f=%5Cmu%3D%5Cfrac%7B14.4%7D%7B4%7D%3D3.6)
#the probability of no accidents in a 15-minute period is :
![P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X=0)=\frac{14.4^0e^{-14.4}}{0!}\\\\=5.574\times10^{-7}](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D%5C%5C%5C%5CP%28X%3D0%29%3D%5Cfrac%7B14.4%5E0e%5E%7B-14.4%7D%7D%7B0%21%7D%5C%5C%5C%5C%3D5.574%5Ctimes10%5E%7B-7%7D)
Hence, the probability of no accident in a 15-min period is ![=5.574\times10^{-7}](https://tex.z-dn.net/?f=%3D5.574%5Ctimes10%5E%7B-7%7D)
b. The the probability of at least one accident in a 15-minute period. is calculated as:
![P(x)=\frac{\mu^xe^{-\mu}}{x!}\\\\P(X\leq 1)=\frac{14.4^0e^{-14.4}}{0!}+\frac{14.4^1e^{-14.4}}{1!}\\\\=5.574\times10^{-7}+8.026\times 10^{-6}\\\\=8.584\times 10^{-6}](https://tex.z-dn.net/?f=P%28x%29%3D%5Cfrac%7B%5Cmu%5Exe%5E%7B-%5Cmu%7D%7D%7Bx%21%7D%5C%5C%5C%5CP%28X%5Cleq%201%29%3D%5Cfrac%7B14.4%5E0e%5E%7B-14.4%7D%7D%7B0%21%7D%2B%5Cfrac%7B14.4%5E1e%5E%7B-14.4%7D%7D%7B1%21%7D%5C%5C%5C%5C%3D5.574%5Ctimes10%5E%7B-7%7D%2B8.026%5Ctimes%2010%5E%7B-6%7D%5C%5C%5C%5C%3D8.584%5Ctimes%2010%5E%7B-6%7D)
Hence, the probability of at least one accident in a 15-minute period is ![8.584\times10^{-6}](https://tex.z-dn.net/?f=8.584%5Ctimes10%5E%7B-6%7D)
c. The probability of four or more accidents in a 15-minute period is calculated as:
![P(X\geq 4)=1-P(X\leq 3)=1-[P(X=0)+P(X1)+P(X=2)+P(X=3)]\\\\=1-[5.574\times10^{-7}+a. \ 8.026\times10^{-6}+\frac{14.4^2e^{-14.4}}{2!}+\frac{14.4^3e^{-14.4}}{3!}]\\\\=1-[8.584\times 10^{-6}+5.779\times10^{-5}+2.774\times10^{-4}]\\\\=0.9997](https://tex.z-dn.net/?f=P%28X%5Cgeq%204%29%3D1-P%28X%5Cleq%203%29%3D1-%5BP%28X%3D0%29%2BP%28X1%29%2BP%28X%3D2%29%2BP%28X%3D3%29%5D%5C%5C%5C%5C%3D1-%5B5.574%5Ctimes10%5E%7B-7%7D%2Ba.%20%5C%208.026%5Ctimes10%5E%7B-6%7D%2B%5Cfrac%7B14.4%5E2e%5E%7B-14.4%7D%7D%7B2%21%7D%2B%5Cfrac%7B14.4%5E3e%5E%7B-14.4%7D%7D%7B3%21%7D%5D%5C%5C%5C%5C%3D1-%5B8.584%5Ctimes%2010%5E%7B-6%7D%2B5.779%5Ctimes10%5E%7B-5%7D%2B2.774%5Ctimes10%5E%7B-4%7D%5D%5C%5C%5C%5C%3D0.9997)
Hence,the probability of four or more accidents in a 15-minute period. is 0.9997
Answer:
$64222.22
Step-by-step explanation:
If we call the original value as x, we can write:
1445 = x * (0.15)² (Note: We write 1 - 0.85 = 0.15 and not 0.85 because 0.85 is the decay factor)
1445 = 0.0225x
x ≈ 64222.22
According to the number of cups, 564 people can be invited to the party.
Step-by-step explanation:
This is a simple question of cross multiplication
<u>DATA:</u>
<em>1. Total number of cups of yogurt is 423 cups</em>
<em>2. 1 serving =
th of a cup</em>
<em>3. Each guest gets
of a cup or 1 serving</em>
<em>4. Find out how many guests can be invited to the party,</em>
Cups : People
: 1
423 : p
<em>5. Cross multiply</em>
p = 423 x 1
3p = 423 x 4
p = ![\frac{1692}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1692%7D%7B3%7D)
p = 564
Therefore, according to the number of cups, 564 people can be invited to the party.
Key word: Multiplication
Learn more about multiplication at
#LearnwithBrainly