It will take 4.3 weeks to complete.
71.25 hours / 16.5 hours per week = 4.3
The third one or last one, i’m thinking the third though
After because if you use it before the discount then the final price will be 1.50 but if you use it after the discount, then the final price is 1 dollar . 4 dollar with 50% discount is 2 dollar, and 2-1 is 1. 4-1 is 3 and 3 dollar with 50% discount is 1.50 dollar
Answer:
(121 - x2) / (11 - x)
Step-by-step explanation:
Answer:
The probability that no more than 6 students belong to a ethnic minority is 0.9815.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?</em>
We can model this with a random variable, with sample size n=10 and probability of success p=0.33.
The probability that k answers are guessed right in the sample is:
![P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}](https://tex.z-dn.net/?f=P%28x%3Dk%29%3D%5Cdbinom%7Bn%7D%7Bk%7Dp%5Ek%281-p%29%5E%7Bn-k%7D%3D%5Cdbinom%7B10%7D%7Bk%7D%5Ccdot0.33%5Ek%5Ccdot0.67%5E%7B10-k%7D)
We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:
![P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\](https://tex.z-dn.net/?f=P%28x%5Cleq6%29%3DP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%2BP%28x%3D3%29%2BP%28x%3D4%29%2BP%28x%3D5%29%2BP%28x%3D6%29%5C%5C%5C%5C%5C%5C)
![P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\](https://tex.z-dn.net/?f=P%28x%3D0%29%3D%5Cdbinom%7B10%7D%7B0%7D%5Ccdot0.33%5E%7B0%7D%5Ccdot0.67%5E%7B10%7D%3D1%5Ccdot1%5Ccdot0.0182%3D0.0182%5C%5C%5C%5C%5C%5CP%28x%3D1%29%3D%5Cdbinom%7B10%7D%7B1%7D%5Ccdot0.33%5E%7B1%7D%5Ccdot0.67%5E%7B9%7D%3D10%5Ccdot0.33%5Ccdot0.0272%3D0.0898%5C%5C%5C%5C%5C%5CP%28x%3D2%29%3D%5Cdbinom%7B10%7D%7B2%7D%5Ccdot0.33%5E%7B2%7D%5Ccdot0.67%5E%7B8%7D%3D45%5Ccdot0.1089%5Ccdot0.0406%3D0.1990%5C%5C%5C%5C%5C%5CP%28x%3D3%29%3D%5Cdbinom%7B10%7D%7B3%7D%5Ccdot0.33%5E%7B3%7D%5Ccdot0.67%5E%7B7%7D%3D120%5Ccdot0.0359%5Ccdot0.0606%3D0.2614%5C%5C%5C%5C%5C%5C)
![P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\](https://tex.z-dn.net/?f=P%28x%3D4%29%3D%5Cdbinom%7B10%7D%7B4%7D%5Ccdot0.33%5E%7B4%7D%5Ccdot0.67%5E%7B6%7D%3D210%5Ccdot0.0119%5Ccdot0.0905%3D0.2253%5C%5C%5C%5C%5C%5CP%28x%3D5%29%3D%5Cdbinom%7B10%7D%7B5%7D%5Ccdot0.33%5E%7B5%7D%5Ccdot0.67%5E%7B5%7D%3D252%5Ccdot0.0039%5Ccdot0.135%3D0.1332%5C%5C%5C%5C%5C%5CP%28x%3D6%29%3D%5Cdbinom%7B10%7D%7B6%7D%5Ccdot0.33%5E%7B6%7D%5Ccdot0.67%5E%7B4%7D%3D210%5Ccdot0.0013%5Ccdot0.2015%3D0.0547%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C)
![P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815](https://tex.z-dn.net/?f=P%28x%5Cleq6%29%3D0.0182%2B0.0898%2B0.1990%2B0.2614%2B0.2253%2B0.1332%2B0.0547%5C%5C%5C%5C%5C%5CP%28x%5Cleq6%29%3D0.9815)
The probability that 6 or less students belong to a ethnic minority is 0.9815.