Sub x = 2-y^2 to Q, we get:
Q = 3(2-y^2)*y^2
let y^2 = k
Q = 3(2-k)k = 3(2k-k^2)
2k-k^2 has a max when k = 1
Then y^2 = 1 -> y = 1 or -1
Answer: 0.0548
Step-by-step explanation:
Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.
Let 
represents the sample mean GPA for each student.
Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:
![P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z](https://tex.z-dn.net/?f=P%28%5Coverline%7BX%7D%3E3.42%29%3DP%28%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%3E%5Cdfrac%7B3.42-3.5%7D%7B%5Cdfrac%7B0.5%7D%7B%5Csqrt%7B100%7D%7D%7D%29%5C%5C%5C%5C%3DP%28Z%3E%5Cdfrac%7B-0.08%7D%7B%5Cdfrac%7B0.5%7D%7B10%7D%7D%29%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3DP%28Z%3E1.6%29%5C%5C%5C%5C%3D1-P%28Z%3C1.6%29%5C%5C%5C%5C%3D1-0.9452%3D0.0548)
hence, the required probability is 0.0548.
If you apply the or both
Only 1 of the students would need to know the "or both", therefore maximizing the remaining amount of students you can put in.
Gerald, let's call him, knows French AND German, so there's only one less student that knows french and german. Gerald is 1 student.
MAXIMUM:
There are now 14 monolinguistic French speakers and 16 monolinguistic German's, 30 students + Gerald=31.
Minimum:
As a bonus, the minimum is 15 students knowing french AND German and only 2 monolinguistic German speakers, so 17.
Answer:
C = 0.65x + 145
Step-by-step explanation:
Assume:
Number of miles = x
Annual maintenance = $145
Total reimbursement = C = $0.65*x + $145 = $0.65x + $145
Answer:
j
Step-by-step explanation:
