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.
Answer: 
Step-by-step explanation:
We know that the standard quadratic equation is ax^2+bx+c=0
Let's compare all the given equation to it and , find discriminant.
1. a=2, b= -7, c=-9
So it has 2 real number solutions.
2. a=1, b=-4, c=4
So it has only 1 real number solution.
3. a=4, b=-3, c=-1
So it has 2 real number solutions.
4. a=1, b=-2, c=-8
So it has 2 real number solutions.
5. a=3, b=5, c=3
Thus it does not has real solutions.
Answer:
Step-by-step explanation:
![volume = \frac{4}{3} \pi {r}^{3} \\ \\ 288\pi = \frac{4}{3} \pi {r}^{3} \\ \\ 3(288\pi) = 4\pi {r}^{3} \\ \\ \frac{3(288\pi)}{4\pi} = {r}^{3} \\ \\ 216 = {r}^{3} \\ \\ r = \sqrt[3]{216} \\ r = 6](https://tex.z-dn.net/?f=volume%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20288%5Cpi%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%203%28288%5Cpi%29%20%3D%204%5Cpi%20%7Br%7D%5E%7B3%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B3%28288%5Cpi%29%7D%7B4%5Cpi%7D%20%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20216%20%3D%20%20%7Br%7D%5E%7B3%7D%20%20%5C%5C%20%20%5C%5C%20r%20%3D%20%20%5Csqrt%5B3%5D%7B216%7D%20%20%5C%5C%20r%20%3D%206)
Answer:22
Step-by-step explanation:
10x2+1x2=
20+2
=22
Can you insert a photo of the question please it would greatly help me answer this
