Answer: do you need help with 1 and 2?
Step-by-step explanation:
Answer:
The nonzero value of c will be:
Step-by-step explanation:
Given the function
![f\left(x\right)=\:x^2-4x-c](https://tex.z-dn.net/?f=f%5Cleft%28x%5Cright%29%3D%5C%3Ax%5E2-4x-c)
![f\left(c\right)=\:c^2-4c-c](https://tex.z-dn.net/?f=f%5Cleft%28c%5Cright%29%3D%5C%3Ac%5E2-4c-c)
as
![f(c) = c](https://tex.z-dn.net/?f=f%28c%29%20%3D%20c)
so
![c=\:c^2-4c-c](https://tex.z-dn.net/?f=c%3D%5C%3Ac%5E2-4c-c)
switching the sides
![c^2-4c-c=c](https://tex.z-dn.net/?f=c%5E2-4c-c%3Dc)
subtract c from both sides
![c^2-4c-c-c=c-c](https://tex.z-dn.net/?f=c%5E2-4c-c-c%3Dc-c)
![c^2-6c=0](https://tex.z-dn.net/?f=c%5E2-6c%3D0)
![c\left(c-6\right)=0](https://tex.z-dn.net/?f=c%5Cleft%28c-6%5Cright%29%3D0)
Using the zero factor principle
![\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)](https://tex.z-dn.net/?f=%5C%3AIf%7D%5C%3Aab%3D0%5C%3A%5Cmathrm%7Bthen%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Bor%7D%5C%3Ab%3D0%5C%3A%5Cleft%28%5Cmathrm%7Bor%5C%3Aboth%7D%5C%3Aa%3D0%5C%3A%5Cmathrm%7Band%7D%5C%3Ab%3D0%5Cright%29)
![c=0\quad \mathrm{or}\quad \:c-6=0](https://tex.z-dn.net/?f=c%3D0%5Cquad%20%5Cmathrm%7Bor%7D%5Cquad%20%5C%3Ac-6%3D0)
so, the solutions to the quadratic equations are:
![c=0,\:c=6](https://tex.z-dn.net/?f=c%3D0%2C%5C%3Ac%3D6)
Therefore, a nonzero value of c will be:
<u>Given</u>:
Given that the data are represented by the box plot.
We need to determine the range and interquartile range.
<u>Range:</u>
The range of the data is the difference between the highest and the lowest value in the given set of data.
From the box plot, the highest value is 30 and the lowest value is 15.
Thus, the range of the data is given by
Range = Highest value - Lowest value
Range = 30 - 15 = 15
Thus, the range of the data is 15.
<u>Interquartile range:</u>
The interquartile range is the difference between the ends of the box in the box plot.
Thus, the interquartile range is given by
Interquartile range = 27 - 18 = 9
Thus, the interquartile range is 9.
Using the normal distribution, it is found that the probability is 0.16.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem, the mean and the standard deviation are given by, respectively,
.
The proportion of students between 45 and 67 inches is the p-value of Z when <u>X = 67 subtracted by the p-value of Z when X = 45</u>, hence:
X = 67:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{67 - 70}{3}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B67%20-%2070%7D%7B3%7D)
Z = -1
Z = -1 has a p-value of 0.16.
X = 45:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{45 - 70}{3}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B45%20-%2070%7D%7B3%7D)
Z = -8.3
Z = -8.3 has a p-value of 0.
0.16 - 0 = 0.16
The probability is 0.16.
More can be learned about the normal distribution at brainly.com/question/24663213