Given:
The given sum is:
![\sum _{k=4}^9(5k+3)](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29)
To find:
The expanded form and find the sum.
Solution:
We have,
![\sum _{k=4}^9(5k+3)](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29)
The expanded form of given sum is:
![\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29%3D%285%284%29%2B3%29%2B%285%285%29%2B3%29%2B%285%286%29%2B3%29%2B%285%287%29%2B3%29%2B%285%288%29%2B3%29%2B%285%289%29%2B3%29)
![\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29%3D%2820%2B3%29%2B%2825%2B3%29%2B%2830%2B3%29%2B%2835%2B3%29%2B%284%2B3%29%2B%2845%2B3%29)
![\sum _{k=4}^9(5k+3)=23+28+33+38+43+48](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29%3D23%2B28%2B33%2B38%2B43%2B48)
![\sum _{k=4}^9(5k+3)=213](https://tex.z-dn.net/?f=%5Csum%20_%7Bk%3D4%7D%5E9%285k%2B3%29%3D213)
Therefore, the correct option is C.
Answer:
If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams
Step-by-step explanation:
Mean = ![\mu = 464](https://tex.z-dn.net/?f=%5Cmu%20%3D%20464)
Standard deviation =![\sigma = 6](https://tex.z-dn.net/?f=%5Csigma%20%3D%206)
We are supposed to find If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than how many grams i.e.P(X>x)=0.02
The mean weight is in the highest 2%, you want to go to a z-table and find the z-score that where the area to the left of the curve is closest to 0.98.
n = 27
Refer the z -table
P(Z>x)=2.06
![\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}=2.06\\\frac{x-464}{\frac{6}{\sqrt{27}}}=2.06\\x-464=2.06 \times \frac{6}{\sqrt{27}}\\x=(2.06 \times \frac{6}{\sqrt{27}})+464\\x=466.37](https://tex.z-dn.net/?f=%5Cfrac%7Bx-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%3D2.06%5C%5C%5Cfrac%7Bx-464%7D%7B%5Cfrac%7B6%7D%7B%5Csqrt%7B27%7D%7D%7D%3D2.06%5C%5Cx-464%3D2.06%20%5Ctimes%20%5Cfrac%7B6%7D%7B%5Csqrt%7B27%7D%7D%5C%5Cx%3D%282.06%20%5Ctimes%20%5Cfrac%7B6%7D%7B%5Csqrt%7B27%7D%7D%29%2B464%5C%5Cx%3D466.37)
So, If 27 fruits are picked at random, then 2% of the time, their mean weight will be greater than 466.37 grams
A is 0.0028
and B is 0.054
B. Domain: [-3, 0]; Range: [- 2, 2]
domain is the x axis, range is the y axis
-7x+6y-6x is simplified to be -13x+6y.