Answer:
Mean = 75
Median = 73.5
Mode = 95
Range = 36
Step-by-step explanation:
Given:
Sort:
To find:
Mean:
![\displaystyle \large{\dfrac{1}{n}\sum_{i =1}^n x_i = \dfrac{x_1+x_2+x_3+...+x_n}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%20%3D1%7D%5En%20x_i%20%3D%20%5Cdfrac%7Bx_1%2Bx_2%2Bx_3%2B...%2Bx_n%7D%7Bn%7D%7D)
Sum of all data divides by amount.
![\displaystyle \large{\dfrac{59+60+70+77+89+95}{6}=\dfrac{450}{6}}\\\\\displaystyle \large{\therefore mean=75}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B59%2B60%2B70%2B77%2B89%2B95%7D%7B6%7D%3D%5Cdfrac%7B450%7D%7B6%7D%7D%5C%5C%5C%5C%5Cdisplaystyle%20%5Clarge%7B%5Ctherefore%20mean%3D75%7D)
Therefore, mean = 75
Median:
If it’s exact middle then that’s the median. However, if two data or values happen to be in <em>middle</em>:
![\displaystyle \large{\dfrac{x_1+x_2}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%7D)
From 59,60,70,77,89,95, since 70 and 77 are in middle:
![\displaystyle \large{\dfrac{70+77}{2} = \dfrac{147}{2}}\\\displaystyle \large{\therefore median = 73.5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B%5Cdfrac%7B70%2B77%7D%7B2%7D%20%3D%20%5Cdfrac%7B147%7D%7B2%7D%7D%5C%5C%5Cdisplaystyle%20%5Clarge%7B%5Ctherefore%20median%20%3D%2073.5%7D)
Therefore, median = 73.5
Mode:
The highest value or/and the highest amount of data. Mode can have more than one.
From sorted data, there are no repetitive data nor same data. Consider the highest value:
Therefore, mode = 95
Range:
or highest value - lowest value
Thus:
![\displaystyle \large{95-59 = 36}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clarge%7B95-59%20%3D%2036%7D)
Therefore, range = 36
Answer:
The 4th term in the sequence is -8.
Step-by-step explanation:
The nth term of the sequence B is given by:
![B(n) = (-2)^{n-1}](https://tex.z-dn.net/?f=B%28n%29%20%3D%20%28-2%29%5E%7Bn-1%7D)
So the fourth term will be given by:
B when n = 4, that is, B(4).
![B(4) = (-2)^{4-1} = (-2)^{3} = -8](https://tex.z-dn.net/?f=B%284%29%20%3D%20%28-2%29%5E%7B4-1%7D%20%3D%20%28-2%29%5E%7B3%7D%20%3D%20-8)
The 4th term in the sequence is -8.
Factory A can produce more machines. 30 more wil be more produced
Answer:
The exact volume of the cone is ![\frac{196}{3}\pi\ in^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B196%7D%7B3%7D%5Cpi%5C%20in%5E%7B3%7D)
Step-by-step explanation:
we know that
The volume of the cone is equal to
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
we have
![r=7\ in](https://tex.z-dn.net/?f=r%3D7%5C%20in)
![h=4\ in](https://tex.z-dn.net/?f=h%3D4%5C%20in)
substitute the values
![V=\frac{1}{3}\pi (7^{2})(4)=\frac{196}{3}\pi\ in^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%287%5E%7B2%7D%29%284%29%3D%5Cfrac%7B196%7D%7B3%7D%5Cpi%5C%20in%5E%7B3%7D)
2.5*6.4=16, 2.5*4.8=12. 12+12+16+16=56