Unless this is a trick question, I think 7 baskets. If you have 7 baskets then you can put 5 peaches in each basket. Hope this is right.
Answer:
a) ![\frac{72x^5}{9x^7}](https://tex.z-dn.net/?f=%5Cfrac%7B72x%5E5%7D%7B9x%5E7%7D)
b) ![=\frac{8}{x^2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8%7D%7Bx%5E2%7D)
c), Yes;![8x^2](https://tex.z-dn.net/?f=8x%5E2)
Step-by-step explanation:
Michael's Weight: ![72x^5](https://tex.z-dn.net/?f=72x%5E5)
Al's weight: ![9x^7](https://tex.z-dn.net/?f=9x%5E7)
a) Ratio of Michael's weight to Al's weight: ![\frac{72x^5}{9x^7}](https://tex.z-dn.net/?f=%5Cfrac%7B72x%5E5%7D%7B9x%5E7%7D)
b) This ratio simplifies to: ![\frac{8\times 9x^5}{9x^5\timesx^2}](https://tex.z-dn.net/?f=%5Cfrac%7B8%5Ctimes%209x%5E5%7D%7B9x%5E5%5Ctimesx%5E2%7D)
![=\frac{8}{x^2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B8%7D%7Bx%5E2%7D)
c) Yes, If the exponent in each expression were negative, then we have:
Ratio of Michael's weight to Al's weight: ![\frac{72x^{-5}}{9x^{-7}}](https://tex.z-dn.net/?f=%5Cfrac%7B72x%5E%7B-5%7D%7D%7B9x%5E%7B-7%7D%7D)
This ratio simplifies to: ![8x^{-5--7}=8x^2](https://tex.z-dn.net/?f=8x%5E%7B-5--7%7D%3D8x%5E2)
The two ratios are not the same.
Explanation
Part A
We can use the formula below to find the mean.
![\text{Mean}=\sum ^{}_{}(\frac{fx}{f})](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Csum%20%5E%7B%7D_%7B%7D%28%5Cfrac%7Bfx%7D%7Bf%7D%29)
We will then have;
![\begin{gathered} \text{Mean = }\frac{5\times3+4\times1+5\times1+6\times2+7\times2+8\times4+9\times3+10\times1}{19}=\frac{15+4+5+12+14+32+27+10}{19} \\ =\frac{119}{19}=6.2632 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BMean%20%3D%20%7D%5Cfrac%7B5%5Ctimes3%2B4%5Ctimes1%2B5%5Ctimes1%2B6%5Ctimes2%2B7%5Ctimes2%2B8%5Ctimes4%2B9%5Ctimes3%2B10%5Ctimes1%7D%7B19%7D%3D%5Cfrac%7B15%2B4%2B5%2B12%2B14%2B32%2B27%2B10%7D%7B19%7D%20%5C%5C%20%3D%5Cfrac%7B119%7D%7B19%7D%3D6.2632%20%5Cend%7Bgathered%7D)
Mean = 6.2632
Part B
Since the data set is odd.
![\begin{gathered} \text{Median}=\frac{(n+1)}{2}^{th}\text{observation} \\ =\text{Value of }\frac{\text{(19+1)}}{2}^{th}\text{observation} \\ =\text{value of 10th observation} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BMedian%7D%3D%5Cfrac%7B%28n%2B1%29%7D%7B2%7D%5E%7Bth%7D%5Ctext%7Bobservation%7D%20%5C%5C%20%3D%5Ctext%7BValue%20of%20%7D%5Cfrac%7B%5Ctext%7B%2819%2B1%29%7D%7D%7B2%7D%5E%7Bth%7D%5Ctext%7Bobservation%7D%20%5C%5C%20%3D%5Ctext%7Bvalue%20of%2010th%20observation%7D%20%5Cend%7Bgathered%7D)
Answer: From the column of cumulative frequency cf, the median is 7
The prime factorization of 18 is: 2 x 3 x 3.
The prime factorization of 45 is: 3 x 3 x 5.
The prime factors and multiplicities 18 and 45 have in common are: 3 x 3.
3 x 3 is the gcf of 18 and 45.
gcf(18,45) = 9.
V = s³. Therefore, s = ³√ V
Hope that helps you