I can't understand this question write it properly please ok plz
Answer: a) 33.88 and b) 2.91.
Step-by-step explanation:
Since we have given that
Sample n₁ = 6
SS = 236
Sample n₂ = 12
SS = 340
So, we need to find the following:
a. Find the pooled variance for the two samples.
![S_{p^2}=\dfrac{SS_1+SS_2}{n_1+n_2-1}](https://tex.z-dn.net/?f=S_%7Bp%5E2%7D%3D%5Cdfrac%7BSS_1%2BSS_2%7D%7Bn_1%2Bn_2-1%7D)
So, it becomes,
![S_p^2=\dfrac{340+236}{12+6-1}=\dfrac{576}{17}=33.88](https://tex.z-dn.net/?f=S_p%5E2%3D%5Cdfrac%7B340%2B236%7D%7B12%2B6-1%7D%3D%5Cdfrac%7B576%7D%7B17%7D%3D33.88)
b. Compute the estimated standard error for the sample mean difference.
![SE=S_p\times \sqrt{\dfrac{1}{n_1}+\dfrac{1}{n_2}}\\\\SE=\sqrt{33.88}\times \sqrt{\dfrac{1}{6}+\dfrac{1}{12}}\\\\SE=5.82\times \sqrt{\dfrac{2+1}{12}}\\\\SE=5.82\times \sqrt{\dfrac{3}{12}}\\\\SE=5.82\times \sqrt{\dfrac{1}{4}}\\\\SE=5.82\times \dfrac{1}{2}\\\\SE=2.91](https://tex.z-dn.net/?f=SE%3DS_p%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B1%7D%7Bn_1%7D%2B%5Cdfrac%7B1%7D%7Bn_2%7D%7D%5C%5C%5C%5CSE%3D%5Csqrt%7B33.88%7D%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B6%7D%2B%5Cdfrac%7B1%7D%7B12%7D%7D%5C%5C%5C%5CSE%3D5.82%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B2%2B1%7D%7B12%7D%7D%5C%5C%5C%5CSE%3D5.82%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B3%7D%7B12%7D%7D%5C%5C%5C%5CSE%3D5.82%5Ctimes%20%5Csqrt%7B%5Cdfrac%7B1%7D%7B4%7D%7D%5C%5C%5C%5CSE%3D5.82%5Ctimes%20%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5CSE%3D2.91)
Hence, a) 33.88 and b) 2.91.
In mathematics, the term "center of dilation" refers to a constant point on a surface from which all other points are either enlarged or compressed. The center of dilation and the scale factor comprise the two properties of a dilation.
Yes it is a 90 degree rotation clockwise.
Answer with Step-by-step explanation:
We are given that
Height of ball after t seconds is given by
![s(t)=-4t^2+20t+2](https://tex.z-dn.net/?f=s%28t%29%3D-4t%5E2%2B20t%2B2)
a.Substitute the value of t=1
![s(1)=-4(1)+20(1)+2=-4+20+2=18 ft](https://tex.z-dn.net/?f=s%281%29%3D-4%281%29%2B20%281%29%2B2%3D-4%2B20%2B2%3D18%20ft)
b.Differentiate w.r.t x
![s'(t)=-8t+20](https://tex.z-dn.net/?f=s%27%28t%29%3D-8t%2B20)
![s'(t)=0](https://tex.z-dn.net/?f=s%27%28t%29%3D0)
![-8t+20=0](https://tex.z-dn.net/?f=-8t%2B20%3D0)
![8t=20](https://tex.z-dn.net/?f=8t%3D20)
![t=\frac{20}{8}=2.5](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B20%7D%7B8%7D%3D2.5)
Again differentiate w.r.t t
![s''(t)=-8](https://tex.z-dn.net/?f=s%27%27%28t%29%3D-8%3C0)
Hence, the height is maximum at t=2.5 s
![s(2.5)=-4(2.5)^2+20(2.5)+2=27](https://tex.z-dn.net/?f=s%282.5%29%3D-4%282.5%29%5E2%2B20%282.5%29%2B2%3D27)
Maximum height of the baseball=27 ft