The sixteen pack because $6.24 divided by 16 is 0.39 per dinner roll
Answer:
Decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence that indicate that there is a significant difference between the two treatments
Step-by-step explanation:
From the question we are told that
The sample size is n = 12
The first mean is ![M_1 = 55](https://tex.z-dn.net/?f=M_1%20%20%3D%20%2055)
The variance is ![s^2_1 = 8](https://tex.z-dn.net/?f=s%5E2_1%20%3D%20%208)
The second mean is
The second variance is ![s^2_2 = 4](https://tex.z-dn.net/?f=s%5E2_2%20%3D%20%204)
Let the level of significance be ![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.05)
The null hypothesis is ![H_o : M_1 = M_2](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20M_1%20%3D%20M_2)
The alternative hypothesis is ![H_a : M_1 \ne M_2](https://tex.z-dn.net/?f=H_a%20%20%3A%20%20M_1%20%5Cne%20M_2)
Generally the test statistics is mathematically
![t = \frac{M_1 - M_2 }{ \sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BM_1%20-%20M_2%20%7D%7B%20%5Csqrt%7B%5Cfrac%7Bs_1%5E2%7D%7Bn_1%7D%20%2B%5Cfrac%7Bs_2%5E2%7D%7Bn_2%7D%7D%20%7D)
=> ![t = \frac{55 - 52 }{ \sqrt{\frac{8}{12} +\frac{4}{12 }} }](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B55%20-%2052%20%7D%7B%20%5Csqrt%7B%5Cfrac%7B8%7D%7B12%7D%20%2B%5Cfrac%7B4%7D%7B12%20%7D%7D%20%7D)
=>
Generally the degree of freedom is mathematically represented as
![df = 12 -1](https://tex.z-dn.net/?f=df%20%3D%2012%20-1)
=>
Generally from the t- distriibution table the critical value of
at a degree of freedom of
is
![t_{0.05 , 11} = 2.20098516](https://tex.z-dn.net/?f=t_%7B0.05%20%2C%2011%7D%20%3D%20%202.20098516)
Here given that the critical value is greater than the t statistics value the
Decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence that indicate that there is a significant difference between the two treatments
Answer:
![=\frac{2x-3}{x}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2x-3%7D%7Bx%7D)
Step-by-step explanation:
![=6x^2\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=\frac{3x\left(4x-6\right)}{2x\cdot \:3x}\\2x\cdot \:3x=6x^2\\=\frac{3x\left(4x-6\right)}{6x^2}\\\mathrm{Cancel\:}\frac{3x\left(4x-6\right)}{6x^2}:\quad \frac{4x-6}{2x}\\=\frac{4x-6}{2x}\\\mathrm{Factor}\:4x-6:\quad 2\left(2x-3\right)\\=\frac{2\left(2x-3\right)}{2x}\\\mathrm{Divide\:the\:numbers:}\:\frac{2}{2}=1\\=\frac{2x-3}{x}](https://tex.z-dn.net/?f=%3D6x%5E2%5C%5C%5Cmathrm%7BRemove%5C%3Aparentheses%7D%3A%5Cquad%20%5Cleft%28a%5Cright%29%3Da%5C%5C%3D%5Cfrac%7B3x%5Cleft%284x-6%5Cright%29%7D%7B2x%5Ccdot%20%5C%3A3x%7D%5C%5C2x%5Ccdot%20%5C%3A3x%3D6x%5E2%5C%5C%3D%5Cfrac%7B3x%5Cleft%284x-6%5Cright%29%7D%7B6x%5E2%7D%5C%5C%5Cmathrm%7BCancel%5C%3A%7D%5Cfrac%7B3x%5Cleft%284x-6%5Cright%29%7D%7B6x%5E2%7D%3A%5Cquad%20%5Cfrac%7B4x-6%7D%7B2x%7D%5C%5C%3D%5Cfrac%7B4x-6%7D%7B2x%7D%5C%5C%5Cmathrm%7BFactor%7D%5C%3A4x-6%3A%5Cquad%202%5Cleft%282x-3%5Cright%29%5C%5C%3D%5Cfrac%7B2%5Cleft%282x-3%5Cright%29%7D%7B2x%7D%5C%5C%5Cmathrm%7BDivide%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A%5Cfrac%7B2%7D%7B2%7D%3D1%5C%5C%3D%5Cfrac%7B2x-3%7D%7Bx%7D)
Answer:
2
Step-by-step explanation:
X= 2
just make a graph and you got the answer
.
X + 3x + 4x = 56
8x = 56
x = 7
The shortest piece is 7 inches
The middle piece is 7*3 = 21 inches.
The longest piece is 4*7 = 28 inches
Check
7 + 21 + 28 = 56 It does check and the lengths are correct.