Answer:
157 - 70x
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5
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the image attached. For two triangles to be congruent, then the sides of UVW is equal to that of TSR
From the diagram given
TR = UW
Given
TR = 50
UW = 3z+14
Equate and find z;
3z+14 = 50
3z = 50-14
3z = 36
z = 36/3
z = 12
VW = RS
Given
VW = 27
RS = 5y - 33
Equate
5y-33 = 27
5y = 27+33
5y = 60
y = 60/5
y = 12
Also TS = UV
TS = 53
UV = 12x+7
Equate:
12x-7 = 53
12x = 53+7
12x = 60
x = 60/12
x = 5
Hence x = 5, y = 12 and z = 12
Answer:
The decision rule is
Reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The population mean is ![\mu = 5.6 \ pounds/inch^2](https://tex.z-dn.net/?f=%5Cmu%20%3D%20%205.6%20%20%5C%20pounds%2Finch%5E2)
The sample size is n = 160
The sample mean is ![\= x = 5.7 \ pounds/ inch^2](https://tex.z-dn.net/?f=%5C%3D%20%20x%20%3D%20%205.7%20%20%5C%20%20pounds%2F%20inch%5E2)
The variance is ![\sigma ^2 = 0.25](https://tex.z-dn.net/?f=%5Csigma%20%5E2%20%3D%20%200.25)
The level of significance is ![\alpha = 0.01](https://tex.z-dn.net/?f=%5Calpha%20%20%20%3D%20%200.01)
The null hypothesis is ![H_o : \mu = 5.6](https://tex.z-dn.net/?f=H_o%20%20%3A%20%20%5Cmu%20%20%3D%20%205.6)
The alternative hypothesis is ![H_a : \mu > 5.6](https://tex.z-dn.net/?f=H_a%20%3A%20%20%5Cmu%20%3E%205.6)
Generally the standard deviation is mathematically represented as
![\sigma = \sqrt{\sigma ^2 }](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%20%5Csqrt%7B%5Csigma%20%5E2%20%7D)
=>
=>
Generally the test statistics is mathematically represented as
![z = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }](https://tex.z-dn.net/?f=z%20%3D%20%20%5Cfrac%7B%5C%3D%20x%20%20-%20%5Cmu%20%7D%7B%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%20%20%7D%20%7D)
=>
=> ![z = 2.53](https://tex.z-dn.net/?f=z%20%3D%20%202.53)
From the z table the area under the normal curve to the left corresponding to 2.53 is
![p-value = P(Z > 2.53 ) =0.0057](https://tex.z-dn.net/?f=p-value%20%3D%20%20P%28Z%20%3E%20%202.53%20%29%20%3D0.0057)
From the value obtained we see that the
hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the believe that the valve performs above the specifications is true
I think you add both of them together and you get 145
Answer: ⇒ last options d. 16√5
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Step-by-step explanation:
First you had to add similar elements.
![13\sqrt{5}+3\sqrt{5}=16\sqrt{5}](https://tex.z-dn.net/?f=13%5Csqrt%7B5%7D%2B3%5Csqrt%7B5%7D%3D16%5Csqrt%7B5%7D)
![=16\sqrt{5}](https://tex.z-dn.net/?f=%3D16%5Csqrt%7B5%7D)
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