Y = 7 + 3.50x
you multiply the number of hours by 3.50$ and add 7$ to that to get total cost
Answer:
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447 gram setting.
![H_0:\mu = 447\\H_a:\mu\neq 447](https://tex.z-dn.net/?f=H_0%3A%5Cmu%20%3D%20447%5C%5CH_a%3A%5Cmu%5Cneq%20447)
Mean = ![\mu = 447\\s = 21\\x = 443](https://tex.z-dn.net/?f=%5Cmu%20%3D%20447%5C%5Cs%20%3D%2021%5C%5Cx%20%3D%20443)
n = 19
Since n < 30 , so we will use t test
![t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D)
Substitute the values :
![t=\frac{443-447}{\frac{21}{\sqrt{19}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B443-447%7D%7B%5Cfrac%7B21%7D%7B%5Csqrt%7B19%7D%7D%7D)
![t=−0.8302](https://tex.z-dn.net/?f=t%3D%E2%88%920.8302)
t calculated = -0.830
degree of freedom = n-1 = 19-1 = 18
A level of significance=α=0.025
![t_{(df,\frac{\alpha}{2})}=2.093](https://tex.z-dn.net/?f=t_%7B%28df%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%29%7D%3D2.093)
t critical = 2.093
t calculated < t critical
So, We failed to reject null hypothesis
Decision rule -0.830< 2.093 So, We failed to reject null hypothesis
It is a scalene triangle.
<h3><u>The height of the top of the ladder from the ground is 4.53 m</u></h3>
Step-by-step explanation:
<h2>Given:</h2>
length of ladder =5 m
Angle formed = 65°
Let h be the Height of the top of the ladder from the ground
<h2>Required:</h2>
Height of the top of the ladder from the ground
<h2>Equation:</h2>
SOH-CAH-TOA
Since the hypotenuse side is given and what we are to solve is the opposite side, use SOH
![sinθ\:=\: \frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=sin%CE%B8%5C%3A%3D%5C%3A%20%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
![sin(65°)\:=\: \frac{opposite}{5\: m}](https://tex.z-dn.net/?f=sin%2865%C2%B0%29%5C%3A%3D%5C%3A%20%5Cfrac%7Bopposite%7D%7B5%5C%3A%20m%7D)
![opposite\:=\:(5 \:m )\:sin(65°)](https://tex.z-dn.net/?f=opposite%5C%3A%3D%5C%3A%285%20%5C%3Am%20%29%5C%3Asin%2865%C2%B0%29)
![opposite\:=\:4.53 \:m](https://tex.z-dn.net/?f=opposite%5C%3A%3D%5C%3A4.53%20%5C%3Am)
<h2>Final Answer:</h2><h3><u>The height of the top of the ladder from the ground is 4.53 m</u></h3>
<em>Please refer to the photo for the illustration</em>