Answer:
1). y = -4/7x 2). y = 7/4x - 65/4
Step-by-step explanation:
1). When a line is parallel, the slope remains the same.
y = -4/7x + b
-4 = -4/7(7) + b
-4 = -4 + b
0 = b
The equation is simply y = -4/7x.
2). When a line is perpendicular, the slope becomes the exact opposite.
y = 7/4x + b
-4 = 7/4(7) + b
-4 = 49/4 + b
-65/4 = b
The equation is y = 7/4x - 65/4.
In the chart of the triangle it shows that the variable b is the base. It also give us the equation for area 1/2bh (half of base * height)
Now we just plug in the values we are given
1/2bh
1/2(10*13)
1/2(130)
65
The area of the triangle is 65 ft
Answer:
16.06
20characterlimitlmasdfdgfds
Answer:
Step-by-step explanation:
Given : A new catalyst is being investigated for use in the production of a plastic chemical. Ten batches of the chemical are produced. The mean yield of the 10 batches is 72.5% and the standard deviation is 5.8%. Assume the yields are independent and approximately normally distributed.
To find : A 99% confidence interval for the mean yield when the new catalyst is used ?
Solution :
Let X be the yield of the batches.
We have given, n=10 ,
, s=5.8%
Since the size of the sample is small.
We will use the student's t statistic to construct a 995 confidence interval.
![\bar X\pm t_{n-1,\frac{\alpha}{2}}\frac{s}{\sqrt n}](https://tex.z-dn.net/?f=%5Cbar%20X%5Cpm%20t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D)
From the t-table with 9 degree of freedom for ![\frac{\alpha}{2}=0.005](https://tex.z-dn.net/?f=%5Cfrac%7B%5Calpha%7D%7B2%7D%3D0.005)
![t_{n-1,\frac{\alpha}{2}}=t_{9,0.005}](https://tex.z-dn.net/?f=t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3Dt_%7B9%2C0.005%7D)
![t_{n-1,\frac{\alpha}{2}}=3.250](https://tex.z-dn.net/?f=t_%7Bn-1%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3D3.250)
The 99% confidence interval is given by,
![CI=72.5 \pm 3.25\frac{5.8}{\sqrt{10}}](https://tex.z-dn.net/?f=CI%3D72.5%20%5Cpm%203.25%5Cfrac%7B5.8%7D%7B%5Csqrt%7B10%7D%7D)
![CI=72.5 \pm 5.96](https://tex.z-dn.net/?f=CI%3D72.5%20%5Cpm%205.96)
![CI=(72.5+5.96),(72.5-5.96)](https://tex.z-dn.net/?f=CI%3D%2872.5%2B5.96%29%2C%2872.5-5.96%29)
![CI=(66.54,78.46)](https://tex.z-dn.net/?f=CI%3D%2866.54%2C78.46%29)
Answer:
9
Step-by-step explanation:
Composite Numbers before 10: 4, 6, 8, and 9
The only one of those 4 that is NOT a multiple of 2: 9