The answer would be (2,1)
Answer:
all of them???
Step-by-step explanation:
Answer:
432 in^2
Step-by-step explanation:
in similar quadrilaterals, the first point of one quad. corresponds to the first point of the other quad, so in this case UA corresponds with CH.
since CH is 3/4 the length of UA, we can also assume that the other sides in ZUCH are 3/4 the length of their corresponding sides in SQUA.
even though we don't know what quadrilateral SQUA and ZUCH are, we know the area of SQUA is 9/16 times less than ZUCH.
want some proof?
lets say SQUA and ZUCH are rectangle/square
ZUCH: 4X4 = 16
SQUA: 3X3 = 9
now lets say they are trapezoids. We will set ZUCH 2nd base to 8 and height to 16, therefore SQUA bases will be 3 and 6, and the height will be 12 (multiply ZUCH lengths by 3/4)
ZUCH = (b1+b2)(h)/2 = (4+8)(16)/2 = 96
SQUA = (b1+b2)(h)/2 = (3+6)(12)/2 = 54
simplify 96/54 = 16/9
now we can multiply 243 by our factor 16/9 to find the area of SQUA.
243 * 16/9 = 432 in^2
Answer:
![\bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{22026.1}{171}=128.81](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%20f_i%7D%7Bn%7D%3D%20%5Cfrac%7B22026.1%7D%7B171%7D%3D128.81)
![s^2 = \frac{2839948.85- \frac{(22026.1)^2}{171}}{171-1}= 16.59](https://tex.z-dn.net/?f=%20s%5E2%20%3D%20%5Cfrac%7B2839948.85-%20%5Cfrac%7B%2822026.1%29%5E2%7D%7B171%7D%7D%7B171-1%7D%3D%2016.59)
![s= \sqrt{16.587}=4.07](https://tex.z-dn.net/?f=%20s%3D%20%5Csqrt%7B16.587%7D%3D4.07)
Step-by-step explanation:
For this case we can calculate the sample variance and deviation with the following table
Class Midpoint (Xi) fi Xi*fi Xi^2 *fi
120.6-123.6 122.1 17 2075.7 253443
123.7-126.7 125.2 49 6134.8 768077
126.8-129.8 128.3 29 3720.7 477365.8
129.9-132.9 131.4 41 5387.4 707904.4
133.0-136.0 134.5 35 4007.5 633158.8
___________________________________________
Total 171 22026.1 2839948.85
For this case we can calculate the mean or expected value with the following formula:
![\bar X = \frac{\sum_{i=1}^n X_i f_i}{n}= \frac{22026.1}{171}=128.81](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%20%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%20f_i%7D%7Bn%7D%3D%20%5Cfrac%7B22026.1%7D%7B171%7D%3D128.81)
Now we can calculate the sample variance with the following formula:
![s^2 =\frac{\sum f_i X^2_i -[\frac{(\sum X_i f_i)}{n}]^2}{n-1}](https://tex.z-dn.net/?f=s%5E2%20%3D%5Cfrac%7B%5Csum%20f_i%20X%5E2_i%20-%5B%5Cfrac%7B%28%5Csum%20X_i%20f_i%29%7D%7Bn%7D%5D%5E2%7D%7Bn-1%7D)
And if we replace we got:
![s^2 = \frac{2839948.85- \frac{(22026.1)^2}{171}}{171-1}= 16.59](https://tex.z-dn.net/?f=%20s%5E2%20%3D%20%5Cfrac%7B2839948.85-%20%5Cfrac%7B%2822026.1%29%5E2%7D%7B171%7D%7D%7B171-1%7D%3D%2016.59)
And the standard deviation would be the square root of the variance and we got:
![s= \sqrt{16.59}=4.07](https://tex.z-dn.net/?f=%20s%3D%20%5Csqrt%7B16.59%7D%3D4.07)