Answer:
12.08
Step-by-step explanation:
For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
![\sqrt{V(X)} = \sqrt{np(1-p)}](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D)
Seventy-six percent of sunflower seeds will germinate into a flower
This means that ![p = 0.76](https://tex.z-dn.net/?f=p%20%3D%200.76)
Samples of 800:
This means that ![n = 800](https://tex.z-dn.net/?f=n%20%3D%20800)
The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
![\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08](https://tex.z-dn.net/?f=%5Csqrt%7BV%28X%29%7D%20%3D%20%5Csqrt%7Bnp%281-p%29%7D%20%3D%20%5Csqrt%7B800%2A0.76%2A0.24%7D%20%3D%2012.08)
Answer:
a = 1
b = - 1
Explanation:
To know the values of a and b, we need to solve the following equation:
![z=\sqrt[]{2}\lbrack\cos (\frac{-\pi}{4})+i\sin (\frac{-\pi}{4})\rbrack](https://tex.z-dn.net/?f=z%3D%5Csqrt%5B%5D%7B2%7D%5Clbrack%5Ccos%20%28%5Cfrac%7B-%5Cpi%7D%7B4%7D%29%2Bi%5Csin%20%28%5Cfrac%7B-%5Cpi%7D%7B4%7D%29%5Crbrack)
So, replacing cos(-π/4) by √2/2 and sin(-π/4) by -√2/2, we get:
![z=\sqrt[]{2}\cdot(\frac{\sqrt[]{2}}{2}+i\frac{-\sqrt[]{2}}{2})](https://tex.z-dn.net/?f=z%3D%5Csqrt%5B%5D%7B2%7D%5Ccdot%28%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D%2Bi%5Cfrac%7B-%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D%29)
Applying the distributive property:
![\begin{gathered} z=\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}-\frac{\sqrt[]{2}\cdot\sqrt[]{2}}{2}i \\ z=\frac{2}{2}-\frac{2}{2}i \\ z=1-1i \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20z%3D%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%5Csqrt%5B%5D%7B2%7D%7D%7B2%7D-%5Cfrac%7B%5Csqrt%5B%5D%7B2%7D%5Ccdot%5Csqrt%5B%5D%7B2%7D%7D%7B2%7Di%20%5C%5C%20z%3D%5Cfrac%7B2%7D%7B2%7D-%5Cfrac%7B2%7D%7B2%7Di%20%5C%5C%20z%3D1-1i%20%5Cend%7Bgathered%7D)
Therefore, we can complete the equation as:
![z=1-1i=a+bi_{}](https://tex.z-dn.net/?f=z%3D1-1i%3Da%2Bbi_%7B%7D)
It means that a = 1 and b = - 1.
The formula for volume is Length x width x height.
Bottom: 18 * 12 * 8 = 1728 cubic centimeters.
Middle: 12 * 8 * 6 = 576 cubic centimeters.
Top = 4 *4*4 = 64 cubic centimeters.
Total: 1728 + 576 + 64 = 2368 cubic centimeters.
Answer:
<h2>
143°</h2>
Step-by-step explanation:
<A and <B are corresponding angles
< A = < B
plugging the values
![7x + 24 = 3x + 92](https://tex.z-dn.net/?f=7x%20%2B%2024%20%3D%203x%20%2B%2092)
Move variable to L.H.S and change its sign
![7x - 3x + 24 = 92](https://tex.z-dn.net/?f=7x%20-%203x%20%2B%2024%20%3D%2092)
Move constant to R.H.S and change its sign
![7x - 3x = 92 - 24](https://tex.z-dn.net/?f=7x%20-%203x%20%3D%2092%20-%2024)
Calculate
![4x = 68](https://tex.z-dn.net/?f=4x%20%3D%2068)
Divide both sides of the equation by 4
![\frac{4x}{4} = \frac{68}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4x%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B68%7D%7B4%7D%20)
Calculate
![x = 17](https://tex.z-dn.net/?f=x%20%3D%2017)
Replacing value
<A = ![7x + 24](https://tex.z-dn.net/?f=7x%20%2B%2024)
![= 7 \times 17 + 24](https://tex.z-dn.net/?f=%20%3D%207%20%5Ctimes%2017%20%2B%2024)
![= 119 + 24](https://tex.z-dn.net/?f=%20%3D%20119%20%2B%2024)
![= 143](https://tex.z-dn.net/?f=%20%3D%20143)
hope this helps...
A line parallel and passing through point (1,5) would be y=-3x+8