I believe it is a parallelogram.
Reasons:
1. It is a quadrilateral. Quadrilaterals have a total amount of 360 degrees. 80+100+100+80=360
2. It has oposite sides that are equal
3. If you look at a parallelogram it has two obtuse angles and two acute.
100= obtuse angle 80= acute angle
Answer:
![P(X=10) = 0.1222](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.1222)
Step-by-step explanation:
Represent Green with G
So,
![G = 50\%](https://tex.z-dn.net/?f=G%20%3D%2050%5C%25)
Required
Determine the probability that 10 out of 16 prefer green
This question is an illustration of binomial distribution and will be solved using the following binomial distribution formula.
![P(X=x) = ^nC_xG^x(1-G)^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%20%3D%20%5EnC_xG%5Ex%281-G%29%5E%7Bn-x%7D)
In this case:
-- number of people
-- those that prefer green
So, the expression becomes:
![P(X=10) = ^{16}C_{10}G^{10}(1-G)^{16-10}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7DG%5E%7B10%7D%281-G%29%5E%7B16-10%7D)
![P(X=10) = ^{16}C_{10}G^{10}(1-G)^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7DG%5E%7B10%7D%281-G%29%5E%7B6%7D)
Substitute 50% for G (Express as decimal)
![P(X=10) = ^{16}C_{10}*0.50^{10}*(1-0.50)^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%7D%2A%281-0.50%29%5E%7B6%7D)
![P(X=10) = ^{16}C_{10}*0.50^{10}*0.50^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%7D%2A0.50%5E%7B6%7D)
Apply law of indices
![P(X=10) = ^{16}C_{10}*0.50^{10+6](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%2B6)
![P(X=10) = ^{16}C_{10}*0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B16)
Solve 16C10
![P(X=10) = \frac{16!}{(16-10)!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%21%7D%7B%2816-10%29%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16!}{6!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%21%7D%7B6%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11*10!}{6!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%2A10%21%7D%7B6%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11}{6!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%7D%7B6%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11}{6*5*4*3*2*1} * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%7D%7B6%2A5%2A4%2A3%2A2%2A1%7D%20%2A%200.50%5E%7B16)
![P(X=10) = \frac{5765760}{720} * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B5765760%7D%7B720%7D%20%2A%200.50%5E%7B16)
![P(X=10) = 8008 * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%208008%20%2A%200.50%5E%7B16)
![P(X=10) = 8008 * 0.00001525878](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%208008%20%2A%200.00001525878)
![P(X=10) = 0.12219231024](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.12219231024)
![P(X=10) = 0.1222](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.1222)
<em>Hence, the required probability is 0.1222</em>
Answer:
sin D
Step-by-step explanation:
i think
or cos D
Answer:
a=6, b=-5
a=12, b=-5
Step-by-step explanation:
We have the equation
![\frac{1}{4}(2a-20x)=3+bx](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%282a-20x%29%3D3%2Bbx)
we will try to resolve for
in terms of
and ![b](https://tex.z-dn.net/?f=b)
Then
![\frac{1}{4}(2a-20x)=3+bx\\\frac{a}{2}-5x=3+bx\\\frac{a}{2}-3=5x+bx\\\frac{a-6}{2}=(5+b)x\\\frac{a-6}{2}\frac{1}{5+b}=x\\\frac{a-6}{10+2b}=x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%282a-20x%29%3D3%2Bbx%5C%5C%5Cfrac%7Ba%7D%7B2%7D-5x%3D3%2Bbx%5C%5C%5Cfrac%7Ba%7D%7B2%7D-3%3D5x%2Bbx%5C%5C%5Cfrac%7Ba-6%7D%7B2%7D%3D%285%2Bb%29x%5C%5C%5Cfrac%7Ba-6%7D%7B2%7D%5Cfrac%7B1%7D%7B5%2Bb%7D%3Dx%5C%5C%5Cfrac%7Ba-6%7D%7B10%2B2b%7D%3Dx)
Note that if the denominator is 0, then the division is undefined and therefore there would be no solution for x.
Then, the denominator is 0 if
.
Then, for the pairs
a=6, b=-5 and a=12, b=-5, there is no solution for x.