Answer:
x=7 multiplicity of 2
Step-by-step explanation:
14x - 49 = x^2
Subtract x^2 from each side
-x^2 +14x - 49 = x^2-x^2
-x^2 +14x - 49 = 0
Multiply by -1
x^2 -14x +49 =0
What 2 numbers multiply together to give you 49 and add together to give you -14
7*-7 = 49
-7+-7 = -14
(x-7) (x-7) = 0
Using the zero product property
x-7 = 0 x-7 =0
x-7+7= 0+7 x-7+7 =0+7
x =7 x=7
Answer:
<h2>C. 71.2 in²</h2>
Step-by-step explanation:
We have the square in the base with side a = 4in and four triangles with base a = 4in and height h = 6.9in.
The formula of an area of a square:
A = a²
Substitute:
As = 4² = 16 in²
The formula of an area of a triangle:
A = (ah)/2
Substitute:
At = [(4)(6.9)]/2 = 27.6/2 = 13.8 in²
The Surface Area:
S.A. = As + 4At
Substitute:
S.A. = 16 + 4(13.8) = 16 + 55.2 = 71.2 in²
Answer:
24
Step-by-step explanation:
you would multiply 12 time 2
Answer:
1. The probability that the student will get exactly 6 correct answers is
.
2. The probability that the student will get more than 6 correct answers is
.
Step-by-step explanation:
From the given information it is clear that
The total number of equations (n) = 10
The probability of selecting the correct answer (p)= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
The probability of selecting the incorrect answer (q)= ![1-p=1-\frac{1}{3}=\frac{2}{3}](https://tex.z-dn.net/?f=1-p%3D1-%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B2%7D%7B3%7D)
According to the binomial distribution, the probability of selecting r items from n items is
![P=^nC_rp^rq^{n-r}](https://tex.z-dn.net/?f=P%3D%5EnC_rp%5Erq%5E%7Bn-r%7D)
where, p is probability of success and q is the probability of failure.
The probability that the student will get exactly 6 correct answers is
![P(r=6)=^{10}C_6(\frac{1}{3})^6(\frac{2}{3})^{10-6}](https://tex.z-dn.net/?f=P%28r%3D6%29%3D%5E%7B10%7DC_6%28%5Cfrac%7B1%7D%7B3%7D%29%5E6%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-6%7D)
![P(r=6)=210(\frac{1}{3})^6(\frac{2}{3})^{4}=\frac{1120}{19683}](https://tex.z-dn.net/?f=P%28r%3D6%29%3D210%28%5Cfrac%7B1%7D%7B3%7D%29%5E6%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B4%7D%3D%5Cfrac%7B1120%7D%7B19683%7D)
Therefore the probability that the student will get exactly 6 correct answers is
.
The probability that the student will get more than 6 correct answers is
![P(r>6)=^{10}C_7(\frac{1}{3})^7(\frac{2}{3})^{10-7}+^{10}C_8(\frac{1}{3})^8(\frac{2}{3})^{10-8}+^{10}C_9(\frac{1}{3})^9(\frac{2}{3})^{10-9}+^{10}C_{10}(\frac{1}{3})^{10}(\frac{2}{3})^{10-10}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D%5E%7B10%7DC_7%28%5Cfrac%7B1%7D%7B3%7D%29%5E7%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-7%7D%2B%5E%7B10%7DC_8%28%5Cfrac%7B1%7D%7B3%7D%29%5E8%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-8%7D%2B%5E%7B10%7DC_9%28%5Cfrac%7B1%7D%7B3%7D%29%5E9%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-9%7D%2B%5E%7B10%7DC_%7B10%7D%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B10%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-10%7D)
![P(r>6)=^{10}C_7(\frac{1}{3})^7(\frac{2}{3})^{3}+^{10}C_8(\frac{1}{3})^8(\frac{2}{3})^{2}+^{10}C_9(\frac{1}{3})^9(\frac{2}{3})^{1}+^{10}C_{10}(\frac{1}{3})^{10}(\frac{2}{3})^{0}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D%5E%7B10%7DC_7%28%5Cfrac%7B1%7D%7B3%7D%29%5E7%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B3%7D%2B%5E%7B10%7DC_8%28%5Cfrac%7B1%7D%7B3%7D%29%5E8%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B2%7D%2B%5E%7B10%7DC_9%28%5Cfrac%7B1%7D%7B3%7D%29%5E9%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B1%7D%2B%5E%7B10%7DC_%7B10%7D%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B10%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B0%7D)
![P(r>6)=120\times \frac{8}{59049}+45\times \frac{4}{59049}+10\times \frac{2}{59049}+1\times \frac{1}{59049}=\frac{43}{2187}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D120%5Ctimes%20%5Cfrac%7B8%7D%7B59049%7D%2B45%5Ctimes%20%5Cfrac%7B4%7D%7B59049%7D%2B10%5Ctimes%20%5Cfrac%7B2%7D%7B59049%7D%2B1%5Ctimes%20%5Cfrac%7B1%7D%7B59049%7D%3D%5Cfrac%7B43%7D%7B2187%7D)
Therefore the probability that the student will get more than 6 correct answers is
.