Answer:
D
Step-by-step explanation:
-3x + 3y = 9 (1)
2x - 7y = -14 (2)
From (1),
3y= 9 + 3x
y = 3 + x
Using (2),
2x - 7(3 + x) = -14
2x - 21 - 7x = -14
-5x = 7
x = -7/5 = -1⅖
y = 3 + x = 3 - 7/5 = 8/5 = 2⅗
Answer:
D. Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he does not. The probability of the student is guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
20 questions
This means that ![n = 20.True/false:For each of them there are 2 answers, one of which is correct, so [tex]p = \frac{1}{2} = 0.5](https://tex.z-dn.net/?f=n%20%3D%2020.%3C%2Fp%3E%3Cp%3E%3Cstrong%3ETrue%2Ffalse%3A%3C%2Fstrong%3E%3C%2Fp%3E%3Cp%3EFor%20each%20of%20them%20there%20are%202%20answers%2C%20one%20of%20which%20is%20correct%2C%20so%20%5Btex%5Dp%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%3D%200.5)
How would you find the probability that the student will get 8 or fewer answers correct?
![P(X \leq 8) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)](https://tex.z-dn.net/?f=P%28X%20%5Cleq%208%29%20%3D%20P%28X%20%3D%200%29%20%2B%20P%28X%20%3D%201%29%20%2B%20P%28X%20%3D%202%29%20%2B%20P%28X%20%3D%203%29%20%2B%20P%28X%20%3D%204%29%20%2B%20P%28X%20%3D%205%29%20%2B%20P%28X%20%3D%206%29%20%2B%20P%28X%20%3D%207%29%20%2B%20P%28X%20%3D%208%29)
That is, it is the same as the cumulative probability for 8.
So the correct answer is:
D. Find the cumulative probability for 8 in a binomial distribution with n = 20 and p = 0.5.
Answer:
N = 3
Step-by-step explanation:
![\frac{28}{4} = \frac{21}{N} \\ \\ 28N = 21 \times 4 \\ 28N = 84 \\ \\ N = \frac{84}{28} \\ \\ N = 3](https://tex.z-dn.net/?f=%20%5Cfrac%7B28%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B21%7D%7BN%7D%20%20%5C%5C%20%20%5C%5C%2028N%20%3D%2021%20%5Ctimes%204%20%5C%5C%2028N%20%3D%2084%20%5C%5C%20%20%5C%5C%20N%20%3D%20%20%5Cfrac%7B84%7D%7B28%7D%20%20%5C%5C%20%20%5C%5C%20N%20%3D%203)
I hope I helped you^_^
It is seen in the figure given that there are three triangles with sides equal to a = 17 inches, b = 17 inches, and c = 20.5. Our angle c is the angle opposite side c and that is 74°. Using the equation given in the question,
A of triangle = ((17 in)(17 in)(sin 74°))(1/2)
= 138.9 in²
Then, we multiply this area by 3 since there are 3 triangles.
total area = (138.9 in²)(3) = 416.7 in²
The area of the figure is most approximately equal to 417 in².