Answer:
0.875 as a decimal
875/1000 or 7/8 as a fraction
explanation:
7/8 = 0.875
875/1000 = 0.875
hope this helps :)
Answer:
Step-by-step explanation:
x is the score she got on the fifth test.
Since her average score is 88, the sum of all five tests is 5×88.
x + 87 + 75 + 93 + 85 = 5×88 = 440
x = 440 - 87 - 75 - 93 - 85
x = 100
She got a 100 on her fifth test.
Answer:
0.173 probability that she gets exactly three questions correct.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for a question 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.
Seven questions:
This means that ![n = 7](https://tex.z-dn.net/?f=n%20%3D%207)
Each question has four choices.
Abby guesses, which means that ![p = \frac{1}[4} = 0.25](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7B1%7D%5B4%7D%20%3D%200.25)
Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.
This is P(X = 3).
![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)
![P(X = 3) = C_{7,3}.(0.25)^{3}.(0.75)^{4} = 0.173](https://tex.z-dn.net/?f=P%28X%20%3D%203%29%20%3D%20C_%7B7%2C3%7D.%280.25%29%5E%7B3%7D.%280.75%29%5E%7B4%7D%20%3D%200.173)
( y - 4 ) ( y² + 4 y + 16 ) =
= y³ + 4 y² + 16 y - 4 y² - 16 y - 64 = y³ - 64
If the result is the polynomial of the form:
y³ + 4 y² + a y - 4 y² - a y - 64
a = 16
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