Answer:
D
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= (x + 4)(3x² - 7)
each term in the second factor is multiplied by each term in the first factor , that is
x(3x² - 7) + 4(3x² - 7) ← distribute both parenthesis
= 3x³ - 7x + 12x² - 28
= 3x³ + 12x² - 7x - 28 ← in standard form
Answer:
The probability that the good exam belongs to student <em>X</em> is 0.8571.
Step-by-step explanation:
It is provided that the probability that <em>X</em> did well in the exam is, P (X) = 0.90 and the probability that <em>X</em> did well in the exam is, P (Y) = 0.40,
Compute the probability that exactly one student does well in the exam as follows:
![P(Either\ X\ or\ Y\ did\ well)=P(X\cap Y^{c})+P(X^{c}\cap Y)\\=P(X)P(Y^{c})+P(X^{c})P(Y)\\=P(X)[1-P(Y)]+[1-P(X)]P(Y)\\=(0.80\times0.60)+(0.20\times0.40)\\=0.56](https://tex.z-dn.net/?f=P%28Either%5C%20X%5C%20or%5C%20Y%5C%20did%5C%20well%29%3DP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%5C%5C%3DP%28X%29P%28Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%29P%28Y%29%5C%5C%3DP%28X%29%5B1-P%28Y%29%5D%2B%5B1-P%28X%29%5DP%28Y%29%5C%5C%3D%280.80%5Ctimes0.60%29%2B%280.20%5Ctimes0.40%29%5C%5C%3D0.56)
Then the probability that <em>X</em> is the one who did well in the exam is:
![P(X\ did\ well\ in\ the\ exam)=\frac{P(X\cap Y^{c})}{P(X\cap Y^{c})+P(X^{c}\cap Y)}\\ =\frac{P(X)[1-P(Y)]}{P(X\cap Y^{c})+P(X^{c}\cap Y)} \\=\frac{0.80\times0.60}{0.56}\\=0.857143\\\approx0.8571](https://tex.z-dn.net/?f=P%28X%5C%20did%5C%20well%5C%20in%5C%20the%5C%20exam%29%3D%5Cfrac%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%5C%5C%20%3D%5Cfrac%7BP%28X%29%5B1-P%28Y%29%5D%7D%7BP%28X%5Ccap%20Y%5E%7Bc%7D%29%2BP%28X%5E%7Bc%7D%5Ccap%20Y%29%7D%20%5C%5C%3D%5Cfrac%7B0.80%5Ctimes0.60%7D%7B0.56%7D%5C%5C%3D0.857143%5C%5C%5Capprox0.8571)
Thus, the probability that the good exam belongs to student <em>X</em> is 0.8571.
Answer:
c
Step-by-step explanation:
!!!
<span>The correct answer for this question is this one: "
Hint 1. Predicting the outcome of the experiment if your hypothesis is supported First, review your hypothesis.
Your hypothesis states that female crickets respond to both the chirp rate of the male’s song and the local temperature when identifying potential mates. From this hypothesis, you make the following prediction: If a female cricket is at a different temperature from a male of the same species, she will not respond to the male’s song.
Hope this helps answer your question.
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