17. Divide using synthetic division, and write a summary statement in fraction form.
1 answer:
<h3>Answer:</h3>
17. 2x^4 + x^3 + x^2 + 4x + 3 + 8/(x -1)
18. x = 2, x = -2
19. The slant asymptote is y = x + 14
<h3>Explanation:</h3>17. See the first attachment for the synthetic division. The summary statement is the expression represented by the result.
18. The denominator is the difference of two squares, so is readily factored to ...
... (x -2)(x +2)
The zeros of this product are the locations of the vertical asymptotes of f(x). They are ...
... x = 2, x = -2.
19. Dividing the numerator by the denominator (using synthetic division, if you like) gives the result ...
... f(x) = x + 14 + 104/(x -8)
The linear expression y=x+14 defines the end behavior when x gets large. That is, it is the slant asymptote of the function. See the second attachment for a graph.
(There will be a horizontal asymptote only when the degrees of numerator and denominator are the same. In this case, they are not.)
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Answer and Step-by-step explanation:
A) For the model to be a probability distribution, it has to follow two conditions:
1) The probability of each value of the discrete random variable is between, and included, 0 and 1:
2) The sum of all probabilities is 1;
In the table shown, the probabilities are from 0 to 0.3 - between 0 and 1;
Adding the probabilities: 0 + 0.3 + 0.1 + 0.3 + 0.3 = 1
Therefore, this model is a valid probability distribution model.
B) They are discrete because each value correspond to a finite number of possible values.
C) Expected value is calculated by
E(X) = 2.6
D) P(X=3) = P(3), which means probability of 3:
P(X=3) = 0.3
E) P(X<4): probabilities of values of X that are less than 4:
P(X<4) = P(0) + P(1) + P(2) + P(3)
P(X<4) = 0 + 0.3 + 0.1 + 0.3
P(X<4) = 0.7
F) P(X>0) = P(1) + P(2) + P(3) + P(4)
P(X>0) = 0.3 + 0.1 + 0.3 + 0.3
P(X>0) = 1
G) P(X=5) = P(5)
There is no probability of P(5) because the model doesn't "cover" that number.
H) P(X=0) = P(0)
P(X=0) = 0
I) The total area of any density curve is 1 because it represents all the possible values a variable can assume.