Which of the following lists all of the positive factors of 18?
1 answer:
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Answer:
f(x) = -19/9(x + 3)² + 5
Step-by-step explanation:
Given the vertex, (-3, 5) and the point, (0, 14):
Use the following quadratic equation formula in vertex form:
f(x) = a(x - h)² + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the graph wide or narrow.
<em>h</em><em> </em>= determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for <em>a</em>:
f(x) = a(x - h)² + k
14 = a(0 + 3)² + 5
14 = a(3)² + 5
14 = a(9) + 5
Subtract 5 from both sides:
-14 - 5 = 9a
-19 = 9a
Divide both sides by 9 to solve for a:
-19/9 = 9a/9
-19/9 = a
Therefore, the quadratic function in vertex form is:
f(x) = -19/9(x + 3)² + 5
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Answer:
c) Is not a property (hence (d) is not either)
Step-by-step explanation:
Remember that the chi square distribution with k degrees of freedom has this formula
Where N₁ , N₂m .... are independent random variables with standard normal distribution. Since it is a sum of squares, then the chi square distribution cant take negative values, thus (c) is not true as property. Therefore, (d) cant be true either.
Since the chi square is a sum of squares of a symmetrical random variable, it is skewed to the right (values with big absolute value, either positive or negative, will represent a big weight for the graph that is not compensated with values near 0). This shows that (a) is true
The more degrees of freedom the chi square has, the less skewed to the right it is, up to the point of being almost symmetrical for high values of k. In fact, the Central Limit Theorem states that a chi sqare with n degrees of freedom, with n big, will have a distribution approximate to a Normal distribution, therefore, it is not very skewed for high values of n. As a conclusion, the shape of the distribution changes when the degrees of freedom increase, because the distribution is more symmetrical the higher the degrees of freedom are. Thus, (b) is true.