19. Given that the lines are parallel, what angle is congruent to angle 6?
1 answer:
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You question is of two parts.
For the first part:
<span>A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.
![\begin{center} \begin{tabular} {|c|c|c|c|c|} & Cats & Dogs & Other & Total \\ [1ex] Male & 42 & 58 & 6 & 106 \\ Female & 52 & 48 & 2 & 102 \\ [1ex] Total & 94 & 106 & 8 & 208 \end{tabular} \end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%0A%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7Cc%7Cc%7Cc%7C%7D%0A%20%26%20Cats%20%26%20Dogs%20%26%20Other%20%26%20Total%20%5C%5C%20%5B1ex%5D%0AMale%20%26%2042%20%26%2058%20%26%206%20%26%20106%20%5C%5C%0AFemale%20%26%2052%20%26%2048%20%26%202%20%26%20102%20%5C%5C%20%5B1ex%5D%0ATotal%20%26%2094%20%26%20106%20%26%208%20%26%20208%0A%5Cend%7Btabular%7D%0A%5Cend%7Bcenter%7D)
</span>Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male.
Find P(B| NOT A).
P(A) = P(choosing cat) + P(choosing dog) =
P(NOT A) =
P(B and NOT A) = P(males that did not choose cat or dog) =
P(B | NOT A) =
For the second part of the question.
<span>Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
If his investment increases by 10%, the value of the investment will be 1.1 x $19 = $20.90 with a probability of 30% or 0.3
The expected value of the investment is given by
Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.
</span>
For the first part:
<span>A group of men and women were asked what their favorite pet was, and the results of the survey were tabulated.
</span>Let event A be defined as randomly choosing someone who picked cats or dogs as their favorite pet. Let event B be defined as a randomly chosen person being male.
Find P(B| NOT A).
P(A) = P(choosing cat) + P(choosing dog) =
P(NOT A) =
P(B and NOT A) = P(males that did not choose cat or dog) =
P(B | NOT A) =
For the second part of the question.
<span>Petey is considering investing $19 in a certain company. Financial advisors forecast that there is a 30% chance that the stock will increase in value by 10%, and a 70% chance he will lose his initial investment. Determine if Petey should make the investment, and find the expected value of the investment.
If his investment increases by 10%, the value of the investment will be 1.1 x $19 = $20.90 with a probability of 30% or 0.3
The expected value of the investment is given by
Therefore, Petey should not make the investment as there is an expectation of a loss from the investment.
</span>
Answer:
,
Step-by-step explanation:
The function of the graph can be written in the vertex form as
, where V(h,k)=V(2,4) is the vertex of the quadratic function.
We substitute the value to obtain;
,
The point (5,1) lies on the graph so we use it to determine the value of a.
,
,
,
The required equation is
,