In Central City, Elm Street and Maple Street are parallel to one another. Oak Street crosses both Elm Street and Maple Street as
shown.
Tell whether each statement is True or False.
Tell whether each statement is True or False.
1 answer:
<h2>Answer:</h2>
a. True.
b. False.
c. True.
d. True.
e. True.
<h2>Step-by-step explanation:</h2>a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.
b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.
c. This statement is true because angles 5 and 1 correspond to each other.
d. This statement is true because angles 7 and 8 form a straight line.
e. This statement is true because they are interior angles that are alternate.
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Answer:
d) 300 times for the first game and 30 times for the second
Step-by-step explanation:
We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.
As the coin is flipped more than one time and calculated the proportion, we have to use the <em>sampling distribution of the sampling proportions</em>.
The mean and standard deviation of this sampling distribution is:
We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.
The probability of getting a proportion within this interval can be calculated as:
referring the z values to the z-score of the standard normal distirbution.
We can calculate this values of z as:
If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.
With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.
For the second game, we win if we get a proportion over 80%.
The probability of winning is:
The z value is calculated as before:
As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).
If our chances of winnings depend on P(z>z*), they become lower as z* increases.
Then, we can conclude that our chances of winning decrease with the increase of the number of trials.
We prefer the option of 30 trials for this game.