help Kyle trying to explain to her friend why the placement of an ange and the concept of rigid motions can be used in determini
ng triangle congruence. She illustrates the SAS triangle corerence and the SSA possibility as shown in the diagram with two pairs of triangles. What do you think Kyle said to her friend about the placement of angles and about the relationship between the triangle pairs in terms of rigid motions? Using Kyle's illustration, write an argument for why the placement of the anges and the concept of rigid motions in proving triangle congruence can be critical A E E
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Answer:
Step-by-step explanation:
As it is a second order equation, it means that it has two possible answers and they are and
.
The famous quadratic formula for solving any second order equation is the following:
Where a is the coefficient of , b is the coefficient of x, and c is the free term. In other words,
as the equation should be in the following form:
Therefore the possible answer should be the following,
by dividing the numerator and denominator by 2, we can deduce the following,
Michael Jordan's Freethrow, the population of the 6 countries and the distribution of the uninsured drivers are illustrations of probabilities
<h3>1. Michael Jordan Freethrow</h3>The given parameter is:
p = 83% -- the percentage of free throws he made
<u>Probability that he misses his 6th throw </u>
The probability that he misses his 6th throw is:
P = P(He made the first 5 throws) * P(He lost the 6th)
This gives
P = (83%)^5 * (1 - 83%)^1
P = 0.0670
<u>Expected number of miss</u>
The expected number till he misses the first free throw is:
E(x) = np
This gives
E(x) = 6 * 83%
E(x) = 4.98
Approximate
E(x) = 5
Hence, the probability that he misses his 6th throw is 0.0670 and the expected number till he misses the first free throw is 5
<h3>2. Country Populations</h3>The given parameters are:
Average population = 268.35 million
Standard deviation = 370.43 million
<u>The z-scores for the United States, Egypt, and Mexico</u>
This is calculated as:
z = (x - )/
So, we have:
US = (332 million - 268.35 million)/ 370.43 million
US = 0.17
Egypt = (104 million - 268.35 million)/ 370.43 million
Egypt = -0.44
Mexico = (128 million - 268.35 million)/ 370.43 million
Mexico = -0.38
<u>The countries from the smallest to the largest </u>
By comparing the z-score of the countries, the order of the countries are:
Egypt, Japan, Mexico, Brazil, United States and India
The countries are ranked that way because the higher the z-score, the higher the population
<h3>3. Uninsured drivers</h3>The given parameter is:
p = 12.6% -- the percentage of uninsured drivers
<u>Probability that exactly 5 drivers of 30 are uninsured</u>
This is calculated as:
P(x) = nCx * p^x * (1 - p)^(n-x)
So, we have:
P(5) = 30C5 * (12.6%)^5 * (1 - 12.6%)^(30-5)
Evaluate the product
P(5) = 0.1561
<u>Probability that the next uninsured driver is the 7th</u>
This is calculated as:
P = P(First 6 are insured) * P(7th is unisured)
This gives
P = (1 - 12.6%)^6 * (12.6%)^1
P = 0.0562
The probability that exactly 5 drivers of 30 are uninsured is 0.1561, and the probability that the next uninsured driver is the 7th is 0.0562
Read more about probability at: