HELPPP!! Triangle ABC is similar to triangle MOP. A = 45 and P = 102. What is the measure of B?
1 answer:
Answer:
Explanation:
The order of the letters naming the triangles is relevant. When it is said that <em>triangle ABC is similar to triangle MOP</em>, means that:
- ∡A ≅ ∡M
- ∡B ≅ ∡O
- ∡C ≅ ∡P
Therefore:
- ∡A = 45º (given)
- ∡P = 102º (given)
- ∡C = 102º (by substitution)
Now, you have two angles of triangle ABC and can find the third one:
- ∡A + ∡B + ∡C = 180º
- ∡B = 180º - ∡A - ∡B
- ∡B = 180º - 45º - 102º = 33º ← answer
You might be interested in
Answer:
The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.
Then, the mean of the distribution of the sum of values of X is given by,
And the standard deviation of the distribution of the sum of values of X is given by,
The information provided is:
<em>μ</em> = $970
<em>σ</em> = $129
<em>n</em> = 102
Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.
Then,
Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.