The tangent of an angle is the opposite side divided by the adjacent side of the triangle, relative to the angle. By tan theta = 3, it means that, the adjacent side is thrice as long as the opposite side.
3a = o
Then, using Pythagorean's theorem:
25² = a² + o²
Substituting o,
25² = a² + (3a)²
25² = a² + 9a²
25² = 10a²
a = 7.9 cm
Then, 3(7.9) = o = 23.7 cm
So, the opposite side is 23.7 cm and the adjacent side is 7.9 cm.
Answer:
$3.10
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
If two events X and Y are mutually exclusive,
Then,
P(X∪Y) = P(X) + P(Y)
Let A represents the event of a diamond card and B represent the event of a heart card,
We know that,
In a deck of 52 cards there are 4 suit ( 13 Club cards, 13 heart cards, 13 diamond cards and 13 Spade cards )
That is, those cards which are heart can not be diamond card,
⇒ A ∩ B = ∅
⇒ P(A∩B) = 0
Since, P(A∪B) = P(A) + P(B) - P(A∩B)
⇒ P(A∪B) = P(A) + P(B)
By the above statement,
Events A and B are mutually exclusive,
Hence, the probability of selecting a 4 of diamonds or a 4 of hearts is an example of a mutually exclusive event is a true statement.
Answer:
0.82% of the graduates will receive the tax break
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:

What percentage of the graduates will receive the tax break
This is the pvalue of Z when X = 15600. So



has a pvalue of 0.0082
0.82% of the graduates will receive the tax break