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Andrej [43]
3 years ago
8

In a right triangle, the acute angles measure x + 15 and 2x degrees. What is the measure of the smallest angle of the triangle?

Mathematics
1 answer:
Nat2105 [25]3 years ago
5 0
The sum of the three angles of a triangle is always 180 degrees. If the triangle is right, which means one of the angles measures 90 degrees, the other two angles should add up to 90 degrees. With this condition and the given above, x + 15 + 2x = 90. Solving for x in the equation gives x = 25. Substituting x to the given expression for the acute angles gives the measurements of 40 and 50 degrees. Thus, the smallest angle of the triangle is <em>40 degrees</em>. 
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Answer:

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Step-by-step explanation:

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Have Retirement Benefits
charle [14.2K]

Answer:

(a) The probability of the intersection of events "man" and "yes" is 0.55.

(b) The probability of the intersection of events "no" and "man" is 0.10.

(c) The probability of the union of events "woman" or "no" is 0.45.

Step-by-step explanation:

The information provided is:

             Yes    No   Total

Men       275   50     325

Women  150   25      175

Total      425   75      500

(a)

Compute the probability that a randomly selected employee is a man and a has retirement benefits as follows:

P(M\cap Y)=\frac{n(M\cap Y)}{N}=\frac{275}{500}=0.55

Thus, the probability of the intersection of events "man" and "yes" is 0.55.

(b)

Compute the probability that a randomly selected employee does not have retirement benefits and is a man as follows:

P(N\cap M)=\frac{n(N\cap M)}{N}=\frac{50}{500}=0.10

Thus, the probability of the intersection of events "no" and "man" is 0.10.

(c)

Compute the probability that a randomly selected employee is a woman or has no retirement benefits as follows:

P(W\cup N)=P(W)+P(N)-P(W\cap N)=\frac{175}{500}+\frac{75}{500}-\frac{25}{500}=0.45

Thus, the probability of the union of events "woman" or "no" is 0.45.

5 0
3 years ago
In the Sahara Desert one day it was 136oF. In the Gobi Desert a temperature of
coldgirl [10]

Answer: 186^{\circ}F

Step-by-step explanation:

Given : In the Sahara Desert one day it was 136°F.

In the Gobi Desert a temperature of  -50°F was recorded.

Clearly ,  136°F> -50°F

Then, the difference between these two temperatures will be :-

136^{\circ}F-(-50)^{\circ}F\\\\=(136+50)^{\circ}F\ \ [\because \text{Product two neagtive sign is positive]}\\\\=186^{\circ}F

Hence, the difference between these two temperatures = 186^{\circ}F

7 0
3 years ago
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Answer:8

Step-by-step explanation:

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So for 7.8 it is closer to eight not seven

8 0
2 years ago
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