Answer:
The probability is 0.97
Step-by-step explanation:
In this question, we are concerned with calculating the probability of a student spending time reading or watching TV.
To calculate this, we simply use a direct mathematical formula.
P( of spending time reading or watching tv) = P(of spending time reading) + P(spending time watching Tv) - P( of spending time watching Tv and reading)
From the question, we identify the probabilities as follows;
P(spending time reading) = 0.1
P(of spending time watching Tv) = 0.9
P(of spending time watching Tv and reading) = 0.03
Now, plugging these values, we have
P( of spending time reading or watching Tv) = 0.9 + 0.1 -0.03
= 1-0.03 = 0.97
Answer:
71.6 degrees
Step-by-step explanation:
Given the vectors
u= <8,4> v = <9.-9> (5 points)
u*v = (8, 4)*(9, -9)
u*v = 8(9)+(4)(-9)
u*v = 72 - 36
u*v = 36
|u| = √8²+4²
|u| = √64+16
|u| = √80
|v| = √9²+9²
|v| = √81+81
|v| = √162
Using the formula
u*v = ||u||v| cos theta
36 = √80(√162)cos theta
36 = √12960 cos theta
cos theta = 36/√12960
cos theta = 36/113.8
cos theta = 0.3162
theta = arccos(0.3162)
theta = 71.56 degrees
Hence the angle between the given vectors to the nearest tenth of a
degree is 71.6 degrees
Answer:
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Answer: 
Step-by-step explanation:
The missing figure is attached.
For this exercise it is important to remember that, by definition, the opposite interior angles of an inscribed quadrilateral are supplementary, which means that their sum is 180 degrees.
Based on this, you can identify that the angle D and the angle B are opposite and, therefore, supplementary.
Knowing that, you can write the following equation:
Now you must solve for "x" in order to find its value. This is:
Then:
You know that:
Therefore, since you know the value of "x", you can substitute it into and then you must evaluate, in order to find the measure of the angle A. This is:
