Complete the similarity statement for the two triangles shown. Enter your answer in the box. △XBR∼△ Two similar triangles B R X
and N J Y. In triangle B R X, side B X is the base. Side B R is labeled 30 centimeters, side R X is labeled 40 centimeters, and side B X is labeled 60 centimeters. In triangle N J Y, side N Y is the base. Side N J is labeled 15 centimeters, side J Y is labeled 20 centimeters, and side N Y is labeled 30 centimeters. The measure of angle B equals the measure of angle N, the measure of angle R equals the measure of angle J, and the measure of angle X equals the measure of angle Y.
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Answer:
0.8894 is the probability that the test result comes back negative if the disease is present .
Step-by-step explanation:
We are given the following in the question:
P(Disco Fever) = P( Disease) =
Thus, we can write:
P(No Disease) =
P(Test Positive given the presence of the disease) = 0.99
P( false-positive) = 4%
We have to evaluate the probability that the test result comes back negative if the disease is present, that is
P(test result comes back negative if the disease is present)
By Bayes's theorem, we can write:
0.8894 is the probability that the test result comes back negative if the disease is present .
Least to greatest, the triples are (2x, x²-1, x²+1). Thus the value in the first column of the table is half the value of the first of the triples. Your completed table will be
Answer:
Step-by-step explanation:
Lets call x,y the numbers we obtain from the calculator. x and y are independent random variables of uniform[0,1] distribution.
Lets note that, since both x and y are between 0 and 1, then 1 is the biggest side of the triangle.
Lets first make a geometric interpretation. If the triangle were to be rectangle, then the side of lenght 1 should be its hypotenuse, and therefore x and y should satisfy this property:
x²+y² = 1
Remember that in this case we are supposing the triangle to be rectangle. But the exercise asks us to obtain an obtuse triangle. For that we will need to increase the angle obtained by the sides of lenght x and y. We can do that by 'expanding' the triangle, but if we do that preserving the values of x and y, then the side of lenght 1 should increase its lenght, which we dont want to. Thus, if we expand the triangle then we should also reduce the value of x and/or y so that the side of lenght 1 could preserve its lenght. With this intuition we could deduce that
x²+y² < 1
Now lets do a more mathematical approach. According to the Cosine theorem, a triangle of three sides of lenght a,b,c satisfies
a² = b²+c² - 2bc* cos(α), where α is the angle between the sides of lenght b and c.
Aplying this formula to our triangle, we have that
, where
is the angle between the sides of lenght x and y.
Since the triangle is obtuse, then , and for those values
is negative , hence we also obtain
1 > x² + y²
Thus, we need to calculate P(x²+y² <1). This probability can be calculated throught integration. We need to use polar coordinates.
(x, y) = (r*cosФ,r*senФ)
Where r is between 0 and 1, and Ф is between 0 and (that way, the numbers are positive).
The jacobian matrix has determinant r, therefore,
As a conclusion, the probability of obtaining an obtuse triangle is .