Question 1
2 answers:
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Answer:
cos(45°) = (√2)/2
Step-by-step explanation:
The cosine of 45° is the x-coordinate of the point on the unit circle where the line y=x intersects it. That is, it is the positive solution to the equation ...
x^2 +x^2 = 1
x^2 = 1/2 = 2/4 . . . . . collect terms, divide by 2, express the fraction with a square denominator
x = √(2/4) . . . . . . take the square root
x = (√2)/2 . . . . . simplify
The cosine of 45° is (√2)/2.
Answer:
0.967 = 96.7% probability the rock sample actually contains raritanium
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Positive reading
Event B: Contains raritanium
Probability of a positive reading:
98% of 13%(positive when there is raritanium).
0.5% of 100-13 = 87%(false positive, positive when there is no raritanium). So
Positive when there is raritanium:
98% of 13%
What is the probability the rock sample actually contains raritanium?
0.967 = 96.7% probability the rock sample actually contains raritanium
Answer:
i.e after the first year ;
there 1344 members in the first age class
84 members for the second age class; and
28 members for the third age class
Step-by-step explanation:
We can deduce that the age distribution vector x represents the number of population members for each age class; Given that in each class of age there are 112 members present.
The current age distribution vector is as follows:
Also , the age transition matrix is as follows:
After 1 year ; the age distribution vector will be :