Answer: a
Step-by-step explanation:
I’m pretty sure that your answer is the last one
1. This question refers to conditional probability and is asking us to find the probability of Q occurring, given that R occurs. What this means is that we must divide the probability of Q and R occurring by the probability of R occurring (this is because we have the condition that R occurs). This may be written as such:
Pr(Q|R) = Pr(Q ∩ R) / Pr(R)
2. Now, the first step is to find Pr(Q ∩ R). This is given by the value in the centre of the Venn Diagram (ie. in the cross-over between the two circles) divided by the total of all the values:
Pr(Q ∩ R) = 3/(8 + 3 + 4 + 22)
= 3/37
3. The next step is to find Pr(R). This is given by the value in the circle denoted R (including the cross-over with Q) divided by the total of all the values.
Pr(R) = (4 + 3)/(8 + 3 + 4 + 22)
= 7/37
4. Thus, we can now subtitute the probabilities we defined in 2. and 3. into the formula for conditional probability we defined in 1.:
Pr(Q|R) = (3/37) / (7/37)
= 3/7
Thus, the answer is B.
Note that technically there is no need to write out the full probabilities before coming to this answer. The same exact answer could be found by using Pr(Q ∩ R) = 3 and Pr(R) = 7. This works because they are part of the same universal set - in other words, since the total of all the values in the Venn Diagram remains constant, the denominators of the two probabilities would be the same (given that no cancelling is done) and these denominators would be cancelled out when dividing Pr(Q ∩ R) by Pr(R). This can be particularly useful for a multiple choice question such as this one.
We use estimation beacause;
Esimation helps us because for example, if there were a can of jellybeans and you had to know the right amount, because you wanted to sell them, and had to put the exact number of jellybeans, then estimation would be about that exact number of jellybeans. Or estimating how much money you earned in your work, or what you shopped for, estimating helps us in everyday life. If you need more examples feel free to ask me.
Hope helps!-Aparri
9514 1404 393
Answer:
see attached
Step-by-step explanation:
13. The difference of two matrices is the term-by-term difference. For example, the bottom right term is the difference of the bottom right terms ...
(-6) -(5) = -11
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14. The scalar multiple of a matrix is the scalar multiplied by each term of the matrix. For example, the upper right term is ...
3(1) = 3
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15. The matrix product is the dot product of the rows of the left matrix with the columns of the right matrix. For example, the product term in row two, column one is the dot product of row 2 of C and column 1 of B:
[9, -2, 4]·[-2, -7, 10] = 9(-2) +(-2)(-7) +4(10) = -18 +14 +40 = 36
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It is convenient to let an appropriate tool help with this. Many graphing calculators and spreadsheets are able to do these functions easily.
