To multiply B and A, the number of columns of B must matc the number of rows of A.
<h3>
When we can multiply two matrices?</h3>
When we multiply two matrices, A and B, we multiply the rows of matrix A by the columns of matrix B.
Now, the number of elements in a row of a matrix, is equal to the number of columns (and the number of elements in a column is equal to the number of rows).
To multiply BxA:
Then, a row on matrix B must have the same number of elements than a column in row A.
Then, to multiply BxA, the number of columns of B must match the number of rows of A, meaning that the correct option is the last one.
If you want to learn more about matrices, you can read:
brainly.com/question/11989522
Let <span>Jacob, Carol, Geraldo, Meg, Earvin, Dora, Adam, and Sally be represented by the letters J, C, G, M, E, D, A, and S respectively. </span>
<span>In part IV we are asked:
</span><span>What is the sample space of the pairs of potential clients that could be chosen?
</span><span>
Since the Sample Space is the set of all possible outcomes, we need to make a set (a list) of all the possible pairs, which are as follows:
{(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S)
, </span>(C, G), (C, M), (C, E), (C, D), (C, A), (C, S)
<span>
</span> , (G, M), (G, E), (G, D), (G, A), (G, S)
<span>
,</span>(M, E), (M, D), (M, A), (M, S)
<span>
, </span>(E, D), (E, A), (E, S) <span>
, </span>(D, A), (D, S)
, (A, S).}
We can check that the number of the elements of the sample space, n(S) is
1+2+3+4+5+6+7=28.
This gives us the answer to the first question: <span>How many pairs of potential clients can be randomly chosen from the pool of eight candidates?
(Answer: 28.)
II) </span><span>What is the probability of any particular pair being chosen?
</span>
The probability of a particular pair to be picked is 1/28, as there is only one way of choosing a particular pair, out of 28 possible pairs.
III) <span>What is the probability that the pair chosen is Jacob and Meg or Geraldo and Sally?
The probability of choosing (J, M) or (G, S) is 2 out of 28, that is 1/14.
Answers:
I) 28
II) 1/28</span>≈0.0357
III) 1/14≈0.0714
IV)
{(J, C), (J, G), (J, M), (J, E), (J, D), (J, A), (J, S)
, (C, G), (C, M), (C, E), (C, D), (C, A), (C, S)
, (G, M), (G, E), (G, D), (G, A), (G, S)
,(M, E), (M, D), (M, A), (M, S)
, (E, D), (E, A), (E, S)
, (D, A), (D, S)
, (A, S).}
Answer:
Year 2030.
Step-by-step explanation
In 1997, Let Tim's age = <em>X</em> years
In 1997, Let Sue's age = <em>Y</em> years
After 5 years in 2002, Tim's age = (<em>X+ 5) </em>years
After 5 years in 2002, Sue's age = <em>(Y + 5)</em> years
Now, According to question,
<em>X </em>+ <em>Y</em> = 32 (sum of their ages) .......(1)
<em>Y </em>= 32 -<em> X</em>
(X + 5) = 2 (Y + 5) .......(2)
Substituting the value of <em>Y</em> in (2)
<em>X </em>+ 5 = 2 (32 - <em>X </em>+ 5)
<em>X </em>+ 5 = 2 (37 - <em>X </em>)
<em>X </em>+ 5 = 74 - 2<em>X </em>
3<em>X </em>=<em> </em>69
<em>X </em>= 69/3 = 23
Now ∵<em> Y</em> = 32 - <em>X </em>and<em> X = </em>23
∴ <em>Y</em> = 32 - 23 = 9
So, In 1997, Tim's age = 23 years and Sue's age = 9 years.
Let the year in which Sue's age will be three-fourth times of Tim's age be t.
Sue's age after<em> t </em>years = (9 +<em> t) </em>years.
Tim's age after<em> t</em> years = (23 + <em>t</em>) years
According to question,
<em>
</em>
<em>
</em>
The Year in which Sue's age will be three-fourth times of Tim's age is:
= (1997 + 33) = 2030.
