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:
15 feet
Step-by-step explanation:
The question talks about;
- A rectangular flower bed whose dimensions are 12 ft by 9 ft
We are required to determine the length of the diagonal
To answer the question, we need to know the following;
- All the angles in a rectangle are right angles
- A diagonal divides a rectangle into two right-angled triangles
- The dimensions of the rectangle acts as the legs of right angled triangle.
Therefore;
Using Pythagoras theorem;
a² + b² = c²
Where, c is the hypotenuse (in this case the diagonal)
a and b are the shorter sides of the right-angled triangle
Therefore;
c² = 12² + 9²
c² = 144 + 81
= 225
c = √225
= 15
Therefore, the length of the diagonal is 15 feet
Answer:
the answer to 248 divided by 9 is 27 remainder 5
Step-by-step explanation:
Step 1) Start by setting it up with the divisor 9 on the left side and the dividend 248 on the right side like this:
Step 2) The divisor (9) goes into the first digit of the dividend (2), 0 time(s). Therefore, put 0 on top:
Step 3) Multiply the divisor by the result in the previous step (9 x 0 = 0) and write that answer below the dividend.
Step 4) Subtract the result in the previous step from the first digit of the dividend (2 - 0 = 2) and write the answer below.
Step 5) Move down the 2nd digit of the dividend (4) like this:
Step 6) The divisor (9) goes into the bottom number (24), 2 time(s). Therefore, put 2 on top:
Step 7) Multiply the divisor by the result in the previous step (9 x 2 = 18) and write that answer at the bottom:
Step 8) Subtract the result in the previous step from the number written above it. (24 - 18 = 6) and write the answer at the bottom.
Step 9) Move down the last digit of the dividend (8) like this:
Step 10) The divisor (9) goes into the bottom number (68), 7 time(s). Therefore put 7 on top:
Step 11) Multiply the divisor by the result in the previous step (9 x 7 = 63) and write the answer at the bottom:
Step 12) Subtract the result in the previous step from the number written above it. (68 - 63 = 5) and write the answer at the bottom.
