Answer:
1. Addition Property of Equality
2. Segment addition
3. Substitution Property of Equality.
4. Transitive Property of Equality.
Step-by-step explanation:
Given: CD = EF and AB = CE
To Show: AB = DF
Following the steps outlined:
1. CD + DE = EF + DE by the (addition) Property of Equality.
This shows that the same value has been added to both sides of the equation.
2. CE = CD + DE and DF = EF + DE through (segment addition).
This indicates that CE and DF are segments, and the length of any segment equals the total of its parts.
3. CE = DF according to the (Addition, subtraction, substitution, transitive) Property of Equality. Recognizing that CE = CD + DE and using the fact that CD = EF allows us to replace CD with EF.
So, CE = EF + ED = FD (via substitution) Property of Equality.
4. Since AB = CE and CE = DF, we can conclude AB = DF by the (transitive) Property of Equality.
This follows the rule that if x = y and y = z, then x = z.
Let Jacob, Carol, Geraldo, Meg, Earvin, Dora, Adam, and Sally be denoted as J, C, G, M, E, D, A, and S respectively. In part IV, we need to identify the pairs of potential clients that could potentially be selected. The sample space consists of all possible outcomes, therefore we create a set of all valid pairs, listed as follows: {(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)}. We can verify the number of elements in the sample space, n(S) is 1+2+3+4+5+6+7=28. This gives us the answer to the first question: What is the count of pairs of potential clients that can be randomly selected from the pool of eight candidates? (Answer: 28.) II) What is the chance of a certain pair being chosen? The chance of picking a specific pair is 1/28, as there’s just one way to select a particular pair out of the 28 possible options. III) What is the probability that the selected pair consists of Jacob and Meg or Geraldo and Sally? The probability of selecting (J, M) or (G, S) is 2 out of 28, which equates to 1/14. Answers: I) 28 II) 1/28 ≈ 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).}
1,107 cc
The scanning consists of 10 intervals:
[0,1.5), [1.5,3), [3,4.5), [4.5,6), [6,7.5), [7.5,9), [9,10.5), [10.5,12), [12,13.5), [13.5,15)
To estimate the volume using the Midpoint Rule, n should be set to 10.
Given that we will use n=5, we will split the range [0,15] into five intervals of lengths 3 each:
[0,3], [3,6], [6,9], [9,12], [12,15] and calculate their midpoints:
1.5, 4.5, 7.5, 10.5, and 13.5.
Next, we will determine the volume V from the five cylinders, where each has a height h=3 and the base area A corresponds to the calculated midpoints' intervals:
Cylinder 1
Midpoint=1.5, corresponding to the 2nd interval
A = 18, V= height * area of the base = 18*3 = 54 cc
Cylinder 2
Midpoint=4.5, corresponding to the 4th interval
A = 78, V= height * area of the base = 78*3 = 234 cc
Cylinder 3
Midpoint=7.5, corresponding to the 6th interval
A = 106, V= height * area of the base = 106*3 = 318 cc
Cylinder 4
Midpoint=10.5, corresponding to the 8th interval
A = 129, V= height * area of the base = 129*3 = 387 cc
Cylinder 5
Midpoint=13.5, corresponding to the 10th interval
A = 38, V= height * area of the base = 38*3 = 114 cc
Thus, the estimated volume is
54 + 234 + 318 + 387 + 114 = 1,107
