Question 7
<h3>Answer: A) 15</h3>
---------------------
Work Shown:
angle B = angle D = 56
angle C = angle F = 64
The missing angle A adds with B and C to get 180
A+B+C = 180
A = 180-B-C
A = 180-56-64
A = 60
Since angles B and D are congruent, and C and F are congruent, this must mean angle A = angle E. I'm using the angle angle (AA) similarity rule.
angle E = angle A
3x+15 = 60
3x = 60-15
3x = 45
x = 45/3
x = 15
Side note: I'm not sure why your teacher marked angle E as the same as angles C and F. They should have used another angle marker to indicate that angles A and E are the same.
================================================
Question 8
<h3>Answer: B) 17</h3>
------------------------------
Work Shown:
Triangle ABC is congruent to triangle EDF. The order is important. We have A first, then B, then C for ABC. Also, we have E first, then D, then F for EDF.
Therefore, we have these three pairings
- angle A = angle E
- angle B = angle D
- angle C = angle F
We'll first need angle C
A+B+C = 180
C = 180-A-B
C = 180-42-108
C = 30
which we'll then solve for x
angle F = angle C
4x-4 = 30
4x = 30+4
4x = 34
x = 34/4
x = 8.5
which doubles to
2x = 2*8.5
2x = 17
Answer:
Mean = 528 ppm
Standard deviation = 90.8 ppm
Step-by-step explanation:
Assuming a basis of 100 trees
6 trees with 350 ppm (minimal growth)
10 trees with 450 ppm (slow growth)
47 trees with 550 ppm (moderate growth)
37 trees with 650 ppm (rapid growth)
Mean = xbar = Σx/N
x = each variable
xbar = mean
N = number of variables = 100
Σx = sum of all variables = sum of all the ppm = (6×350) + (10×450) + (47×550) + (37×550) = 52800
xbar = 52800/100 = 528 ppm
Standard deviation = σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 528
N = number of variables = 12
Σ(x - xbar)² = [6(350 - 528)²] + [10(450 - 528)²] + [47(550 - 528)²] + [37(650 - 528)²] = 824400
σ = √[Σ(x - xbar)²/N] = √(824400/100) = 90.8 ppm
Answer:
34.75 ( that's round to the nearest hundredth )
Step-by-step explanation:
do the math
