Answer:
x = 23
y = 110
Step-by-step explanation:
70 and 3x+1 are alternate exterior angles and that means they are equal
70 =3x+1
Subtract 1 from each side
69 = 3x
Divide by 3
69/3 =3x/3
23 =x
70 and y are same side exterior angles and that means they are supplementary ( add to 180)
70+y = 180
y = 180-70
y = 110
Answer:
30
Step-by-step explanation:
1. x + 40 = 3x - 20
2. 40 = 2x - 20
3. 60 = 2x
4. 30 = x
Answer:
0.0918
Step-by-step explanation:
We know that the average amount of money spent on entertainment is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.
The mean and standard deviation of average spending of sample size 25 are
μxbar=μ=95.25
σxbar=σ/√n=27.32/√25=27.32/5=5.464.
So, the average spending of a sample of 25 randomly-selected professors is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.
The z-score associated with average spending $102.5
Z=[Xbar-μxbar]/σxbar
Z=[102.5-95.25]/5.464
Z=7.25/5.464
Z=1.3269=1.33
We have to find P(Xbar>102.5).
P(Xbar>102.5)=P(Z>1.33)
P(Xbar>102.5)=P(0<Z<∞)-P(0<Z<1.33)
P(Xbar>102.5)=0.5-0.4082
P(Xbar>102.5)=0.0918.
Thus, the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.5 is 0.0918.
Answer: 36
Step-by-step explanation:
4 + 2h < -3
2h < -7
h < -3.5
x ∈ (-∞, -3.5)
