<span>For the Vertical Angle theorem, if a slant line is intersected by a horizontal, the opposite angles must be equal. In here, he stated that the sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees. It means that the sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. </span>
Answer: P(22 ≤ x ≤ 29) = 0.703
Step-by-step explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703
Answer:
B. 1,900
Step-by-step explanation:
Answer:
x = 15
Step-by-step explanation:
angles 2 and 4 are supplementary so they add up to 180
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15