Answer:
68%
Step-by-step explanation:
The attached normal table shows area under the standard normal curve that are to the left of a particular z-score.
To find the area between two z-scores, say , find the area to the left of
then subtract the area to the left of
. That difference is the area between the two z-scores.
38 minutes has a z-score
46 minutes has a z-score
Find z= 1.0 in the table. The area in that row is .8413.
Find z=-1.0 in the table. The area in that row is .1587.
The difference, .8413 - .1587 = .6826 is the area under the normal curve between z=-1 and z=1.
.6826 is about 68%
Answer:
(96.91, 101.09)
Step-by-step explanation:
To calculate the interval, you require the Z value at 95% confidence interval. The Z value is 1.96. The formula to calculate the confidence interval:
Where X is the mean and s is the standard deviation and x the sample size:
The interval is (96.91, 101.09)
y = 90°
Solution:
The reference image for the answer is attached below.
The sum of opposite interior angles is equal to the exterior angles.
m∠BAC + m∠ACB = 110°
m∠BAC + 70° = 110°
m∠BAC = 110° – 70°
m∠BAC = 40°
m∠BAD + m∠DAC = 40°
x + x = 40°
2x = 40°
Divide by 2 on both sides of the equation.
x = 20°
In triangle DAC,
Sum of all the angles of a triangle = 180°
m∠DAC + m∠ACD + m∠CDA = 180°
20° + 70° + m∠CDA = 180°
90° + m∠CDA = 180°
m∠CDA = 180° – 90°
m∠CDA = 90°
∠CDA and y lies on the straight line. So they form a linear pair.
y + m∠CDA = 180°
y + 90° = 180°
y = 180° – 90°
y = 90°
The value of y is 90°.
