Answer/Step-by-step explanation:
1. <ABC and <BCD are alternate interior angles. Alternate interior angles are equal, therefore, since m<ABC = 38°, then m<BCD = 38°
2. m<ECF = m<BCD (corresponding angles)
m<ECF = 38° (substitution)
3. m<DCF + m<ECF = 180° (linear pair)
m<DCF + 38° = 180° (substitution)
m<DCF = 180° - 38° (Subtraction property of equality)
m<DCF = 142°
Answer:
The length of the yard is 60 feet while the width is 30 feet.
Step-by-step explanation:
If the length of Mr. Timmon's backyard is double the width, then the dimensions are related by the following expression:
length = 2*width
We also know the perimetter, since he has the exact length of fence to surround his whole yard, which is 180 feet. The perimeter of a rectangle is given by:
perimeter = 2*length + 2*width
Therefore,
180 = 2*length + 2*width
With the length being double the width, we have:
180 = 2*(2*width) + 2*width
180 = 4*width + 2*width
6*width = 180
width = 180/6 = 30
length = 2*width = 2*30 = 60
The length of the yard is 60 feet while the width is 30 feet.
Answer:
Note that we need calculate the scores between the mean (
) and the mean plus 3 times the standard deviation. It is 3 times since the distance between the values given (513 and 759) divided by the standard deviation is 3 (
)
So the rule say that 99.7% of data is between 
and 
, as it is a normal distribution half of 99.7% is between 
and 
. Hence 49.85% of people score between 513 and 759.
