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Find x :
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Sum of adjacent angles on a straight line is 180.
∠ABY + ∠YBC = 180
x + 25 + 2x + 50 = 180
3x + 75 = 180
3x = 105
x = 35
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Check if AC is parallel to DF :
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If AC is parallel to DF,
∠YBC = ∠BEF (Corresponding angles)
∠YBC = 2x + 50 = 2(35) + 50 = 120
∠BEF = 5x - 55 = 5(35) - 55 = 120
Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer: Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer:
4
Step-by-step explanation:
Answer:
Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ.
Step-by-step explanation:
Start with a line segment PQ that we will copy. Mark a point R that will be one endpoint of the new line segment. Set the compasses' point on the point P of the line segment to be copied. Adjust the compasses' width to the point Q. The compasses' width is now equal to the length of the line segment PQ.
Answer: B) 4.963±0.019.
Step-by-step explanation:
Confidence interval for population mean ( when population standard deviation is not given) is given by :-
, where 
= Sample mean
n= Sample size
s= sample standard deviation
t* = critical t-value.
As per given:
n= 50
Degree of freedom = n-1 =49
s= 0.067 lb
For df = 49 and significance level of 0.05 , the critical two-tailed t-value ( from t-distribution table) is 2.010.
Now , substitute all values in the formula , we get
Hence, a 95% confidence interval for the mean weight (in pounds) of the mulch produced by this company is 
.
Thus , the correct answer is B) 4.963±0.019.
Step-by-step explanation:
1) see the attached picture;
2) 120+80=200 (persons).
PS. change the design according to local requirements.
