Answer:
Given: ABCD is a parallelogram,
In which E ∈ BC and F lies on the extension of DC,
Such that line segment EF goes through the vertex A.
To prove:
Proof:
Since, By the definition of parallelogram,
By the Alternative interior angle theorem,
Also, ( vertically opposite angles )
Thus, By AA similarity postulate,
Hence proved.
Answer:
The 95% confidence interval based on this sample is =
[6.41, 7.79]
Step-by-step explanation:
The formula for Confidence Interval =
Mean ± z × standard deviation/√n
Sample mean = 7.1 hours
Standard deviation = 5 hours
n = 200 students
z = 95% confidence interval z score
= 1.96
C.I = 7.1 ± 1.96 × 5/√200
C.I = 7.1 ± 0.693
Hence, Confidence Interval
= 7.1 - 0.693
= 6.407
Approximately = 6.41
= 7.1 + 0.693
= 7.793
Approximately = 7.79
Therefore, the 95% confidence interval based on this sample is
[6.41, 7.79]
Answer:
.50 cents per minute
Step-by-step explanation:
8.50 divided by 17= 0.50
to check- 0.50 times 17 equals 8.50
Oleg, Sasha, and Dima shared 600 toys. Sasha had twice as many toys as Oleg. Dima had 40 more toys than Oleg.
Let the number of toys Oleg has = x
Let the number of toys Sasha has = y
Let the number of toys Dima has = z
Sasha had twice as many toys as Oleg
So y = 2*x= 2x
Dima had 40 more toys than Oleg.
z = x + 40
Oleg, Sasha, and Dima shared 600 toys
x + y + z= 600
We know y=2x and z=x+40
Replace it for y and z
Subtract 40 on both sides
Divide by 4 on both sides
Oleg had 140 toys
Answer:
Use feet for greater measurements, such as heights.<u><em> </em></u><u><em>Use yards to measure distances, such as the length of a football field.</em></u> Use miles to measure great distances, such as the distance between cities. Choose the most reasonable unit of measure.
Step-by-step explanation: