Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other
2 answers:
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Answer:
To get maximum area, the dimensions will be;
l = 200 and b = 100
Step-by-step explanation:
Given the data in the question;
No fencing is needed on this side as the farmer wants to fence 3 sides of a rectangular field with 400 m fencing.
now, let the two vertical length sides be x meter and the horizontal length be 400 - 2x
as shown in the image below;
so,
Area of rectangle = (400 - 2x) × x = 400x - 2x²
now, to maximize area 'A', we will make A' = 0
⇒ 400 - 2(2x) = 0
400 = 4x
x = 400/4 = 100
so
⇒ (400 - 2x) = 400 - 2(100) = 400 - 200 = 200
∴ Maximum area = ( 400 - 2x) × x
= 200 × 100
= 20000 m²
∴ To get maximum area, the dimensions will be;
l = 200 and b = 100
Answer:
The value of t test statistics is 4.518.
Step-by-step explanation:
We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.
He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.
<em>Let </em><em> = mean length of commercials on his station.</em>
So, Null Hypothesis, :
= 24 seconds {means that the mean length of commercials on his station is equal to 24 seconds}
Alternate Hypothesis, :
24 seconds {means that the mean length of commercials on his station is different from 24 seconds}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample average length of these commercials = 26.3 seconds
s = sample standard deviation = 7.2 seconds
n = sample of commercials = 200
So, <u><em>test statistics</em></u> = ~
= 4.518
The value of t test statistics is 4.518.