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KatRina [158]
4 years ago
11

The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2) pa

rtitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
A. 0
B. 2/5
C. 4/7
D. 1
E. 7/4
Mathematics
1 answer:
Pie4 years ago
7 0

Answer:

The answer is A

Step-by-step explanation:

The rectangular has a height of 4 unit and has a width of 7 units. Area of the rectangular is:

4*7=28

28 unit square.

The point of (2,2) is on the middle height of rectangular shape. The point has 2 unit distance to base and ceiling of the rectangular.

The line y=2 is passing thought on (2,2) and also divides rectangular into two rectangular which have 14 unit square area.

Therefor, the slope is 0

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Answer:

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We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305

The degrees of freedom for this sample size are:

df=n-1=50-1=49

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

MOE=t\cdot s_M=2.01 \cdot 0.305=0.61

Then, the lower and upper bounds of the confidence interval are:

LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95

The 95% confidence interval for the mean is (5.73, 6.95).

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