Hello from MrBillDoesMath!
Answer:
l = 12 feet, w = 5.5
Discussion:
Let w be the width of the pen and "l" the length. From the problem statement
l = w + 6.5 and the perimeter, P, of the fence -= 35.
Now the perimeter of the rectangle is given by the formula
P = 2l + 2w.
In our case, P = 35 and l = w + 6.5 so the equation becomes:
35 = 2(w+6.5) + 2w =>
35 = 2w + 13 + 2w =>
35 = 4w + 13 => (subtract 13 from both sides)
35-13 = 4w =>
22 = 4w =>
w = 22/4 = 5.5 feet
As, l = w + 6.5, l = 5.5 + 6.5 = 12 feet
Thank you,
MrB
Answer:
Part A) 82% of $5.00 is $4.10.
Part B) Less, because $5.00 is 2x as much as $2.50, therefore anything over 50% would be less, and anything under would be more.
The tangents are equal length, so
.. 8x = x^2
We presume their length is not zero, so we can divide by x to get
.. 8 = 2x
.. 4 = x
Then the length of each tangent is 8*4 = 32 units.
Answer:
108 miles
Step-by-step explanation:
Given the points (0.5, 135) and (2,81)
Diatnce between two points :
D = √(x2 - x1)² + (y2 - y1)²
X1 = 0.5 ; y1 = 135 ; x2 = 2 ; y2 = 81
D = √(2^2 - 0.5^2) + (81^2 - 135^2)
D = √(4 - 0.25) + (6561 - 18225)
D = √3.75 −11664
D = 107.98263
D = 108 miles
Answer:
Yes
Step-by-step explanation:
First, suppose that nothing has changed, and possibility p is still 0.56. It's our null hypothesis. Now, we've got Bernoulli distribution, but 30 is big enough to consider Gaussian distribution instead.
It has mean μ= np = 30×0.56=16.8
standard deviation s = √npq
sqrt(30×0.56×(1-0.56)) = 2.71
So 21 is (21-16.8)/2.71 = 1.5494 standard deviations above the mean. So the level increased with a ˜ 0.005 level of significance, and there is sufficient evidence.
