Answer:
Step-by-step explanation:
Find the digram attached.
Perimeter of the track = perimeter of the rectangle + perimeter of the 2semicircles
Perimter of a rectangle = 2(x+r) where:
x is the length
2r is the width of the rectangle = diameter of the semicircle
Perimeter of semicircle = 2πr/2 = πr
Perimeter of 2semicirle = 2πr
Perimeter of the track = 2(x+2r) + 2πr
r is the radius if the semicircle
Expand
Perimeter of the track = 2x+4r + 2πr
Perimeter of the track = 2(x+2r+πr)
b) Given P = 2(x+2r+πr), we are to make x the subject of the formula.
P = 2x+4r+2πr
P-4r-2πr = 2x
Divide both sides by 2.
(P-4r-2πr)/2 = 2x
x = (P-4r-2πr)/2
c) Given
P = 600fr
r = 50ft
x = (600-4(50)-2π(50))/2
x = (600-200-100(3.14))/2
x = 400-314/2
x = 86/2
x = 43ft
Hence the value of x to nearest foot is 43ft
Answer:
a) 0.7403
b)0.0498
c)0.2240
Step-by-step explanation:
Given: The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution
We know that to calculate expected number of flaws use
expected number of flaws =10×0.03 =0.3
a) probability that there are no surface flaws in an auto's interior =P(X=0)=
e^-0.3 =0.7408
b) probability that none of the 10 cars has any surface flaws =(e^-0.3)^10 =0.0498
c) probability that at most one car has any surface flaws =P(X<=1)=P(X=0)+P(X=1)
this means
=10C_0(1-0.7408)^0(0.7408)^10+10C_1(1-0.7408)^1(0.7408)^9=0.2240
Given:
Scatter plot of weight loss plan.
To find:
how many pounds were lost per month with 4 hours of weekly.
Solution:
Take any two points on the trend line.
Let the points are (3, 4) and (5, 7).
Slope of the line:
m = 1.5
Using point-slope formula:
Add 4 on both sides.
Approximate equation of a line is y = 1.5x - 0.5
Substitute x = 4.
y = 1.5(4) - 0.5
y = 6 - 0.5
y = 5.5
Which is nearly equal to 6.
Also see in the scatter plot, y-value for the corresponding value of 4 in x-axis is 6.
Hence 6 pounds lost per month with 4 hours of weekly aerobic activity.
