Speed skiing takes place on a course that is 2/3 mile long. How many feet long is the course? Show work too
2 answers:
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Answer:
Area of Circle A = 1133.54
Circumference of Circle A= 119.32
Step-by-step explanation:
Given: Sum of both circle diameters= 49 feet.
Circle A radius= Three feet less than twice the diameter of circle B.
Lets assume diameter of Circle B is "x"
∴ Circle A radius (r)=
We know, the diameter of circle is
Diameter of Circle A is
Next as given sum of both circle diameter is 49 feet.
∴
distributing 2 with 2x and -3
⇒
⇒
Adding both side by 6
⇒
Cross multiplying both side.
⇒
∴ Diameter of circle B is 11 feet.
Next, subtituting the value of x to get the value of radius for Circle A.
Radius of circle A=
⇒ Radius of circle A=
∴ Radius of circle A= 19 feet.
Area of circle=
Taking π= 3.14
Area of circle A=
∴ Area of circle A= 1133.54
Circumference of circle= 2πr
Circumference of Circle A=
∴ Circumference of Circle A= 119.32
Answer:
a) 20.16; b) 20.49 and 21.51
Step-by-step explanation:
We use z scores for each of these. The formula for a z score is
.
For part a, we want the 20th percentile; this means we want 20% of the data to be lower than this. We find the value in the cells of the z table that are the closest to 0.20 as we can get; this is 0.2005, which corresponds with a z score of -0.84.
Using this, 21 as the mean and 1 as the standard deviation,
-0.84 = (X-21)/1
-0.84 = X-21
Add 21 to each side:
-0.84+21 = X-21+21
20.16 = X
For part b, we want the middle 39%. This means we want 39/2 = 19.5% above the mean and 19.5% below the mean; this means we want
50-19.5 = 30.5% = 0.305 and
50+19.5 = 69.5% = 0.695.
Looking these values up in the cells of the z table, we find those exact values; 0.305 corresponds with z = -0.51 and 0.695 corresponds with z = 0.51:
-0.51 = (X-21)/1
-0.51 = X-21
Add 21 to each side:
-0.51+21 = X-21+21
20.49 = X
0.51 = (X-21)/1
0.51 = X-21
Add 21 to each side:
0.51+21 = X-21+21
21.51 = X