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aksik [14]
2 years ago
14

The distances (in yards) for nine holes of a golf course are listed.

Mathematics
1 answer:
k0ka [10]2 years ago
5 0

Answer:

A.) 358; 375

B.) 1074 ; 1125

C.) Both the mean and median values in feets could be obtained by just multiplying the values in yards by 3

D.) If we have our median and mean of thee original dataset in inches, we just divide the values by 36 to get our mean and median values in yard.

Step-by-step explanation:

Given the data (in yards)

Rearranged data : x (in yards) :

441, 531, 1008, 1080, 1125, 1179, 1224, 1512, 1566

Mean, m : Σx/n

ΣX = 3222 ; n = sample size, n = 9

m = 3222 / 9

m = 358

Median :

0.5(n +1) th term

0.5(9 + 1)th term

0.5(10) = 5th term = 375

Converting the data to feets :

147, 177, 336, 360, 375, 393, 408, 504, 522

1 yard = 3 feets

In Feets:

441, 531, 1008, 1080, 1125, 1179, 1224, 1512, 1566

Mean, m : Σx/n

ΣX = 9666 ; n = sample size, n = 9

m = 9666 / 9

m = 1074

Median :

0.5(n +1) th term

0.5(9 + 1)th term

0.5(10) = 5th term = 1125

C) Both the mean and median values in feets could be obtained by just multiplying the values in yards by 3

D.) since 1 yard = 36 inches

If we have our median and mean of thee original dataset in inches, we just divide the values by 36 to get our mean and median values in yard.

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To solve this problem, we need to know 2 relationships:

<h2>1. AC = AB + BC</h2>

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AC = AB + BC

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<h2>2. AB = BC</h2>

The distance of AB is the same as AC.

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We know this since B is in the middle of AC, so the distance from B to A (BA) is the same as the distance from B to C (BC).

You can see the attached image (at the bottom) for a visualization of this.

<h2>Putting them together</h2>

Since we know the values of AB and BC...

AB = x+9\\BC = 3x-7

...we can put these values into our 2nd equation and solve for x:

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Knowing x, we can find the distance of AC using our first equation.

AC = AB + BC

Let's put in the values of AB and BC:

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We group x and 3x and add those together. Then we subtract 7 from 9.

With this equation, we can put in x = 8:

AC = 4x +2\\AC = 4*8 + 2

Since 4 * 8 = 32:

AC = 4 * 8 + 2\\AC = 32 + 2\\AC = 34

Finally, we have found both x and AC.

<h2>Answer</h2>

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