Solve the word problem. Round your final result to the nearest hundredth.

Mathematics

1 answer:

fenix001 [56]3 years ago

4 0

Answer:

1)Area of circle: 64 $\pi$

2)Area of semicircles: 128 $\pi$

3)Area of quarter-circles: 128 $\pi$

4)Total area of pattern: 320 $\pi$

Step-by-step explanation:

r = 8cm

Given: 1 circle, 4 semicircles, and 8 quarter-circles.

Area of a circle: $\pi r^{2}$

1) A = $\pi r^{2}$ where r = 8

A = 64 $\pi$

2) 4 semicircles = 2 circles

so the answer is 2*A = 128 $\pi$

3) 8 quarter-circles = 2 circles

Therefore, the answer here is the same as the answer for #2!

4)There are 5 circles total because:

1 circle = 1 circle

4 semicircles divided by 2 = 2 circles (because $\frac{1}{2}$ times 4)

8 quarter-circles divided by 4 (think about what "quarter" means) = 2 circles

So ... 1 + 2 + 2 = 5 circles

Now we need to find the area of 5 circles which is just 5*A

5*A = 320 $\pi$

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One year Ron had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched)

Arada [10]

Answer:

Ron's ERA has a z-score of -2.03.

Karla's ERA has a z-score of -1.86.

Due to the lower z-score, Ron had a better yean than Karla relative to their peers.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Since the lower the ERA, the better the pitcher, whoever's ERA has the lower z-score had the better year relative to their peers.

Ron

ERA of 3.06, so $X = 3.06$