If a circle has a circumference of C, what is the area of the circle in terms of C?

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First you have to write down the formula on how to get the circumference of the circle (C = 2pi * Radius) and the Area of the circle which is (A=Pi*Radius^2). In getting the radius you need to transform the formula of the circumference by making the radius to be the unknown variable so it would become(R=C/2pi), after that you need to replace the radius in the formula of the area by the transformed formula of the circumference and you will come up of the formula of (A=Pi(C/2pi)^2).

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The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a

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Answer:

The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.

Step-by-step explanation:

We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.

The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.

Let X = time for this event for boys in secondary school

SO, X ~ Normal( $\mu=460,\sigma^{2} =40^{2}$ )

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean time = 460 seconds

$\sigma$ = standard deviation = 40 seconds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;

P(X > x) = 0.10 {where x is the required time which boy need to beat}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-460}{40}$ ) = 0.10