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3 years ago

The function y = f(x) is graphed below. What is the average rate of change of the

Mathematics

1 answer:

stepladder [879]3 years ago

7 0

Answer:

Average rate of change = 1

Step-by-step explanation:

Average rate of change of a function between x = a and x = b is defined by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

We have to find the average rate of change of the function in the interval 2 ≤ x ≤ 4

Therefore, average rate of change of the function = $\frac{f(4) - f(2)}{4-2}$

From the graph attached,

f(4) = 4

f(2) = 2

Average rate of change = $\frac{4-2}{4-2}$

= 1

Therefore, average rate of change of the function in the given interval is 1.

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AlekseyPX

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( $\mu=460,\sigma^{2} =40^{2}$ )

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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}

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