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Pani-rosa [81]
3 years ago
7

Please help i dont understand thank you

Mathematics
1 answer:
Alenkasestr [34]3 years ago
8 0

Answer:

Part a)

We need to find the equation of a straight line passing through two given points in slope-intercept form

Part b)

The information given; we are given two points where the line passes through; (0, -4) and (-2, 2)

Part c)

We shall first determine the slope of the line using the formula;

change in y/change in x. Next, we determine the value of the y-intercept using the general form of the equation of a straight line in slope-intercept form; y = mx+c

Part d)

The slope of the line is calculated as;

(2--4)/(-2-0) =6/-2 = -3

The equation of the line in slope-intercept form becomes;

y = -3x +c

We use the point (0, -4) to determine the value of c;

-4 = -3(0)+c

c = -4

Part e)

Final solution thus becomes;

y=-3x-4

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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
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.

<u><em>Let X = time for this event for boys in secondary school</em></u>

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.

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

       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

        P(Z > \frac{x-460}{40} ) = 0.10

<em>So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;</em>

<em>                   </em>      \frac{x-460}{40} =1.2816

                         {x-460}{} =1.2816\times 40

<em>                           </em>x = 460 + 51.264 = <u>511.264 seconds</u>

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

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