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3 years ago

A soccer player stands in the southeast corner of a 76-meter by 57-meter field and kicks a

Mathematics

1 answer:

sukhopar [10]3 years ago

3 0

Answer:

228m

Step-by-step explanation:

Let's draw a rectangle ABCD, A being its bottom left point, B bottom right, C top right and D top left.

That is our soccer field. The player stands in the southeast corner, which is top right corner or, in our case point B. He passes the ball to the player in the opposite corner, which is corner D. He then passes the ball to the player in the southwest corner, which is corner A. And he finally passes it back to the player in the corner B.

So, the ball goes from B to D to A to B. That means that the ball went along the circumference of the triangle DAB.

So, to answer how long the ball travelled we need to find the circumference of the triangle. The circumference is the sum of its three sides. One side is the field's length (76m) and the othet is field's width (57m). We only need to find the triangle's hypotenuse, side BD, using Pythagoras theorem:

BD² = AB² + AD²

BD² = 76² + 57²

BD = 95

So, the circumference of the triangle is 76+57+95=228m

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3 years ago

Suppose that the sample standard deviation was s = 5.1. Compute a 98% confidence interval for μ, the mean time spent volunteerin

NISA [10]

Answer:

The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

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