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g100num [7]
3 years ago
9

A goat is placed in a circular pen with a radius of 15 feet. The formula for the area of a circle is A=πr2, where r is the radiu

s. If π=3.14, on how many square feet of grass can the goat graze in the pen?
Mathematics
1 answer:
matrenka [14]3 years ago
7 0

Answer:

area of circular pen=πr²=3.14×15²=706.5ft²

706.5ft²of grass can goat graze in the pen.

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How long is the rail? Round your answer to the nearest tenth.
ziro4ka [17]

Answer:

D. 15.7 yards

Step-by-step explanation:

The safety rail makes a curved side of a quarter circle.

The length of the safety rail = circumference of the curved part only of a quarter circle = ¼*2πr

Where,

radius = 10 yards

π = 3.14

Plug in the values

= ¼*2*3.14*10

= 15.7 yards.

✅The rail is 15.7 yards long.

8 0
2 years ago
With a height of 68 ​in, Nelson was the shortest president of a particular club in the past century. The club presidents of the
Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: \\ z = -1.1739 \approx -1.174 (Nelson's height is <em>below</em> the population's mean 1.174 standard deviations units).

d. Nelson's height is <em>usual</em> since \\ -2 < -1.174 < 2.

Step-by-step explanation:

The key concept to answer this question is the z-score. A <em>z-score</em> "tells us" the distance from the population's mean of a raw score in <em>standard deviation</em> units. A <em>positive value</em> for a z-score indicates that the raw score is <em>above</em> the population mean, whereas a <em>negative value</em> tells us that the raw score is <em>below</em> the population mean. The formula to obtain this <em>z-score</em> is as follows:

\\ z = \frac{x - \mu}{\sigma} [1]

Where

\\ z is the <em>z-score</em>.

\\ \mu is the <em>population mean</em>.

\\ \sigma is the <em>population standard deviation</em>.

From the question, we have that:

  • Nelson's height is 68 in. In this case, the raw score is 68 in \\ x = 68 in.
  • \\ \mu = 70.7in.
  • \\ \sigma = 2.3in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

That is, <em>the positive difference is 2.7 in</em>.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many <em>standard deviations</em> is that, we need to divide that difference by the <em>population standard deviation</em>. That is:

\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174

In words, the difference found in part (a) is 1.174 <em>standard deviations</em> from the mean. Notice that we are not taking into account here if the raw score, <em>x,</em> is <em>below</em> or <em>above</em> the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

\\ z = \frac{x - \mu}{\sigma}

\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}

\\ z = \frac{-2.7\;in}{2.3\;in}

\\ z = -1.1739 \approx -1.174

This z-score "tells us" that Nelson's height is <em>1.174 standard deviations</em> <em>below</em> the population mean (notice the negative symbol in the above result), i.e., Nelson's height is <em>below</em> the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

\\ -2 < z_{Nelson} < 2

\\ -2 < -1.174 < 2

Then, Nelson's height is <em>usual</em> according to that statement.  

7 0
3 years ago
Write the equation for the line that goes through point (1, 1) with slope m = -9
DENIUS [597]

1) Since we have the slope, and one point we can find that linear equation using this point-slope formula. Plugging them we have:

\begin{gathered} (y-y_0)=m(x-x_0) \\ y-1=-9(x-1) \\ y-1=-9x+9 \\ y=-9x+9+1 \\ y=-9x+10 \end{gathered}

2) Note that we had to add 1 to both sides, to keep the "y "on the left.

3) Therefore, y=-9x+10 is the answer.

7 0
1 year ago
Find the equation of a line parallel to y=2x-4 that contains the points (5,1)
Alex73 [517]
The correct answer is
y=2x-9

Since the lines are parallel, they will gave the same slope (in this case it’s 2)

Our equation will be
y=mx+b

We know the slope is 2, and they’ve given us x and y coordinates. Plugging it in to the slope equation we get

1=2(5)+b

1=10+b

Subtract 10 from both sides and you get

-9=b

Putting it together our new parallel line will be

y = 2x - 9
5 0
3 years ago
Which of the following is not an example of replication?
Vitek1552 [10]

Solution: Which of the following is not an example of replication?

Answer: Replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. Therefore option A is not an example of replication

A. Conducting different experiments on the same groups

3 0
3 years ago
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