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3 years ago

If the circumference of the circle is 37.68 units, what is the area? (Use 3.14 for pi .)

Mathematics

1 answer:

cricket20 [7]3 years ago

3 0

Answer:

Area of the circle = $113.04\;units^2$

Step-by-step explanation:

Circumference = $37.68\;units$

Circumference of the circle = $2\times \pi \times r$

As,

$\pi =\dfrac{22}{7}=3.14$

$37.68=2\times \pi \times r\\\\37.68=2\times 3.14 \times r\\\\37.68=6.28\times r\\\\r=\dfrac{37.68}{6.28} \\\\r=6\;units$

Area of a circle = $\pi \times r^2$

$=3.14\times (6\times 6)\\\\=3.14\times 36\\\\=113.04\;units^2$

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Because of staffing decisions, managers of the Gibson-Marion Hotel are interested in the variability in the number of rooms occu

olchik [2.2K]

Answer:

a) $s^2 =30^2 =900$

b) $\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

c) $23.818 \leq \sigma \leq 41.112$

Step-by-step explanation:

Assuming the following question: Because of staffing decisions, managers of the Gibson-Marimont Hotel are interested in the variability in the number of rooms occupied per day during a particular season of the year. A sample of 20 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 30 rooms

Part a

For this case the best point of estimate for the population variance would be:

$s^2 =30^2 =900$

Part b

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The degrees of freedom are given by:

$df=n-1=20-1=19$

Since the Confidence is 0.90 or 90%, the significance $\alpha=0.1$ and $\alpha/2 =0.05$ , the critical values for this case are:

$\chi^2_{\alpha/2}=30.144$

$\chi^2_{1- \alpha/2}=10.117$

And replacing into the formula for the interval we got:

$\frac{(19)(30)^2}{30.144} \leq \sigma^2 \leq \frac{(19)(30)^2}{10.117}$

$567.28 \leq \sigma^2 \leq 1690.224$

Part c

Now we just take square root on both sides of the interval and we got:

$23.818 \leq \sigma \leq 41.112$

5 0

4 years ago

A bullet is fired straight up from a gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the form

Dafna1 [17]

Answer:

70 seconds

Step-by-step explanation:

Given that;

The initial velocity $v_o$ of the bullet fired = 1120 ft/s

Initial height h = 8 feet

The expression to determine how many seconds it takes the bullet to hit the ground is:

$h = -16t^2 +v_ot + 8$

Thus;

Replacing the value of $v_o$ = 1120 and h = 0 (i.e. when h =0) in the above expression; we have:

$0= -16t^2 +(1120)t + 8$

$= -16t^2 +(1120)t + (8-0)$

= -16t² + 1120t + 8

mulitiply through by (-)

= 16t² -1120t - 8

Divide through by 8

= 2t² - 140t - 1

The above expression forms a quadratic equation.

where;

a = 2

b = -140

c = - 1

So, by using the quadratic formula $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$ , we have:

$= \dfrac{-(-140) \pm \sqrt{(-140)^2-4(2)(-1)}}{2(2)}$

$= \dfrac{140 \pm \sqrt{19600-(-8)}}{4}$

$= \dfrac{140 \pm \sqrt{19608}}{4}$

$= \dfrac{140 \pm 140}{4}$

$=\dfrac{140+ 140}{4} \ \ \ OR \ \ \ \dfrac{140-140}{4}$

$=\dfrac{280}{4} \ \ \ OR \ \ \ 0$

= 70

Thus, the time (in seconds) it took the bullet to it the ground = 70 seconds

6 0

3 years ago

What is 3×1 and 3/5 A) 2 and 2/5 B) 4 and 3/5 C) 4 and 4/5 D) 7 and 4/5

Bas_tet [7]

Option C is your answer.

1 3/5 is the same as 8/5

3(8/5) = 24/5 = 4 and 4/5

3 0

3 years ago

I'm having trouble figuring out what the difference between two positive numbers are. The numbers are 3.9 and 8.3 and I'm not su

Tju [1.3M]

To find the difference between these numbers you need to subtract 8.3 - 3.9
and that equals 4.4

8 0

3 years ago

Read 2 more answers

Write an algebraic expression for the phrase five less than the product of six and N

GenaCL600 [577]

Answer:

6N - 5

Step-by-step explanation:

five less than the product of six and N: 6N

five less than the product of six and N: 6N - 5

Answer: 6N - 5

6 0

3 years ago