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3 years ago

Another set of 10 points

Mathematics

2 answers:

kenny6666 [7]3 years ago

6 0

I’m not sure why you don’t feel good about it I just want you

Vanyuwa [196]3 years ago

5 0

The circumference of the circle is 12.56 km

You might be interested in

Water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the v

Cloud [144]

Answer:

Step-by-step explanation:

Given that water leaks from a vertical cylindrical tank through a small hole in its base at a rate proportional to the square root of the volume of the water remaining. The tank intitially contains 300 liters and 23 liters leak out during the first day

Let V represent the volume at time t.

Rate of change of V is $\frac{dV}{dt} = k\sqrt{v}$

where k represents the constant of proportionality

We separate the variables and integrate

$\frac{dV}{\sqrt{v} } =kdt\\2\sqrt{V} =kt +C\\$

Use the fact when t =0, V =300

$2\sqrt{300} =C\\$

Now use the fact when t =1 V= 300-23 = 277

$2\sqrt{277} =k+2\sqrt{300} \\k = 2(-0.67719) = -1.3544$

k is negative because there is leak

So equation is

$2\sqrt{V} =-1.3544t+2\sqrt{300} \\V= (-0.6772t+\sqrt{300} )^2$

Using this

A) when half empty V = 150

t = $\frac{2\sqrt{150} -2\sqrt{300}}{-1.3544} \\=3.75$

so it takes 3.75 days

B) When t =3

V = 233.7515

6 0

4 years ago

Farmer Ed has 1.000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not f

Lady_Fox [76]

Answer:

1000 m of fence can make a 3-sided enclosure of 125,000 m²

Step-by-step explanation:

Let x represent the length of fence parallel to the river. Then the perpendicular dimension is ...

width = (1000 -x)/2

and the enclosed area is ...

area = length×width = (x)(1000 -x)/2

This describes a downward-opening parabola with zeros at x=0 and x=1000. The vertex (maximum) is halfway between, at x=500.

Then the maximum area is ...

area = (500)(1000 -500)/2 = 125,000 . . . . square meters

7 0

3 years ago

If 9 batteries cost 25 dollars what is the rate and unit rate

sergij07 [2.7K]

Answer: 2.77777778

Step-by-step explanation:

25/9=2.77777778

check

2.77777778*9= 25 dollars

8 0

3 years ago

In a data set with a normal distribution, the mean is 59 and the standard deviation is 3.

Delicious77 [7]

Answer:

Part A: 81.5%

Part B: About 95% of the data lie between 53 and 65.

Step-by-step explanation:

Note: the percentages marked in red and blue never change

For Part A, we add the percentages that are between 53 and 62. So, 34% + 34% + 13.5% which is 81.5%

For Part B, we can look at this graph and seen that 95% of this data set lies between 53 and 65

Hope this is correct and of help!

4 0

2 years ago

g A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. In a rando

Tema [17]

Answer:

We accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

Step-by-step explanation:

A sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50.

This means that the null hypothesis is:

$H_{0}: \mu = 50$

And the alternate hypothesis is:

$H_{a}: \mu \neq 50$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

50 tested at the null hypothesis:

This means that $\mu = 50$

In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.

This means that $n = 36, X = 50.67, \sigma = 3.9$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{50.67 - 50}{\frac{3.9}{\sqrt{36}}}$

$z = 1.03$

p-value:

Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03.

z = 1.03 has a pvalue of 0.8485

1 - 0.8485 = 0.1515

2*0.1515 = 0.3030

0.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.

5 0

3 years ago