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2 years ago

7

At the AoPS office, mice vary inversely with cats, that is, $\text{mice}=\frac{k}{\text{cats}}$, for some value of $k$. When the

re are $3r-19$ cats, there are $2r+1$ mice, and when there are $6r-27$ mice, there are $r-5$ cats. Find $k$. I really need help, thanks.

1 answer:

lesya692 [45]2 years ago

5 0

Answer:

540

Step-by-step explanation:

im terrible at explaining so-

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A disk with radius 3 units is inscribed in a regular hexagon. Find the approximate area of the inscribed disk using the regular

Oksi-84 [34.3K]

Answer:

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

$m\angle AOM =30^o$

In the right triangle OAM

$tan(30^o)=\frac{(a/2)}{r}=\frac{a}{2r}\\\\tan(30^o)=\frac{\sqrt{3}}{3}$

so

$\frac{a}{2r}=\frac{\sqrt{3}}{3}$

we have

$r=3\ units$

substitute

$\frac{a}{2(3)}=\frac{\sqrt{3}}{3}\\\\a=2\sqrt{3}\ units$

Find the area of six equilateral triangles

$A=6[\frac{1}{2}(r)(a)]$

simplify

$A=3(r)(a)$

we have

$r=3\ units\\a=2\sqrt{3}\ units$

substitute

$A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2$

Therefore

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

6 0

3 years ago

Jeremy is going on rides at a carnival he starts the rides a 12:30 by 12:45 he had gone on 1/5 of the carnival rides at the rate

MArishka [77]

Answer:

1.25 hours or 1 hour and 15 minutes

Step-by-step explanation:

12:45 - 12:30 = :15

15 minutes equates to 1/5 of the rides

So, we multiply 15 by 5 to find the total time taken to ride all the rides.

15 x 5 = 75

75/60 = 1.25

It would take him 1.25 hours to ride all the rides at the carnival or 1 hour and 15 minutes.

8 0

3 years ago

The midpoint between (-4, 4) and (-2, 2)

Sav [38]

The midpoint is (-3,3)

5 0

3 years ago

Read 2 more answers

Plz halp. I just need #20, and please write out the equation so I know how to do it for future problems, thanks!

FrozenT [24]

The number you need is 16 all you have to do is work out the problem and try to understand it they are trying to confuse you don't need an equation.
Hope this help!
Have a Great day mate !!

6 0

3 years ago

Explain the difference between each pair of concepts.

Fynjy0 [20]

Answer:

a. B. Frequency is the number of times a particular distinct value occurs. Relative frequency is the ratio of the frequency of a value to the total number of observations.

b. A. A relative frequency is the same as a percentage expressed as a decimal.

Step-by-step explanation:

Frequency is the number of repetitions of a particular observation.

Relative Frequency is the ratio of the frequency of particular observation to the sum of frequencies of all the observations.

The percentage is the proportion of the whole.

Thus, In question (a)

Option B is the only correct answer.

and in question (b)

Option A is the only correct answer.

7 0

3 years ago