jfan17

1. The angles in the dilation are the exact same, as they are both similar since their corresponding sides are all proportional to each other in a scale factor of 2.

2. I'd imagine there's some kind of tool to measure angle. Use that on both of these triangles, and you should find that they have the same angle measurements

3. That would be true for any angles in dilation, since dilating these triangles are just "stretching them", or magnifying their sides by a certain factor, leaving the same proportion between the original and the dilated triangle, meaning they remain similar, and thus, have the same angle measurements.

My advice would be to use complementary counting. In otherwords, you take the total number of ways to form a 3 senator committee, and subtract from it the number of ways that a single party can hold all 3 seats. That simplifies the problem immensely.

We then have:

100 * 99 * 98 ways to form a 3 member senate. If we had a committe with all 3 seats belonging to one party, there are two cases:

Democrats occupy all of them, of which there are:

47*46*45 ways to do this

Republicans occupy all of them, of which there are:

53*52*51

We add these two cases up, and then subtract it from the total number of ways to form a 3 member senate.

970200- 237846= 732354 ways(check me if I'm wrong)

No worries!  :)

The formula for volume of a cylinder is as follows:

given r as the area of one of its circular bases, and H as the height, 

the volume of the cylinder = \(\pi*r^2*h\)

The volume of the cylinder given in this problem has an 18 inch diameter, meaning the radius is 9

The volume is then:

\(\pi * 9^2 * 15 = 1215\pi\) in.³

Next, to calculate how much total water is within the cylinder, we just need to subtract the volume of the 6 inch diameter ball from the cylinder(since that ball takes up volume).

The volume of a sphere is as follows:

given r as its radius, its volume is then:

\(\frac43 * \pi * r^3\)

We are given that the diameter of this ball is 6 inches, so the radius is then 6/2 = 3 inches

The volume is then:

\(\frac43 * \pi * 3^3 = \frac43 * 27 * \pi = 36\pi\) in.³

Our total volume of water is then:

\(1215\pi - 36\pi = 1179\pi\)in.³

Oh right, oops on my part! The problem didn't say whether we have to find the smallest one tho, but I'm assuming it does :)

It says it's a quadratic, which means it has a degree of 2 if that answers your question. "Let f(x) be a quadratic polynomial"

When you divide fractions, yo\(\)u just multiply by their reciprocal. For example, if you have:

\(\frac4{\frac8{3}}\), this is equivalent to:

\(\frac4{1} * \frac3{8} = \frac{12}{8} = \frac32\)

For this question, it asks us to do 

\(\frac{2}{\frac73}\)

This is equivalent to:

\(\frac21 * \frac37 = \frac67\), so our answer is 6/7

1. Upon death of a specified person, a family or designated person will receive money based on the insurance policy's terms. This is important in the case of losing a key provider for a family.

2. In many cases, life insurance is necessary to provide "breathing room" for one's children or spouse in the case of a loss, in the form of an extra cash surplus

3. If looking at a business, life insurance could possibly save a small company (or even a big one) in the case of the loss of a key figure within the company. (the extra cash would keep the company afloat).

Many of these answers are along the same lines:

Life insurance acts as a "safety net" against any sort of financial blowback that comes as a result of someone's death

Hey guest! In this problem, we can make use of some number theory.

First we can write the following equivalences:

\(x \equiv 2 \pmod3\)

\(x \equiv 3 \pmod5\)

\(x \equiv 2 \pmod 7\)

Here, let's assume the first two conditions are true. 

We then get:

x = 3k + 2

x = 5j + 3

Let's start with x = 0, 1, 2, 3.....

for 3k + 2:

2, 5, 8, 11, 14, 17, 20, 23...... 38 etc.

for 5j + 3:

3, 8, 13, 18, 23, ....... 38, etc.

Do you see what's going on here now?

Every 15, starting from 8, the two sequences share a common element. This is because 15 is the lcm of 3 and 5, which makes sense in the context of this problem. We can then write that x would be of the form:

x = 15w + 8

Now let's look at the third and last equation.

We can write:

x = 7h + 2

Let's do the same sequences pattern. 

for 15w + 8:

8, 23, 38, 53....... 128

for x = 7h + 2:

2, 9, 16, 23, 30, 37, 44, 51.... 128

Here, the lcm of 15 and 7 is 105. 

The shared elements are of the form:

This is a combination of all three modulo equations.

105k + 23.

All solutions that hold true for this equation will satisfy the three modulo equations. Assuming that we are trying to find the smallest one(the problem doesn't say what to find exactly), if k =1, we get:

128 as our final answer. 

I posted an answer to this problem here:

https://web2.0calc.com/questions/reposted-again-bc-a-certain-user-kept-complaining