KnockOut

So lets start out by figuring out what fraction of the whole circumference the arc takes up.

The arc has a length of \(\frac{8}{5}\), or \(1.6\), out of a circle with circumference \(12\).

The arc takes up \(\frac{1.6}{12} = \frac{16}{120} = \frac{2}{15}\)of the whole circumference. 

This also means that the central angle of the arc takes up \(\frac{2}{15}\) of the entire \(360\) degree angle.

So the central angle of the arc is \(\frac{2}{15}\) of \(360\), which is \(\boxed{48 \space \text{degrees}}\).

https://www.mathcounts.org/resources/video-library/mathcounts-minis/mini-87-using-geometric-models-determine-probability

Follow the link and a guy that looks like  will explain it to ya.

Another way of approaching the problem is by setting up equations.

Let \(b = \text{ # of chocolate bars}\), and \(c = \text{# of gummy candy}\)

Because the total number of bars and candies sold was \(275\),

We can set up the equation \(b + c = 275\)

Next, we have the individual price for the chocolate bars, the individual price for the gummies, and the total price. We can set up another equation using these three.

\($1.25 ( \text{# of chocolate bars} ) + $0.75 ( \text{# of gummy bears} ) = \text{total price}\),

Therefore,

\(1.25b + 0.75c = 272.25\)

Now we have our two equations,

\(b + c = 275\)

\(1.25b + 0.75c = 272.25\)

You can either use substitution or elimination to solve for the two equations,

Which leaves us with our final answers:

\(\boxed{b = 132 , c = 143}\)

Multiply the length of the wooden board by the cost per foot to get your answer.

In this case (assuming the values are 745 and 0.70 because your numbers seem to have repeated when you typed the question out)

Your answer would be the value of 745 x 0.70

Hey!

So let's start off by doing some conversions.

(Whisper) there's \(5280\) feet in a mile (Whisper)

Ok, since we already know that \(1\) mi = \(5280\) ft,

We can set up a ratio to figure out that \(15.5\) mi = \((15.5 \times 5280\)) = \(81,840\) ft.

Now, that's not our answer just yet.

We have to do the second conversion.

Because we know how time works, there's \(60\) minutes in an hour.

We need the speed in \(\frac{\text{ft}}{\text{min}}\), so we have \(\frac{81840}{60}\) = \(\boxed{1,364 \frac{\text{ft}}{\text{min}}}\)

\(\boxed{\boxed{\boxed{3}}}\)

Hey but let's be honest, you knew that 

Hey!

Let's start by setting two variables, 

\(S = \text{sheep}\)

\(C = \text{chicken}\)

Once we have our variables we can go ahead and make our equations:

1.) The easiest equation that we can make with these two variables is with the total # of animals.

The number of sheep + The number of chickens = The total # of animals,

So we get the equation: \(S + C = 20\).

2.) Now, we are given that sheep have \(4\) legs and chickens have \(2\) legs.

(The number of sheep x The number of legs each sheep has) + (The number of chickens x The number of legs each chicken has) = The total # of legs.

So we get the equation \(4S + 2C = 64\)

Now that we have our two equations,

\(4S + 2C = 64\)

\(S + C = 20\),

You can use the two equations to either substitute the variables or eliminate them to find your answer. 

This isn't a full question?

@Rom don't you need to apply the -1 to both sides of the inequality?

\(-4 \le 2x+1 \le 6\)

\(-5 \le 2x \le 5\)

\(-\frac{3}{2} \le x \le \frac{5}{2}\)

\(x \in \{-2, -1, 0, 1, 2, \}\)

\(\text {5 integers satisfy the inequality}\)