Hmmmm

How did you box your answer?

Percent is in the form of:

$$x/100$$
 

So we try to get:

$$14/70 = x/100$$

We simplify the right side fraction:

$$2/10 = x/100$$
 

We multiply the right side by 10 on the numerator and denominator:

$$20/100 = x / 100$$
 

So x = 20

So your answer is 20%

~Hmmmm

Probability is:

successes/total

We start by finding the total number of draws that you can do:

6 * 5 * 4 * 3 * 2 * 1

Now, we have to find the probability that you actually draw your pair:

6 * 1 

-> For the first pair:

4 * 1

-> After taking out the second pair:

2 * 1 

-> For the third pair

So, successes are: (6 * 4 * 2)/(6 * 5 * 4 * 3 * 2 * 1)

1/(5 * 3)

1/15

So the probability is 1/15.

I might be incorrect as I'm not the best at this, so if you find it incorrect please tell me.

We have the equation:

X + 1 = 0

Subtract 1 from both sides:

X = -1

Well, if there is only 3 games, and 1/5 probability for each, I believe you just do:

1/5 * 1/5 * 1/5

= 1/125 probability that the Bears actually win the tournament.

However, if I am wrong, please tell me, as I would be happy to learn what my mistake was and how I could have corrected it!

I don't see "the 5 boxes below"...

If x = 12, then your equation simplifies to:

$$36 + y = a$$

and

$$24 + 5y = 2a$$

We can substitute a for 36 + y:

$$24 + 5y = 72 + 2y$$

$$3y = 48$$

$$y = 16$$

We now know that y is 16, and we substitute that into our first equation:

$$36 + 16 = a$$

$$52 = a$$

$$a = 52$$

So the value of a is 52.

If I am wrong, please tell me as I would be happy to fix it!

Oh, right, you could also solve it using discriminants. Didn't even think of that 

Pretty sure your answer is just a repeat. Check out this one:

Alright, so we're going to write a system of equations and define the variables:

d = the number of drinks Jordan buys

t = the number of tacos Jordan buys

We know that he bought 4 more tacos than drinks so:

$$t = 4 + d$$

Our next equation is:

$$2.50 \cdot d + 2 \cdot t = 26$$

Since t = 4 + d, we substitute this into our equation:

$$2.50 \cdot d + 2 \cdot (d + 4) = 26$$

We simplify:

$$2.50d + 2d + 8 = 26$$

Subtract 8 from both sides:

$$2.50d + 2d = 18$$

$$4.50d = 18$$
 

We divide by 4.50

$$d = 4$$

So we know that he bought 4 drinks, and when we do d + 4 = 8 tacos.

If anything is wrong, please tell me as I would be happy to help!

Hmmm...

We have the equation:

$$2x^2 + 5x + c = x^2 - 4x$$

We subtract x^2 from both sides:

$$x^2 + 5x + c = -4x$$
We add 4x to both sides:

$$x^2 + 9x + c = 0$$

Now, I want to clarify one thing, when finding the largest product, there is a pretty easy way to do this with intuition.

Try multiplying:

$$7*\cdot3 = 21$$

$$6\cdot4 = 24$$

$$5\cdot5 = 25$$

When doing this similar multiplication process with other numbers, you will realize that the closer the numbers are, the greater their product is:

So, when we want the max value of our constant, we have to use the closest numbers together.

We also notice that our two numbers (r and s) have to equal 9. Since we need the closest numbers, then r = s.

$$2r = 9$$

$$r = 4.5$$

So our equation would be in the form:

$$(x + 4.5)(x + 4.5) = x^2 + 9x + 20.25$$

Therefore the greatest constant value is 20.25.

Expressing this answer in a fraction can either be 20 1/4 or 81/4

Please tell me if I am incorrect as I would be happy to fix it!

I'm pretty sure this is an illogical question, because I don't see any numbers, and you have unnecessary spaces where numbers should be. Please fix that...

I'm new here so maybe I'm missing something, but I don't see any grid below, is there something wrong with your question, or am I missing something?

@Guest, I'm getting something different hopefully you can help me with the problem I'm having here:

Say our coins were in the form of:

_ _ _ _ _ _ _ _ _ _

Where each "_" is either a head or a tail. We need 8 of the tosses to be heads, so we do:

choose 8 of 10

This is 45, then for the other two, we have 2 * 2 = 4 options for what those can be, so I'm getting

45 * 4 = 180

So that's my answer (but it's probably incorrect, and if it is, please tell me so I can fix it!)

Hmmm...

I'm going to try and solve this in the best way possible (although I might get the answer wrong, so I advise you to read through my explanation first)

Before I start my answer, I want to clarify what you should know:

- how percents work

- how to define a variable

- how to solve a simple algebraic expression

If you don't know any of these, than I advise you to learn as these are major concepts which will help you later on, to make sure that you understand and read my explanation, I will only be giving you the answer to a) so that you can work out (hopefully) the other ones.

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Let's start by clarifying the question, we have:

red potion  contains 50% of the syrup

blue potion contains 15% of the syrup

We want to know how much red potion should be added to 300 ml of blue potion to get a potion which is 20% syrup.

We have 300 ml of blue potion. Let's start by figuring out how much syrup is in the 300 ml.

We have 15% of 300 = 45 ml of syrup

We want 20% of the total to be syrup

We define x as the amount of red potion that goes in to be 20%

Our equation is:

(.50x + 45)/(300 + x) = 20/100

We multiply by 300 + x

(.50x + 45)(100) = (6000+20x)

50x + 4500 = 6000 + 20x

30x = 1500

x = 50

So our equation says that we will add 50ml of red potion, let's confirm:

50 ml of red potion has 25 ml of syrup:

(45 + 25)/(300+50)
70/350 = 20/100 = 1/5

So for part a) we need 50ml of red potion, hope you can solve the other ones because I think I gave a pretty solid solution! (If it is wrong please tell me, as I will be happy to fix it!)

~ Hmmmm

I'm new here so maybe I'm missing something, but I don't see any grid below, is there something wrong with your question, or am I missing something?