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By the Principle of Inclusion-Exclusion, there are 8 students who are in both classes.

19x +86 + 16 = 16x + 90

x = - 4

∠RPS = 19x + 86 = - 76 + 86 = 10º

∠QPS = 16x + 90 = - 64 + 90 = 26º  

Oh dear, my teacher is going to hunt me down for such a mistake!

anyways, thanks for the reminder! I just edited my answer, happy?

ilorty: Because you CAN repeat the letters, you have: 3^3 = 27 permutations.

AAA, AAB, AAC, ABA, ABB, ABC, ACA, ACB, ACC, BAA, BAB, BAC, BBA, BBB, BBC, BCA, BCB, BCC, CAA, CAB, CAC, CBA, CBB, CBC, CCA, CCB, CCC, Total No = 27 permutations

Notice how there are 39 numbers in the sequence, 78/2. Also notice how 2+78 = 80. We want to make this the easiest for us, so we should try to find all the pairs that sum to 80. 

Seeing as there are 39 numbers, there will be one solo. that means there will be 19 pairs all summing to 80. 19*80 = 1520. But we are still missing one number. Since there are 19 pairs, our last integer will be in the center. Between the 19th integer and the 19th to last integer, 38 and 42, respectively, is 40. So adding them, our answer is 1,520 + 40 = 1,560.

Nice job A.

@SHADOWwolf

Must be learning counting! If you'd pay attention in class, or at least even read/try the question, it come across as not very much of "HELP ASAP" worthy.

Let me spare you some time from doing your work, but you'll have to face the "doom" of reading my entire answer. Or else it would be done in vain. Maybe you'll use the few seconds I spared you to take one last look at that headless chicken you saw on the Internet. Maybe.

We begin placing each place. Use whatever you want, but for the headless chicken's sake, I will make a podium

                        ____________

                        |                       |
                        |                       |

                        |                       |___________

____________                          |                      |

|                       |                       |                      |

|                       |                       |                      |

|       3rd           |        1st          |        2nd        |

You have no idea how long that took. But I'm proud of it.

Now, for some permutations, which is just a fancy way to say: "Kids, we will learn multiplication today. Why do I bother teaching 12 year olds what they learned in second grade?"

Each number is the amount of choices for each spot:

We see there are 8 choices for 1st, 7 choices for 2nd, and 6 choices for 3rd.

8 * 7 * 6 = 336

336 possible combinations, what are the odds that I will win?

Now you may go hang out with the headless chicken 🐔 <------ i found the head!

:)

No guest! That answer is not 18, and you know it could not possibly be such a large number!

Think of the word as three spaces:

______  _______ _______
 

Now, each value on top of the spaces is how many options we can choose from:

    3             3              3

______  _______  _______

Now, multiply:

3 * 3 * 3

There! 27.

How could that possibly be 18? Last time I checked, 18 did not equal 27...

Still don't believe me? How many more can you find? Oh, so you found another one? Let me hear. ABCDEFGH? Lovely, maybe I forgot about that one....

:)
 

The question is not hard at all: it's funny how some people don't get the similarity between this and the Pythagorean theorem!

The formula for right triangle: c^2 = a^2 + b^2

Formula for distance between opposite points of rectangular prism: d^2 = x^2 + y^2 + z^2

See how simple it is? It probably faster than the time it takes for me to open my front door! (Really, that creature is super unruly, maybe oil will help)

Do you really want an answer? An answer you want, an answer you get.

Using the formula, we see that the diagonal squared is:

d^2 = 3^2 + 4^2 + 12^2

Evaluate:

3^2 + 4^2 + 12^2 = 9 + 14 + 144 = 167

Now root that:

And....your answer is sqrt(167)

maybe if you paid attention in class (I am assuming they gave a lecture) you would have known this simple formula. you could even do a quick google search!

maybe I finally entered my house after hours of trying to swing the door open...

:)

If the round trip took 6 hours, then:

Let the distance to Big Foot = D

D / 70  +  D / 50 = 6, solve for D

D = 175 miles - one-way distance to Big Foot.

175 / 70 = 2.5 hours - time it took him to get to Big Foot

ABCD = 162

It took 4 hours to get to bigfoot.

f^{-1}(-3) + f^{-1}(0) + f^{-1}(3) = -11.

We need to sharpen our trig skills, because believe it or not, this problem involves trig!

Anyways, I assume we are allowed to use calculators. 
 

For the community: Please don't submit solutions to this problem. This is a homework problem for an online course that does not allow students to search for answers to specific problems outside of the school.

For the original poster: We realize that homework can be challenging. If you wish to receive help from the staff or other students, we encourage you to use the resources that the online classes provide. Please don't ask or search online for homework help. We understand that it's common in today's information age to look for resources online, and in some contexts, that's a great thing! However, it's against our Honor Code. You can ask for help on the message boards, and you can learn from the official solution after you submit your answer.

This calls for "casework", though not much of counting...

We first need to figure out a "not so specific" range for quarters. We see that:

25 - 17 = 8

Which means, she can have from 1 to 8 quarters, but that is not specific enough. We also need to calculate the total amount of dimes she has:

0.1 * 17 = 1.7

Now, we can start:

If there were 1 quarter:

Not possible: not enough for the minimum amount of money

If there were 2 quarters:

Not possible: not enough for the minimum amount of money

If there were 3 quarters:

Not possible: not enough for the minimum amount of money

If there were 4 quarters:

Not possible: not enough for the minimum amount of money

If there were 5 quarters:

Not possible: not enough for the minimum amount of money

If there were 6 quarters:

Not possible: not enough for the minimum amount of money

If there were 7 quarters:

Not possible: not enough for the minimum amount of money

If there were 8 quarters:

Not possible: not enough for the minimum amount of money

so leave your answer blank.

BUT!

We could have saw from before whether there would have been enough money or not!

If we multiply: 8 * 0.25 = 2, and add that to 1.7, we get 3.7. Not possible.

What I don't understand about this problem is: If they literally said that Akana had some dimes and quarters, and they said that this was true, why did they give a possibility of "not possible"? Akana, you probably discovered Roman Numeral 0.

:)

In my opinion, there's no point of that extra triangle, maybe just there as a red herring...

Thanks! Maybe I'll practice my explaination skills, so that it won't be that hard to understand my answers....

deleted

:)

Future Population =FP

Present Population=PV

FP =PV x [1 + R]^N, where R=Rate of growth, N= Number of Periods.

6400 = 4000 x 1.02^N

6400/4000 = 1.02^N

1.6 = 1.02^N             Take the log of both sides

N =Log(1.6) / Log(1.02)

N =23.73 =~24 Years for town's population to grow from 4000 to 6400.

When the customer recieves both gift cards (i wish i were that guy! who doesn't like free money?), it would be the LCM of 20 and 45. Then we could do some math, and voila! the answer

LCM (20, 45)

How to do this? Let's go back to what we learned in third grade: GCF and LCM (or was it fourth? it has been such a long time...)

This one isn't hard: we don't need to use the "prime factorization method", we can use the "list out the numbers" method we learned:

20: 20, 40, 60, 80, 100, 120, 140, 160, 180

45: 45, 90, 135, 180

So, now we know that the 180th customer got 2 gift cards

But we are not done yet! We need to know how many people have recieved the gift card!

Let's get some counting ready!

There are 9 $10 (90 total) gift cards, and 4 $15 (60 total) gift cards, so add that together, and we have a total of $150 worth of gift cards.

Here are the answers, for your conveniance:

1. 180th person

2. $150 worth of gift cards

:)

The LCM(20, 45) = 180

So, it will be the 180th customer who will receive both gift cards.

180 / 20 = 9 - $10 gift cards were given away

180 / 45 = 4 - $15 gift cards were given away

[9  x $10] + (4 x $15] =$90 + $60 =$150 worth of gift cards were given away in that period of 180 days.

There were 20% * 100 = 20 more boys, and 18% * 50 = 9 more girls, so in total 29 more students got on the honor roll. From 150 to 179, the percentage is 29/150 = 19.3%.

You are very welcome!

:P