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I think since sqrt(9) = +- 3, it can be all numbers other than -6 to 6  (non inclusive)

=^._.^=

Oh no, it looks like we have different answers. 

I'm rechecking and my answer is wrong. 

9^2-7^2 = 32

32+1 = 33

83 - 33 = 50

Yep, 50 is correct. 

Thank you to geno for helping me get the right one. :))

=^._.^=

HELLLLP

I think that it is  50.

Now, draw out the spiral and tell us which one of us is correct ...

24,332,000 :)

83 is quite close to 81. 

At 81, there will be a 9 by 9 square, meaning at 83, it will be 9 less than 83. 

83 - 9 = 74

I hope that's correct. 

=^._.^=

Agreed

Price of 6 forks and 6 spoons = 106.4 - 60.2 = 46.2

Price of 1 fork and 1 spoon = 46.2/6 = 7.7

Price of 5 forks and 5 spoons = 7.7 * 5 = $38.5

I don't think that this is a great solution because there are many wonderful guests. 

Having an account doesn't make someone a cheater/not a cheater. 

=^._.^=

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total 55,692. The variable costs will be 11.50 per book. The publisher will sell the finished product to bookstores at a price of 24.25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Hello Strayer!

\(x\cdot 24.25=x\cdot 11.50+55692\\ x(24.25-11.50)=55692\\ x=\dfrac{55692}{24.25-11.50}\)

\(x = 4368\)

The publisher must sell at least 4368 books.

  !

S + 4C   =      $ ( w+4 )

S + 2C   =      $ ( w+2 )

      2C   = $2

      1C    = $1

      1S   = $ ( w+2 ) - 1 - 1 = w

        1 Cheese Bun -> $1

        1 Sandwich -> $w

If it is a multiple of 5, and is even, then the last digit must be 0. But, 0 is not from 1-6, so there are no solutions and the probability is 0.

The solutions are 19, 19+43 so their sum is 38+43 = 81.

What is the smallest real number x in the domain of the function \(g(x) = \sqrt{(x^2 - (x - 15)^2)}\)?
 

Two reasons why a number might not be included in the domain is that it makes an expression in the denominator of a fraction equal to 0, or it makes the expression be the square root of a negative number. These are big no-nos.

Keeping this in mind, let's find what values of x don't work, so then we can find the ones (the smallest one in particular) that do. For x not to work, we would have to have:

\(\sqrt{x^{2}-(x-15)^{2}} < 0\).

Simplifying, we get:

\(-30x+225<0\)

\(30x<225\).

I'll let you finish!

First, let's find the prime factorization of \(10! \cdot 11!\): 

\(10! \cdot 11! = 11 \cdot 10 \cdot10 \cdot9 \cdot9 \cdot8 \cdot8 \cdot7 \cdot7 \cdot6 \cdot6 \cdot5 \cdot5 \cdot4 \cdot4 \cdot3 \cdot3 \cdot2 \cdot2 \cdot1 \cdot1 = 2^{16} \cdot3^{8} \cdot5^{4} \cdot7^{2} \cdot11^{1}\)

Next, let's test values for x (by using the prime factorizion, of course!):

x = 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, ...

I will let you finish the problem. Keep in mind that the highest x can be is \(2^{5}\cdot3^{2}\cdot5=1440\).

Caution: It is important to note that the question says "integers" instead of "positive integers." The cube of a negative number is still negative, so it will not change the answer to this particular problem. However, if x was squared or raised to any even power, we would have to include the negatives.

same. this idea is just 

The idea makes sense, but many people (like me) come here to answer people's questions instead of post questions for others to solve.

Ok, then about 90% of the guest users will be unable to use the forum, and a small percentage will sign in, this idea is.... 🤦‍♂️ 

it is (12/6) *3

135/360 = 0.375*5 = 1.875?

When the linear dimensions of an object are doubled, any surface area would be 4-tupled (2^2) and any volume would be 8 times (2^3) as large. The liquid contents of a container are measured by their volume; so any volume of water that is transferred from A to B would see its level ( or height, a linear measure) reduced to one eightth of what it was in A.

There must have the orders of factors, 

5 5 4 3 1: 5!/2! =60

5 5 3 2 2: 5!/2!2! =30

6 5 5 2 1: 5!/2! =60

60+30+60=150

150 is the answer.

Well, there actually is only one way, because if each person has to sit in-between the two people of the opposite party, then due to symmetry, there is, again, only one way to seat them.

DRDRDRDR 

(d=democrat, r = republican) Hope this helps! :) 

The rolls must be 1, 2, 5, 5, 6 in some order, so there are 5!/2 = 60 ways.