BuilderBoi

Inequality 1: \(3n + 8< 30\)

Subtract 8 from both sides: \(3n <22\)

Divide by 3: \(n < {22 \over 3}\)

Inequality 2: \(2n - 9 > -4\)

Add 9 to both sides: \(2n > 5\)

Divide both sides by 2: \(n > {5 \over 2}\)

So our range becomes \({5 \over 2} < n < {22 \over 3}\)

The integers that work are 3, 4, 5, 6, and 7.

So the answer is \(3 \times 4 \times 5 \times 6 \times 7 = \color{brown}\boxed{2520}\)

here: https://web2.0calc.com/questions/help-due-in-1-hour#r1

Multiplying the entire equation by \(x^3 - x^2 - 21x + 45\): \(1 = A(x-3)(x-3) + B(x+5)(x-3) + C(x-5)\)

Simplify the right-hand side: \(1 = A(x^2 - 6x + 9) + B(x^2 + 2x - 15) + C(x-5)\)

Equating terms to get the following system: \(Ax^2 + Bx^2 = 0\)

                                                                     \(-6Ax + 2Bx + Cx = 0\)

                                                                    \(9A - 15B - 5C = 1\)

Removing the x's from the system gives us a simpler system: \(A + B = 0\)

                                                                                                   \(-6A + 2B + C = 0\)

                                                                                                   \(9A - 15B - 5C = 1\)

Now, just solve for a. 

:)

The formula for the radius of the sphere is \(4 \pi r^2\). We know that this is equal to \(196 \pi\). Setting these equal and solving for r, we find that \(r = 7\), meaning the circumference is \(2 \pi r = \color{brown}\boxed{14 \pi}\)

You can't hear other guesses tho...

that part alone makes it soo hard 

Let the amount of money Jeri owns be \(j\). Off the bat, we know \(j \geq 200\).

Represent the first part as \({2 \over 3}(j-80) + 80\). The second part represents how much money Jeri has in her right pocket, and the latter represents the amount of money in her left pocket. The second part is just \(j - 200\).

So we have the inequality: \({2 \over 3}(j-80) + 80 > j-200\)

Solving, we find \(j<680\), but because we know \(j \geq 200\), we have \(200 \leq j < 680\), which equals \(\color{brown}\boxed{[200, 680)}\) in interval notation. 

From the first equation and second equations, we have \(p = 2q\) and \(q = 2r\), meaning \(p = 2 \times 2r = 4r\)

Substituting this into the third equation gives us \(r = 1\). Plugging this value into the second equation gives us \(q - 2 = 0\), meaning \(q = 2\)

Finally, substituting \(q = 2\) into the first equation \(p - 4 = 0 \), meaning \(p = 4\)

So, the solution is \(\color{brown}\boxed{(4,2,1)}\)

There are \(8! \div 8 = 7! \) ways to put the mages, but we have to divide by \(2! \times 3! = 12\) to get \({7! \div 12} = \color{brown}\boxed{420}\) 

Note that in standard form (Ax + By = C), the slope of the equation is just \(-{A \over B}\).

So, we have \(-{A \over B} = -{1 \over 3}\), meaning \(3A = B\)

Now, substitute the point \((-7, 2)\) into the equation. This gives us \(-7A + 2B = 3\)

Now, just solve the system for A and B, then do B - A

:)

https://web2.0calc.com/questions/need-help-plz_17

answered on original :)

We know there must be five 1's, two 2's, and four 3's. 

There are \({11! \over 2! \times 5! \times 4!} = \color{brown}\boxed{6930}\) numbers that work. 

How many two-digit numbers are there?

How many numbers can you list out that have at least 1 7?

If you are still confused, feel free to ask for further help 

1 x 60 x 60 x 24 x 365 x 15 = 473,040,000

Wait, I see my mistake... I subtracted 300 instead of 360. 

So the correct answer becomes \(3360- 360-600-1200 = \color{brown}\boxed{1200}\).

Now, GingerAle and I are in agreement. 

Multiply the ratio by 3 to get 15:24.

I assume you can take it from here...