NotThatSmart

Let's look at the number 512. 

We know that $512=2^9$ , which means it has 10 divisors. 
Since it's divisble by 2 and two is the smallest prime, 

our final answer is 2. 

Thanks! :)

Let's calculate the number of ways we can seat the children and adults seperately. 

First, there are $4! = 24$  ways to seat the children and  $4! = 24$ ways to seat the adults. 

We now multiply these values together to get

$24*24=576$

So 576 is our answer. 

Thanks! :)

Let's write an equation to solve this pronlem. 

First off, let's let x be the tens digit and the other be y. 

From the first of the problem, we have the equation

$10x+y = 10y+x +72$

From the second part of the problem, we have the equation

$x=2y-1$

Solving this system, we get that $x=17,\:y=9$

This equation cannot be satisfied. 

From the first equation, we have that $y=x-8$

There are only two possibilities. One is where x is 9 and y is 1, so we have 91. 

The other possibility is x is 8 and y is 0. 

Neither of these satisfy the conditions given.

Thanks! :)

I'm sorry, I used symbolab. 

I graphed the answer, where I replaced t with x for the graph. I got

Thanks! :)

There actually is no minimum value. 

The larger x gets, the smaller the fraction becomes, therefore meaning there is no minimum value. 

The range is  $y <1$, meaning no minimum value is present. 

Here's an image

The horizontal asymtote is $y=0$

Thanks! :)

If the number 5 is in the units digit, then the original number that was squared must end with 5. 

Let's set a variable to help us solve this question. 

Let's let a be a number that is the multiple of 10. We have

$(a + 5) (a + 5) = \\ a^2 + 10a + 25$

a^2 will always end with a 0 or two 0s, so it has no effect on the final digit

10a will always end with a 0 or two 0s, so it has no effect on the final digit 

This means we always have 25. 

So 2 is our answer. 

Thanks! :)

I'm not clear on what the problem states, but I'm assuming it means that 0,1,2,3,4 are plugged in as x. 

So, see...

What the equation is saying is that x^5 must be divisble by 5. 

Let's plug in numbers

$0^5 \equiv 0 \pmod{5}$ so it works

$1^5 = 1 \equiv 1 \pmod5$ so it doesn't work

$2^5 = 32 \equiv 2 \pmod5$ so it doesn't work

$3^5=243\equiv3 \pmod 5$ so it doesn't work

$4^5 = 1024 \equiv 4 \pmod 5$ so it doesn't work

So the only one that works is 0. 

Then again, residue is usually used as the remainder, but I hope my asusmption is correct.

Thanks! :)

First, let's convert 1/288 into base 13. 

Since 1 is the smae in every base, and we have

$(192)_{13} = (1 × 13^2) + (9 × 13^1) + (2 × 13^0) = (288)_{10}$

This means that

$\frac{1}{192}_{13} = \frac{1}{288}_{10}$

Now, we complete base division. The answer is approximately 

$0.0078229A44BC67118933...$

I don't think the number is repeating, although I am not sure. 

If I had to geuss with the first 20 digits, it isn't repeating, but maybe it is. 

Thanks! :)

https://web2.0calc.com/questions/number-theory_13663

the answer is $2$