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The circle (x+1)^2 +(y−3)^2 ≤ 4 has an area of 4, and the circle (x+1)^2 +(y−3)^2 ≤ 9 has an area of 9, so the fraction is 4/9.

nice answer, cat! i was wondering though, what if the question meant more than two numbers? 

for example, 2*3*4 multiplies to 24, but they don't add up to 13. would there maybe be more than just a pair of numbers that could work? 

39 hours is 3 half lives

64 * 1/2 * 1/2 * 1/2 =   69 * 1/8 = ....... grams left

using distance = rate * time, i used the information in the question to set up this equation: 756 = 12 * rate

then, dividing both sides of the equation, i got Salma's rate, which is 756/12 = 63 miles per hour.

now, plugging some more thing into the distance = rate * time rule: 567 = 63 * time

so, we can conclude that it will take Salma 567/63, or 9 hours to drive 567 miles.

hope this helped! please correct me if i am wrong :)

567 m   / (756 m / 12 hr   ) =     567 * 12/756   hr = .........

The area is 3*pi - 1.

oh wait I got it it's 6

idk its in latex

Hi Guest!

You're really close, but the first digit only has 4 options since it can't be 0. 

4*5*5*5*5 = 2500

=^._.^=

Edit:

I've made a dumb error... >:(((

So I forgot that numbers exist that aren't 5 digit.-.-

So please ignore that previous response. 

As for why the 2 guests have gotten different answers is because 0 is also counted using the method: 5^5 = 3125, so you just have to subtract 1. 

Nice job to our guests for solving the problem... I'm quite sad that I've made such a dumb mistake. 

=^._.^=

Find two consecutive positive integers such that the square of the smaller increased by 4 times thelarger is 64  

I like 6 and 7 for this one.  6² + (4)(7)  =  36 + 28  =  64 

_.

99 000 or less

5 choices for each digit  

            5⁵ = 3125

They all look good to me.

Given  y = -7/3 x +18       when y = 0     the x intercept is   -18 * (-3/7) = .........

Multiply first equation by   4  to get

2s - 12 t = -4

-2s+3t = 3              now add the two equations tegether ....then you can solve for t

                                 use this value of 't' in either of the equations to calculate 's'  

It does not say that the hand should be at 10 to 2.

It says the hands should be on 10 and 2.

This is not a time question.

Like   two  and three ?

The hands should be 3 and 9  that it 180 degrees apart

they are on 2 and 10 that is 120 degrees apart

The DECREASE is  60 degrees

Since 7 is a prime number, the number of 7's in the prime factorization of n! is equal to \(\left \lfloor{\frac{n}{7}}\right \rfloor+\left \lfloor{\frac{n}{7^2}}\right \rfloor+\left \lfloor{\frac{n}{7^3}}\right \rfloor+...\) , where \(\left \lfloor{x}\right \rfloor\) is just the floor of x, which is just the smallest integer less than or equal to x. 

We want the number of 7's in the prime factorization of n! to be equal to 10, and we want it to be as small as possible, which means that n will also be a multiple of 7.

Trying out some reasonable values, we find that \(\boxed{63}\) is the smallest possible value, since \(\left \lfloor{\frac{63}{7}}\right \rfloor+\left \lfloor{\frac{63}{7^2}}\right \rfloor = 9+1 = 10\) (notice that I didn't test the floors of larger values since they will all be zero).

Each hour is 30 degrees      9 oclock is   270

                                              3 oclock is    90              270 - 90 = 180 degrees

Look at a clock face   9   and 3 are opposites....180 degrees

10 oclock is   60 degrees short of vertical   2 oclock is 60 degrees past vertical   60 + 60 = 120

 The way to do this question is:

For first place, we have 13 choices,

13 x__ x__

For second place, we have 12 choices,

13 x 12 x __

And for third place, we have 11 choices.,

13 x 12 x 11 = 1716 ways

This is also a permuation.

13! / (13-3)! = 1716

Hope it helps!!! :)

🙃🙃👌

I am not sure about that because when we calculate the angle of a clock dont we use something like Angle = Minute *60/360. What I am not sure is do I assume it to be 3:45 and 2:50 or 9:15 and 10:10. The angle value I get when I assume the clock hands as 3:45 and 2:50 is 12.5 while 9:15 and 10:10 gives me the answer 57.5. and there is my confusion

The total amount of boys is 40%. And 50% of boys chose blue as their favourite colour. This means that 1/2 of the boys chose blue as their favourite colour which means 20% of boys chose blue as their favourite colour. 20% is 20/100 = 2/10 = 1/5.

By SFFT, p = 3 and t = 10.  You can then work out the answer from there.

This question could have many possible answers. One such answer could be:

Jimmy had 80 marbles. His friend had only x amount of marbles. So Jimmy decided to give him 3x amount of marbles. When he is done, he now has 53 marbles. What is the value of x?