A cube has 6 faces.

There is only 1 way to paint the cube's faces all blue.

So the probability is: \(\dfrac{1}{2^6}=\dfrac{1}{64}\)

ANSWER: 1/64

There are 80 numbers from 1 to 80.

There are 22 numbers are prime from 1 to 80.

So the probability is: \(\dfrac{22}{80}=\dfrac{11}{40}\)

ANSWER: 11/40

The probability is: \(\dfrac{7}{7+6+5+4+3+2+1}=\dfrac{7}{28}=\dfrac{1}{4}\) 

(The dominos are: 0-0;1-1;2-2;3-3;4-4;5-5;6-6)

The value of n is: \(\left[\left(1450-1300\right)\cdot2+3000\right]:3=1100\left(lemnings\right)\)

We have: 19   20   21   22   23   24   25   26

                BC  DE  FG  HI  JK  LM  NO  PQ

So the letter has a 6 in the number 26 is Q

The area of the dodecagon is: \(4\cdot5-\left(1^2\cdot4\right)=20-4=16\left(cm^2\right)\)

The possible sums are: 1 + 1 + 1 + 1 + 1; 1 + 1 + 1 + 2; 1 + 1 + 2 + 1;  2 + 1 + 1 + 1; + 1 + 2 + 1 + 1; 1 + 2 + 2; 2 + 2 + 1; 2 + 1 + 2

So there are: 8 different ordered sequences can be written by Siddarth as a sum.

The numbers from 1 to 25 (total 25 numbers): 

+ Divisible by 2 are: \(2;4;6;8;10;12;14;16;18;20;22;24\left(12-numbers\right)\)

+ Divisible by 3 (but not divisible by 2) are: \(3;9;15;21\left(4-numbers\right)\)

+ Because \(4⋮2\) => The numbers divisible by 4 (but not divisible by 2 and 3) is: \(\varnothing\)

+ Divisible by 5 but not divisible by 2 and 3 is: \(5\) 

So the probability is: \(\dfrac{12+4+1}{25}=\dfrac{17}{25}\)

Call the bigger number is a and the smaller number is b

We have:  \(a+b=3b+18\)

=> \(a=2b+18\) but \(a=4b\)

=> \(4b-2b=18\)

<=> \(2b=18\) <=> \(b=18:2=9\)

There are: \(23\cdot27=621\left(chairs\right)\) in the room.

\(\dfrac{3}{m}=\dfrac{27}{72}\) <=> \(3\cdot72=27\cdot m\) <=> \(m=\left(3\cdot72\right):27=8\)

The answer the question ask is the maximum number of socks she must take to be assured that she has a matching pair. Because 6 > 5 so she must take: \(6+1=7\left(socks\right)\) to be sure that she has a matching pair.

Because the integers are continuously so the average is the median of the integers. So the average of the integers is 22

There are: \(4\cdot3=12\left(ways\right)\) to form a two-digit number.

The prime numbers can be make are: 23;27;31;37;13;17;73 so there are 7 prime numbers can be make.

So the probability is: \(7:12=\dfrac{7}{12}\)

There are: \(10\cdot25\%=2,5\left(lbs\right)\) sugar in the sugar syrup.

From the question, we have: \(40\%+\left(10\cdot x\right)=2,5+x\). Therefore, we get \(x=2,5\left(lbs\right)\)

ANSWER: 2,5lbs

There are: \(\left(752-138\right):1+1=615\left(numbers\right)\) between 138 and 752.

We have: \(1+2^1=3\) ; \(3+2^2=7\) ; ... ; \(15+2^5=31\) so the number in the blank is: \(31+2^6=63\)

ANSWER: 63

First, we have: \(5^2+2=27\left(2nd\right)\) so we have number 7

Second, we have: \(7^2+2=51\left(3rd\right)\) so we have number 1

Third, we have: \(1^2+2=3\left(4th\right)\) so we have number 3

Fourth, we have: \(3^2+2=11\left(5th\right)\) so we have number 1

So the sequence from the 6th number will be the numbers 3 and 1. Since 100 is an even number so the 100th-term number is 3

This question is asked 2 times before.

5 apples equals to: \(1-\dfrac{1}{2}=\dfrac{1}{2}\) of the number of Anna's apples

So Anna has: \(5:\dfrac{1}{2}=10\left(apples\right)\)