All Answers 358090 Answers

52 p 2 = 2652 ways    this is   52 ! / 50!       or    52 cards for first choice * 51 cards for second choice = 2652 ways 

https://web2.0calc.com/questions/help_95630

x = worker days needed to complete the job

x/5  =  days for 5 to complete 

x/(5+1) = x/5 - 8     

x/6 = x/5 - 8 

5x/30 - 6x/30 = - 8

     solve for x = 240 worker days 

Now for 28 days less:

240/ ( 5 + n) =  240/5 -28      where n = number of additional workers

240/(5+n) = 20 

n = 7 additional workers needed above the original 5 

A = pizza eaten by A

3/2 A = pizza eaten by B 

A + 3/2 A = 1   whole pizza

5/2 A = 1 

A = 2/5  of the pizza       so:    2/5 * $ 18 = $ 7.20 = A share       and       B  pays the rest = $ 10.80

Strictly speaking, an exponent tower is one of the few operations in mathematics that is evaluated from the "top" of the tower to the "bottom" of the tower. Unfortunately, this number is too large to write down. Although, we can attempt to write an approximation.

\({{3^3}^3}^3 = {3^3}^{27} = 3^{7\;625\;597\;484\;987} \approx {10^{10}}^{12.5609}\). The exponent is too large, so this number cannot be written down realistically. This number has about one trillion digits, which is far too many.

This question is a bit too broad, but I assume you want to simplify the expression \(5(3x^2 + 9x) - 14\) as much as possible? If so, there is not much to do to simplify this particular expression other than do the expansion within the parentheses. 

\(5(3x^2 + 9x) - 14 = 15x^2 + 45x - 14\)

Saying that the arithmetic mean of x and y is 18 mathematically means that \(\frac{x + y}{2} = 18\). Also, saying that x and y have a geometric mean of \(\sqrt{47}\) means that \(\sqrt{xy} = \sqrt{47}\). With this information, we want to find the value of \(x^2 + y^2\). We can use clever algebraic manipulation to find this value without too much trouble.

\(\frac{x + y}{2} = 18; \sqrt{xy} = \sqrt{47} \\ x + y = 36; xy = 47 \\ (x + y)^2 = 36^2 \\ x^2 + 2xy + y^2 = 1296 \\ x^2 + y^2 = 1296 - 2xy \\ x^2 + y^2 = 1296 - 2 * 47 \\ x^2 + y^2 = 1202 \)

Sometimes, it is hard to wrap one's head around how to determine how one quantity is related to another without a visual picture. As a result, I decided to create a Venn diagram that should make the situation clearer. I have included all the given information in the Venn diagram.

The given information states that there are twice as many students in the cooking club as in the drama club. Since we are using the a-variable to represent the number of students in the drama club, this means that 2a students are in the cooking club. We are letting the b-variable be in the middle; this represents the students who are members of both clubs. Our objective is to find an expression that represents the students in the one of the two clubs but not both.

I will start with the cooking club. The cooking club has 2a members. With the help of the diagram, it is clear there are b students who are members of both. Therefore, 2a - b represents the number of students who are only apart of the cooking club.

Considering the drama club, there are a total members. There are b students who are members of both. Therefore, a - b represents the number of students only participating in the drama club.

Now, we just find the sum of these parts. \(2a - b + a - b = 3a - 2b\) students who are members of one of the clubs but not both.

I see nowhere where the problem specifies that at least three of the squares must be of the color red.

The leftmost square is essentially a free choice; there is no restriction on this choice. Therefore, the leftmost square can take any of the 3 colors.

The square directly to the right of the leftmost square is somewhat restricted. Because no consecutive squares can have the same color, there will be 2 other choices for the square directly to the right of the leftmost square in all cases.

All squares after the leftmost square are under the same restriction of having only 2 choices in all cases.

This means there are \(3 * 2 * 2 * 2 * 2 = 3 * 2^4 = 3 * 16 = 48\) ways of coloring these squares.