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jolli1 [7]
3 years ago
6

Dwayne plays five games of rock-paper-scissors. In order to seem unpredictable, he never chooses the same move (rock, paper, or

scissors) twice in a row. How many different sequences of moves can Dwayne go through?
Mathematics
1 answer:
Andreyy893 years ago
6 0

Answer:

48

Step-by-step explanation:

First, in this problem, you would assume that there are five numbers to multiply since Dwayne played 5 games.  

 

                                                                                       

 

In the first blank, he could choose any move, and there are three, rock, paper, and scissors. In the first blank, you would put 3. Then, since you already picked one, you can't repeat it, so you would end up with 2 for the second blank. Continuing with the next blanks, the third, fourth, and fifth spaces would be 2 choices because you cannot have the one choice you chose previously. In the end, the blanks would look somewhat like this:

 

3    2    2    2    2

 

And you would multiply all the numbers.

 

3  x  2  x  2  x  2  x  2

                                                                  = 6 x 8

                                                                  = 48

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Find UX and the area of △UVW.
Mkey [24]

Answer:

UX ≈ 4.5

△UVW = 49.5 ft²

Step-by-step explanation:

[] We can assume that UX is the midline of this triangle.

22 ft / 2 = 11 ft

XW and VX = 11 ft

[] Now that we have 2 sides of a right traingle, we can find the third.

a² + 11² = 12²

a² + 121 = 144

a² = 20

a = about 4.5, which is side UX

[] Since we have all three sides of the triangle, we can also solve for the total triangle's area. To solve for the area of a triangle, we do base times height divided by 2

22 * 4.5 = 99

99 / 2 = 49.5 ft²

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

7 0
3 years ago
What is the algebraic expression for the difference between seven times a number and three times that number?​
anastassius [24]

Given

An algebraic expression is the difference between seven times a number and three times that number.

To find:

The algebraic expression.

Solution:

Let x be the unknown number.

Multiplication is used for times and subtraction is used for difference.

7 times of a number = 7x

3 times of that number = 3x

The difference between seven times a number and three times that number is

Difference = 7x-3x

Difference =4x

Therefore, the algebraic expression for the given statement is 7x-3x and its simplified form is 4x.

6 0
3 years ago
Read 2 more answers
What are the solutions to the system of equations? {−x+y=4y+12=x2+x
monitta

Answer:Since -2 can not equal 0, there is no solution. The lines are parallel. It is an inconsistent system.

Step-by-step explanation:

The first step in solving a system of equations by substitution is solving one of the equations for one of the variables

x - y = 0 Equation 1

x - y + y = 0 +y Add y to each side

x = y Simplify

After solving an equation for one of the variables, substitute that value into the other equation. In this problem, I can substitute y for x.

x - y - 2 = 0 Equation 2

y - y - 2 = 0 Substitute the value of x from equation 1

0 - 2 = 0 Inverse Property of addition

-2 = 0 Identity Property of addition

5 0
3 years ago
What is the surface area?<br>18 cm<br>18 cm<br>19 cm​
wariber [46]

Answer:

If it is a rectangular prism (this formula only works with that 3d shape, the answer is 2016 cm²

Step-by-step explanation:

SA=2(hl+hw+lw)

SA=2(18×19+18×18+18×19)

Sa=2(342+324+342)

sa=2(1008)

sa=2016 cm²

3 0
3 years ago
What is the following quotient?
Sergio039 [100]

Answer:

\frac{\sqrt{3} }{4}

Step-by-step explanation:

\frac{1}{1+\sqrt{3} }

basically we want to get rid of the √3 on the denominator

to do so we multiply it by itself so it is a perfect square

but whatever we do to the top we must do to the bottom so we multiply the numerator and denominator by √3

\frac{1*\sqrt{3} }{1+\sqrt{3}*\sqrt{3}  }=\frac{\sqrt{3} }{1+\sqrt{9} } =\frac{\sqrt{3} }{1+3} =\frac{\sqrt{3} }{4}

notes : √3 × √3 = √9 which is a perfect square that simplfies to 3

3 0
2 years ago
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