<span>In order to find the standard deviation, we first have to calculate the mean (average) of the numbers. To get this we add all the numbers together and then divide by 12 since there are 12 numbers. The mean = 782. Next, we take each number and subtract the mean, taking the result and squaring it. For this we get: 6724, 2209, 10404, 11664, 729, 1764, 12544, 9, 529, 71824, 1444, 1024. Now we sum all of these up and take the average by dividing the sum by 12. Doing this we get 120868/12=10072. The last step is the take the square root of that number to get the standard deviation. The final result is 100.</span>
Vertical angles are equal and supplementary angles add to 180 degrees
Answer:

Step-by-step explanation:
This is a hard one
We have to use the rational root theorem
= 0
We have to find all the factors of a and d and put them in a fraction

We then plug them into the equation to see if any of them work
The equation isn't true when plugging 1, but is true when plugging in 1/2
factored form of 1/2 is (2x-1)
Then we divide the original equation by (2x-1) (you can use synthetic division or long division, it would be hard to type out the process for that) to get 
So now the equation is 
Solve the second half of this equation using the quadratic formula to get
and 
We already know the solution for the first half of the equation (1/2)
So the final answers are:

Answer: a rectangles area is length x width. You need to find the numbers that represent the length and the width and multiply them
Step-by-step explanation:
Answer:
a) 0.00031
b) 0.0017
c) 0.31
d) 0.00018
Step-by-step explanation:
attached below is the detailed solution
Total number of 7-poker cards are 52P7 = 133784560
A) Determine the probabilities of Seven-card straight
probability of seven-card straight = 0.00031
B) Determine the probability of four cards of one rank and three of a different rank
P( four cards of one rank and three of different rank ) = 0.0017
C) Determine probability of three cards of one rank and two cards of each two different ranks
P( three cards one rank and two cards of two different ranks ) = 0.31
D) Determine probability of two cards of each of three different ranks and a card of a fourth rank
P ( two cards of each of three different ranks and a card of fourth rank ) = 0.00018