Question 1
There are 5 letters (B, O, K, E, R) and there is a total of 10 letters to make up the word.
There are

ways of arranging the letters, which equal to 210 ways
Question 2
There are seven swimmers in total.
There are

ways of choosing the first winner, which is 7 ways
There are

ways of choosing the second winner, which is 6 ways
There are

ways of choosing the third winner, which is 5 ways
There are 7×6×5=210 ways of choosing first, second, and third winner
Question 3
The probability of eating an orange and a red candy is

×

, which equals to

The probability of eating two green candies is

×

which equals to
7y +8= 9+3y+2y
Combine like terms.
7y+8= 9+5y
Subtract 5y on both sides.
2y+8=9
Subtract 8 on both sides.
2y=1
Your answer is 2y=1
I hope this helps!
~kaikers
For part A: two transformations will be used. First we will translate ABCD down 3 units: or the notation version for all (x,y) → (x, y - 3) so our new coordinates of ABCD will be:
A(-4,1)
B(-2,-1)
C(-2,-4)
D(-4,-2)
The second transformation will be to reflect across the 'y' axis. Or, the specific notation would be: for all (x,y) → (-x, y) New coordinates for A'B'C'D'
A'(4,1)
B'(2,-1)
C'(2,-4)
D'(4,-2)
Part B: The two figures are congruent.. We can see this a couple of different ways.
- first after performing the two transformations above, you will see that the original figure perfectly fits on top of the image.. exactly the same shape and size.
- alternatively, you can see that the original and image are both parallelograms with the same dimensions.
Answer:
280 hours
Step-by-step explanation:
Amount paid + profit = cost of a lesson per hour
$2000 + $5000 = $25(h)
7000 = 25h
7000/25 = h
280 = h