‼️WILL GIVE BRAINLIEST (Please answer all questions!)

ΔABC is translated 4 units to the left and 8 units up. Answer the questions to find the coordinates of A after the translation.

1. Give the rule for translating a point 4 units left and 8 units up. (2 points)

2. After the translation, where is A located? (2 points)

Now reflect the figure over the y-axis. Answer the questions to find the coordinates of A after the reflection.

3. Give the rule for reflecting a point over the y-axis. (2 points)

4. What are the coordinates of A after the reflection? (2 points)

5. Is the final figure congruent to the original figure? How do you know? (2 points)

1) (x-4 , y+8)

2) (3,13)

3) (x,y) -> (-x,y)

4) (-7,5) This after reflection of original triangle

5) Yes, reflections don't change size, only position

Step-by-step explanation:

1. 0.445 or 0.5

2. 0.167 or 0.2

3. Yes and No

Step-by-step explanation:

2 coins are fair and the 3rd is two-headed

So there are 2 tails and 4 heads altogether.

(A) He randomly picks one, flips it and gets a head. What is the probability that the coin is a fair one?

The probability that the coin is a fair one is: Probability of a fair coin x Probability of obtaining a head

= 2/3 x 4/6 = 0.445 to 3 decimal places

(B) He randomly picks one and flips it twice. Compute the probability that he gets 2 tails

This is = [the sum of the probability that each coin produces a tail 2 times when flipped twice] divided by 3.

For Coin 1,  0.5 is the probability of getting tails. For two consecutive tails, the probability would be 0.5 x 0.5 = 0.25

Same goes for Coin 2 which is the second fair coin.

For Coin 3, the probability of getting a tail at all is 0.

So [0.25 + 0.25 + 0] / 3  = 0.167 to 3 d.p.

(C) Suppose B = the event that the first result is head

Suppose C = the event that the second result is also head

- Are B and C independent (if the two-headed coin wasn't picked)?

YES

- Are B and C independent (if the two-headed coin was picked)?

NO