To the nearest tenth, what is the perimeter of the triangle with vertices at (−2, 3), (3, 6), and (2, −2)?
1 answer:
9514 1404 393
Answer:
20.3
Step-by-step explanation:
The distance formula can be used to find the side lengths.
d = √((x2 -x1)^2 +(y2 -y1)^2)
For the first two points, ...
d = √((3 -(-2))^2 +(6 -3)^2) = √(5^2 +3^2) = √34 ≈ 5.83
For the next two points, ...
d = √((2 -3)^2 +(-2-6)^2) = √(1 +64) = √65 ≈ 8.06
For the last and first points, ...
d = √((-2-2)^2 +(3-(-2)^2) = √(16 +25) = √41 ≈ 6.40
Then the sum of the side lengths is ...
5.83 +8.06 +6.40 = 20.29 ≈ 20.3
The perimeter of the triangle is about 20.3 units.
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Answer: The events are independent
a) p = 1/36 b) p = 5/216
Step-by-step explanation: both events are independent because the fact that the first die shows it sample space {1, 2, 3, 4, 5, 6} does not stop the second die from showing it own sample space too which is {1, 2, 3, 4, 5, 6}.
The sample space of first die = {1, 2, 3, 4, 5, 6}
The sample space of second die = {1, 2, 3, 4, 5, 6}
The sample space of 2 dice rolled at once is seen as attachment to this answer, find attachment below.
Probability that an event will occur = number of time the event will occur / total number of possible outcome of the event
a)
Probability that first die will show 3 = number of times 3 shows up in the event / total number of outcome of the die = P (3)
P (3) = 1/6
Probability that 2 dice sum up to give 7 = 6/ 36 = 1/6 ( from the sample space for 2 dice attached, it is seen that the sum of 7 comes out 6 times and the total sample space is 36)
P (first die show 3) = 1/6
P ( 2 dice sum to 7) = 1/6
P ( first die show 3) and P ( 2 dice sum to 7) = 1/6 * 1/6 = 1/36.
b)
Probability of the first die showing 4 = P(4) = 1/6
Probability of 2 die sum up to give 8 = 5/36
P ( first die show 8) and P ( 2 die sum up to give 8) = 1/6 * 5/36 = 5/216
