Given:
The three vertices of a parallelogram are (-3,8), (4,5), (2,-5).
To find:
The fourth vertex of the parallelogram.
Solution:
Let the vertices of the parallelogram are A(-3,8), B(4,5), C(2,-5) and D(a,b).
We know that, diagonals of a parallelogram bisect each other. It means midpoints of both diagonals are same.
Midpoint formula:

Two diagonals of ABCD are AC and BD.
Midpoint of AC = Midpoint of BD


On comparing both sides, we get




And,




Therefore, the coordinates of fourth vertex are (-5,-2).
Answer:
There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which
x is the number of sucesses
is the Euler number
is the mean in the given time interval.
The problem states that:
The number of phone calls that Actuary Ben receives each day has a Poisson distribution with mean 0.1 during each weekday and mean 0.2 each day during the weekend.
To find the mean during the time interval, we have to find the weighed mean of calls he receives per day.
There are 5 weekdays, with a mean of 0.1 calls per day.
The weekend is 2 days long, with a mean of 0.2 calls per day.
So:

If today is Monday, what is the probability that Ben receives a total of 2 phone calls in a week?
This is
. So:


There is a 0.73% probability that Ben receives a total of 2 phone calls in a week.
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So there are five candy bars.
Herself and two sisters equals 3 people in total.
This is a graph of 5 candy bars, each line being 1/2.
━ ━
━ ━
━ ━
━ ━
━ ━
If she ate half of one... the graph would become this.
━ ━
━ ━
━ ━
━ ━
━
Now there are 9 halves. You need to split the 9 halves for 3 people. 9 divided by 3 is 3.
Each person gets 3 halves, or 1 and 1 half.
Mai: ━ ━ ━
Sister 1: ━ ━ ━
Sister 2: ━ ━ ━
Altogether that is 9 halves, AKA the number of halves Mai had after she ate 1/2.
The amount Mai ate in the first place: ━
9 halves plus 1 half, equals 10 halves. Each whole has 2 halves. 10 divided by 2 is 5, AKA the number of candy bars she had in the first place.
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The answer would be B C E hope this helps :)