Our basis for this equality is the pythagorean theorems of trigonometry. There are three equations for the pythagorean theorems. These are:
sin²x + cos²x =1
1 + tan²x = sec² x
1 + cot² x = csc² x
These are all derived from circle geometry on the cartesian plane. Now, the useful trigonometric property to be used is the third one. Rearranging this, we come up with
cot²x - csc²x = -1
This coincided with the given equation. Therefore, this is true. This is because it is already established from the pythagorean theorems.
Answer:
16
Step-by-step explanation:
5-4 = 1 so total profit would be $1 for each bag.
Because he makes 1 dollar per bag this is a fairly simple to see how many he has but we will pretend its not so you have an idea of how to do this later.
You should divide the final profit he's made by the total he gets per each, which would give you how many he has made.
$16/$1 = 16 bags produced.
Answers:
a. Given
b. Transitive property of congruence
c. Vertical angles are congruent
d. Transitive property of congruence
Let me know if you need any clarification as to how I got those answers. They should be self-explanatory but I'm happy to clarify further if needed.
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.
Answer:3 and 1/4 is closer to 3 and 3/5 is closer to 4
Step-by-step explanation: one is closer on the number scale then the other
