Last Option
Rita will spend $25
5(8-3)
Answered by Gauthmath must click thanks and mark brainliest
In order to find out what the value is when x=π, we have to model the function. It says it is a cosine wave, and a amplitude of 1/3 so we start as
1/3(cos(x))
It says a period of π/3. So the period of a cosine function is
2π/n
Where n is cos(nx)
So to find n, we set the period and that equal to each other
Finding n we get 6. So now we have
1/3(cos(6x))
The shift is -2π. When we have a shift of something, we put the opposite sign with the x. So now it's
1/3(cos(6x+2π))
Factor out a 6 and we get
1/3(cos(6(x+π/3))
If we add the period to x, nothing happens so it remains
1/3(cos(6x))
The vertical shift is -3 so we just add that to everything so it becomes
1/3(cos(6x))-3
Plugging in x=π we get
1/3(cos(6π))-3
Cos(6π) is 1 so it is 1/3 - 3, or -8/3
Answer: after 40 seconds, the two tanks will have the same amount of water.
Step-by-step explanation:
Let x represent the number of seconds after which both tanks will have the same amount of water.
A fish tank has 150 gallons of water and is being drained at a rate of 1/2 gallons each second. It means that the number of gallons of water that would be in the tank after t seconds is
150 - 0.5t
A second fish tank has 120 gallons and it is being filled at a rate of 1/4 gallons each second. It means that the number of gallons of water that would be in the tank after t seconds is
120 + 0.25t
For the volume of both tanks to he the same, then
120 + 0.25t = 150 - 0.5t
0.25t + 0.5t = 150 - 120
0.75t = 30
t = 40 seconds
Answer:
If she wants at least one comedy, there are 1484 different combinations.
Step-by-step explanation:
The order in which she wants to pick the movies is not important. So, we use the combinations formula to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
In this question:
She wants combinations of 3 movies, with at least one comedy. The easiest way to find this is finding the total number of combinations of 3 movies, from the set of 25(18 children's and 7 comedies), and subtract by the total number without comedies(which is 3 from a set of 25). So
Total:
3 from a set of 25.
Without comedies:
3 from a set of 18.
At least one comedy:
If she wants at least one comedy, there are 1484 different combinations.