The time intervals when the riders could see Niagara falls are; 0.834 < t < 1.416 and (3.084, 3.666)
<h3>How to interpret Cycle Graphs?</h3>
From the diagram attached, we can say that;
Period = 2π/k
where;
k = 2π/2.25
k = 8π/9
Thus;
h(t) = -(48/2) cos (8π/9)t + ((48/2) + 0.5)
h(t) = -24cos (8π/9)t + 24.5
Riders can see Niagara falls if they are higher than 41 meters above the ground. Thus;
41 = -24cos (8π/9)t + 24.5
41 - 24.5 = -24cos (8π/9)t
16.5 = -24cos (8π/9)t
-0.6875 = cos (8π/9)t
cos⁻¹0.6875 = (8π/9)t
t = 0.834 min
Thus, time interval is between;
0.834 < t < (2.25 - 0.834)
⇒ 0.834 < t < 1.416 and
(2.25 + 0.834) < t < (2.25 + 1.416)
⇒ (3.084, 3.666)
Read more about Cycle Graphs at; brainly.com/question/24461724
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We will see that the probability of x taking on a value between 75 to 90 is P = 0.5
<h3>
How to get the probability?</h3>
We know that x is a continuous random variable uniformly distributed between 65 and 85.
This means that the probability that x value y in the range is such that:
1 = P(y)*(85 - 65) = P(y)*20
1/20 = P(y).
Now, the probability of x taking a value between 75 and 85 is:
P(75 to 85) = (1/20)*(85 - 75) = 10/20 = 0.5
And the probability between 85 and 90 is zero (because the maximum value that x can take is 85, so this part does not affect).
Then we conclude that the probability of x taking a value between 75 to 90 is:
P(75 to 90) = P(75 to 85) + P(85 to 90) = 0.5 + 0 = 0.5
If you want to learn more about probability, you can read:
brainly.com/question/251701
Answer:
we get the all equation of given condition
&
Step-by-step explanation:
Given that,
Number of painting made by Gloria every month is 2.
Gloria creates depends on the number of paintings p, Gloria paints over m months if she meet her goal.
we have to check all the apply.
According to question,
M is the independent variable and P is dependent variable.
So, Relation formed by given statement is 
Case(1): P is increased by 2 as M is increased by 1.
Then, 


This is Equation of the given case(1).
Again, P is the independent variable and M is dependent variable.
∴ 
Case (2) M is increased by 2 as P increased by 1.
Then, 


Hence,
we get the all equation of given condition
& 