Suppose a worker needs to process 100 items. The time to process each item is exponentially distributed with a mean of 1 minute,
1 answer:
Answer: 0.0368
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
, where is the mean of the distribution.
Given : The time to process each item is exponentially distributed with a mean of 1 minute .
In hour, the mean time to process each item = hour
Then , the probability that the worker finishes in less than 2.25 hours :-
Hence, the probability that the worker finishes in less than 2.25 hours = 0.0368
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<em>Question:</em>
<em>Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. </em>
<em>The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is . </em>
<em>The solution to the inequality is . </em>
<em>Sal’s mother would have to keep the second cell phone plan for at least months in order for it to be less expensive.</em>
Answer:
a.
b.
c. At least 13 months
Step-by-step explanation:
Given
First Phone;
<em>(monthly)</em>
Second Phone;
<em /><em> (monthly)</em>
<em></em>
Solving (a): The inequality
<em></em>
Represent the number of months with x
The first phone is expressed as:
The second phone is expressed as:
For the second to be less expensive that the first, the inequality is:
Solving (b): Inequality Solution
Collect Like Terms
Solve for x
Solving (c): Interpret the solution in (b)
implies 13, 14, 15....
Hence, She'll keep the second phone for a period of at least 13 months
Answer: P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T =
C is the phase shift or horizontal shift:
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
<u>Amplitude</u>:
a =
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a =
a = 1.25
<u>b</u>
A time period for Pluto is T=66 years:
66 =
b =
<u>Vertical</u> <u>Shift</u>
It can be calculated as:
d =
d =
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin(.t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin(.t) + 5.65