The displacement (in meters) of a particle moving in a straight line is given by the equation of motion
1 answer:
Answer:
Step-by-step explanation:
the displacement of the particle is given by
The rate of change of position gives the value of velocity.
So, v = ds/dt
Differentiate the position function with respect to time.
Now, at t = a
v = -18/a³ m/s
At t = 1
v = - 18 m/s
At t = 2
v = - 18 / 8 = - 2.25 m/s
At t = 3
v = - 18 / 27 = 0.67 m/s
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Answer:
27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.
Step-by-step explanation:
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
What is the probability that the mean volume of a random sample of 144 bottles is less than 12 oz
This is the pvalue of Z when
By the Central Limit Theorem
has a pvalue of 0.2743.
So there is a 27.43% probability that the mean volume of a random sample of 144 bottles is less than 12 oz.
Solution:
Given :
.............(1)
where, B = aP = birth rate
D = = death rate
Now initial population at t = 0, we have
= 220 ,
= 9 ,
= 15
Now equation (1) can be written as :
.................(2)
Now this equation is similar to the logistic differential equation which is ,
where M = limiting population / carrying capacity
This gives us M = a/b
Now we can find the value of a and b at t=0 and substitute for M
and
So,
=
= 132
Now from equation (2), we get the constants
k = b =
=
The population P(t) from logistic equation is calculated by :
As per question, P(t) = 110% of M
Now taking natural logs on both the sides we get
t = 36.216
Number of months = 36.216