Answer:
See Below
Step-by-step explanation:
The function is a piecewise function defined as:
a)
We need to find the limit of the function as t goes to infinity. This means what is the max value of fish in the pond given times goes to infinity (on an on).
We will take the 2nd part of the equation since t falls into that range, t is infinity, which is definitely greater than 8.
This means the maximum number of fish at this pond is 1600, no matter how long it goes on.
b)
A function is continuous at a point if we have the limit and the functional value at that point same.
Functional value at t = 8 is (we use 2nd part of equation):
We do have a value and limit also goes to this as t approaches 8.
So, function is continuous at t = 8
c)
We want to find is there a "time" when the number of fishes in the pond is 250, during t from 0 to 6. We plug in 250 into N(t) and try to find t. Make sure to use the 1st part of the piece-wise function. Shown below:
The time is 4 years when the number of fishes in the pond is 250
Answer:
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Step-by-step explanation:
Problems of normally distributed samples can be 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.
In this question:
Find the score that separates the lower 5% of the class from the rest of the class.
This score is the 5th percentile, which is X when Z has a pvalue of 0.05. So it is X when Z = -1.645.
The score that separates the lower 5% of the class from the rest of the class is 55.6.
Answer: Angle addition postulate.
Explanation: If 
and 
here, if we have to prove x=30
If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate, we can say that 
⇒
But,
In option (1) substitution property of equality
If there is condition that 
then we can use substitution property of equality,
And, in this case 
⇒
which is wrong. So, we can not use this property here.
In option (3) subtraction property of equality
There is no use of this property to find the value x.
In option (4) addition property of equality
There is no use of this property to find the value x.
