A coordinate plane linear graph shows inequalities. A line goes through (0, 1) and (2, minus 1). Another line goes through (0, m
1 answer:
The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph attached.
<h3>What is Inequality ?</h3>When two algebraic expressions are equated by an inequality operator then the mathematical statement formed is called inequality
It is given that a line passes through the points (0, 1) and (2, minus 1)
The equation of the line representing this is given by
y = mx+c
m = -1
y = -x+1
and the other line passing through the points of (0, minus 3) and (2, 1) is
m = 2
y = 2x -3
These are plotted on the graph
From intersection, region to the right of it is A, below is D, to the left is C, and above is B.
These are noted ion the graph
Then the inequalities are plotted y ≥ 2x − 3 and y ≤ -x + 1
The region in the graph that represents the solution of the system of linear inequalities y ≥ 2x − 3 and y ≤ -x + 1 is given by C region , This can be clearly understood from the graph.
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Answer:
a) There is a 9% probability that a drought lasts exactly 3 intervals.
There is an 85.5% probability that a drought lasts at most 3 intervals.
b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation
Step-by-step explanation:
The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.
It has the following probability density formula:
In which p is the probability of a success.
The mean of the geometric distribution is given by the following formula:
The standard deviation of the geometric distribution is given by the following formula:
In this problem, we have that:
So
(a) What is the probability that a drought lasts exactly 3 intervals?
This is
There is a 9% probability that a drought lasts exactly 3 intervals.
At most 3 intervals?
This is
Previously in this exercise, we found that
So
There is an 85.5% probability that a drought lasts at most 3 intervals.
(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?
This is .
We are working with discrete data, so 3.66 is rounded up to 4.
Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:
There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation
Answer:
The % growth rate is 15.8%.
Step-by-step explanation:
Let the function is given by , where f(w) is the number of a specific product produced after w weeks.
Now, given for w = 0, f(0) = 190 = a
So, the function becomes ............. (1)
Now, it is also give that at w = 1, f(1) = 220.
So, from equation (1) we get,
⇒ b = 1.15789.
Now, b = 1 + r
⇒ 1.15789 = 1 + r
⇒ r = 0.15789
Therefore, the % growth rate is 0.15789 × 100% = 15.8% (Approx.)