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2 answers:
<u>Answer</u>:
the length of chicken coop and the garden is of 40 feet.
<u>Explanation</u>:
Given that the garden is the length of the chicken coop, equal length
→ 3x + 12 = 6x – 16
→ 3x - 6x = -16 - 12
→ -3x = -28
→
→
→ x = 9.33 feet.
- The garden length = 3(
) + 12 → 40 feet
- the chick coop length should be same as the garden length.
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Answer: The required probability of event B is P(B) = 0.37.
Step-by-step explanation: For two events A and B, we are given the following probabilities :
P(A) = 0.34, P(A ∩ B) = 0.27 and P(A ∪ B) = 0.44.
We are to find the probability of event B, P(B) = ?
From the laws of probability, we have
Thus, the required probability of event B is P(B) = 0.37.
The correct option is ''The value of 135 because it is not greater than 136.5 values is outside the 99% confidence interval for the population mean''
<h2>Given that,</h2>A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34.
<h3>We have to find,</h3>Which of the following values is outside the 99% confidence interval for the population mean?
<h3>According to the question,</h3>A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard deviation of 34.
Sample space n = 85,
Mean = 146
And standard deviation = 34
Then, The standard error of the sample is,
Then, z-critical value for 99% is 2.58,
Margin of error = ±9.515
Confidence interval for lower bound is,
= 146 - 9.515 = 136.485
And confidence interval upper bound is,
= 146 + 9.515 = 155.515
Here, 135 is less than the lower bound,
Therefore, 135 does not lie within a 99% confidence interval.
For more details about Lower bound refer to the link given below.
9514 1404 393
Answer:
a) f(x)
b) g(x)
c) for all values of x > 1, g(x) has a greater rate of change
Step-by-step explanation:
a) The rate of change of f(x) is the x-coefficient: 4. The average rate of change of g(x) on an interval can be found by dividing the change by the interval width. Here, the width of the interval of interest is 1-0 = 1, so the average rate of change is g(1) -g(0) = 4-2 = 2.
On the interval [0, 1], f(x) has the greater rate of change.
__
b) The interval [2, 3] also has a width of 1, so the rate of change of g(x) on that interval is g(3) -g(2) = 20 -10 = 10. This value is greater than 4, so ...
on the interval [2, 3], g(x) has the greater rate of change.
__
c) Part (b) demonstrates that g(x) will have a greater rate of change on some intervals. In fact, for any interval whose center is greater than x=1, g(x) will have a greater rate of change than f(x).
_____
In calculus terms, the rate of change of g(x) is g'(x) = 4x. This will be greater than 4 for any x > 1. The graph shows the rate of change is 4 at x=1, and is higher for x > 1. The average rate of change will be greater than 4 on any interval whose center is greater than x=1.
We can figure the average rate of change on the interval [a, b] as ...
m = (g(b) -g(a))/(b -a)
m = ((2b² +2) -(2a² +2))/(b -a) = 2(b² -a²)/(b-a) = 2(b+a)
For the average rate of change to exceed 4, the sum of the ends of the interval must exceed 2, which is to say the midpoint must exceed 1.
