Answer:
a) the proportion of 95% confidence intervals that include the population proportion approaches 0.95
b) Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
Step-by-step explanation:
a)
Given the the data in the question, confidence level is 95%.
In this case as the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 0.95. hence the expected value of the proportion.
b)
Given the the data in the question, confidence level is 95% and sample proportion
we know that In normal distribution 68% confidence indicate one standard deviation, 95% confidence indicate 2 standard deviation while 99.97% confidence indicate 3 standard deviation.
The sample proportion does not include the population proportion, in 95% confidence from the standard normal table 0.95 value lies within the critical value of 1.96 approximately 2.
hence ( z =2 ) that satisfied the 1.96 standard error from the population proportion
hence, Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion
Answer:
(2,5)) ,(-2,-3),(8,2),(4,-6)
Step-by-step explanation:
it is rotated by 180 degree so evrything becomes positve beside the -6
Answer:
B. -5
C. 5
Step-by-step explanation:
The absolute value means make it positive.
When solving an equation with an absolute value it means we have two solutions, a positive and a negative
|x| =5
x = 5 and x = -5
I would compute sqrt(1 + 160pi^2) first to get approximately 39.75093337
Add this to 1 and we have 40.75093337
Then divide over 2pi to get a final approximate result of 6.48571248
So x = 6.48571248 is one approximate solution
In short, I computed 
only focusing on the plus for now.
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If you were to compute 
you should get roughly -6.167402596 as your other solution. Each solution can then be plugged into the original equation to check if you get 0 or not. You likely won't land exactly on 0 but you'll get close enough.
Answer:
Maximum Value: ∞
General Formulas and Concepts:
<u>Calculus</u>
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 3x² + x³
<u>Step 2: Find Derivative</u>
- Basic Power Rule: f'(x) = 2 · 3x²⁻¹ + 3 · x³⁻¹
- Simplify: f'(x) = 6x + 3x²
<u>Step 3: Analyze</u>
We see that our derivative is the graph of some sort of parabola. The parabola would be opening upwards.
Therefore, the maximum value of the derivative would be ∞, as the parabola's output <em>y</em> infinitely increases.
