Answer:
CI = 21 ± 0.365
Step-by-step explanation:
The confidence interval is:
CI = x ± SE * CV
where x is the sample mean, SE is the standard error, and CV is the critical value (either t score or z score).
Here, x = 21.
The standard error for a sample mean is:
SE = σ / √n
SE = 3.2 / √510
SE = 0.142
The critical value is looked up in a table or found with a calculator. But first, we must find the alpha level and the critical probability.
α = 1 - 0.99 = 0.01
p* = 1 - (α/2) = 1 - (0.01/2) = 0.995
Using a calculator or a z-score table:
P(x<z) = 0.995
z = 2.576
Therefore:
CI = 21 ± 0.142 × 2.576
CI = 21 ± 0.365
Round as needed.
Answer:
75%
Step-by-step explanation:
The computation of the percent of the professional professors there are tenured is shown below;
Given that
academic professors A = 60%
professors tenured P = 70%
professors at Paracelsus University = 90%
Based on the above information
As we know that 90% of the professors could be academic professors or tenured or both
so here we can say that the percent of academic professors is
= 60 + 70 - 90
= 40
Therefore professors tenured will be
= 70 - 40
= 30
Now the percentage of professional professor that is tenured is
= 30 ÷ 40 × 100
= 75%
D.
The formula to find the circumference of a circle is:
Where "C" is circumference and "d" is diameter.
Substituting your values in, we have:
Which, when rounded, is 37.7.
Lets assume height as x
so width will be 2x
and length will be 3x similarly.
so,
Volume of prism = w * h * l
384 = 2x * x * 3x
384 = 6x^3
dividing both sides by 6
64 = x^3 ( taking cube root of 64)
4 = x
So,
Height = 4
width = 4 * 2 = 8
length = 4 * 3 = 12
Hope this helps.. :)
Answer:
(b) domain: (-∞, ∞)
(c) f(x) = 3 only at x=1
(d) range: (-∞, 3]
Step-by-step explanation:
(b) The domain is the horizontal extent of the region over which the function is defined. The function f(x) is defined for all x, from -∞ to +∞. The arrowheads on the ends of the graph mean the graph extends to infinity in x and y directions from those points (y goes to -∞, while x goes to ±∞).
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(c) Locate the horizontal grid line y=3 on the graph. Find all the points where it intersects the graph. There is only one: (1, 3). That is, x=1 is the only x-value for which f(x) = 3.
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(d) The range of the function is its vertical extent. The graph of f(x) extends from y = -∞ up to y = 3, so that is the range.
