There are 48 available subjects. Researchers should select 4 of them for their experiment.
We should find the number of possible different random samples. The order of the selected subjects is not important. This means that we need to find how many different combinations of subjects from total 48 are possible. <span>A </span>formula<span> for the number of possible </span>combinations<span> of </span>r<span> objects from a </span>set<span> of </span>n<span> objects is: n!/r!(n-r)!. In our case n=48 and r=4:
C=48!/44!*4!=48*47*46*45*44!/44!*4!=</span><span>48*47*46*45/4*3*2*1=4669920/24=
194580.</span>
Given:
n = 50, sample size

, sample mean
s = 2.4 min, sample standard deviation.
The confidence interval is

At the 99% confidence level, t* (from the student's t-distribution) is
t* = 2.68
Therefore
t*(s/√n) = 2.68*(2.4/√50) = 0.9096
The confidence interval is
(23.6-0.9096, 23.6+0.9096) ≈ (22.69, 24.51)
Answer: (22.7, 24.5)
The answer is C because it is telling you to subtract 180 degrees from 54 degrees to get the final answer which is 126 I got that because 54 is that angle and it is asking for the whole amount so it would be C
Answer:
Step-by-step explanation:
Distance upstream = (34-c)(39/60) miles
--------------------------
Distance downstream = (34+c)(29/60) miles
-----------------------------------------------
Equation:
distance = rate*time
distance up = distance down
(34-c)(39/60) = (34+c)(29/60)
Multiply both sides by 60 to get:
39(34-c) = 29(34+c)
39*34 - 39c = 29*34 + 29c
68c = 340
c = 5 mph speed of the current
There are 2 tangent lines that pass through the point

and

Explanation:
Given:

The point-slope form of the equation of a line tells us that the form of the tangent lines must be:
![[1]](https://tex.z-dn.net/?f=%5B1%5D)
For the lines to be tangent to the curve, we must substitute the first derivative of the curve for
:



![[2]](https://tex.z-dn.net/?f=%5B2%5D)
Substitute equation [2] into equation [1]:
![[1.1]](https://tex.z-dn.net/?f=%5B1.1%5D)
Because the line must touch the curve, we may substitute 

Solve for x:




± 
±
<em> </em>

There are 2 tangent lines.

and
