In this
problem, the given values are:
x = average =
30.4
s = standard
deviation = 7.1
n = number of
samples = 25
Degrees of
freedom = n -1 =24
Using the
t-distribution table for a normal curve at 90% CI, we get t-crit:
t-crit = 1.711
Now the Margin
of Error (E) is calculated as:
E = t-crit*(s/ 
)
By substituting the known values into the equation:
E = 1.711 * (7.1/ 
)
E = +- 4.30
Therefore, the margin of error is 4.36. Hence, the commute time
is between 26.1 minutes and 34.7 minutes.
<span> </span>
Answer: 90.51 square units
Explanation:
1) The rectangle has one length on the x-axis.
2) Call x, the x-coordinate of the right lower corner of the rectangle.
And the point is (x,0)
3) The x-coordinate of the lef lower corner will be - x.
And the point is (-x,0)
4) The right upper point of the rectangle will be (x,y) where y = 24 - x²
5) The left upper point of the rectangle will be (-x,y) where y = 24 - x² .
6) The area of such rectantle is the length of the base times the length of the height.
The length of the base is 2x
The lenght of the height is y
So, the area is A = 2x(y) = 2x(24 - x²) = 48x - 2x³
7) Now to find the maximum area you have to derivate the function and make it equal to zero:
dA
---- = A' = 48 - 6x² = 0 =>
dx
4x² = 48 => x² = 48/6 = 8 =>
x = (+/-)√8
Then, y = 24 - x² = 24 - (√8)² = 24 - 8 = 16
8) Therefore the area of the rectangle is
A = 2x(y) = 2(√8)(16) = 90.51.
9) You can see if x is a greater or smaller.
For example x = 2 and x = 3
x = 2 => y = 24 - (2)² = 20 => A = 2(2)(20) = 80 which is less than 90.51
x = 3 => y = 24 - (3)² = 15 => A = 2(3)(15) = 90 which is less than 90.51
So, that tells you that your result should be right.
A=1/2 9+20×15
1/2. 29×15
217.5
Answer:closed
Step-by-step explanation:
Classify the two given samples as independent or dependent.
sample 1: the scores of 20 students who took the act
sample 2: the scores of 20 different students who took the sat
Solution: The two given samples are independent samples because in both the samples, the scores of one student will not affect the scores of other students.
Independent samples are samples that are selected randomly so that its observations do not depend on the values other observations.
