Answer:
a) 
b) 
Step-by-step explanation:
1) Data given and notation
n=900 represent the random sample taken
X=372 represent the students were pursuing liberal arts degrees
estimated proportion of students were pursuing liberal arts degrees
represent the significance level
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
p= population proportion of students were pursuing liberal arts degrees
2) Solution to the problem
The confidence interval would be given by this formula
For the 99% confidence interval the value of 
and 
, with that value we can find the quantile required for the interval in the normal standard distribution.
The margin of error is given by:
If we replace we have:
And replacing into the confidence interval formula we got:
And the 99% confidence interval would be given (0.371;0.455).
We are confident (99%) that about 37.1% to 45.5% of students were pursuing liberal arts degrees.
Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.
On this exercise is asked to find the scale factor by which the triangle ABC was
dilated to produce the triangle A'B'C'.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
As can be see on the picture the dilation produce was an enlargement meaning that the image is larger that the preimage.
Of this form you can discard the choices A and B as possible solutions.
Lets try 5/2 as the possible scale factor:
(x,y)-- (kx, ky)
A(0,2)--(5/2(0),5/2(2))=A'(0,5)
B(2,2)--(5/2(2),5/2(2))=B'(5,5)
C(2,0)--(5/2(2),5/2(0))=C'(5,0)
Lets try 5/1 or 5 as the scale factor:
A(0,2)--(5(0),5(2))=A'(0,10)
B(2,2)--(5(2),5(2))=B'(10,10)
C(2,0)--(5(2),5(0))=C'(10,0)
As said at the beginning of the question the triangle was not only dilated.
After a dilation and a translation, the scale factor of the dilation is letter C or 5/2.
Answer:x=5
Step-by-step explanation: x^2−2x−15=0
(x−5)=0 x−5=0 x=5
Answer:
212m
Step-by-step explanation:
The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.
Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;
Since we have the angle theta = 45° and opposite = 150m
According to SOH;
Sin theta = opposite/hypotenuse.
Sin45° = 150/hyp
hyp = 150/sin45°
hyp = 150/(1/√2)
hyp = 150×√2
hyp = 150√2 m
hyp = 212.13m
Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m
Answer:
a.0.126
b.100.6356
c.5.010
Step-by-step explanation:
