Answer:

Step-by-step explanation:
The picture of the question in the attached figure
we know that
The domain of a function is the set of all possible values of x
The domain of the line with negative slope is the interval [1,3)
The domain of the line with slope equal to zero (horizontal line ) is the interval [3,5)
so
The domain of the piece-wise function is the interval [1,5)

The value of x=1 is included in the domain set
The value of x=5 is not included in the domain set
The question is missing the figure. So, it is in the atachment.
Answer: MN = x
LN = 
Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.
For the triangle <u>on the left</u> of the altitude:
45+90+angle=180
angle = 45
For the triangle <u>on the right</u>:
30+90+angle=180
angle = 60
With the angles, use the Law of Sines, which is relates sides and angles, as follows:

For MN:

MN = 
MN = x
For LN:

LN = 
We can determine sin (105) as:
sin(105) = sin(45+60)
sin(105) = sin(45)cos(60) + cos(45)sin(60)
sin(105) = 
sin(105) = 
LN = 
LN = 
LN = 
The expressions for:
MN = x
LN = 
Answer: No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.
Step-by-step explanation:
Since we have given that
n the California state university system take 4.5 years, on average, to finish their undergraduate degrees.
So, the hypothesis would be

Mean = 5.1
Standard deviation = 1.2
n = 49
So, test statistic value would be

At 1% level of significance, critical value is 2.58
Since 2.58>-3.53.
So, we will accept the null hypothesis.
Hence, No, the data does not support the claim at 1% level as the mean time is no longer than 4.5 years.
You have 11 items and you need to choose 5 of the 11.
There are 462 ways to choose them.
The formula is :
11! / (5!6!)
n!/(r!(n-r)!)