Answer:
b. The values X and Y are independent therefore, the mean is 34 seconds and the standard deviation is 50 seconds
Step-by-step explanation:
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds.
This means that 
After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds.
This means that 
Which of the following is true about the distribution of X-Y?
They are independent, so:


This means that the correct answer is given by option b.
Answer:


Step-by-step explanation:
The question is 
<em>We let
, so the equation becomes:</em>

Where 
Putting it in the quadratic formula, we have:
<u>Quadratic formula:</u> 
Substituting we have: 
<em>We let
, so x is:</em>
<em>
</em>
<em>and</em>
<em>
</em>
The solutions of the equation is
(rounded to 2 decimal places), and
(rounded to 2 decimal places)
The postulate that is used in order to prove the congruency of the triangles is the ASA which means (Angle – Side – Angle). The property that is applicable for the congruency of DB to itself is the reflexive property. Therefore, the answer to this item is the second choice.
Hope I helped! :)
Let x = the length of the rectangle
Let w= the width
Two sections are required, hence 2w of fence required
2x+3w=500
this can be written as:
3w=1500-2x
w=(1500-2x)/3
Area=x*w
replacing w with our expression:
A=x(1500-2x)/3
A=(500x-2x^2)/3
This is a quadratic equation, if we find the axis of symmetry we will know what value of x gives maximum area:
Axis of symmetry: x=-b/2a
From our equation we get:
a=-2/3; b=1500/3
thus
x=(1500/3)/(-(-2/3))
x=750
thus the maximum area will be given by length of 750