Answer: 
Step-by-step explanation:
<h3>
The complete exercise is: "Line segment YV of rectangle YVWX measures 24 units. What is the length of line segment YX?"</h3><h3>
The missing figure is attached.</h3>
Since the figure is a rectangle, you know that:

Notice that the segment YV divides the rectangle into two equal Right triangles.
Knowing the above, you can use the following Trigonometric Identity:

You can identify that:

Therefore, in order to find the length of the segment YX, you must substitute values into
and then you must solve for YX.
You get that this is:

Answer:
6.78ft/sec
Step-by-step explanation:
From the question, dx/dt= 3.9 ft/sec
We are looking for Dy/dt
From geometry,vof this case the relationship between x and y is needed here, there is two similar triangle that exhibited by the man and the lamb
12/y= 5.1/(y-x)
Then ,cross multiply, we have
12(y-x)=5.1y
12y-12x=5.1y
12y-5.1y=12x
6.9y=12x
y=( 12/6.9)x
Differentiating implicitly the bother sides with respect to t, we have
Dy/dt= ( 12/6.9)dx/dt
But dx/dt= 3.9 ft/sec
Then Dy/dt= ( 12/6.9)× 3.9
Dy/dt=6.78ft/sec
Hence, the rate that the tip of the person's shadow moves away from the lamppost when the person is 9 ft away from the lampost is 6.78ft/sec
CHECK THE ATTACHMENT FOR THE FIQURE
Answer:

Step-by-step explanation:
Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.
The probability to select red marble is
Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.
The probability to select red marble is
Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.
The probability to select red marble is
The probability to choose each urn is the same and is equal to 
Thus, the probability that the marble is red is
