Answer:
<em>Average rate of change is </em><em>-78.</em>
Step-by-step explanation:
A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round.
The table that shows the number of contestants in each round of the competition is,
x f(x)
1 243
2 81
3 27
4 9
5 3
Average rate of change is the change in the y-value divided by the change in the x-value for two points on the graph.
i.e 
So, the average rate of change of 
from 
to 
is,
Since f(x) is decreasing, so rate of change is negative.
Answer:
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
Step-by-step explanation:
- The diagonal of a rectangle is represented by
. - Area of rectangle is = length×width
- Perimeter of a rectangle = 2(length+width).
Assume x be the width of the rectangle.
The length of the rectangle is to be 6 cm more than twice the width.
The length of the rectangle is= (2x+6) cm
Then the diagonal of the rectangle is
cm
According to the problem,
Squaring both sides
⇒5x²+45x-21x-189=0
⇒5x(x+9)-21(x+9)=0
⇒(x+9)(5x-21)=0
⇒x+9=0 or, 5x-21=0
⇒x= -9, 4.2
Since the width of a rectangle can not negative.
So, x=4.2 cm
The width of rectangle is = 4.2 cm
The length of the rectangle is =(2×4.2+6)
=14.4 cm
She should make a rectangle with dimensions 14.4 cm by 4.2 cm.
P=0.15
P^ is the sample proportion which comes from the data
In this case the p^=12/50=0.24
