Answer:
The required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.
Step-by-step explanation:
From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.
Here, 

The common ratio of GP is 1/2.



The first term of the sequence is 20.
The formula for sequence is

Where a is first term and r is common difference.
The required sequence is

The formula for rate of change is

The average rate of change from n = 1 to n = 3 is



Therefore the required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.
Answer:
y = 4.5 x
Step-by-step explanation:
Answer:
Probability of no black bead is adjacent to the yellow bead is = 0.966
Step-by-step explanation:
First to arrange all the beads without restrictions = 6! = 720
Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 /720
= 0.0333
Probability of no black bead is adjacent to the yellow bead is
= 1- Probability the black bead is adjacent to Yellow bead
= 1-0.033
= 0.966
Consider the absolute value, because we only worry about the quadrant later.


Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.
The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

Since angle A is in the third quadrant, the tangent function will produce a positive angle.


Answer:
15 units.
Step-by-step explanation:
The distance between the points (x1, y1) and (x2, y2) is
√(x1-y1)^2 + (y1-y2)^2))
So here it is:
√(10- -2)^2 + (6- -3)^2)
= √(144+81)
= √225
= 15.