Answer:
The rate of return is 14%
Step-by-step explanation:
The rate of return can be determined by,
RR = 
x 100%
where:
RR is the rate of return
is the final amount = $690 - $6 = $684
is the initial amount = $15 x 40 = $ 600
So that,
RR = 
x 100%
= 0.14 x 100%
= 14%
Therefore, the rate of return is 14%.
The Answer is A
Explanation:
The standard form equation for an ellipse is:
(x - h)² / a² + (y - k)² / b² = 1
So looking at the picture above you can see that the center of the ellipse is at the origin which is (0;0) making both h and k zero.
It is then observed that the x-intercepts are at 12 meaning a=12 and y- intercepts are at approximately square root of 95 which is 9.746... which are 'k'
So you can conclude by saying that:
x²/12² + y²/(sqrt of 95)² = 1
then giving you the answer of A which is:
x²/144 + y²/95 = 1
Step-by-step explanation:
Left hand side:
4 [sin⁶ θ + cos⁶ θ]
Rearrange:
4 [(sin² θ)³ + (cos² θ)³]
Factor the sum of cubes:
4 [(sin² θ + cos² θ) (sin⁴ θ − sin² θ cos² θ + cos⁴ θ)]
Pythagorean identity:
4 [sin⁴ θ − sin² θ cos² θ + cos⁴ θ]
Complete the square:
4 [sin⁴ θ + 2 sin² θ cos² θ + cos⁴ θ − 3 sin² θ cos² θ]
4 [(sin² θ + cos² θ)² − 3 sin² θ cos² θ]
Pythagorean identity:
4 [1 − 3 sin² θ cos² θ]
Rearrange:
4 − 12 sin² θ cos² θ
4 − 3 (2 sin θ cos θ)²
Double angle formula:
4 − 3 (sin (2θ))²
4 − 3 sin² (2θ)
Finally, apply Pythagorean identity and simplify:
4 − 3 (1 − cos² (2θ))
4 − 3 + 3 cos² (2θ)
1 + 3 cos² (2θ)
Answer:
Constant of proportionality(X:Y) = 1:6
Step-by-step explanation:
Given:
X- 5, 6, 7, 8, 9
Y- 30, 36, 42, 48, 54
Find:
Constant of proportionality
Computation:
X/Y = 5/30 = 6/36 = 7/42 = 8/48 = 9/54
X/Y = 1/6 = 1/6 = 1/6 = 1/6 = 1/6
So;
Constant of proportionality(X:Y) = 1:6
Option four is the answer bc 8^2 is 64 and so is 4^3. so for the answer to be correct, it should say = and not ≠
