4900=4200(1+r/2)^(2*4)
Solve for r
R=(4900/4200)^(1/8))-1)*2
R=((4,900÷4,200)^(1÷8)−1)×2
R=0.039*100=3.9%
1) gradient of line = Δ y ÷ Δ x
= (5 -2) ÷ (3 - (-6))
= ¹/₃
using the point-slope form (y-y₁) = m(x-x₁)
using (3,5)
(y - 5) = ¹/₃ (x -3)
y - 5 = ¹/₃x - 1
⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1)
<span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6
³/₂ x = 1
x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6
y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A]
This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B]
Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
Answer:
16.053 inches
Step-by-step explanation:
Many such probability questions are easily answered by a suitable calculator or spreadsheet.
Answer:
$102,677.20
Step-by-step explanation:
The present value of an annuity due is determined by the following expression:
Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.
With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:
The present value of your winnings is $102,677.20.
R^2=(x-6)^2+(y-4)^2
r^2=(6-2)^2+(4-1)^2, r^2=16+9=25
(x-6)^2+(y-4)^2=25
