Answer:
6194.84
Step-by-step explanation:
Using the formula for calculating accumulated annuity amount
F = P × ([1 + I]^N - 1 )/I
Where P is the payment amount. I is equal to the interest (discount) rate and N number of duration
For 40 years,
X = 100[(1 + i)^40 + (1 + i)^36 + · · ·+ (1 + i)^4]
=[100 × (1+i)^4 × (1 - (1 + i)^40]/1 − (1 + i)^4
For 20 years,
Y = A(20) = 100[(1+i)^20+(1+i)^16+· · ·+(1+i)^4]
Using X = 5Y (5 times the accumulated amount in the account at the ned of 20 years) and using a difference of squares on the left side gives
1 + (1 + i)^20 = 5
so (1 + i)^20 = 4
so (1 + i)^4 = 4^0.2 = 1.319508
Hence X = [100 × (1 + i)^4 × (1 − (1 + i)^40)] / 1 − (1 + i)^4
= [100×1.3195×(1−4^2)] / 1−1.3195
X = 6194.84
Answer:
The area of the shaded region is about 38.1 square centimeters.
Step-by-step explanation:
We want to find the area of the shaded region.
To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.
The given circle has a radius of 6 cm.
And the given sector has a central angle of 150°.
The area for a sector is given by the formula:
In this case, r = 6 and θ = 150°. Hence, the area of the sector is:
Now, we can find the area of the triangle. We can use an alternative formula:
Where a and b are the side lengths, and C is the angle between them.
Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.
And the angle C is 150°. Hence, the area of the triangle is:
The area of the shaded region is equivalent to the sector minus the triangle:
Therefore:
Use a calculator:
The area of the shaded region is about 38.1 square centimeters.
Answer:
-3
Step-by-step explanation:
cause positive = negative
the answer is = negative
Answer: $222.73
===========================================
Work Shown:
x = pre-GST price
10% of x = 0.10x = tax amount
x + 0.10x = 1.10x = post-GST price = 245
1.10x = 245
x = 245/1.10
x = 222.7272 approximately
x = 222.73 is the price before tax.
------------
Check:
10% of 222.73 = 0.10*222.73 = 22.273 = 22.27
The tax amount ($22.27) is added to the pre-GST price to get
22.27+222.73 = 245
which matches the post-GST price mentioned.
The answer is confirmed.
Or another way to confirm the answer is to calculate this
1.10*222.73 = 245.003 = 245
Answer:
b (1/15)
Step-by-step explanation:
