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 base of the rectangular prism is:
- <u>18 square centimeters</u>.
The height of the rectangular prism is:
The volume of the rectangular prism is:
- <u>108 cubic centimeters</u>.
Step-by-step explanation:
To find the area of the base of the prism, you must remember that it corresponds to the rectangle formed by the points ABCD, with this in mind we apply the area formula that is equal to:
- Area of a rectangle = base * height.
Since the rectangle formed by the mentioned points has a base of 9 cm and a height of 2 cm, these values are the ones we use in the formula:
- Area of a rectangle = 9 cm * 2 cm
- <u>Area of a rectangle = 18 cm^2
</u>
Since the height requested by the second question is not from the rectangle at the base but from the entire prism, you should look at the height formed by the AW points, which as you can see is:
- <u>Prism height = 6 cm
</u>
Once we have these two data, it is very easy to calculate the volume since they are what we require in the volume formula:
- Volume = area * height.
- Volume = 18 cm^2 * 6 cm
- <u>Volume = 108 cm^3</u>
Answer:
bc is 26
Step-by-step explanation:
Answer:
x = 6
Step-by-step explanation:
To find the missing side, write a proportion using side lengths from each similar shape. A proportion is an equation that sets equal two ratios.
Find x by cross multiplying numerator and denominator of each fraction.
4(18) = 12x
72 = 12x
6 = x
