how much fencing would be required to fence a square field with an area of 118 sq.meters and 81 sq.decimetres
2 answers:
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Answer:
Step-by-step explanation:
Answer:
a. The amount that is saved at the expiration of the 5 year period is $22,769.20¢
b. The amount of interest is $2,769.20¢
Step-by-step explanation:
Since the amount that is deposited every year for a period of five years is $4,000 and the rate of the interest is 6.5%. We can always calculate the amount that is saved at the expiration of the five years.
We will first state the formula for calculating the future value of annuity:-
Future value of annuity =
Where P is the amount deposited per year.
r is the rate of interest
t is the time or period
and in this case, the actual value of P = $4,000
rate of interest, r is 6.5% = 0.065
time, t is 5 years.
Substituting e, we have:
Fv of annuity =
= 4,000 × [((1.065)^5)- 1/0.065]
= 4,000 × [(1.37 - 1)/0.065]
= 4,000 × (0.37/0.065)
= 4,000 × 5.6923
= $22,769.20¢
a. Therefore the amount that is saved at the end of the five (5) years is $22,769.20¢
b. To find the interest, we will calculate the amount of deposit made during the period of five years and subtract the sum from the current amount that is saved ($22,769.29¢).
Since I deposited 4,000 every year for five years, the total amount of deposit I made at the period =
4,000 × 5 = $20,000
The amount of interest is then = $22,769.20¢ - $20,000 = $2,769.20¢
Answer:
a)0.7
b) 10.03
c) 0.0801
Step-by-step explanation:
Rate of return Probability
9.5 0.1
9.8 0.2
10 0.3
10.2 0.3
10.6 0.1
a.
P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)
P(Rate of return is at least 10%)=0.3+0.3+0.1
P(Rate of return is at least 10%)=0.7
b)
Expected rate of return=E(x)=sum(x*p(x))
Rate of return(x) Probability(p(x)) x*p(x)
9.5 0.1 0.95
9.8 0.2 1.96
10 0.3 3
10.2 0.3 3.06
10.6 0.1 1.06
Expected rate of return=E(x)=sum(x*p(x))
Expected rate of return=0.95+1.96+3+3.06+1.06=10.03
c)
variance of the rate of return=V(x)=
Rate of return(x) Probability(p(x)) x*p(x) x²*p(x)
9.5 0.1 0.95 9.025
9.8 0.2 1.96 19.208
10 0.3 3 30
10.2 0.3 3.06 31.212
10.6 0.1 1.06 11.236
sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681
variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²
variance of the rate of return=V(x)=100.681-(10.03)²
variance of the rate of return=V(x)=100.681-100.6009
variance of the rate of return=V(x)=0.0801
Given that diameter of the base of the cylinder = 8 ft
Given that height of the cylinder = 6 ft
We have to find the surface area of the cylinder in terms of pi.
So we need to use formula of surface area of the cylinder which is
where h= height = 6
r= radius = diameter/2 = 8/2 = 4
Now plug these values into above formula
Hence final answer is
square ft