Answer:
a. 6
b. 9
Step-by-step explanation:
a. The product modulo 7 can be found from the product of the individual numbers modulo 7:
(88·95·36·702) mod 7 = (88 mod 7)·(95 mod 7)·(36 mod 7)·(703 mod 7) mod 7
= (4·4·1·3) mod 7 = 48 mod 7 = 6
__
b. Powers of 4 mod 11 repeat with period 5:
4 mod 11 = 4
4^2 mod 11 = 5
4^3 mod 11 = 9
4^4 mod 11 = 3
4^5 mod 11 = 1
So, 4^83 mod 11 = 4^3 mod 11 = 9
Answer:
Base = 24 ft; height = 47 ft
Step-by-step explanation:
The formula for the area of a triangle is
A = ½bh
Let x = the base. Then
2x - 1 = the height
We reject the negative value, so x = 24 ft
Base = x = 24 ft
Height = 2x - 1 = 2(24)-1 = 48 - 1 = 47 ft
Check:
564 = ½ × 24 × 47
564 = 564
OK
2+2+2=(6
(a2)
(b2)
2×2=4+2=6
Answer:
FV= $70,887.15
Step-by-step explanation:
<u>First, we need to calculate the future value of the $130 deposit for 5 years:</u>
FV= {A*[(1+i)^n-1]}/i
A= monthly deposit= $130
i= 0.08/12= 0.0067
n= 5*12= 60 months
FV= {130*[(1.0067^60) - 1]} / 0.0067
FV= $9,561.96
<u>Now, using the following formula, the future value of the investment after 25 years:</u>
<u />
FV= PV*(1 + i)^n
n= 25*12= 300
FV= 9,561.96*(1.0067^300)
FV= $70,887.15
