Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
Answer: x = 0; y = 2; z = 5
Step-by-step explanation:
x+2y+z=9
x-y+3z=13
2z=10
==
Start with the last equation: 2z = 10, therefore z = 5 [easy]
Let's rewrite the second equation with 1) z=5, and 2) rearrange to find x:
x-y+3z = 13
x - y +3*5 = 13
x = y-2
Now use the values for x [(y-2)] and y [5] in the first equation:
X+2y+z=9
(y-2) +2y + 5 = 9
3y +3 = 9
3y = 6
y = 2
Now that we have y [2] and z [5], let's use the first equation to solve for x:
x+2y+z=9
x + 4 + 5 = 9
x + 9 = 9
x = 0
====
Try the three values (x=0, y=2, and z=5) in any of the formulas. The result should/will equal the number shown.
Answer:
m=76
Step-by-step explanation:
Ration of minutes of television to commercial is 35:7.8
3 hours and 50 minutes is 230 minutes
230:X
35:7.8
Multiply both sides by 6.6
X=51.5 minutes
There is about 51.5 minutes of commercials
Answer:
B)6.25
Step-by-step explanation: