Answer:
8 days
Step-by-step explanation:
On day 8, Isabella will save 256 nickels, bringing her total to 510.
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The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.
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The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.
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The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...
an = a1·r^(n-1) = 2·2^(n-1) = 2^n
The sum of n terms of the sequence is ...
S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)
S = 2^(n+1) -2
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We want S > 500, so ...
500 < 2^(n+1) -2
502 < 2^(n+1)
251 < 2^n
log(251) < n·log(2)
n > log(251)/log(2)
n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels
Answer:
Width = 40 meters
Length = 167 meters
Step-by-step explanation:
Let
Width of the pool = x meters
Then
Length of the pool = 4x + 7 meters
and
Perimeter meters
Hence,
Answer: B) $4,000
Step-by-step explanation:
The formula for determining simple interest is expressed as
I = PRT/100
Where
I represents interest paid on the loan.
P represents the principal or amount taken as loan
R represents interest rate
T represents the duration of the loan in years.
Considering Cathy's loan,
P = $20,000
R = 5.2%
T = 10 years
I = (20000 × 5.2 × 10)/100
I = $10400
Considering Steven's loan,
P = $20,000
R = 4.8%
T = 15 years
I = (20000 × 4.8 × 15)/100
I = $14400
The difference between the amounts of interest Cathy and Steven paid for their loans is
14400 - 10400 = $4000
Answer:
Step-by-step explanation:
Given
Required
Solve for x
Subtract 5 from both sides
Divide through by 3
Answer:
find he domain by finding where the equation is defined. the range is the set of values that correspond with the domain.