Two weeks before an examination day, a librarian monitored the number of students who visited the library. Then they compared it with the number of visits made in an average week. Approximately 2×103 visits were reflected in their logbook during this two-week period, while only about 5×102 were reflected on an average week. How many times higher is the number of library visits before examination day compared to the library visits in an average week? Your answer should be a whole number.
I apologize for the incorrect response.
To find the number of times higher the number of library visits before the examination day compared to an average week, we need to divide the number of visits before the examination day by the number of visits in an average week.
Number of library visits before examination day = 2×10^3
Number of visits in an average week = 5×10^2
Number of times higher = (2×10^3) / (5×10^2)
= (2/5) × (10^3/10^2)
= (2/5) × (10^(3-2))
= (2/5) × (10^1)
= (2/5) × 10
= 4
Therefore, the number of library visits before the examination day is 4 times higher than the number of visits in an average week.
Apologies for the previous incorrect response.
To solve for the actual monthly deposit, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The final amount ($15,528.23)
P = The principal amount (monthly deposit)
r = Annual interest rate (as a decimal) = 0.05
n = Number of times interest is compounded per year = 12
t = Number of years = 10
We need to solve for P, the monthly deposit amount.
Rearranging the formula, we have:
P = A / [(1 + r/n)^(nt)]
Plugging in the values, we have:
P = 15528.23 / [(1 + 0.05/12)^(12*10)]
P ≈ 82.02173
Rounding to the nearest whole dollar, we find:
P ≈ $82
Therefore, the actual monthly deposit amount should be approximately $82. The amount $15,528.23 can be expressed as 2 × 10^4 in the form of a × 10^n where a is a single digit.
To find the number of times higher the number of library visits before the examination day compared to an average week, we need to divide the number of visits before the examination day by the number of visits in an average week.
Number of library visits before examination day = 2×10^3
Number of visits in an average week = 5×10^2
Number of times higher = (2×10^3) / (5×10^2)
= (2/5) × (10^3/10^2)
= (2/5) × 10^(3-2)
= (2/5) × 10^1
= 2 × 10
= 20
Therefore, the number of library visits before the examination day is 20 times higher than the number of visits in an average week.
that is incorrect
It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a×10^n where a is single digit
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The final amount
P = The principal amount (monthly deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, we have:
P = $100
r = 0.05 (5% as a decimal)
n = 12 (compounded monthly)
t = 10 years
Plugging in these values, we get:
A = 100(1 + 0.05/12)^(12*10)
Simplifying this expression, we find:
A ≈ 100(1.00417)^(120)
A ≈ 100(1.6470094)
A ≈ 164.70094
Rounding this to the nearest place value, we have:
A ≈ $164.70
Therefore, the amount $15,528.23 can be expressed as 1.647 x 10^4 (rounded to the nearest place value in the required form).
incorrect
Apologies for the previous incorrect response.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = The final amount
P = The principal amount (monthly deposit)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, we have:
P = $100
A = $15,528.23
r = 0.05 (5% as a decimal)
n = 12 (compounded monthly)
We need to solve for t, the number of years.
Using the formula, we can rearrange it to solve for t:
t = log(A/P) / (n * log(1 + r/n))
Plugging in the values, we have:
t = log(15528.23/100) / (12 * log(1 + 0.05/12))
Calculating this expression, we find:
t ≈ 11.5493
Since we are given that it takes exactly 10 years for the amount to reach $15,528.23, this means the monthly deposit time was rounded.
To find the actual monthly deposit, we can use the formula:
P = A / [(1 + r/n)^(nt)]
Plugging in the values, we have:
P = 15528.23 / [(1 + 0.05/12)^(12*10)]
P ≈ 81.6337
Rounding to the nearest whole dollar, we find:
P ≈ $82
Therefore, the monthly deposit should be approximately $82. The amount $15,528.23 cannot be expressed in the form a × 10^n where a is a single digit in this case.
How many times is 4 × 10^4 larger than 2 × 10^2
How many times less is 10^2 than 10^6 ? Express your answer as an integer power of 10.(1 point)
Responses
a. 10^−4
b. 10,000
c. 0.0001
d. 10^4