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.
To find the number of times higher the number of library visits before the examination day is compared to an average week, we need to compare the number of visits in the two-week period to the number of visits in one average week.
The number of visits in the two-week period is 2 × 10^3.
The number of visits in one average week is 5 × 10^2.
To find the number of times higher, we divide the number of visits in the two-week period by the number of visits in one average week:
(2 × 10^3) / (5 × 10^2) = (2/5) × (10^3/10^2) = (2/5) × 10^1 = 0.4 × 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.
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×10n where a is single digit.
To find the value of "n" for the expression a×10n, we can use the formula:
P = A / (1 + r)^n
Where:
P = initial deposit ($100)
A = final amount ($15,528.23)
r = interest rate per period (5% or 0.05)
n = number of periods (months or years)
Since the interest is compounded monthly, we need to convert the 10-year period into months:
n = 10 years * 12 months/year = 120 months
Substituting the given values into the formula:
100 = 15,528.23 / (1 + 0.05)^120
Now we solve for (1 + 0.05)^120:
(1.05)^120 ≈ 4.3219
So, 4.3219 * 100 ≈ 432.19
Therefore, the value of "a" is approximately 4, and the value of "n" is 2.
Thus, $15,528.23 can be expressed as 4.32x10².
To find out how many times higher the number of library visits before the examination day is compared to an average week, we need to calculate the ratio between the two.
The number of visits during the two-week period is given as 2x10^3.
The number of visits during an average week is given as 5x10^2.
To calculate the ratio, we divide the number of visits during the two-week period by the number of visits during an average week:
Ratio = (2x10^3) / (5x10^2)
Next, we can simplify the ratio:
Ratio = (2/5) x (10^3 / 10^2)
Ratio = (2/5) x 10^(3-2)
Ratio = (2/5) x 10^1
Ratio = 2
Therefore, the number of library visits before the examination day is 2 times higher than the number of visits during an average week.
To find the number of times higher the number of library visits before the examination day is compared to the visits in an average week, we need to calculate the ratio between these two numbers.
First, let's find the number of visits during the two-week period:
Number of visits before examination day = 2 × 10^3 visits
Next, let's find the number of visits in an average week:
Number of visits in an average week = 5 × 10^2 visits
Now, we can calculate the ratio:
Ratio = Number of visits before examination day / Number of visits in an average week
Ratio = (2 × 10^3) / (5 × 10^2)
Simplifying the ratio, we can cancel out the common factors in the numerator and denominator:
Ratio = (2 × 10^3) / (5 × 10^2)
= (2/5) × (10^3/10^2)
= (2/5) × 10^(3-2)
= (2/5) × 10^1
= (2/5) × 10
= 2 × 2
= 4
Therefore, the number of library visits before the examination day is 4 times higher compared to the visits in an average week.