The calendar obviously has an integral number of years and months in 400 years. If it has an integral number of weeks, then it will repeat itself after that time. The rules of the calendar eliminate a leap year in 3 out of the four century years, so there are 97 leap years in 400 years. The number of excess days of the week in 400 years can be found by ...
(303·365) mod 7 + (97·366) mod 7 = (2·1 + 6·2) mod 7 = 14 mod 7 = 0
Thus, there are also an integral number of weeks in 400 years.
The first day of the week is the same at the start of every 400-year interval, so the calendar repeats every 400 years.
Answer:
It was an exponential increase
In 3 months, the bill will be $285.61
Step-by-step explanation:
First, this scenario is exponential, because the price of food is increasing with a percentage, based on the price that it was the previous amount.
Next, to find what the bill will be in 3 months, an equation needs to be made representing the situation.
Use the standard exponential equation: y = ab^x, where a is the initial amount, b is the growth rate, and x is the amount of time.
Plug in the values we know:
y = 130(1.3)^3
Solve for y
y = 285.61
So, 3 months later, the bill will be $285.61
We are given two binomials: x+4 , x^2-9.
x+4 can't be factored. Therefore, it is a prime.
Let us work on x^2-9.
9 could be written as 3^2.
Therefore, x^2-9 = x^2 - 3^2.
Now, we can apply difference of the squares formula to factor it.
We know a^2 -b^2 = (a-b) (a+b).
Therefore, x^2 - 3^2 can be factored as (x-3) (x+3).
So, x^2-9 is not a prime binomial because it can be factored as (x-3) (x+3).
Answer:
The amount of sale is approximately 5714.
Step-by-step explanation:
Let x be the sales made that will result to the same salary and let y be the same weekly salary.
We can represent both salaries as follows:
300 + 0.04x = y
100 + 0.075x = y
Subtracting the second equation from the first, we have:
200 – 0.035x = 0
0.035x= 200
x = 200/0.035
x ≈ 5714.
Therefore, the amount of sale is approximately 5714.
Answer:
T = 67.5
V = 22.5
Step-by-step explanation:
The Sum of triangle angles = 180
180 = W + T + V
180 = 90 + 3X + X
X = 22.5
