Answer:
The sales figure for the third year is ![[\frac{32\ \text{mn}-x\ \text{mn}}{x\ \text{mn}}\times 100\%]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B32%5C%20%5Ctext%7Bmn%7D-x%5C%20%5Ctext%7Bmn%7D%7D%7Bx%5C%20%5Ctext%7Bmn%7D%7D%5Ctimes%20100%5C%25%5D)
.
Step-by-step explanation:
Since sales data for the second year is unavailable, we denote it as x million.
Year 3's total sales amount to 32 million.
Calculate the sales account for year 3 as follows:
Triangle XYZ is an equilateral triangle, meaning the sector's central angle measures 120 degrees, which is equivalent to 2π/3 radians. To find the area of a sector corresponding to a central angle β, we use the formula A = (1/2)r²*β, where β is expressed in radians. For this sector, the area calculation is A = (1/2)*2²*(2π/3) = 4π/3 square units.
Answer: The other two observations are 97 and 107.
Explanation:
We know that
Mean = 100
Mode = 98
Range = 10
And from the formula,
Range = Highest - Lowest.
Let’s set the highest observation as x and the lowest as y.
Thus, we have the equation x - y = 10 (equation 1).
The observations can be represented as:
x, 98, 98, y.
Using the mean formula yields:
Mean = 
.
This means our second equation is:
x + y = 204.
By applying the elimination method to solve these linear equations, we find:
x = 97.
and
.
Therefore, the other two observations are 97 and 107.
Response:
x² + -6x = -13
Detailed breakdown:
8x² - 48x = -104
Rearranging gives us x² - 6x = -13
For team one, they have to compete against 12 different teams, which amounts to 12 days of play.
Team two, which has already played team one, will only need to participate in 11 more days.
Team three has already faced teams one and two, leaving them with 10 additional days.
Continuing this pattern results in a total of 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78 days.
Alternatively, you can calculate the number of unique matches as 13*12 / 2! = 78.
Another way is by calculating combinations of 13 taken 2 at a time: 13C2 = 13! / [(2!)(11!)] = 13*12*11! /(2!*11!)= 13*12/2 = 78.
