Answer:
4989600 ways
Step-by-step explanation:
From the question,
The word MATHEMATICS can be arranged in n!/(r₁!r₂!r₃!)
⇒ n!/(r₁!r₂!r₃!) ways
Where n = total number of letters, r₁ = number of times M appears r₂ = number of times A appears, r₃ = number of times T appears.
Given: n = 11, r₁ = 2, r₂ = 2, r₃ = 2
Substitute these value into the expression above
11!/(2!2!2!) = (39916800/8) ways
4989600 ways
Hence the number of ways MATHEMATICS can be arranged without duplicate is 4989600 ways
Answer:
Linearly, because the table shows that the sunflowers increased by the same amount each month
Step-by-step explanation:
Given the table
![\begin{array}{lcccc}\text{Month}&1&2&3&4\\ \\\text{Sunflowers}&15&17.2&19.4&21.6\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcccc%7D%5Ctext%7BMonth%7D%261%262%263%264%5C%5C%20%5C%5C%5Ctext%7BSunflowers%7D%2615%2617.2%2619.4%2621.6%5Cend%7Barray%7D)
Note that months change one-by-one (21-1, 3-2=1, 4-3=1).
Also
![17.2-15=2.2\ [\text{from month 1 to month 2}]\\ \\19.4-17.2=2.2\ [\text{from month 2 to month 3}]\\ \\21.6-19.4=2.2\ [\text{from month 3 to month 4}]](https://tex.z-dn.net/?f=17.2-15%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%201%20to%20month%202%7D%5D%5C%5C%20%5C%5C19.4-17.2%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%202%20to%20month%203%7D%5D%5C%5C%20%5C%5C21.6-19.4%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%203%20to%20month%204%7D%5D)
This means the number of sunflowers increases linearly, because the table shows that the sunflowers increased by the same amount each month
Im thinking 226.08
v=1/3pie r^2 h
v=1/3Pie (6) ^2 (6)
v=1/3 pie (36) (6)
v=1/3 pie (216)
v=72 pie
72 x 3.14=226.08
Given:
Two vectors (u) and (w) and the angle between them θ
![\begin{gathered} |u|=50 \\ |w|=12 \\ \theta=35\degree \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%7Cu%7C%3D50%20%5C%5C%20%7Cw%7C%3D12%20%5C%5C%20%5Ctheta%3D35%5Cdegree%20%5Cend%7Bgathered%7D)
the sketch of the vectors will be as shown in the following figure:
As shown, the resultant vector is the blue line segment
The vector R has a magnitude = 60.22
And the angle between u and R = 5.56°
Answer:
1/7
Step-by-step explanation: