The first step for each of these is adding or subtracting the coefficient to isolate your terms with variables. And then divide to isolate the variable itself.
Let's assume that the statement "if n^2 is odd, then is odd" is false. That would mean "n^2 is odd" leads to "n is even"
Suppose n is even. That means n = 2k where k is any integer.
Square both sides
n = 2k
n^2 = (2k)^2
n^2 = 4k^2
n^2 = 2*(2k^2)
The expression 2(2k^2) is in the form 2m where m is an integer (m = 2k^2) which shows us that n^2 is also even.
So this contradicts the initial statement which forces n to be odd.
Answer:
2.5, -2.61, 0.81, -0.12
Step-by-step explanation:
The taylor series of the function sin(x) around zero is given by
Therefore,
![\sin(\frac{5}{2})=\dfrac{5}{2}-\dfrac{[\frac{5}{2}]^3}{3!}+\dfrac{[\frac{5}{2}]^5}{5!}-\dfrac{[\frac{5}{2}]^7}{7!}+...](https://tex.z-dn.net/?f=%5Csin%28%5Cfrac%7B5%7D%7B2%7D%29%3D%5Cdfrac%7B5%7D%7B2%7D-%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E3%7D%7B3%21%7D%2B%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E5%7D%7B5%21%7D-%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E7%7D%7B7%21%7D%2B...)
hence the first four nonzero terms of the series are
![\dfrac{5}{2}=2.5\\\\-\dfrac{[\frac{5}{2}]^3}{3!} \approx -2.61\\\\\dfrac{[\frac{5}{2}]^5}{5!} \approx 0.81\\\\-\dfrac{[\frac{5}{2}]^7}{7!} \approx -0.12](https://tex.z-dn.net/?f=%5Cdfrac%7B5%7D%7B2%7D%3D2.5%5C%5C%5C%5C-%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E3%7D%7B3%21%7D%20%5Capprox%20-2.61%5C%5C%5C%5C%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E5%7D%7B5%21%7D%20%5Capprox%200.81%5C%5C%5C%5C-%5Cdfrac%7B%5B%5Cfrac%7B5%7D%7B2%7D%5D%5E7%7D%7B7%21%7D%20%5Capprox%20-0.12)
Answer:
total number of brown sugar cubes = 3
total number of white sugar cubes = 1
total number of sugar cubes = total no of brown sugar cubes + total no of white sugar cubes = 3 + 1 = 4
probability to select one brown sugar cube = total number of brown sugar cube / total number of sugar cube = 3/ 4
therefore the probability of selecting a brown sugar cube is 3/4 or 0.75
