Answer:
The leg is 8 cm long
Step-by-step explanation:
An isosceles right triangle has the length of its hypotenuse and opposite equal
Let us call the length x
From Pythagoras’ , the square of the hypotenuse equals the sum of the squares of the two other sides
Thus, we have ;
x^2 + x^2 = (8 √2)^2
2x^2 = 128
x^2 = 128/2
x^2 = 64
x= √64
x = 8 cm
and
are independent and identically distributed with PMF
![\mathrm{Pr}(X = x) = \begin{cases}1/6 & \text{if } x \in\{1,2,3,4,5,6\} \\ 0 & \text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cmathrm%7BPr%7D%28X%20%3D%20x%29%20%3D%20%5Cbegin%7Bcases%7D1%2F6%20%26%20%5Ctext%7Bif%20%7D%20x%20%5Cin%5C%7B1%2C2%2C3%2C4%2C5%2C6%5C%7D%20%5C%5C%200%20%26%20%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
If
, then
has range/support
{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
where we can get
- -5 = 1 - 6 in 1 way, hence with probability 1/36
- -4 = 1 - 5 = 2 - 6 in 2 ways, with probability 2/36 = 1/18
- -3 = 1 - 4 = 2 - 5 = 3 - 6 in 3 ways, with probability 3/36 = 1/12
and so on, so that the PMF of
is
![\mathrm{Pr}(Z=z) = \begin{cases}1/36 & \text{if } z\in\{-5,5\} \\ 2/36 & \text{if } z\in\{-4,4\} \\ 3/36 & \text{if }z\in\{-3,3\} \\ 4/36 & \text{if } z\in\{-2,2\} \\ 5/36 & \text{if } z\in\{-1,1\} \\ 6/36 & \text{if } z =0 \\ 0 & \text{otherwise}\end{cases}](https://tex.z-dn.net/?f=%5Cmathrm%7BPr%7D%28Z%3Dz%29%20%3D%20%5Cbegin%7Bcases%7D1%2F36%20%26%20%5Ctext%7Bif%20%7D%20z%5Cin%5C%7B-5%2C5%5C%7D%20%5C%5C%202%2F36%20%26%20%5Ctext%7Bif%20%7D%20z%5Cin%5C%7B-4%2C4%5C%7D%20%5C%5C%203%2F36%20%26%20%5Ctext%7Bif%20%7Dz%5Cin%5C%7B-3%2C3%5C%7D%20%5C%5C%204%2F36%20%26%20%5Ctext%7Bif%20%7D%20z%5Cin%5C%7B-2%2C2%5C%7D%20%5C%5C%205%2F36%20%26%20%5Ctext%7Bif%20%7D%20z%5Cin%5C%7B-1%2C1%5C%7D%20%5C%5C%206%2F36%20%26%20%5Ctext%7Bif%20%7D%20z%20%3D0%20%5C%5C%200%20%26%20%5Ctext%7Botherwise%7D%5Cend%7Bcases%7D)
Answer:
153.3852
Step-by-step explanation:
After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2
Answer:
Step-by-step explanation:
cosθ = ⅘
sin²θ = 1-cos²θ = 9/25
since θ is in quadrant I, sinθ = √(9/25) = ⅗
sin(2θ) = 2sinθcosθ = 2(⅗)(⅘) = 24/25
Cuz 14/4 and 56/16 are equal ... just divide both of them and you get 3.5 for both
if you multiply both the denomintor and numerator of 14/4 by 4 you get 56/16 so that's how u know they're equal because if you multiply both by the same number you should get a fraction equal to that one
idk I'm new to this app just checking it out