Answer: 1/2
Step-by-step explanation:
The sample space when a six sided die is thrown once is :
{ 1,2,3,3,5,6}
The even numbers are :
{2,4,6}
Therefore :
P(even) = n(even) / total number
That is
P(even) = 3/6
P(even) = 1/2
6. 3X6= 4xm
18=4m
Divide by 4
M=4.5
7.14 x5= b^2
70=b^2
Sq rt of 70
8.4
Answer:ion know
Step-by-step explanation:
<h3>
Answer:</h3>
![\frac{1}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B9%7D)
<h3>
Step-by-step explanation:</h3>
We know that
, so substitute that into the equation. ![y=3^{-2}](https://tex.z-dn.net/?f=y%3D3%5E%7B-2%7D)
With negative powers, instead of making the result negative, you divide one by it. Mathematically speaking,
. This makes our equation: ![y=\frac{1}{3^2}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B3%5E2%7D)
Finally, simplify the exponent. ![y=\frac{1}{9}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B9%7D)
<u>Solution</u><u>:</u>
The rationalisation factor for
is ![a + \sqrt{b}](https://tex.z-dn.net/?f=a%20%2B%20%5Csqrt%7Bb%7D%20)
So, let us apply it here.
![\frac{1}{5 - \sqrt{2} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%20-%20%20%5Csqrt%7B2%7D%20%7D%20)
The rationalising factor for 5 - √2 is 5 + √2.
Therefore, multiplying and dividing by 5 + √2, we have
![= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B5%20-%20%20%5Csqrt%7B2%7D%20%7D%20%20%5Ctimes%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B%285%20-%20%20%5Csqrt%7B2%7D%29%285%20%2B%20%20%5Csqrt%7B2%7D%20%29%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B%20%7B%285%29%7D%5E%7B2%7D%20-%20%28%20%5Csqrt%7B2%7D%29%5E%7B2%7D%20%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B25%20-%20%202%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B23%7D%20)
<u>Answer:</u>
<u>
</u>
Hope you could understand.
If you have any query, feel free to ask.