There are 13 diamonds in the deck, so
ways of drawing 3 diamonds.
There is a total of
ways of drawing any 3 cards from the deck.
So the probability of drawing 3 diamonds is
![\dfrac{\binom{13}3}{\binom{52}3}=\dfrac{11}{850}\approx0.012941](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cbinom%7B13%7D3%7D%7B%5Cbinom%7B52%7D3%7D%3D%5Cdfrac%7B11%7D%7B850%7D%5Capprox0.012941)
where
.
Answer:
- Inscribed angle is half of the intercepted arc.
- Central angle is the same size as the intercepted arc.
<u>As per above two statements we have:</u>
and
Answer:
Ten times a number minus 3 is greater than three times the number plus eleven
Step-by-step explanation:
we have the inequality
10x-3 > 3x+11
Let
x ----> a number
As a word problem will be
10x -----> Ten times a number x
+ ----> plus
-3 -----> negative 3
> greater than
3x ----> three times a number x
11 ----> eleven
therefore
Ten times a number minus 3 is greater than three times the number plus eleven
Answer:
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.
Step-by-step explanation:
Given equations are:
4x + 5y = 10
Ax + By = 16
The general form of linear equation in two variables is given by:
![ax+by = c](https://tex.z-dn.net/?f=ax%2Bby%20%3D%20c)
Here a, b and c are constants and x,y are variables.
In the given equations, after comparing with the general form
![a_1 = 4\\b_1 = 5 \\c_1 = 10\\a_2 = A\\b_2 =B\\c_2 = 16](https://tex.z-dn.net/?f=a_1%20%3D%204%5C%5Cb_1%20%3D%205%20%5C%5Cc_1%20%3D%2010%5C%5Ca_2%20%3D%20A%5C%5Cb_2%20%3DB%5C%5Cc_2%20%3D%2016)
"In order for a system of equations to have infinity many solutions,
"
Putting the values we get
![\frac{4}{A} = \frac{5}{B} = \frac{10}{16}\\\frac{4}{A} = \frac{5}{B} = \frac{5}{8}\\Now\\\frac{4}{A} = \frac{5}{8}\\\frac{A}{4} = \frac{8}{5}\\A = \frac{8}{5} * 4\\A = \frac{32}{5}\\And\\\frac{5}{B} = \frac{5}{8}\\\frac{B}{5} = \frac{8}{5}\\B = 8](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B10%7D%7B16%7D%5C%5C%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5CNow%5C%5C%5Cfrac%7B4%7D%7BA%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5C%5Cfrac%7BA%7D%7B4%7D%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5C%5CA%20%3D%20%5Cfrac%7B8%7D%7B5%7D%20%2A%204%5C%5CA%20%3D%20%5Cfrac%7B32%7D%7B5%7D%5C%5CAnd%5C%5C%5Cfrac%7B5%7D%7BB%7D%20%3D%20%5Cfrac%7B5%7D%7B8%7D%5C%5C%5Cfrac%7BB%7D%7B5%7D%20%3D%20%5Cfrac%7B8%7D%7B5%7D%5C%5CB%20%3D%208)
Hence,
For A = 32/5 and B = 8 the system of equations will have infinitely many solutions.