Answer:
67
Step-by-step explanation: 67 is 100% of itself duh
We are given first equation: −2x+3y=12.
Converting it in slope-intercept form
3y=2x + 12
y= 2/3 x + 12/3
y= 2/3 x + 4.
Slope of the given equation is 2/3.
<u>Note:</u><em> When slopes are same, lines would be parallel.</em>
<em>When slope are negative reciprocals, lines would be perpendicular.</em>
<em>When neither same nor negative reciprocal, the lines neither parallel nor perpendicular.</em>
1) First option : -2x+y=12.
In slope-intercept form y = 2x +12.
Slope is 2 there.
<h3>Neither parallel nor perpendicular to the line −2x+3y=12.</h3>
2) 3x+2y=-2
In slope-intercept form y = -3/2 x - 1.
Slope = -3/2.
Slope are negative reciprocal to slope of −2x+3y=12 equation.
<h3>Therefore, lines are perpendicular.</h3>
3) y=2/3x-1
Slope = 2/3.
<h3>Slopes are same therefore lines are parallel.</h3>
4) -2x+3y=11
y = 2/3 x + 11/3.
<h3>Slopes are same therefore lines are parallel.</h3>
Subtract 6 from both sides
15x= 195
Divide both sides by 15
x=13
Final answer: x=13
Check:
15(13)+6
195+6
201
201=201
First, we add everything together, so; 3 + 3 + 4 + 2 = 12. This means every marble has a 8.33% chance of being chosen, however since there are more than others we add those separate percentages together.
Pink: 25%
Violet: 25%
Yellow: 33.33%
Brown: 16.66%
These are the chances of you getting either color. Since the problem asks what is the probability of finding a violet marble,we just look at the written percentages to see we have a 25% chance of choosing a violet marble.
The next step is to see what is the probability of choosing a pink marble, except we have to change things up a bit. Since we removed 1 marble, that changes ALL the percentages again, so we must rewrite the percentages. 12 - 1 is easily solved as 11, and so this means every marble has a 9.0909091% of being chosen. Let's rewrite the grouped percentages now:
Pink: 27.27%
Violet: 18.18%
Yellow: 36.36%
Brown: 18.18%
Now we see that with one marble removed, and that marble not being pink, we have a 27.27% chance of picking a pink marble.
Your Answer: 25% of Violet first time, 27.27% of Pink second time.
(How To Get Percentages?): Simple, you divide 100 (since whatever number we start out with as long as it claims nothing is missing equal 100%) by whatever number of objects you have. So as an example, if I have 5 objects, 100 / 5 = 20. This means every individual object has a 20% chance of being chosen. But we then arrange everything into whatever groups (in your problems case, colors) and multiply by the amount. So say I have 3 green balls and 2 white balls, 3 x 20 = 60 and 2 x 20 = 40 so I have a 60% of getting a green ball and 40% chance of a white ball.
Hope this helps and I hope even more you learned something :D
