Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = y intercept
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
From the information given,
comparing the equation given,
y=4x+1 with the slope intercept equation, y = mx + c
Slope, m = 4
When two slopes are perpendicular, their product is -1
Let the slope of the perpendicular line to the one given by the above equation be m1. Therefore,
m × m1 = -1
4 m1 = -1
m1 = -1/4
Inputting m1 = 4 into the slope intercept equation, it becomes
y = -1/4×x + c
y = -x/4 + c
Okay, lets write down what we do know...
4 out of the 12 cups are decaf, so the odds of selecting a decaf cup by random is 4/12 or 1/3
Alternatively 8 of the 12 cups are caffeinated, so the odds of selecting a caffeinated cup by random is 8/12 or 2/3
P(decaf)=1/3
P(caf)=2/3
But those odds are only for the first cup picked. The second cup has 4 probabilities...
1. Picking a decaf cup for the second time
2. Picking a decaf cup for the first time
3. Picking a caf cup for the second time
4. Picking a caf cup for the first time
So lets find the probability of each event...
1. Picking a decaf cup for the second time. If a decaf cup has already been picked, then the odds of drawing another one is 3/11
2. Picking a decaf cup for the first time. If a decaf cup hasn't already been picked, then the odds of drawing one is 4/11
3. Picking a caf cup for the second time. If a caf cup has already been picked, then the odds of drawing one is 7/11
4. Picking a caf cup for the first time. If a car cup hasn't already been picked, then the odds of drawing one is 8/11.
Okay, so now we can solve for the various possibilities.
1. Picking a decaf cup for the second time
1/3*3/11=3/33
2. Picking a decaf cup for the first time
2/3*4/11=8/33
3. Picking a caf cup for the second time
2/3*7/11=14/33
4. Picking a caf cup for the first time
2/3*8/11=16/33
Both cups were caffeinated, so neither were decaf.
Answer= Neither cup is decaf.
Answer:
622.2 miles 1,001.3 kilometers