Answer:
That something unexpected is about to happen.
Step-by-step explanation:
Such an equation would be y + 8x = - 25 (standard form) OR y = -8x - 25 (y-intercept form)
Deriving The Answer:
By using the point-slope form of the equation of a line, by knowing the gradient of that line and a point on that line, the equation of this line can be derived.
Now, the point-slope form exists as y - y₁ = m ( x - x₁)
since slope = -8 and the point on the line = (-4 , 7)
Then m = - 8
x₁ = - 4
y₁ = 7
⇒ y - 7 = -8 ( x - (-4))
⇒ y - 7 = -8x - 32
⇒ y + 8x = - 25
Answer:
£90
Step-by-step explanation:
Let M = Malachy's share
and P = Paul's share
and B = Brian's share.
We have three conditions:
(1) M = 2P
(2) P = 3B
(3) M + P + B = 150
Solve for B:
Substitute (2) into (3) (4) M + 3B + B = 150
(5) M + 4B = 150
Substitute (2) into (1) M = 2(3B)
(6) M = 6B
Substitute (6) into (5) 6B + 3B + B = 1 50
(7) B = 15
Solve for P:
Substitute (7) into (2) P = 3×15
(8) P = 45
Solve for M:
Substitute (8) into (1) M = 2×45
M = 90
Malachy gets £90.
Experimental probability = 1/5
Theoretical probability = 1/4
note: 1/5 = 0.2 and 1/4 = 0.25
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How I got those values:
We have 12 hearts out of 60 cards total in our simulation or experiment. So 12/60 = (12*1)/(12*5) = 1/5 is the experimental probability. In the simulation, 1 in 5 cards were a heart.
Theoretically it should be 1 in 4, or 1/4, since we have 13 hearts out of 52 total leading to 13/52 = (13*1)/(13*4) = 1/4. This makes sense because there are four suits and each suit is equally likely.
The experimental probability and theoretical probability values are not likely to line up perfectly. However they should be fairly close assuming that you're working with a fair standard deck. The more simulations you perform, the closer the experimental probability is likely to approach the theoretical one.
For example, let's say you flip a coin 20 times and get 8 heads. We see that 8/20 = 0.40 is close to 0.50 which is the theoretical probability of getting heads. If you flip that same coin 100 times and get 46 heads, then 46/100 = 0.46 is the experimental probability which is close to 0.50, and that probability is likely to get closer if you flipped it say 1000 times or 10000 times.
In short, the experimental probability is what you observe when you do the experiment (or simulation). So it's actually pulling the cards out and writing down your results. Contrast with a theoretical probability is where you guess beforehand what the result might be based on assumptions. One such assumption being each card is equally likely.
