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.
Answer:
a.7(6xy-2z)
=7*6xy-7*2z
=42xy-14z
b.5(2w+3)-6(w+2)
=5*2w+5*3-6*w-6*2
=10w+15-6w-12
=4w+3
c.2f(2f+g-3)
=2f*2f+2f*g-2f*3
=4f^2+2fg-6f
Step-by-step explanation:
Answer:
y=3.14x
Step-by-step explanation:
if you graph this on a calculator you can just visually see what line lines up with all the points. but you can also plug in one of the points into the equations to see if its true or not and if its true choose that equation. like use the first points (2, 6.28) and plug them into the equations and see which one is true.
Answer:
y = 100,000 + 3500x
$142,000
Step-by-step explanation:
a. The fixed cost is 100,000 while appreciation is 3, 500/year.
Now after x years, total appreciation equals 3,500 × x = 3500x
The total amount in dollars is thus :
y = 100,000 + 3500x.
b. The value of the house in 12 years.
Since y = 100,000 + 3500x, here, y = ? and x = 12.
y = 100,000 + 3500(12) = 100,000 + 42,000 = $142,000
64 is counterexample that proves that the conjecture below is false. "Other than the number 1, there are no numbers less than 100 that are both perfectsquares and perfect cubes.
<span>8*8 = 64 </span>
<span>4*4*4 = 64
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