A coin has one of two outcomes: heads or tails.
Each has an equal probability of occurring, meaning that they each have a 50% chance to occur. (They need to add up to 100% because they include all the outcomes, divide that into two equal parts and...)
This is what we call theoretical probability. It's a guess as to how probability <em>should</em> work. Like in the experiment, it's not always going to be 50-50.
What <em>actually happens</em> is called experimental probability. This may vary slightly from theoretical probability because you can't predict probability with complete certainty, you can only say what is <em>most likely to happen</em>.
We want to find the probability of getting heads in our experiment so we can compare it to the theoretical outcome. To do this, we need to compare the number of heads to the total number of outcomes.
We have 63 heads, and a total of 150 coin flips.
That makes the probability of getting a heads 63/150.
The hard part is getting this ratio into a percent.
You can try simply dividing, but you should be able to notice something here.
SInce the top and the bottom of our fraction are both divisible by 3, we can <em>simiplify</em>.
63 ÷ 3 = 21
150 ÷ 3 = 50
So we could say that 63/150 = 21/50.
A percent is basically a fraction out of 100.
Just like you can divide the parts of a ratio by the same number and it will stay the same, you can also multiply. To get the fraction out of 100, let's multiply by 2.
(since 50 × 2 = 100)
21 × 2 = 42
50 × 2 = 100
21/50 = 42/100 = 42%
Comparing our experimental probability to the theoretical one...it is 8% lower.
We know f(x)=5x+1. Plug in f(x) in the g(x) function.
We get
Distribute the 2 to 5x and 1.
Simplify to get
Now, we plug in -1 for x.
A number that can add up to 10 and multiplies to 11 is 1 since 11 is a prime number
ANSWER
EXPLANATION
The given expression is
We can see that (x+2) is the greatest common factor.
We factor to obtain;
The correct choice is C.
Answer:
f (x) = -2 (x + 6)^2 + 2
Step-by-step explanation:
f (x) = -2x^2 - 24x - 70 <--- divide out -2 out of the first two terms...
f (x) = -2 (x^2 + 12x) - 70 <-- divide the x coefficient by 2 and then square it, then add AND subtract it)
f (x) = -2 (x^2 + 12x + (12/2)^2 - (12/2)^2) - 70
f (x) = -2 (x^2 + 12x + 36 - 36) - 70 <--- distribute the -2 onto -36 to get it out of the brackets..
f (x) = -2 (x^2 + 12x + 36) + 72 - 70 <-- combine constants and factor perfect square trinomial...
f (x) = -2 (x + 6)^2 + 2 <-- standard form...
