Answer:
, , and
Step-by-step explanation:
1.
Let's find a common denominator:
=
2/(x-1)x(x+1)
2.
Distribute exponents:
2^3(y^2)^3
__________
8^2(y)^2
Numerator:
2 to the power of 3 equals (2 · 2 · 2) = 8
y to the power of 2 to the power of 3 equals, y to the power of 6 (this is because when exponents in parenthesis are held to the power of another number outside of the parenthesis, you multiply them)
Now let's simplify the denominator:
8 to the power of 2 equals (8 · 8) = 64
y to the power of 2 is just y to the power of 2, so our new expression is:
Let's cancel the terms further:
8/64 can be simplified to 1/8
And when you cancel exponents, you subtract the denominator's exponent from the numerator's exponent ( = )
Now put them together:
Which is,
=
y^4/8
3.
The common denominator for both fractions is 3t, so let's make -1/3's denominator 3t by multiplying t to both the numerator and the denominator:
-1 · t
_____ = -1(t)/3t = -t/3t
3 · t
Now let's solve for the numerator:
(t + 2) - t, the t's cancel out, t - t + 2 = 2
And the denominator stays the same, so it will still equal 3t
Finally, you'll get an answer of
=
2/3^2
Your Question:
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
My answer:
each dice has these 6 numbers
1,2,3,4,5,6
the even out of all of the numbers are
2,4,6
The others are odd (obviously)
1,3,5
So 1/2 are odd.
1/2 of 60 is the number of times it would get even numbers,
1/2 of 60=1/2 times 60=30
My prediction was 30!
→Jessie←
Outcome Club Diamond Heart Spade
Number of trials 8 12 11 9
A.
17%
B.
20%
C.
25%
D.
30%