The ratio 9:7 gives you following statement:
- Carl will win in 9 cases from 9+7=16;
- Carl will lose in 7 cases from 16.
Then the probability that Carl will lose is
Answer:
Alright so start of with solving 1 1/8+5/6
Solve and you get 1 23/24
Now to subtract you have your answer subtracted by 1/2:
1 23/24-1/2=1 11/24
And so you get 1 11/24
~Evie
First we note symmetry in the expression's coefficients.
We also note that 7*3=21, and 7+3=10.
From the rational roots theorem, we are tempted to try with 3 and 7 as coefficients of the factors.
Try
(7b+3)(3b+7)=21b^2+(49+9)b+21
By switching the sign of 3b+7 to 3b-7, we get the signs right, to check:
(7b+3)(3b-7)=21b^2+(9-49)b-21=21b^2-40b-21 ....right!
So
(7b+3)(3b-7)=21b^2-40b-21
It must be 6 since the length sides r doubled and it's similar
Recall that the derivative of a function f(x) at a point x = c is given by
By substituting h = x - c, we have the equivalent expression
since if x approaches c, then h = x - c approaches c - c = 0.
The two given limits strongly resemble what we have here, so it's just a matter of identifying the f(x) and c.
For the first limit,
recall that sin(π/3) = √3/2. Then c = π/3 and f(x) = sin(x), and the limit is equal to the derivative of sin(x) at x = π/3. We have
and cos(π/3) = 1/2.
For the second limit,
we observe that e²ˣ = 1 if x = 0. So this limit is the derivative of e²ˣ at x = 0. We have
and 2e⁰ = 2.