You and a friend have a hula hoop competition. you win 3 out of every 7 trials. your friend wins 5 more trials than you. how many trials are in the competition?

We have been given that me and my friend have a hula hoop competition. I win 3 out of every 7 trials. My friend wins 5 more trials than me.  

Probability of my winning is and probability of my friend's winning is .    

Let there be n numbers of trials. Therefore, my score after n trials is and my friend's score after n trials is .

Therefore, trials my friend won more than be would be,

We have been given that my friend won 5 more trials than me. So upon equating these two quantities we will get,

Therefore, total number of trials is 35.

Let us verify our answer.

After 35 trials I will win trials and my friend will win trials. Hence, my friend won 5 more trials than me.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!

let's solve your equation step-by-step.

24−3x=−27

step 1: simplify both sides of the equation.

24−3x=−27

24+−3x=−27

−3x+24=−27

step 2: subtract 24 from both sides.

−3x+24−24=−27−24

−3x=−51

step 3: divide both sides by -3.

−3x

−3

=

−51

−3

x=17

answer:

x=17

step-by-step explanation:

mark brainliest and have a great day!