A box of jerseys for a pick-up game of basketball contains 9 extra-large jerseys, 6 large jerseys, and 5 medium jerseys. If you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 medium jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

1/114 or 0.008772

Step-by-step explanation:

I am not very sure, my answer seems unlikely, but here's what I think:

There are 20 jerseys in the box to begin with, and 5 medium jerseys that you can have.

Therefore, the probability of you randomly grabbing a medium sized jersey is 5/20 or 1/4.

After taking out one medium sized jersey, there are 19 jerseys in the box and 4 medium jerseys you can pick from.

The probability of you randomly grabbing a medium sized jersey is 4/19.

After taking out another medium sized jersey, there are 18 jerseys left in the box and 3 medium jerseys you can pick from.

The probability of you randomly grabbing a medium sized jersey is 3/18.

To get the answer, you do 1/4 * 4/19 * 3/18, and get 1/114, or 0.00877192982.

If you round that to the nearest millionth, it's 0.008772

Don't judge me, it might not be correct.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

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}

step-by-step explanation:

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!