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zaharov [31]
3 years ago
7

There are 135 people in a sport centre.

Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
5 0

Answer:

\dfrac{1}{9}

Step-by-step explanation:

4 people use all three facilities, then

  • 16 - 4 = 12 people use the gym and the track and do not use the pool;
  • 9 - 4 = 5 people use the pool and the track and do not use the gym;
  • 19 - 4 = 15 people use the gym and the pool and do not use the track.

At least two facilities use 4 + 12 + 5 + 15 = 36 people, 4 of them use all three facilities. Thus, the probability that a randomly selected person which uses at least two facilities, uses all the facilities is

\dfrac{4}{36}=\dfrac{1}{9}

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3 years ago
Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.
Leni [432]

Answer:  \dfrac{2x^2-1}{x(x^2-1)}

Step-by-step explanation:

The given function : y=\ln(x(x^2 - 1)^{\frac{1}{2}})

\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}    [\because \ln(ab)=\ln a +\ln b]

\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}  [\because \ln(a)^n=n\ln a]

Now , Differentiate both sides  with respect to x , we will get

\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1) (By Chain rule)

[Note : \dfrac{d}{dx}(\ln x)=\dfrac{1}{x}]

\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)

[ \because \dfrac{d}{dx}(x^n)=nx^{n-1}]

=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}

Hence, the derivative of the given function is \dfrac{2x^2-1}{x(x^2-1)} .

8 0
4 years ago
What is the equation of the line that passes through the point (-4,1) and has a<br> slope of -3/4
Rashid [163]

Answer:

y = -3/4x - 2

Step-by-step explanation:

y = -3/4x + b

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y = -3/4x -2

8 0
3 years ago
What is the second term of (p+q)^5<br> 1. 25p^4<br> 2. 5p^4q<br> 3. 25p^4q<br> 4. 125p^4q
yaroslaw [1]
I hope this helps you

4 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!
Semmy [17]
You should put 4 as x, -3 as y and a as slope to make an equation :
- 3 =  a \times 4
then you can find the slope and the correct equation of the line :

the slope is :
- 3 = 4a \\ a =  \frac{ - 3}{4}
so the equation of the line will be
y =  \frac{ - 3}{4}  x
D is true
hope this helps
5 0
3 years ago
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