Please help! Due today!

The mean age of 11 women in an office is 31 years old.

BlackZzzverrR [31]

Answer: 30.2

Explanation:

The mean is calculated by taking the sum of the values and dividing by the count.

For instance, for the 6 women, with the mean being 31, we can see that the ages summed to 186:

186

6

=

31

And we can do the same for the men:

116

4

=

29

And now we can combine the sum and count of the men and women to find the mean for the office:

186

+

116

10

=

302

10

=

30.2

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Show all work to identify the asymptotes and zero of the function f(x) = 6x / x^2 - 36

eduard

Answer:

Zero of the function f(x) is at x = 0

Vertical Asymptotes at x = ±6

Horizontal Asymptotes at y = 0

Step-by-step explanation:

<h3>Vertical Asymptotes </h3>

For a given function f(x):

Vertical Asymptotes are obtained at those values of x, where the function f(x) tends to infinity, I.e.,

When x approaches some constant value but the curve moves towards infinity.

If f(x) is a fraction, it'll tend to infinity when it's denominator becomes zero.

Vertical Asymptotes of the given function can be obtained by walking thru the following steps:

Step I

(Factorise the numerator and denominator)

$\mathsf{ f(x) = \frac{6x}{ {x}^{2} - 36 } }$

x² - 36 can be factorised into (x + 6)(x - 6)

and, ofcourse, we can write 6x as 6(x - 0)

$\mathsf{ f(x) = \frac{6(x - 0)}{ (x + 6)(x - 6) } }$

Step II

(Reduce the fraction to its simplest form by canceling out the common factors)

There aren't any common factors in the numerator and denominator in this case.

Step III

(Look for the values of x which cause the denominator to be zero)

If we put x = 6

denominator becomes 0

Also,

If we substitute x with -6

denominator becomes 0.

The two values of x indicate the two Vertical Asymptotes of the function f(x).

Therefore,

Vertical Asymptotes of the given function f(x) are:

$\boxed{ \mathsf{x = \pm6}}$

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

<h3 /><h3>Horizontal Asymptotes:</h3>

Horizontal Asymptotes are obtained When x tends to infinity and y approaches some constant value.

I'll be using the concept of limits for this.

$\mathsf{y = \frac{6x}{ {x}^{2} - 36 } }$

dividing and multiplying by x² (Yep! so if x becomes infinity 1/ x and 1/ x² all such terms become 0, 'cause 1/ ∞ is 0)

$\implies \mathsf{y = lim_{x \rightarrow \infty }( \frac{ \frac{6x}{ {x}^{2} } }{ \frac{ {x}^{2} - 36 }{ {x}^{2} } } ) }$

$\implies \mathsf{y = lim_{x \rightarrow \infty }( \frac{ \frac{6}{ x } }{ 1- \frac{36 }{ {x}^{2} } } ) }$

Substitute x with ∞, you get zero/ 1

$\implies \boxed{\mathsf{y = 0}}$

So, the horizontal Asymptote of the function is y = 0, that is the x axis

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

<h3>Zeroes of a function:</h3>

The values of x that reduces f(x) to zero are called the zeroes of f(x).

Here, only x = 0 acts as the zero of the function.

[NOTE:

For finding Vertical Asymptotes,Equate the denominator to 0. And
For finding Zeroes, Equate the numerator to 0]

__________________

[That's what it's graph looks like. ]

3 0

3 years ago

Solve each equation for all values of x. 3 cot2x-5=-4

Anni [7]

1is answer

Step-by-step explanation:

1ttttttyyuiio

4 0

2 years ago

# 18 What is 5.6 less than 14.52

kramer

Answer:

8.92

Step-by-step explanation:

14.52 - 5.6 =

less than means subtract

6 0

3 years ago

Read 2 more answers

What are the missing lengths ???

lesantik [10]

Answer:

1. c = 13

2. a = 20

Step-by-step explanation:

1. 12² + 5² = x²

144 + 25 = x

144 + 25 = 169

√169 = 13

2. 29² - 21² = x²

841 - 441 = x

841 - 441 = 400

√400 = 20

7 0

3 years ago