There are 12 men and 24 women in a chorus. What percent of the entire chorus is composed of women?

Tanya runs a catering business. Based on her records, her weekly profit can be approximated by the function LaTeX: f\left(x\righ

Shtirlitz [24]

The function

$2x^2-44x-150$

is a parabola concave up, whose solutions are

$2x^2-44x-150=0 \iff x^2-22x-75=0$

from here, you can use the quadratic formula

$x_{1,2} = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

to find that the solutions of the parabola are $-3,\ 25$

So, the parabola is positive if $x$ (which wouldn't make sense in our case) or $x$

So, if Tanya caters 25 meals she breaks even, and starting with the 26th meal she will begin to profit.

4 0

3 years ago

Here is a list of numbers: 6 , 14 , 1 , 16 , 16 , 14 , 15 , 9 , 11 , 10 State the median.

zvonat [6]

Answer:

12.5

Step-by-step explanation:

8 0

3 years ago

How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)

kaheart [24]

Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0. Factor out x^(5/3): x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3.

To solve this: mult. both sides by x^(-2/3). Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3), or 4 = 3x^(-2/3). It'd be easier to work with this if we rewrote it as

4 3
--- = --------------------
1 x^(+2/3)

Then

4
--- = x^(-2/3). Then, x^(2/3) = (3/4), and x = (3/4)^(3/2). According to my 3 calculator, that comes out to x = 0.65 (approx.)

Check this result! subst. 0.65 for x in the given equation. Is the equation then true?

My method here was a bit roundabout, and longer than it should have been. Can you think of a more elegant (and shorter) solution?

7 0

3 years ago

Read 2 more answers

Let g be the function given by g(x)=limh→0sin(x h)−sinxh. What is the instantaneous rate of change of g with respect to x at x=π

lorasvet [3.4K]

The instantaneous rate of change of g with respect to x at x = π/3 is 1/2.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The instantaneous rate of change at a given value of $x$ can be found by concept of derivative, which is described below:

$g(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Where $h$ is the difference rate.

In this question we must find an expression for the instantaneous rate of change of $g$ if $f(x) = \sin x$ and evaluate the resulting expression for $x = \frac{\pi}{3}$ . Then, we have the following procedure below: