3 years ago

Set up a proportion to predict the outcome of the given event

Mathematics

2 answers:

pickupchik [31]3 years ago

8 0

It is 4
Hope this helps good luck

I am Lyosha [343]3 years ago

4 0

It is 4.
The proportion of chocolate to the containers of ice cream sold is 1:5
Or 1 to 5.

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Karen is buying pens and pencils for the new school year. She wants to have no more than 25 writing utensils in all. She also wa

bezimeni [28]

For this case, the first thing we must do is define variables.
We have then:
x: number of pens
y: number of pencils
We now write the system of inequations:
$x + y \leq 25

y \geq (x - 3) ^ 2
$
The solution to the system of inequations is given by the shaded region.
Note: see attached image.

3 0

3 years ago

Use the four-step definition of the derivative to find f'(x) if f(x) = −4x^3 −1.

guapka [62]

$\stackrel{de finition \textit{ of a derivative as a limit}}{\lim\limits_{h\to 0}~\cfrac{f(x+h)-f(x)}{h}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[-4(x+h)^3-1]~~ - ~~[-4x^3-1]}{h} \\\\\\ \cfrac{[-4(x^3+3x^2h+3xh^2+h^3)-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{[-4x^3-12x^2h-12xh^2-4h^3-1]~~ ~~+4x^3+1}{h} \\\\\\ \cfrac{-4x^3-12x^2h-12xh^2-4h^3-1+4x^3+1}{h}\implies \cfrac{-12x^2h-12xh^2-4h^3}{h}$

$\cfrac{h(-12x^2-12xh-4h^2)}{h}\implies -12x^2-12xh-4h^2 \\\\\\ \lim\limits_{h\to 0}~-12x^2-12xh-4h^2\implies \lim\limits_{h\to 0}~-12x^2-12x(0)-4(0)^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \lim\limits_{h\to 0}~-12x^2~\hfill$