Multiply all whole numbers from 1 through 100, the largest power of 4 is a factor of the product of?

If 3% of ties sold in the United States are bow ties, what is the probability of randomly selecting three ties that were purchas

Luda [366]

Given that 3 ties were selected and the probability of selecting a bow tie is 3%, the probability of selecting 3 bow ties will be:
P(selecting 3 ties)=P(selecting a bow tie)*P(selecting a bow tie)*P(selecting a bow tie)
=(0.03)*(0.03)*(0.03)
=0.000027

7 0

3 years ago

Cecile packages snack mix at a health food store.

Sedaia [141]

Answer:
her supply has 18 pounds

Explanation:
Assume that the number of pounds in her supply is x.
We are given that:
She uses 1/3 x in salted mix and 2/9 x in unsalted mix.
This means that:
Total amount used = 1/3 x + 2/9 x = 5/9 x of her supply

Now, we are also given that:
She used 10 pounds of her supply.
This means that:
5/9 x = 10
5x = 9*10 = 90
x = 18 pounds

Hope this helps :)

5 0

2 years ago

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How to find the derivative of cos^2x? i seem to be confused.

slamgirl [31]

If you're using the app, try seeing this answer through your browser: brainly.com/question/2927231

————————

You can actually use either the product rule or the chain rule for this one. Observe:

• Method I:

y = cos² x

y = cos x · cos x

Differentiate it by applying the product rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x\cdot cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{dx}(cos\,x)\cdot cos\,x+cos\,x\cdot \dfrac{d}{dx}(cos\,x)}$

The derivative of cos x is – sin x. So you have

$\mathsf{\dfrac{dy}{dx}=(-sin\,x)\cdot cos\,x+cos\,x\cdot (-sin\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=-sin\,x\cdot cos\,x-cos\,x\cdot sin\,x}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

—————

• Method II:

You can also treat y as a composite function:

$\left\{\!
\begin{array}{l}
\mathsf{y=u^2}\\\\
\mathsf{u=cos\,x}
\end{array}
\right.$

and then, differentiate y by applying the chain rule:

$\mathsf{\dfrac{dy}{dx}=\dfrac{dy}{du}\cdot \dfrac{du}{dx}}\\\\\\
\mathsf{\dfrac{dy}{dx}=\dfrac{d}{du}(u^2)\cdot \dfrac{d}{dx}(cos\,x)}$

For that first derivative with respect to u, just use the power rule, then you have

$\mathsf{\dfrac{dy}{dx}=2u^{2-1}\cdot \dfrac{d}{dx}(cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2u\cdot (-sin\,x)\qquad\quad (but~~u=cos\,x)}\\\\\\
\mathsf{\dfrac{dy}{dx}=2\,cos\,x\cdot (-sin\,x)}$

and then you get the same answer:

$\therefore~~\boxed{\begin{array}{c}\mathsf{\dfrac{dy}{dx}=-2\,sin\,x\cdot cos\,x}\end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: <em>derivative chain rule product rule composite function trigonometric trig squared cosine cos differential integral calculus</em>

3 0

3 years ago

What is the value of 43.7891

tankabanditka [31]

Answer:

the value of 43.7891 will obviously be 43.7891

3 0

2 years ago

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Suppose you invest $63 a month in an annuity that earns a 3.3% APR

lisov135 [29]

Answer: $3227.93 APEX

4 0

3 years ago