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3 years ago

Find the cost of one item to the nearest cent. Round if necessary. a dozen donuts for $4.00

Mathematics

2 answers:

kondaur [170]3 years ago

5 0

Answer:

33 cents

Step-by-step explanation:

4/12=1/3=0.33=33 cents

Molodets [167]3 years ago

4 0

Answer:

= $1/3

Step-by-step explanation:

A dozen contains 12 items

Therefore;

a dozen of doughnuts contains 12 doughnuts

12 doughnuts = $ 4.00

1 doughnuts = 4/12

= $ 1/3

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2 years ago

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dalvyx [7]

Answer:

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Step-by-step explanation:

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$\displaystyle B(t)=24.6\sin(\frac{\pi t}{10})(8-t)$

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$\displaystyle B^\prime(t)=\frac{d}{dt}[24.6\sin(\frac{\pi t}{10})(8-t)]$

We can move the constant outside:

$\displaystyle B^\prime(t)=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)]$

Now, we will utilize the product rule. The product rule is:

$(uv)^\prime=u^\prime v+u v^\prime$

We will let:

$\displaystyle u=\sin(\frac{\pi t}{10})\text{ and } \\ \\ v=8-t$

Then:

$\displaystyle u^\prime=\frac{\pi}{10}\cos(\frac{\pi t}{10})\text{ and } \\ \\ v^\prime= -1$

(The derivative of u was determined using the chain rule.)

Then it follows that:

$\displaystyle \begin{aligned} B^\prime(t)&=24.6\frac{d}{dt}[\sin(\frac{\pi t}{10})(8-t)] \\ \\ &=24.6[(\frac{\pi}{10}\cos(\frac{\pi t}{10}))(8-t) - \sin(\frac{\pi t}{10})] \end{aligned}$

Therefore:

$\displaystyle B^\prime(6) =24.6[(\frac{\pi}{10}\cos(\frac{\pi (6)}{10}))(8-(6))- \sin(\frac{\pi (6)}{10})]$

By simplification:

$\displaystyle B^\prime(6)=24.6 [\frac{\pi}{10}\cos(\frac{3\pi}{5})(2)-\sin(\frac{3\pi}{5})] \approx -28.17$

So, the slope of the tangent line to the point (6, B(6)) is -28.17.

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