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lidiya [134]
3 years ago
10

A toy factory makes 15 teddy bears every 10 minutes. The factory makes teddy bears for 8 hours each work day. What is the fewest

number of work days the factory will need to make 5,000 teddy bears? Write an explanation to show how you determined your answer
Mathematics
1 answer:
Kay [80]3 years ago
6 0
Ok so if they make 15 bears every 10 mins then they will make 90 bears in one hour.

15 x 6 = 90

If they work for 8 hours then they’ll make 720 bears in one work day.

90 x 8 = 720

Let x be the number of days...

720x = 5000

5000 / 720 = 6.9444444.....

Round up because they want the least number of work days

So the answer is 7 work days

Hope this helps! Any questions let me know :)
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Step-by-step explanation:

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Given sin x = -4/5 and x is in quadrant 3, what is the value of tan x/2
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bearing in mind that, on the III Quadrant, sine as well as cosine are both negative, and that hypotenuse is never negative, so, if the sine is -4/5, the negative number must be the numerator, so sin(x) = (-4)/5.


\bf sin(x)=\cfrac{\stackrel{opposite}{-4}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{adjacent}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2-(-4)^2}=a\implies \pm\sqrt{9}=a\implies \pm 3=a \\\\\\ \stackrel{III~Quadrant}{-3=a}~\hfill cos(x)=\cfrac{\stackrel{adjacent}{-3}}{\stackrel{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill

\bf tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}\qquad \leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\[-0.35em] ~\dotfill

\bf tan\left( \cfrac{x}{2} \right)=\cfrac{~~\frac{-4}{5}~~}{1-\frac{3}{5}}\implies tan\left( \cfrac{x}{2} \right)=\cfrac{~~\frac{-4}{5}~~}{\frac{2}{5}}\implies tan\left( \cfrac{x}{2} \right)=\cfrac{-4}{5}\cdot \cfrac{5}{2} \\\\\\ tan\left( \cfrac{x}{2} \right)=\cfrac{-4}{2}\cdot \cfrac{5}{5}\implies tan\left( \cfrac{x}{2} \right)=-2

4 0
4 years ago
Read 2 more answers
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kodGreya [7K]

Answer:

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Step-by-step explanation:

For functions, the two notations mean the exact same thing, but "f (x)" gives you more flexibility and more information. You used to say "y = 2x + 3; solve for y when x = –1". Now you say "f (x) = 2x + 3; find f (–1)" (pronounced as "f-of-x equals 2x plus three; find f-of-negative-one").

6 0
3 years ago
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