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liq [111]
3 years ago
15

In August, Nancy's Clothing Store sold 266 shirts with the ratio of short sleeve to long sleeve being 4:10. How many short sleev

e shirts were sold?
Mathematics
1 answer:
Akimi4 [234]3 years ago
6 0

Answer:

The number of short sleeve sold was 76

Step-by-step explanation:

Let

x ----> the number of short sleeve sold

y ----> the number of long sleeve sold

we know that

\frac{x}{y}=\frac{4}{10}

x=\frac{4}{10}y -----> equation A

x+y=266 -----> equation B

substitute equation A in equation B

\frac{4}{10}y+y=266

solve for y

\frac{14}{10}y=266\\\\y=266(10)/14\\y=190

Find the value of x

x=\frac{4}{10}(190)=76

therefore

The number of short sleeve sold was 76

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Write each expression as an algebraic​ (nontrigonometric) expression in​ u, u > 0.
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Answer:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

Step-by-step explanation:

We want to write the trignometric expression:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)\text{ where } u>0

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First, we can focus on the inner expression. Let θ equal the expression:

\displaystyle \theta=\sec^{-1}\left(\frac{u}{10}\right)

Take the secant of both sides:

\displaystyle \sec(\theta)=\frac{u}{10}

Since secant is the ratio of the hypotenuse side to the adjacent side, this means that the opposite side is:

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Using an double-angle identity:

=2\sin(\theta)\cos(\theta)

We know that the opposite side is √(u² -100), the adjacent side is 10, and the hypotenuse is u. Therefore:

\displaystyle =2\left(\frac{\sqrt{u^2-100}}{u}\right)\left(\frac{10}{u}\right)

Simplify. Therefore:

\displaystyle \sin\left(2\sec^{-1}\left(\frac{u}{10}\right)\right)=\frac{20\sqrt{u^2-100}}{u^2}\text{ where } u>0

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3 years ago
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Then change the 4% into a decimal= 1.04 

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