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Mariulka [41]
3 years ago
12

A 16-cup container of laundry detergent costs $13.60. What is the price per quart?

Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

$0.21

Step-by-step explanation:

So, first let's find the cost of a single cup.

16/13.60 = 1/0.85

Now, we know that each cup is approximately $0.85. Next, we must convert cups into quarts. 1 cup = 0.25 quarts.

1/0.85 = 0.25/0.21

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A sector of a circle makes a 127° angle at its centre. If the arc of the sector has length 36 mm, find
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Answer:

Approximately 68.5\; \rm mm.

Step-by-step explanation:

Convert the angle of this sector to radians:

\begin{aligned}\theta &= 127^{\circ} \\ &= 127^{\circ} \times \frac{2\pi}{360^{\circ}} \\ &\approx 2.22\end{aligned}.

The formula s = r\, \theta relates the arc length s of a sector of angle \theta (in radians) to the radius r of this sector.

In this question, it is given that the arc length of this sector is s = 36\; \rm mm. It was found that \theta = 2.22 radians. Rearrange the equation s = r\, \theta to find the radius r of this sector:

\begin{aligned} r&= \frac{s}{\theta} \\ &\approx \frac{36\; \rm mm}{2.22} \\ &\approx 16.2\; \rm mm\end{aligned}.

The perimeter of this sector would be:

\begin{aligned}& 2\, r + s \\ =\; & 2 \times 16.2\; {\rm mm} + 36\; {\rm mm} \\ =\; & 68.5\; \rm mm\end{aligned}.

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2 years ago
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