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Pachacha [2.7K]
3 years ago
13

Mr rowley has 16 homework papers and 14 exit tickets to return. Ms ribera has 64 homework papers and 60 exit tickets to return.

For each teacher, write a ratio to represent the number of homework papers to number of exit tickets they have to return. Are the ratios equivalent? Explain.
Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
7 0
Mr. Rowley has 16 homework papers to 14 exit tickets; Ms. Rivera has 64 homework papers to 60 exit tickets. No, the ratios are not equivalent because Mr. Rowley’s unit rate is 8/7, or approximately 1.14, and Ms. Rivera’s unit rate is 16/15, or approximately 1.07
Alexxx [7]3 years ago
7 0

no, the ratios are not equivalent because Ms. Rowley's unit rate is 8/7 and Ms. Rivera's unit rate is 16/15

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8 0
3 years ago
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Find the area of the shaded region ​
o-na [289]

so hmmm let's get the area of the whole hexagon, and then get the area of the circle inside it, then <u>subtract the area of the circle from that of the hexagon's</u>, what's leftover is what we didn't subtract, namely the shaded part.

\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cot\stackrel{\stackrel{degrees}{\downarrow }}{\left( \frac{180}{n} \right)}~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ n=\stackrel{hexagon}{6}\\ s=\frac{9}{2} \end{cases}\implies A=\cfrac{1}{4}(6)\left( \cfrac{9}{2} \right)^2 \cot\left( \cfrac{180}{6} \right)

A=\cfrac{1}{4}(6)\cfrac{9^2}{2^2} \cot(30^o)\implies A=\cfrac{243}{8}\cot(30^o)\implies A=\cfrac{243\sqrt{3}}{8} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{4}{5} \end{cases}\implies A=\pi \left( \cfrac{4}{5} \right)^2\implies A=\cfrac{16\pi }{25} \\\\[-0.35em] ~\dotfill

\stackrel{\textit{area of the hexagon}}{\cfrac{243\sqrt{3}}{8}}~~ - ~~\stackrel{\textit{area of the circle}}{\cfrac{16\pi }{25}}\implies \cfrac{6075\sqrt{3}-128\pi }{200}

5 0
2 years ago
Suppose that $2000 is invested at a rate of 2.6% , compounded semiannually. Assuming that no withdrawals are made, find the tota
EleoNora [17]

Answer:

$2,589.52

Step-by-step explanation:

A = P(1 + \dfrac{r}{n})^{nt}

We start with the compound interest formula above, where

A = future value

P = principal amount invested

r = annual rate of interest written as a decimal

n = number of times interest is compound per year

t = number of years

For this problem, we have

P = 2000

r = 0.026

n = 2

t = 10,

and we find A.

A = $2000(1 + \dfrac{0.026}{2})^{2 \times 10}

A = $2589.52

8 0
3 years ago
Read 2 more answers
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