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allochka39001 [22]
3 years ago
15

Mr. Tindell divided a 6th grade class Of 80 students an into equal groups the number of students in each group was a prime numbe

r how many groups did he make how many were in each group?
Mathematics
1 answer:
zubka84 [21]3 years ago
3 0

Answer:

He made 16 groups which means 5 Students in each group

Step-by-step explanation:

Because 80 divided by 16 is 5 and 5 is a prime number

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The shelf is 4 feet wide and 2/3 feet deep. what is the area of the shelf?
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Answer:

Area of the self will be =4\times \frac{2}{3}=\frac{8}{3}=2.666ft^2

Step-by-step explanation:

We have given that self is 4 feet wide and \frac{2}{3} feet deep

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The figure shown below is composed of a semicircle and a non-overlapping equilateral triangle and contains a hole that is also c
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Check the picture below.

since we know the radius of the larger semicircle is 8, thus its diameter is 16, which is the length of one side of the equilateral triangle.  We also know the smaller semicircle has a radius of 1/3, and thus a diameter of 2/3, namely the lenght of one side of the small equilateral triangle.

now, if we just can get the area of the larger figure and the area of the smaller one and subtract the smaller from the larger, we'll be in effect making a hole/gap in the larger and what's leftover is the shaded figure.

\bf \stackrel{\textit{area of a semi-circle}}{A=\cfrac{1}{2}\pi r^2\qquad r=radius}~\hspace{10em}\stackrel{\textit{area of an equilateral triangle}}{A=\cfrac{s^2\sqrt{3}}{4}\qquad s=\stackrel{side's}{length}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\left[ \stackrel{\textit{larger figure}}{\cfrac{1}{2}\pi 8^2~~+~~\cfrac{16^2\sqrt{3}}{4}} \right]\qquad -\qquad \left[ \cfrac{1}{2}\pi \left( \cfrac{1}{3} \right)^2 +\cfrac{\left( \frac{2}{3} \right)^2\sqrt{3}}{4}\right]}

\bf \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\frac{4}{9}\sqrt{3}}{4} \right] \\\\\\ \left[ 32\pi +64\sqrt{3} \right]\qquad -\qquad \left[ \cfrac{\pi }{18}+\cfrac{\sqrt{3}}{9} \right]~~\approx~~ 211.38 - 0.37~~\approx~~ 211.01

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