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Harrizon [31]
3 years ago
10

What are the median mode and range of the data set 16,17,17,17,19,21,23,24

Mathematics
1 answer:
Sav [38]3 years ago
3 0
Mode 17,
Mean is 19.3
Median 18.
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Flauer [41]

 

\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\

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\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276

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\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}    

 

 

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Which two statements are missing in steps 3 and 4?
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\dfrac{AB}{ZY}=\dfrac{BC}{YX}=2

2. \angle B and \angle Y are right angles - given

3.  \angle B\cong \angle Y two right angles are always congruent.

4. \triangle ABC\sim \triangle ZYX by SAS similarity theorem.

SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

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