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frez [133]
2 years ago
8

The histogram to the right represents the weights​ (in pounds) of members of a certain​ high-school math team. How many team mem

bers are included in the​ histogram? A histogram has a horizontal axis labeled from less than 115 to 235 plus in intervals of 20 and a vertical axis labeled from 0 to 6 in intervals of 1. Vertical bars, 20 units wide and centered on the horizontal axis values, have heights as follows: 115, 1; 135, 4; 155, 3; 175, 1; 195, 5; 215, 2; 235, 3. 115 135 155 175 195 215 235 0 2 4 6 The histogram represents nothing math team members.
Mathematics
1 answer:
Luden [163]2 years ago
5 0

Answer:

19

Step-by-step explanation:

The vertical axis of a histogram indicates the total amount of people that meet the weights indicated in the x-axis in the analysed population.  From data we can construct the following table:

x-axis   y-axis  

115        1

135       4

155       3  

175        1  

195       5  

215       2  

235      3

So there are: 1+4+3+1+5+2+3 = 19 team members included in the​ histogram.

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\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

\rm \:  =  \: \dfrac{5 \times  { {(5}^{2} )}^{n + 1}  -  {5}^{2}  \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {( {5}^{2} )}^{n + 1} }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

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