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3 years ago

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Wilt Chamberlin holds the record for the highest number of points scored in a single NBA basketball game. Chamberlin scored 100

points for Philadelphia against the New York Knicks on March 2, 1962. Chamberlain made a total of 64 baskets consisting of field goals (worth 2 points) and foulshots (worth 1 point). Find the number of field goals and the number of foul shots that chamberlain mad

1 answer:

Genrish500 [490]3 years ago

3 0

Answer:

field goals = 36, foul shots = 28.

Step-by-step explanation:

Given:

Chamberlin scored 100 points.

Chamberlain made a total of 64 baskets consisting of field goals and foulshots.

Each field goal worth = 2 points

Each foulshot worth = 1 points

Question asked:

Find the number of field goals and the number of foul shots that chamberlain made ?

Solution:

Let number of field goals = $x$

<u>As total of 64 baskets, he made:</u>

Then number of foul shots = $64-x$

Now, total points, he scored is given 100,

<u><em>Number of field goals </em></u> $\times$ <u><em> 2 + Number of foul shots </em></u> $\times$ <u><em> 1 = 100</em></u>

$x\times2+(64-x)\times1=100\\2x+64-x=100\\x+64=100$

Subtracting both sides by 64

$x+64-64=100-64\\x=36$

Number of field goals = $x$ = 36

Then number of foul shots = $64-x$ = 64 - 36 = 28

Therefore, 36 field goals and 28 foul shots made by chamberlain.

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An arithmetic progression is simply a progression with a common difference among consecutive terms.

<em>The sum of multiplies of 6 between 8 and 70 is 390</em>
<em>The sum of multiplies of 5 between 12 and 92 is 840</em>
<em>The sum of multiplies of 3 between 1 and 50 is 408</em>
<em>The sum of multiplies of 11 between 10 and 122 is 726</em>
<em>The sum of multiplies of 9 between 25 and 100 is 567</em>
<em>The sum of the first 20 terms is 630</em>
<em>The sum of the first 15 terms is 480</em>
<em>The sum of the first 32 terms is 3136</em>
<em>The sum of the first 27 terms is -486</em>
<em>The sum of the first 51 terms is 2193</em>

<em />

<u>(a) Sum of multiples of 6, between 8 and 70</u>

There are 10 multiples of 6 between 8 and 70, and the first of them is 12.

This means that:

$\mathbf{a = 12}$

$\mathbf{n = 10}$

$\mathbf{d = 6}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

$\mathbf{S_{10} = \frac{10}2(2*12 + (10 - 1)6)}$

$\mathbf{S_{10} = 390}$

<u>(b) Multiples of 5 between 12 and 92</u>

There are 16 multiples of 5 between 12 and 92, and the first of them is 15.

This means that:

$\mathbf{a = 15}$

$\mathbf{n = 16}$

$\mathbf{d = 5}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

$\mathbf{S_{16} = \frac{16}2(2*15 + (16 - 1)5)}$

$\mathbf{S_{16} = 840}$

<u>(c) Multiples of 3 between 1 and 50</u>

There are 16 multiples of 3 between 1 and 50, and the first of them is 3.

This means that:

$\mathbf{a = 3}$

$\mathbf{n = 16}$

$\mathbf{d = 3}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

$\mathbf{S_{16} = \frac{16}2(2*3 + (16 - 1)3)}$

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<u>(d) Multiples of 11 between 10 and 122</u>

There are 11 multiples of 11 between 10 and 122, and the first of them is 11.

This means that:

$\mathbf{a = 11}$

$\mathbf{n = 11}$

$\mathbf{d = 11}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

$\mathbf{S_{16} = \frac{11}2(2*11 + (11 - 1)11)}$

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The sum of n terms of an AP is:

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The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

$\mathbf{S_{20} = \frac{20}2(2*3 + (20 - 1)3)}$

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The given parameters are:

$\mathbf{a = 4}$

$\mathbf{d = 4}$

$\mathbf{n = 15}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

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$\mathbf{n = 32}$

The sum of n terms of an AP is:

$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

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Substitute known values

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<u>(h) Sum of first 51 terms</u>

The given parameters are:

$\mathbf{a = -7}$

$\mathbf{d = 2}$

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$\mathbf{S_n = \frac n2(2a + (n - 1)d)}$

Substitute known values

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Read more about arithmetic progressions at:

brainly.com/question/13989292

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