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1 year ago

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A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 16 cm, a width of 6 cm, and a height

of 8 cm. The pyramid has a height of 14 cm. Find the volume of the composite space figure.

1 answer:

blondinia [14]1 year ago

3 0

Answer:

<u>1,216 cm³</u>

Step-by-step explanation:

Volume (composite space figure) = Volume (pyramid) + volume (prism)

⇒ [16 x 6 x 14 / 3] + [16 x 6 x 8]
⇒ 96 [14/3 + 8]
⇒ 96 [14/3 + 24/3]
⇒ 96 x 38/3
⇒ 32 x 38
⇒ <u>1,216 cm³</u>

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Katen [24]

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

<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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2 years ago

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ANTONII [103]

Answer:

The Answer would be "B"

Step-by-step explanation:

14.1005 - 11.023 = 3.0775

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Ghella [55]

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2 years ago

A recent poll of 80 randomly selected Californians showed that 38% ( = 0.38) believe they are doing all that they can to conserv

Elanso [62]

The margin of error given the proportion can be found using the formula

$z* \sqrt{ \frac{p(1-p)}{n} }$

Where
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$n$ is the sample size

We have
$z*=2.58$
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Plugging these values into the formula, we have:
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Hitman42 [59]

Answer:

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