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yan [13]
2 years ago
9

Simplify: {(12)^1 + (13)^-1}/[(1/5)^-2 × {(1/5)^-1 + (1/8)^-1}^-1]​

Mathematics
2 answers:
GaryK [48]2 years ago
4 0
Answer : 1/20

Explanation:

CaHeK987 [17]2 years ago
3 0

Step-by-step explanation:

\underline{\underline{\sf{➤\:\:Solution}}}

\sf \dashrightarrow \:  \dfrac{ \left(\left(12 \right)^{ - 1}  + \left(13 \right)^{ - 1}  \right) }{\left( \dfrac{1}{5}\right) ^{ - 2}  \times\left( \left( \dfrac{1}{5}  \right) ^{ - 1}  +\left( \dfrac{1}{8}  \right) ^{ - 1}  \right) ^{ - 1}}

\sf \dashrightarrow \:  \dfrac{ \left(\dfrac{1}{12}  + \dfrac{1}{13} \right) }{\left( \dfrac{5}{1}\right) ^{ 2}  \times\left( \dfrac{5}{1}  + \dfrac{8}{1}   \right) ^{ - 1}}

  • LCM of 12 and 13 is 156

\sf \dashrightarrow \:  \dfrac{ \left(\dfrac{1 \times 13 = 13}{12 \times 13 = 156}  + \dfrac{1 \times 12 = 12}{13 \times 12 = 156} \right) }{\ \dfrac{25}{1} \times\left( \dfrac{5 + 8}{1}    \right) ^{ - 1}}

\sf \dashrightarrow \:  \dfrac{ \left(\dfrac{13}{156}  + \dfrac{12}{156} \right) }{\ \dfrac{25}{1} \times\left( \dfrac{13}{1}    \right) ^{ - 1}}

\sf \dashrightarrow \:  \dfrac{ \left(\dfrac{13 + 12}{156}  \right) }{\ \dfrac{25}{1} \times\dfrac{1}{13} }

\sf \dashrightarrow \:    \dfrac{25}{156} \div    \dfrac{25}{13}

\sf \dashrightarrow \:    \dfrac{ \cancel{25}}{156}  \times    \dfrac{13}{ \cancel{25} }

\sf \dashrightarrow \:     \dfrac{13}{156}

\sf \dashrightarrow \:     \dfrac{1}{12}

\sf \dashrightarrow \:    Answer =   \underline{\boxed{ \sf{ \dfrac{1}{12} }}}

━━━━━━━━━━━━━━━━━━━━━━━━

\underline{\underline{\sf{★\:\:Laws\:of\: Exponents :}}}

\sf \: 1^{st} \: Law = \bigg( \dfrac{m}{n} \bigg)^{a} \times \bigg( \dfrac{m}{n} \bigg)^{b} = \bigg( \dfrac{m}{n} \bigg)^{a + b}

\sf 2^{nd} \: Law =

\sf Case : (i) \: if \: a > b \: then, \bigg( \dfrac{m}{n}\bigg) ^{a} \div \bigg( \dfrac{m}{n}\bigg)^{b} = \bigg( \dfrac{m}{n}\bigg)^{a - b}

\sf Case : (ii) \: if \: a < b \: then, \bigg( \dfrac{m}{n}\bigg) ^{a} \div \bigg( \dfrac{m}{n}\bigg)^{b} = \dfrac{1}{\bigg( \dfrac{m}{n}\bigg)^{b - a}}

\sf \: 3^{rd} \: Law = \bigg\{ \bigg( \dfrac{m}{n} \bigg)^{a} \bigg\}^{b} = \bigg( \dfrac{m}{n} \bigg)^{a \times b} =\bigg( \dfrac{m}{n} \bigg)^{ab}

\sf \: 4^{th} \: Law = \bigg( \dfrac{m}{n} \bigg)^{ - 1} = \bigg( \dfrac{n}{m} \bigg) =\dfrac{n}{m}

\sf \: 5^{th} \: Law = \bigg( \dfrac{m}{n} \bigg)^{0} = 1

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A cone has a slant length of 10 and a diameter of 8. Height is unknown.
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Step-by-step explanation:

Hi, to answer this question we have to apply the next formulas:

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Where r is the radius and h is the height (unknown)

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8 = 2r

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Before calculating the volume we have to apply the Pythagorean Theorem to find h. (where the slant is the hypotenuse and h and r are the sides of the triangle)

10 ² = h² + 4²

Solving for h

100 = h² + 16

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A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the
iris [78.8K]

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

Event\ 1 = \{1,2,3,4,5,6\}

Next, we list out the sample space of F

Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\

6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}

In (1): the sample space of E is:

E = \{1\}

So:

P(E) = \frac{n(E)}{n(Event\ 1)}

P(E) = \frac{1}{6}

In (2): the sample space of F is:

F = \{5,5,5,5\}

So:

P(F) = \frac{n(F)}{n(Event\ 2)}

P(F) =\frac{4}{36}

P(F) =\frac{1}{9}

For E and F to be independent:

P(E\ and\ F) = P(E) * P(F)

Substitute values for P(E) and P(F)

This gives:

P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}

P(E\ and\ F) = \frac{1}{54}

However, the actual value of P(E and F) is 0.

This is so because E = \{1\} and F = \{5,5,5,5\} have 0 common elements:

So:

P(E\ and\ F) = 0

Compare P(E\ and\ F) = \frac{1}{54} and P(E\ and\ F) = 0.

These values are not equal.

Hence: the two events are not independent

6 0
3 years ago
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