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Montano1993 [528]

3 years ago

5

Rahm spent 2 1\2 hoirs writing a n essay. it took hime 4 times as long to finish his science project. how long did it take him t

o complete both the essay and the science project?

1 answer:

Ivahew [28]3 years ago

3 0

Answer: it took him 12 1/2 hours to complete both projects.

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A five-digit number starts with a number between 4-9 in the first position, with no restrictions on the remaining 4 digits. a

Maurinko [17]

Answer:

(a) $Pr = 0.3024$

(b) $Pr = 0.6976$

(c) $Pr = \frac{^9P_{n-1}}{10^{n-1}}$

Step-by-step explanation:

Given

$Start = \{5,6,7,8\}$ i.e. between 4 and 9

$n(Start) =4$

$Digits = 5$

Solving (a): Probability that each of the 5 digit are different

Since there is no restriction;

The total possible selection is as follows:

$First\ digit = 4$ (i.e. any of the 4 start digits)

$Second\ digit = 10\\$ (i.e. any of the 10 digits 0 - 9)

$Third\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

$Fourth\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

$Fifth\ digit = 10$ (i.e. any of the 10 digits 0 - 9)

So, the total is:

$Total = 4 * 10 * 10 * 10 * 10$

$Total = 40000$

For selection that all digits are different, the selection is:

$First\ digit = 4$ (i.e. any of the 4 start digits)

$Second\ digit = 9$ (i.e. any of the remaining 9)

$Third\ digit = 8$ (i.e. any of the remaining 8)

$Fourth\ digit = 7$ (i.e. any of the remaining 7)

$Fifth\ digit = 6$ (i.e. any of the remaining 6)

So:

$Selection =4 * 9 * 8 * 7 * 6$

$Selection =12096$

So, the probability is:

$Pr = \frac{Selection}{Total}$

$Pr = \frac{12096}{40000}$

$Pr = 0.3024$

Solving (b): At least 1 repeated digit

The probability calculated in (a) is the all digits are different i.e. P(None)

So, using laws of complement

We have:

$P(At\ least\ 1) = 1 - P(None)$

So, we have:

$Pr= 1 - 0.3024$

$Pr = 0.6976$

Solving (c): An expression to model the probability.

<em>Using (a) as a point of reference, we have;</em>

$Pr = \frac{Selection}{Total}$

Where

$Selection =4 * 9 * 8 * 7 * 6$ ---- for selection of 5 i.e. n = 5

$Total = 4 * 10 * 10 * 10 * 10$

$Selection =4 * 9 * 8 * 7 * 6$

This can be rewritten as:

$Selection = 4 * ^9P_4$

4 can be expressed as: 5 - 1

So, we have:

$Selection = (5-1) *^9P_{5-1}$

Substitute n for 5

$Selection = (n-1) *^9P_{n-1}$

$Selection = (n-1)^9P_{n-1}$

$Total = 4 * 10 * 10 * 10 * 10$

This can be rewritten as:

$Total = 4 * 10^4$

$Total = (5-1) * 10^{5-1}$

$Total = (n-1) * 10^{n-1}$

$Total = (n-1) 10^{n-1}$

So, the expression is:

$Pr = \frac{(n-1)^9P_{n-1}}{(n-1)10^{n-1}}$

$Pr = \frac{^9P_{n-1}}{10^{n-1}}$

<em>Where n represents the digit number</em>

5 0

3 years ago

Evaluate<br> 5! 4!<br> ____<br> 7! 2!<br> Simple as much as possible

shepuryov [24]

The value of the factorial is 5!4!/7!2! = 2/7

<h3>What is factorial?</h3>

The product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point.

Given:

5!4!/7!2!

= 5!* 4*3*2!/7*6*5!*2!

=4*3/7*6

=12/42

=4/14

=2/7

Hence, 5!4!/7!2! = 2/7.

Learn more about factorial here:

brainly.com/question/1357774

#SPJ1

8 0

2 years ago

Factor completely <br> 4(x+1)^2/3 + 12(x+1)^-1/3

wolverine [178]

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
\left.\qquad \qquad \right.\textit{negative exponents}\\\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}
\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\qquad \qquad 
a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}
\\\\
-------------------------------\\\\
%4(x+1)^2/3 + 12(x+1)^-1/3
4(x+1)^{\frac{2}{3}}+12(x+1)^{-\frac{1}{3}}\implies 4(x+1)^{\frac{2}{3}}+12\cfrac{1}{(x+1)^{\frac{1}{3}}}
\\\\\\$

$\bf 4(x+1)^{\frac{2}{3}}+\cfrac{12}{(x+1)^{\frac{1}{3}}}\impliedby \textit{so, our LCD is }(x+1)^{\frac{1}{3}}
\\\\\\
\cfrac{4(x+1)^{\frac{2}{3}}\cdot (x+1)^{\frac{1}{3}}+12}{(x+1)^{\frac{1}{3}}}\implies \cfrac{4(x+1)^{\frac{2}{3}+\frac{1}{3}}+12}{(x+1)^{\frac{1}{3}}}
\\\\\\
\cfrac{4(x+1)^{\frac{3}{3}}+12}{(x+1)^{\frac{1}{3}}}\implies \cfrac{4(x+1)+12}{(x+1)^{\frac{1}{3}}}\implies \cfrac{4x+4+12}{(x+1)^{\frac{1}{3}}}
\\\\\\
\cfrac{4x+16}{(x+1)^{\frac{1}{3}}}\implies \cfrac{4(x+4)}{\sqrt[3]{x+1}}$

3 0

4 years ago

Read 2 more answers

6570 ÷ 16 <br><br><br>410<br><br><br>410 1/16<br><br><br>410 3/8<br><br><br>410 5/8

UNO [17]

Answer:

Exact Form:

3285

8

Decimal Form:

410.625

Mixed Number Form:

410

5

8

thats what i got i hope this helps

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

the cost of a family membership at a health club $58 per month plus a one time 129 start up fee . if a family spent 651 , how ma

Lady_Fox [76]

Answer:

9 months

Step-by-step explanation:

651=58x+129

-129 -129

522=58x divide 522 by 58

=9

7 0

3 years ago