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4 years ago

Evaluate ( 25/36)^ 1/2.

Mathematics

2 answers:

Aleks [24]4 years ago

7 0

ANSWER:

5 / 6

When ( 25 / 36 )^1/2 is evaluated, the answer is 5 / 6.

STEP-BY-STEP EXPLANATION:

= ( 25 / 36 )^1/2

= ( 25^1/2 ) / ( 36^1/2 )

= 5 / 6

sergiy2304 [10]4 years ago

7 0

Answer:

The correct option is C.

Step-by-step explanation:

The given expression is

$(\frac{25}{36})^{\frac{1}{2}$

It can be written as

$\sqrt{\frac{25}{36}}$ $[\because x^{\frac{1}{2}=\sqrt{x}]$

Using the property of radical expression, we get

$\frac{\sqrt{25}}{\sqrt{36}}$ $[\because \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}]$

$\frac{5}{6}$

The value of given expression is 5/6. Therefore the correct option is C.

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3 years ago

How many permutations of the 26 letters of the English alphabet do not contain any of the strings fish, rat, or bird

NARA [144]

The number of permutations of the 26 letters of the English alphabet that do not contain any of the strings fish, rat, or bird is 402619359782336797900800000

Let

$\mathcal{E}=\{\text{All lowercase letters of the English Alphabet}\}\\\\B=\overline{\{b,i,r,d\}} \cup \{bird\}\\\\F=\overline{\{f,i,s,h\}} \cup \{fish\}\\\\R=\overline{\{r,a,t\}} \cup \{rat\}\\\\FR=\overline{\{f,i,s,h,r,a,t\}} \cup \{fish,rat\}$

Then

$Perm(\mathcal{E})=\{\text{All orderings of all the elements of } \mathcal{E}\}\\\\Perm(B)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing bird}\}\\\\Perm(F)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing fish}\}\\\\Perm(R)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing rat}\}\\\\Perm(FR)=\{\text{All orderings of all the elements of } \mathcal{E} \text{ containing both fish and rat}\}\\$

Note that since

$F \cap R=\varnothing$ , $Perm(F)\cap Perm(R)\ne \varnothing$

But since

$B \cap R \ne \varnothing$ , $Perm(B)\cap Perm(R)= \varnothing$

and

$B \cap F \ne \varnothing$ , $Perm(B)\cap Perm(F)= \varnothing$

Since

$|\mathcal{E} |=26 \text{, then, } |Perm(\mathcal{E})|=26! \\\\|B|=26-4+1=23 \text{, then, } |Perm(B)|=23!\\\\|F|=26-4+1=23 \text{, then, } |Perm(F)|=23!\\\\|R|=26-3+1=24 \text{, then, } |Perm(R)|=24!\\\\|FR|=26-7+2=21 \text{, then, } |Perm(FR)|=21!\\$