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3 years ago

6

What is the slope between (10,4) and (7,4)?

1 answer:

Inga [223]3 years ago

3 0

Slope is rise/run to find it we do (y1-y2)/(x1-x2) y1 means the 1st y and y2 means the second y in (x,y) form y1=4 y2=4 x1=10 x2=7 (4-4)/(10-7)=0/3=0 slope is 0

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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

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

where $|Perm(X)|=\text{number of possible permutations of the elements of X taking all at once}$

and

$|Perm(F) \cup Perm(R)| = |Perm(F)| + |Perm(R)| - |Perm(FR)|\\= 23!+24!- 21! \text{ possibilities}$

What we are looking for is the number of permutations of the 26 letters of the alphabet that do not contain the strings fish, rat or bird, or

$|Perm(\mathcal{E})|-|Perm(B)|-|Perm(F)\cup Perm(R)|\\= 26!-23!-(23!+24!- 21!)\\= 402619359782336797900800000 \text{ possibilities}$

This link contains another solved problem on permutations:

brainly.com/question/7951365

6 0

2 years ago

Which biconditional is NOT a good definition? A. Two line segments are congruent if and only if they are of same length. B. An a

Natasha2012 [34]

The answer is C, because 2 shapes can have the same area, but that doesn't necessarily mean they're congruent.

8 0

3 years ago

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3 2/3 divided by 2 2/3

Goshia [24]

Answer:

1 3/8

Step-by-step explanation:

3 2/3 = 11/3

2 2/3 = 8/3

11/3 / 8/3 = 11/3*3/8 = 11/8 = 1 3/8

5 0

3 years ago

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A triangle has vertices (3,5), (5,2), and (2,0). Is the triangle a right triangle?

Artyom0805 [142]

Answer:

No, this is not a right triangle

Step-by-step explanation:

8 0

3 years ago

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A triangular courtyard has a perimeter of 120 meters. The lengths of two sides are 30 meters and 50 meters. How long is the thir

Masja [62]

Answer:

the third side is 40 m long

Step-by-step explanation:

The perimeter of the triangle is the sum of its three sides, and they give you what that value in meters is (120 m)

Your are given the length of two of them: 30 m and 50 m, and need to find the third one (let's call it "x" for this unknown side)

Now set the following equation:

Perimeter = side 1 + side 2 + side 3 --> replace these with the info you know

120 m = 30 m + 50 m + x --> add 30 m and 50 m obtaining 80 m

120 m = 80 m + x --> now solve for x (isolate the x on one side) by subtracting 80 m from both sides

120 m - 80 m = x --> perform the subtraction 120 m - 80 m = 40 m

40 m = x

Which tells us that the third unknown side has a length of 40 m

7 0

3 years ago

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