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2 years ago

It is 8 kilometers from Lucy's house to the nearest mailbox. How far is it in meters?

Mathematics

1 answer:

allochka39001 [22]2 years ago

3 0

Answer:

8000

Step-by-step explanation:

multiply the length value by 1000

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Solve the equation 5,4g+10=2.4g+25. a. Find the value of g. b. Explain how you can check that the value you found for g is corre

Marianna [84]

Answer:

G=5

Step-by-step explanation:

Input the answer into the formula. If it is correct then its correct but if it doesn't work it is incorrect

6 0

2 years ago

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Determine the total number of roots of each polynomial function using the factored form.

Tanzania [10]

Answer:

3 roots

Step-by-step explanation:

The roots of a function is the x intercepts.

x=-1

x=3

x=4

6 0

3 years ago

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Solve this equation -9h - 6 + 12h + 40 = 22

schepotkina [342]

$-9h - 6 + 12h + 40 = 22\\\\3h=-12\\\\h=-4$

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2 years ago

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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

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2 years ago

Find the simple interest earned on $2600 invested for 3 years at 12% per annum

Aleks04 [339]

Answer:

$936

Step-by-step explanation:

Simple interest is money you can earn by initially investing some money (a.k.a the principal). In return, a percentage (a.k.a the interest) of the initial money invested is added to the principal, this is what makes your initial investment grow.

The equation for simple interest is:

I = P x r x t

P = Principal, $2600

r = interest rate, 12%

t = time involved, 3 years

Fill in the values:

2600 × 0.12 × 3 = $936.00

5 0

2 years ago

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