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Stella [2.4K]
3 years ago
10

How to solve piecewise functions step by step?

Mathematics
1 answer:
Zanzabum3 years ago
5 0
If you can graph a function, you can graph piecewise functions.  Each one of them is a different line or curve within the domain for that specific line of curve.  If the domain states it's less than or greater than a number, you circle that point on the line.  If the domain states it's also possibly equal to the point at the beginning or the end, you make a closed dot.  

I"m sure that's clear as mud, please respond with any additional questions.
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Find the rule, solve for n
Andrej [43]
Try this option:
note, that the difference between 8 and 10 is 2, between 9 and 12 is 3, between 11 and 16 is 5. It is possible when f(x) is linear function, 2x-6, therefore f(14)=2*14-6=22

Answer: 22.
6 0
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!\\

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
Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent. How many text messag
professor190 [17]

Given that Kimora’s cell phone company charges her $35 a month for phone service plus $.05 for each text message sent.

Kimora's cell phone bill for one month is $52.

We need to determine the number of text messages Kimora sent for one month.

Also, we need to write and equation and solve it.

<u>The equation:</u>

Let x denote the number of text messages Kimora sent for one month.

Thus, the equation is given by

35+0.05x=52

Therefore, the equation for the number of text messages Kimora sent for one month is 35+0.05x=52

<u>Solving the equation:</u>

We need to solve the equation 35+0.05x=52

Subtracting both sides of the equation by 35, we get;

0.05x=17

Dividing both sides of the equation by 0.05, we get;

x=340

Therefore, the number of messages sent is 340.

3 0
3 years ago
A volunteer group picked up 3 times as many plastic bottles as cans in their community. The number of papers they picked up was
sweet-ann [11.9K]

try 4,320 for your answer

4 0
2 years ago
At the space center, Karen bought a model of a shuttle. She started working on the model the next day at 11:13 A.M. She worked u
goblinko [34]

Answer:

58 minutes.

Step-by-step explanation:

From the question, Karen worked on the model in two windows;

1) 11.13 AM - 11.54 AM = 41 minutes

2) 1.29 PM - 1.46 PM = 17 minutes.

Hence, the total amount of time Karen spent working on the Shuttle model is:

41minutes + 17minutes = 58 minutes.

3 0
3 years ago
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