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3 years ago

8 people are boarding a plane 2 have tickets for first class and board before everyone. In how many ways can these people board

the aircraft?

Mathematics

1 answer:

mixer [17]3 years ago

3 0

$2!6!=2\times1\times6\times5\times4\times3\times2\times1=1440$

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Consider the function f(x) = 3x and the function g, which is shown below.

VLD [36.1K]

Answer:

B. The graph of g is the graph of f shifted 2 units down

Step-by-step explanation:

Graph of Functions

We have two functions:

f(x)=3^x

g(x)=3^x-2

Since g(x)=f(x)-2 it will be represented as an identical graph as that for f(x), but vertically displaced 2 units down. Let's check it by plugging some points

f(0)=3^0=1

g(0)=3^0-2=-1

f(1)=3^1=3

g(1)=3^1-2=1

f(3)=3^3=27

g(3)=3^3-2=25

We can notice the values of g(x) are always 2 units below f(x), thus the correct answer is

B. The graph of g is the graph of f shifted 2 units down

7 0

3 years ago

What polynomial identity will prove that 49-4=45

Svetach [21]

49 is a square given by 7x7 as is clear in your equation, 4 is a square given by 4x4 the operator given is - ( minus) you have two squares, and a difference sign a^2 - b^2 = (a-b)(a+b) 7^2 -2^2 = (7-2)(7+2) = (5)(9) = 45 it is the diffeernce of two squares

3 0

3 years ago

Which one is the right answer

Jobisdone [24]

Answer: A. f(g(x)) =x and g(f(x))=x and f and g are inverses.

Step-by-step explanation:

A function g is the inverse of function f if

f(g(x)) = g(f(x))=x

Given: f(x)= x+4 , g(x) = x-4

f(g(x)) = f(x+4) = (x-4)+4

= x-4+4 = x

i.e. f(g(x)) =x

g(f(x))= g(x-4) = (x-4)+4 =x

i.e. g(f(x))=x

Hence, f(g(x)) =x and g(f(x))=x and f and g are inverses.

8 0

3 years ago

Caroline has some dimes and some quarters. She has a maximum of 15 coins worth at least $2.85 combined. If Caroline has 3 dimes,

gayaneshka [121]

Answer:

11, 12.

Step-by-step explanation:

Let q represent number of quarters.

We have been given that Caroline has a maximum of 15 coins worth at least $2.85 combined. We are also told that Caroline has 3 dimes. This means that total coins are less than or equal to 15.

We can represent this information in an inequality as:

$q+3\leq 15...(1)$

We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.

We know that each dime is worth $0.10 and each quarter is worth $0.25.

$0.25q+3(0.10)\geq 2.85...(2)$

Now, let us solve our system of inequalities.

From 1st inequality, we will get:

$q+3-3\leq 15-3$

$q\leq 12$

From 2nd inequality, we will get:

$0.25q+0.30\geq 2.85$

$0.25q+0.30-0.30\geq 2.85-0.30$

$0.25q\geq 2.55$

$\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}$

$q\geq 10.2$

Upon combining our both inequalities, we will get:

$10.2\leq q\leq 12$

This means that numbers of quarters would be greater than or equal to 10.2 and less than or equal to 12.

Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.

6 0

3 years ago

What are two factors to add to give negative 4 and multiply to give negative 10?

SIZIF [17.4K]

-5*-2=-10 The factors to multiply to give negative 10 is -5 and 2 6 plus negative two gives you negative four. The factors to add to give you -4 is 6 and -2

6 0

3 years ago