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2 years ago

In how many ways can people be lined up to get on a bus if a particular person always boards the bus first or last?

1 answer:

6 0

Incomplete question. I Assumed the number of people is 6. In other words, In how many ways can 6 people be lined up to get on a bus if a particular person always boards the bus first or last?

Answer:

6

Step-by-step explanation:

Note, this question involves the use of the permutation formula; which helps determine the arrangement or rearrangement of a set of objects in an ordered way. Since we are told a particular person (ie 1 person) from among the group always boards first or last, it forms our r.

P(n,r)= $\frac{n!}{(n-r)!}$ where n = number of people; r = the difference taken at a time.

P(n,r) = $\frac{6!}{(6-1)!}$ = $\frac{720}{120} = 6$

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Which pair of funtions is not a pair of inverse functions? please help!!

antiseptic1488 [7]

Answer:

$f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Step-by-step explanation:

we know that

To find the inverse of a function, exchange variables x for y and y for x. Then clear the y-variable to get the inverse function.

we will proceed to verify each case to determine the solution of the problem

case A) $f(x)=\frac{x+1}{6} , g(x)=6x-1$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y+1}{6}$

Isolate the variable y

$6x=y+1$

$y=6x-1$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=6x-1$

therefore

f(x) and g(x) are inverse functions

case B) $f(x)=\frac{x-4}{19} , g(x)=19x+4$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y-4}{19}$

Isolate the variable y

$19x=y-4$

$y=19x+4$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=19x+4$

therefore

f(x) and g(x) are inverse functions

case C) $f(x)=x^{5}, g(x)=\sqrt[5]{x}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=y^{5}$

Isolate the variable y

fifth root both members

$y=\sqrt[5]{x}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\sqrt[5]{x}$

therefore

f(x) and g(x) are inverse functions

case D) $f(x)=\frac{x}{x+20} , g(x)=\frac{20x}{x-1}$

Find the inverse of f(x)

Let

y=f(x)

Exchange variables x for y and y for x

$x=\frac{y}{y+20}$

Isolate the variable y

$x(y+20)=y$

$xy+20x=y$

$y-xy=20x$

$y(1-x)=20x$

$y=20x/(1-x)$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=20x/(1-x)$

$\frac{20x}{1-x}\neq \frac{20x}{x-1}$

therefore

f(x) and g(x) is not a pair of inverse functions

7 0

2 years ago

Read 2 more answers

Write the following expression as a function of a positive acute angle. tan 245

weeeeeb [17]

Answer:

I think it’s A, Good luck!

Step-by-step explanation:

6 0

2 years ago

a local little League has a total of 60 players of whom 20%are left handed .how many left handed players are there?

valentinak56 [21]

Answer:

Step-by-step explanation:

left handed players : 20% of 60

turn ur percent to a decimal...." of " means multiply

0.20 * 60 = 12 are left handed

7 0

3 years ago

Read 2 more answers

Describe how to transform the graph of f(x) = x2 to obtain the graph of the related function g(x).

olga55 [171]

9514 1404 393

Answer:

left 1 unit
down 2 units

Step-by-step explanation:

The transformation g(x) = f(x -h) +k is a translation of f(x) to the right by h units and up k units.

1. h = -1, so the graph of g(x) is the graph of f(x) shifted left 1 unit. (blue)

2. k = -2, so the graph of g(x) is the graph of f(x) shifted down 2 units. (green)

6 0

2 years ago

If a solution has 24g of sugar in 130ml of water, what is its concentration?

Jobisdone [24]

Answer: concentration = 15.58%

Step-by-step explanation:

Given: mass of sugar = 24 g = 24 ml [ ∵ 1 g = 1 ml]

Volume of solution = Quantity of water + quantity of solute

= 130 +24 ml

= 154 ml

Concentration = $\dfrac{mass\ of\ solute}{Volume\ of\ solution}\times100$

$=\dfrac{24}{154}\times 100\\\\\approx15.58\%$

Hence, the concentration =15.58%

3 0

2 years ago