What is the correct decimal form of 12%

If APQR - ASTU, which statement must be true?

pashok25 [27]

The answer is C since the sides are congruent

3 0

2 years ago

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

3 years ago

Read 2 more answers

A high school band program sold a total of 350 tickets for a jazz concert. Student tickets were $5 each and general admission ti

dmitriy555 [2]

Answer:

look at picture

Step-by-step explanation:

x: student tickets

y: general tickets

7 0

4 years ago

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of ce

ExtremeBDS [4]

Answer:

a) Poisson probability distribution

b) The probability of no faulty cell phones will be produced tomorrow is 0.1653

c) The probability of 3 or more faulty cell phones were produced in today's run is 0.2694

Step-by-step explanation:

Poisson distribution is used for independent events which occur at a constant rate within a given interval of time

The Poisson probability distribution formula is P(x; μ) = (e^-μ) (μ^x) / x! where

x is the actual number of successes that result from the experiment

e is approximately equal to 2.71828

μ is the mean of the distribution

The number of faulty cell phones in a production run of cell phones is usually small and that the quality of one day's run seems to have no bearing on the next day

That means the probability of finding faulty phones in first day not depend on finding another days

Then the model might you use to model the number of faulty cell phones produced in one day is Poisson probability distribution

a) Poisson probability distribution

∵ The mean number of faulty cell phones is 1.8 per day

∴ μ = 1.8

∵ There is no faulty cell phones will be produced tomorrow

∴ x = 0

- Use the formula above to find the probability

∵ P(0 ; 1.8) = (e^-1.8) (1.8^0) / 0!

- Remember 1.8^0 = 1 and 0! = 1

∴ P(0 ; 1.8) = (e^-1.8)(1)/(1)

∴ P(0 ; 1.8) = 0.1653

b) The probability of no faulty cell phones will be produced tomorrow is 0.1653

∵ The mean number of faulty cell phones is 1.8 per day

∴ μ = 1.8

∵ There is 3 or more faulty cell phones were produced in today's run

∴ x ≥ 3

∵ P(x ≥ 3) = 1 - P(x = 0) - P(x = 1) - P(x = 2)

- Let us find P(1 ; 1.8) and P(2 ; 1.8)

∵ P(1 ; 1.8) = (e^-1.8) (1.8^1) / 1!

∵ 1.8^1 = 1.8

∵ 1! = 1

∴ P(1 ; 1.8) = (e^-1.8)(1.8)/(1)

∴ P(1 ; 1.8) = 0.2975

∵ P(2 ; 1.8) = (e^-1.8) (1.8^2) / 2!

∵ 1.8^2 = 3.24

∵ 2! = 2

∴ P(2 ; 1.8) = (e^-1.8)(3.24)/(2)

∴ P(2 ; 1.8) = 0.2678

Substitute them in the rule above

∵ P(x ≥ 3 ; 1.8) = 1 - 0.1653 - 0.2975 - 0.2678

∴ P(x ≥ 3 ; 1.8) = 0.2694

c) The probability of 3 or more faulty cell phones were produced in today's run is 0.2694

7 0

3 years ago

Which graph has a rate of change oqual to in the interval botwoon 0 and 3 on the x-axis?

son4ous [18]

Answer:

what

Step-by-step explanation:

8 0

3 years ago