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3 years ago

Find the number of ways to purchase 5 different kinds of juices from a selection of 10 juices

1 answer:

8 0

Formula for combinations:
(n!)/(r!(n-r)!)

For you, this is:
10!/(5!(10-5)!) = 10!/5!5! = (10•9•8•7•6•5•4•3•2)/(5•4•3•2)(5•4•3•2) = (10•9•8•7•6)/(5•4•3•2) = 30240/120=252 different ways.

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The function h(x)=4/3x-1 represents the composite h(x)=f(g(x)).if f(x)=2x-1,what is g(x)

Hunter-Best [27]

Answer:

$g( x) = \frac{2}{3}x$

Step-by-step explanation:

Given:

Composite Function:

$h( x)=f( g( x))$

Also,

$h( x)=\frac{4}{3}x-1$

To find:

$g( x ) = ?$

Solution:

First of all, let us learn about a composite function.

Composite function $f( g( x))$ means to write $g( x)$ in place of $x$ in the function $f( x)$ .

Let $g( x) = y$

So, $f( g( x))$ = $f( y )$ .

Therefore,

$h( x) =f( g( x)) = f( y)$

So, $f( y) = 2y-1$

We have to solve for $y$ in terms of $x$ to find the value of $g(x)$ :

$\Rightarrow \frac{4}{3}x-1 = 2y-1\\\Rightarrow 2y=\frac{4}{3}x\\\Rightarrow y = \frac{2}{3}x$

Hence, the answer is $g( x ) = \frac{2}{3}x$ .

Checking whether the answer is correct or not:

$f( g( x)) = f( \frac{2}{3}x) = 2\times \frac{2}{3}x -1 = \frac{4}{3}x-1$

which is $h( x)$ .

Hence, our answer $g( x ) = \frac{2}{3}x$ is correct.

6 0

3 years ago

Read 2 more answers

If you can could you help with 27-30 please

neonofarm [45]

Answer:

27. 98% of 15 is 14.7 (rounding to the nearest tenth, this would be 15)

28. 250% of 25 is 62.5 (rounding to the nearest tenth, this would be 63)

29. 108% of $50 is $54

30. 75.2% of 130 is 97.76 (this would be 98)

Step-by-step explanation:

3 0

2 years ago

Make both statements true<br>1. {y=x+13<br> {xy=30<br>2. {2l+2w=38<br> {l×w=78

4vir4ik [10]

12345678 M's in my bank account

4 0

3 years ago

Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1,5).

lisov135 [29]

Answer:

Step-by-step explanation:

y=a(x-0)(x-2)

=a(x^2-2x)

=a(x^2-2x+1-1)

or y=a(x-1)^2-a

(1,5) lies on it.

5=a(1-1)^2-a

5=0-a

or a=-5

so y=-5(x-1)^2+5

8 0

2 years ago

A retailer sells volleyball nets for $36 that were acquired at a cost of $16. What percentage is the mark-up?

Marat540 [252]

Answer:

5.76

Step-by-step explanation:

5 0

2 years ago