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3 years ago

What is the range of the exponential function shown below?

Mathematics

1 answer:

Alika [10]3 years ago

3 0

Answer:

Option B $y> 0$

Step-by-step explanation:

we have

$f(x)=9(2^{x})$

This is a exponential function of the form

$y=a(b^{x})$

where

a is the initial value

b is the base

r is the rate

b=1+r

In this problem

a=9

b=2

r=2-1=1=100%

The domain for x is the interval ------> (-∞,∞)

All real real numbers

The range is the interval -----> (0,∞)

$y> 0$

All real numbers greater than zero

see the attached figure to better understand the problem

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

(a) The books in any order

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

(b) The mathematics book, not together

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

(c) The novels must be together and the chemistry books, together

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

(d) The mathematics must be together and the chemistry books, not together

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

3 years ago

I need help plz, i dont understand it, its english class, i dont like english class

TiliK225 [7]

The first one is the answer. Hope i helped you, have a blessed day :)

7 0

3 years ago

Read 2 more answers

If the area of a circle is 58 square feet, find the circumference

Blizzard [7]

Answer:

C≈27 feet

Step-by-step explanation:

A=πr²

A/π=r²

√A/π =r or –√A/π=r (refused)

then r =√(A/π) =√(58/π) =4.297829403 feet

C=2πr=2π(4.297829403)=27.00405856≈27 feet

7 0

3 years ago

Read 2 more answers

Helllllppppp plzzzzzzzzzzz

PtichkaEL [24]

Answer:

The answer is C.

Step-by-step explanation:

2x+1+x+4

3x+5

8 0

3 years ago

What is 7x + 6x = ?

viva [34]

Answer:

Step-by-step explanation:

Two ways to solve

1.) Expand each term in the equation

7x = x · x · x · x · x · x · x

6x = x · x · x · x · x · x

Count all the x’s ⇒ There are 13 x’s ⇒ 13x

2.) Add the coefficients

7 + 6 = 13
7x + 6x = 13x

Hence,

Answer = 13x

8 0

3 years ago