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sp2606 [1]
3 years ago
12

A salesman's commission rate is 6%. What is the commission from the sale of 36,000 worth of furnaces?

Mathematics
1 answer:
borishaifa [10]3 years ago
6 0

Answer:

2160

Step-by-step explanation:

36000*6/100=2160

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Suppose that f: R --> R is a continuous function such that f(x +y) = f(x)+ f(y) for all x, yER Prove that there exists KeR su
Pachacha [2.7K]
<h2>Answer with explanation:</h2>

It is given that:

f: R → R is a continuous function such that:

f(x+y)=f(x)+f(y)------(1)  ∀  x,y ∈ R

Now, let us assume f(1)=k

Also,

  • f(0)=0

(  Since,

f(0)=f(0+0)

i.e.

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

i.e.

2f(0)-f(0)=0

i.e.

f(0)=0  )

Also,

  • f(2)=f(1+1)

i.e.

f(2)=f(1)+f(1)         ( By using property (1) )

i.e.

f(2)=2f(1)

i.e.

f(2)=2k

  • Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

i.e.

f(m)=f(1)+f(1)+f(1)+.......+f(1) (m times)

i.e.

f(m)=mf(1)

i.e.

f(m)=mk

Now,

f(1)=f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=f(\dfrac{1}{n})+f(\dfrac{1}{n})+....+f(\dfrac{1}{n})\\\\\\i.e.\\\\\\f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=nf(\dfrac{1}{n})=f(1)=k\\\\\\i.e.\\\\\\f(\dfrac{1}{n})=k\cdot \dfrac{1}{n}

Also,

  • when x∈ Q

i.e.  x=\dfrac{p}{q}

Then,

f(\dfrac{p}{q})=f(\dfrac{1}{q})+f(\dfrac{1}{q})+.....+f(\dfrac{1}{q})=pf(\dfrac{1}{q})\\\\i.e.\\\\f(\dfrac{p}{q})=p\dfrac{k}{q}\\\\i.e.\\\\f(\dfrac{p}{q})=k\dfrac{p}{q}\\\\i.e.\\\\f(x)=kx\ for\ all\ x\ belongs\ to\ Q

(

Now, as we know that:

Q is dense in R.

so Э x∈ Q' such that Э a seq belonging to Q such that:

\to x )

Now, we know that: Q'=R

This means that:

Э α ∈ R

such that Э sequence a_n such that:

a_n\ belongs\ to\ Q

and

a_n\to \alpha

f(a_n)=ka_n

( since a_n belongs to Q )

Let f is continuous at x=α

This means that:

f(a_n)\to f(\alpha)\\\\i.e.\\\\k\cdot a_n\to f(\alpha)\\\\Also\\\\k\cdot a_n\to k\alpha

This means that:

f(\alpha)=k\alpha

                       This means that:

                    f(x)=kx for every x∈ R

4 0
2 years ago
Express the distance 48,000,000 meters using scientific notation in meters and then in millimeters
KengaRu [80]

Answer:

Meters:4.8x10 to the 6th power

Millimeters:4.8x 9th power.

Be doin Pearson MathXL

I did 1 today.

8 0
2 years ago
Read 2 more answers
A rectangular prism had a volume of 252 cubic centimeters. The length of the prism is 14 centimeters and the width of the prism
mojhsa [17]
<h2>Answer:</h2>

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. A rectangular prism is a solid whose base is a rectangle. Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

V=L\times W\times H

FOR THE ORIGINAL PRISM WE HAVE THE FOLLOWING DIMENSIONS:

L=14cm \\ \\ W=6cm \\ \\ H=3cm

In fact, the volume is 252cm^3 because:

V=14\times 6\times 3 \therefore V=252cm^3

Now the height of the prism was changed from 3 centimeters to 6 centimeters to create a new rectangular prism, therefore:

FOR THE NEW PRISM WE HAVE THE FOLLOWING DIMENSIONS:

L=14cm \\ \\ W=6cm \\ \\ H=6cm

So the new volume is:

V=14\times 6\times 6 \therefore V=504cm^3

<h3><em>What do we know about the volume of the new prism?</em></h3>

<em>Well, the volume has increased from </em>252cm^3 \ to \ 504cm^3 <em>and since</em> 504=2\times 252 <em>we can say that the new volume is two times the original volume.</em>

8 0
2 years ago
Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function.
marishachu [46]

Answer:

\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18

Step-by-step explanation:

We have been given the function

f(x)=-2x^2+4x^3+3x^2+18

From the rational zeros theorem, we have

\text{Possible rational zeros}=\pm\frac{\text{Factors of constant term}}{\text{Factors of leading coefficient}}

From the given function,

Leading coefficient = 2

Factors of 2 are 1,2

Constant term = 18

Factors of constant term = 1, 2, 3, 6, 9, 18

Hence, we have

\text{Possible rational zeros}=\pm\frac{1,2,3,6,9,18}{1,2}\\\\\text{Possible rational zeros}=\pm1,\pm\frac{1}{2},\pm2,\pm3,\pm\frac{3}{2},\pm6,\pm9,\pm\frac{9}{2},\pm18

6 0
3 years ago
The radius of a sphere is 6 units.
worty [1.4K]

Answer: 5 radius

Step-by-step explanation: because 6 units- 1 radius

7 0
3 years ago
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