1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
matrenka [14]
2 years ago
6

Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one’s annual income to

the average (arithmetic mean) of 100 units of Country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in Country R’s currency, for a person in that country whose annual income is I ?
A. 50 + I/200
B. 50 + 3I/100
C. 50 + I/40
D. 100 + I/50
E. 100 + 3I/100
Mathematics
1 answer:
Vedmedyk [2.9K]2 years ago
6 0

Answer:

Option C)

50 + \dfrac{I}{40}          

Step-by-step explanation:

We are given the following in the question:

I is the annual income of a person in a country R

2 percent of one’s annual income =

\dfrac{2}{100}\times I = 0.02I

1 percent of one’s annual income =

\dfrac{1}{100}\times I = 0.01I

Average of  100 units of Country R’s currency and 1 percent of one’s annual income.

=\dfrac{0.01I + 100}{2}

Income tax =

2 percent of one’s annual income + Average of  100 units of Country R’s currency and 1 percent of one’s annual income.

= 0.02I + \dfrac{100+0.01I}{2}\\\\=50 + \dfrac{0.04I + 0.01I}{2}\\\\=50 + \dfrac{0.05I}{2}\\\\= 50 + \dfrac{I}{40}

Thus, income tax is given by

Option C)

50 + \dfrac{I}{40}

You might be interested in
Explain how to use multiplication to find
Sindrei [870]

A fraction x/y is a ratio between two numbers x and y.

The ratio is preserved if both x and y are scaled up or down by the same number n.

This means you can obtain any fraction equivalent to x/y by multiplying both x and y by n, i.e. (n*x)/(n*y).

Then we have 1/4 = (2*1)/(2*4) = 2/8, for example.

5 0
3 years ago
3. The values for p and q represent the equilibrium point. As related to the troupe's
svp [43]

Answer: The equilibrium point represents the raising or lowering the price in response to changes in the supply or demand.

If the price of a good is above equilibrium, this means that the quantity of the good supplied exceeds the quantity of the good demanded.

If the quantity is below the equilibrium point, it will create a shortage. because the quantity supplied is less than quantity demanded.

Hope this helps!

Step-by-step explanation:

5 0
2 years ago
What is the approximate side length of a square rug with an area of 64ft^2
DochEvi [55]
It could be 8ft, if the area is 64.
8 0
2 years ago
EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =
Taya2010 [7]

Answer:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

\bigtriangledown  f=\lambda \bigtriangledown  g

for some scalar \lambda called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

\bigtriangledown  f=\lambda \bigtriangledown  g+\mu \bigtriangledown  h

The gradient of f is

\bigtriangledown  f=

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in x,y,z,\lambda,\mu.

We have

f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0

Let's compute the partial derivatives

f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0

The Lagrange condition leads to

1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)

Operating and simplifying

1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11

Replacing the value of \lambda in the two first equations, we get

1=11+2x\mu\\2=-11 +2y\mu

From the first equation

\displaystyle 2\mu=\frac{-10}{x}

Replacing into the second

\displaystyle 13=y\frac{-10}{x}

Or, equivalently

13x=-10y

Squaring

169x^2=100y^2

To solve, we use the restriction h

x^2 + y^2 = 1

Multiplying by 100

100x^2 + 100y^2 = 100

Replacing the above condition

100x^2 + 169x^2 = 100

Solving for x

\displaystyle x=\pm \frac{10}{\sqrt{269}}

We compute the values of y by solving

13x=-10y

\displaystyle y=-\frac{13x}{10}

For

\displaystyle x= \frac{10}{\sqrt{269}}

\displaystyle y= -\frac{13}{\sqrt{269}}

And for

\displaystyle x= -\frac{10}{\sqrt{269}}

\displaystyle y= \frac{13}{\sqrt{269}}

Finally, we get z using the other restriction

x - y + z = 1

Or:

z = 1-x+y

The first solution yields to

\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}

\displaystyle z = \frac{-23\sqrt{269}+269}{269}

And the second solution gives us

\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}

\displaystyle z = \frac{23\sqrt{269}+269}{269}

Complete first solution:

\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0
3 years ago
A group of 5 men and 5 women are applying for a job at a local company. Each of the 10 job candidates has the same chance of rec
Zielflug [23.3K]

Answer: 1/4

Explanation: Because there is a 1/2 chance that a female will get the first job, and a half chance that a lady will get a second job. So (1/2)*(1/2)=(1/4)

7 0
2 years ago
Other questions:
  • Paula spent 3/8 on her allowance on clothes and 1/6 on entertainment. What fraction of her allowance did she spend on other item
    6·2 answers
  • I NEED THIS ASAP WHOEVER GIVES ME THE CORRECT ANSWER GETS BRAINLEST!!! The diagram below represents which percent?
    8·2 answers
  • Which of the following represents 3x 5/7
    15·2 answers
  • This one also I needed help on
    8·1 answer
  • After Rockwell farms installed an irrigation system, their yield per acre of corn rose 15% from 150 bushels per acre. what was t
    15·1 answer
  • PLEASE.HELP. 3. In how many years will Mr. Nunez be twice as old as Mr. Springstein?
    10·1 answer
  • How do I solve this?​
    6·1 answer
  • Blank minus 1/2 equals 3/4​
    12·1 answer
  • A meteor crater is 4000 feet in diameter. approximate the distance around the crater.
    9·1 answer
  • Which expressions are equivalent to the given expression.<br> y^-8y^3x^0x^-2​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!