a) The monthly basic salary of the married Chief of Army Staffs (COAS) General is Rs 79,200 with Rs 2,000 dearness allowance. He gets Dashain allowance which is equivalent to his basic salary of one month. He contributes 10% of his basic salary in Employee's Provident Fund (EPF) and he pays Rs 50,000 as the premium of his life insurance. Given that 1% social security tax is levied upon the income of Rs 6,00,000, 10% and 20% taxes are levied on the next incomes of Rs 2,00,000 and up to Rs 3,00,000 respectively. Answer the following questions. What is his monthly basic salary? (ii) Find his taxable income. (iii) Find the total income tax paid by him.​

Answer:

Step-by-step explanation:

Consistent Independent = exactly ONE solution

Consistent Dependent = INFINITELY many solutions

Inconsistent = NO solution

Answer:

M = $2.5; V = $5

Step-by-step explanation:

We need to set up a system of equations to find the price for both movies (M) and video games (V).

We can use 2M + 5V = 30 and 8M + 3V = 35

We can use elimination:

[tex]-4(2m+5v=30)\\8m+3v=35\\\\-8m - 20v = -120\\8m+3v=35\\-17v=-85\\v=5\\\\2m+5(5)=30\\2m+25=30\\2m=5\\m=5/2 ;m=2.5[/tex]

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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You are expected to lose $ 10 on an average per game

Probability of sum of 7 = 6 / 36

Probability of sum of 7 = 1 / 6

Amount won per game = (1 / 6) × 90

Amount won per game = $ 15

Probability of sum 6 or 8 = 10 / 36

Probability of sum 6 or 8 = 5 / 18

Amount lose per game = (5 / 18) × 90

Amount lose per game = $ 25

Expected earnings = Amount won per game - Amount lose per game

Expected earnings = 15 - 25

Expected earnings = -$ 10

Thus, you are expected to lose $ 10 on an average per game

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The ratio between 40,000 and 200 is 200 : 1

The numbers are given as:

40,000 and 200

Express as ratio

Ratio = 40000 : 200

Divide each number by 200

Ratio = 200 : 1

Hence, the ratio between 40,000 and 200 is 200 : 1

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Answer: 77 degrees

mLON is the total angle. mLOM is part of the angle, and is 55 degrees. To find the missing degree, subtract the part we know from the part the whole. In this case, subtract 55 from 132. mMON is 77 degrees.

Answer:

1) y > x² + 4x - 5, y > x + 5

2) Rational

Step-by-step explanation:

For a parabola, if the shade is inside the curve then the value of y will be greater or equal to:

For a line, if the shade is above it then the value of y will be greater or equal to:

Therefore, since parabola doesn't have solid curve (--- graph) then the inequality is ">"

Therefore, the inequality for parabola is y > x² + 4x - 5

For a line, it does not have solid graph so the inequality is ">"

Therefore, the inequality for line is y > x + 5

-----------

The graph of function describes the shape of rational function. It cannot be exponential as exponential only has one curve. It cannot be logarithm  for same reason as exponential. It cannot be polynomial as polynomial is continuous function but the graph is discontinuous at specific point x = 0.

That being said, all choices except rational are all continuous function by default but rational function isn't and since the graph is discontinuous then we can say that it's rational function.

The resulting equation will represent a line whose slope is 1/2 times the slope of the line

The equation of the line is given as:

y = 3x/a + 5

The constant a is a positive constant.

So, when the value of a in the equation is doubled, we have:

y = 3x/2a + 5

A linear equation is represented as

y = mx + b

Where m represents the slope.

So, we have:

m1 = 3/a

m2 = 3/2a

Substitute m1 = 3/a in m2 = 3/2a

m2 = 1/2 * m1

Hence, the resulting equation will represent a line whose slope is 1/2 times the slope of the line

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The selling price of an equipment costing $150.00 with 35% markup is $202.50

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given that the mark up is 35%, hence:

Markup = [(selling price - cost price)/cost price] * 100%

Substituting:

$202.50

Selling price = $202.50

The selling price of an equipment costing $150.00 with 35% markup is $202.50

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Answer:

[tex]\sqrt{65}[/tex], so [?] = [65]

Step-by-step explanation:

This is a classic Pythagorean Theorem problem :)

We are given a right triangle with 2 sides, so all we have to do is plug it into the formula a² + b² = c², or in simple terms: the square of one side plus the square of the other equals the square of the hypotenuse.

line h is going to bisect the diameter of the circle (8) so one side will be 4. We're given 9 as our hypotenuse, so:

(4)² + (h)² = (9)².

16 + h² = 81

h² = 81 - 16, h² = 65, h = [tex]\sqrt{65}[/tex].

Answer:

perpendicular

Step-by-step explanation:

We'll find the slope of both lines and see what it tells us.

If the slopes are the same, the lines are parallel. If the slopes are opposite sign and flipped (negative reciprocals) then they are perpendicular.

The slope is y-Y on top of a fraction and x-X on the bottom.

Slope of AB:

m = 2-1 / -3 -5

= 1/-8 = -1/8

Slope of CD:

m = 7- -1 / 2-1

= 8/1 = 8

Since the slopes are -1/8 and 8, the lines are perpendicular, because they are opposite sign and flipped (negative reciprocals)

Applying the angles of intersecting secants theorem, the measure of arc XY is: 32°.

According to the angles of intersecting secants theorem, m∠XZY = 1/2(arc VW - arc XY).

Plug in the values:

39 = 1/2(110 - arc XY)

2(39) = 110 - arc XY

78 = 110 - arc XY

78 - 110 = - arc XY

-32 = - arc XY

Arc XY = 32°

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The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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Answer:

55

Step-by-step explanation:

61.621 rounded to the nearest whole number is 62. We know this by looking at the whole number "61" and rounding its last digit by the digit to the right of it, depending if its <5 or >5. In this case, the right ones digit is "6", being greater than 5 means we can round 61.621 to 62.

The same applies to 7.173, given that "1" is less than 5, we don't round down (because we are rounding up), instead we replace remaining digits with 0, leaving us with 7.

To find the difference means to subtract;

62-7 = 55.

The conversion is given as 1, 760 feet per second

We need to convert 20miles per hour to feet per second

First, we should convert miles to feet

1 mile = 5280 feet

Then,

20 miles = x

Cross multiply

20 × 5280 = x

x = 105, 600

Per hour = I hour = 60 seconds

To find the conversion, we divided the conversion to feet by that of the time

= 105, 600/60

= 1, 760 feet per second

Thus, the conversion is given as 1, 760 feet per second

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Answer: 4n - 7 = 21, n = 7

Step-by-step explanation:

A difference indicates subtraction of two terms. Four times a number indicates that a number of any value has to be multiplied by 4.

Hence, the equation that is represented by the question is

[tex]4x - 7 = 21[/tex]

We can also solve this equation (i.e., find the value of x that makes this equation true).

Adding 7 to both sides, we get

[tex]4x - 7 + 7 = 21 + 7[/tex]

Since the -7 and 7 add to 0, the equation becomes

[tex]4x = 28[/tex]

To get x by itself, we can divide both sides by 4, making the equation

[tex]x=7[/tex]

Hence, x must be 7 to make the equation true, or 7 is a solution to the equation.

The general-form equation of the circle is:

A. [tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

This circle has center at (4,4), hence:

[tex]x_0 = 4, y_0 = 4[/tex]

The radius is of 3 units(distance of A and B from the center), hence the equation is:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

[tex](x - 4)^2 + (y - 4)^2 = 3^2[/tex]

We expand the equation to find the general form, hence:

[tex]x^2 - 8x + 16 + y^2 - 8y + 16 = 9[/tex]

[tex]x^2 + y^2 - 8x - 8y + 23 = 0[/tex]

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The answer is 14.

First, we need to find X using the first statement.

Now, we have to substitute this in the required expression.

The kind of symmetry that would be shown in the design is an axial symmetry.

It should be noted that an axial symmetry simply means a symmetry around an axis.

In this case, the capital letter E has an acid of symmetry. Therefore, an axial symmetry is appropriate.

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The correct statement is Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A.

Given that in a coordinate plane, triangle A is reflected across the x-axis to form triangle B. Triangle A is rotated to form triangle C.

From the given figure , it says that Triangle B is a reflection of triangle An across the x-pivot. Triangle C isn't a reflection of triangle A" in light of the fact that Triangle A is in the main quadrant and its appearance with x-axis makes the triangle-B in the fourth quadrant and the triangle C which is in second quadrant can not be a reflection and annot be a rotation of triangle-A. Triangle C is drawn by taking firstly the reflection of triangle A and then rotate on the same place and increased x+3 units in above direction.

Hence, the statement correctly describes the diagram is "Triangle B is a reflection of triangle A across the x-axis. Triangle C isn't a reflection of triangle A".

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Answer:

A. Triangle B is a reflection of triangle A across the x-axis. Triangle C is not a reflection of triangle A..

Step-by-step explanation:

goodluck

Considering the definition of an equation and the way to solve it, 43 female contestants have signed up to compete.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.

The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.

To solve an equation, keep in mind:

Being "m" the number of male contestants, and knowing that:

the equation in this case is:

m + (m+36) = 50

Solving:

m + m = 50 - 36

2m= 14

m= 14 ÷ 2

m= 7

Since there are 36 more female contestants than male contestants, then m +36= 7 + 36= 43

Finally, 43 female contestants have signed up to compete.

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Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]

Put f(x) = y

[tex]\displaystyle y=\frac{x}{5} -2[/tex]

Swap x and y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Now, solve for y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Add 2 to both sides

[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]

Multiply 5 to both sides

[tex]5(x+2)=y[/tex]

Distribute

[tex]5x + 10 =y[/tex]

Put y = f⁻¹(x)

[tex]\boxed{f^{-1}(x)=5x+10}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

the third option, x = –3, –1, 3

Step-by-step explanation:

Answer:

lcm of 3,6,9 is 18

The y-intercept of this function represents C. the minimum amount of electricity consumed

The function is given as:

y = 0.503x + 3.31

The y-intercept of a function represents the minimum or the initial value of the function

This means that the y-intercept of this function represents C. the minimum amount of electricity consumed

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The linear equations are given as follows:

A linear function is modeled by:

y = mx + b

In which:

For diagonal AC, the line contains points (-3,3) and (3,-3), hence the line is:

y = -x.

In standard form:

[tex]x + y = 0, -3 \leq x \leq 3[/tex].

For diagonal BD, the line contains points (3,3) and (-3,-3), hence the line is:

y = x.

In standard form:

[tex]x - y = 0, -3 \leq x \leq 3[/tex].

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Answer is (n + 3) + (n - 7)

Simplified to 2n - 4

Using “n” for number

The solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

The given equation is:

[tex]3p^2-9p=6[/tex]

This can be re-written as:

[tex]3p^2-9p-6=0[/tex]

Solve for p by factorization

[tex]3p^2-3p-6p+6=0\\\\3p(p-1)-6(p-1)=0\\\\(3p-6)(p-1)=0[/tex]

Equate each of the factors to zero

3p - 6 = 0

3p = 6

p = 6/3

p = 2

p - 1 = 0

p = 1

Therefore, the solution to the equation [tex]3p^2-9p-6=0[/tex] are p = 1, p = 2

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