A yearly rent estimate of a building is Rs 5800. Of this 10% is exempt from tax for purpose of
repairs etc, and the remaining rent is liable to 10 ½% general tax,7 ¼% water tax, and 2 ¼ for
cleaning charges. What is the net monthly income from the building?

Answer:

Step-by-step explanation:

14

Answer:

The formula for the volume of a cone is:

V = (1/3)πr^2h

where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cone is 144π cubic inches and the height is 12 inches. So we can plug these values into the formula and solve for r:

144π = (1/3)πr^2(12)

144 = 4r^2

r^2 = 36

r = ±6

Since a negative radius doesn't make sense in this context, we can discard the negative solution and conclude that the radius of the cone is 6 inches.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}[/tex]

Answer:

6:20

Step-by-step explanation:

The time 50 minutes before 07:10 will be 06:20.

Step-by-step explanation:

The perimeter of a rectangle = 2L + 2W = 98.

W is 15 less than L, or L - 15 = W, or W + 15 = L

Substituting from Eq 2 back into Eq 1,

2(W+15) + 2W = 98

2W + 30 + 2W = 98

4W + 30 = 98

4W = 68

W = 17

Recalling L = W+15

L = 17 + 15 = 32

Now to check our solution

Does the perimeter = 98?

2(32) + 2(17) = ??

64 + 34 = 98

Done!

Here's the complete chart:

Month  Balance Interest Payment New Balance

0  $1,357.56     -            -          $1,357.56

1 $1,383.54 $23.98 $150 $1,257.52

2 $1,409.62 $26.08 $150 $1,266.06

3 $1,435.81 $27.19 $150 $1,473.61

Percent is a way of expressing a fraction or a ratio as a number out of 100. The word "percent" comes from the Latin per centum, which means "per hundred." Percentages are commonly used in many areas, including finance, economics, and statistics. For instance, interest rates, inflation rates, and stock market returns are often expressed as percentages. In addition, percentages are used to calculate discounts, markups, and taxes.

Here,

To calculate the new balance by the end of the 3rd month, we need to use the formula for the balance after n months with monthly payments:

B(n) = (1 + r)ⁿ * B(0) - (PMT/r) * [(1 + r)ⁿ-1]

where B(0) is the initial balance, r is the monthly interest rate, PMT is the monthly payment, and n is the number of months.

In this case, we have:

B(0) = $1357.56

r = 1.7% per month = 0.017

PMT = $150

n = 3 months

Plugging these values into the formula, we get:

B(3) = (1 + 0.017)³ * $1357.56 - ($150/0.017) * [(1 + 0.017)³ - 1]

= $1473.61

Therefore, the new balance by the end of the 3rd month is $1473.61.

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On a coordinate plane,

The point (-3,-1) lies in the III Quadrant

The point (3,-1) lies in the IV Quadrant

Both the points are 3cms away from the y axis.

They have a common ordinate.

Answer:

$30

Step-by-step explanation:

x = original price

0.8x = 24

8x = 240

x = 30

Answer:

Step-by-step explanation:

volume of cylinder=πr²h

=3.14×(0.5)²×2

≈1.57 cm³

The number z such that 44% of all observations from a standard Normal distribution are greater than z is given as follows:

z = 0.15.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, we want the 100 - 44 = 56th percentile, which is Z with a p-value of 0.56, so Z = 0.15.

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Answer: 1/9, or 3^-2

Step-by-step explanation: -3^-2 is equivalent to 1/-3^2, which is 1/9

Answer:

-11

Step-by-step explanation:

[tex]1. \: - 9 - 2 \\ 2. \: - 11[/tex]

Using product and power rule to find the derivative f'(-1) of the given function is; f'(-1) = -17

The power rule is used when finding the derivative of a variable base, raised to a fixed power. However, the product rule allows us to find the derivative of a function that is defined as the product of another two (or more) functions

We are given;

f(x) = x⁸h(x)

h(-1) = 4

h'(-1) = 7

Finding the derivative of f(x) gives;

f '(x) = 8x⁷h(x) + x⁸h'(x)

Thus, f'(-1) gives us;

f'(-1) = 8(-1)⁷(4) + (-1)⁸(7)

= -24 + 7

= -17

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Answer:

The ball with diameter 8 ( radius 4) is
8 times bigger
than the ball with diameter 4 (radius  2)

Step-by-step explanation:

We will use volume as an indication of bigger and smaller

For a spherical ball, volume

[tex]V = \dfrac{4}{3}\pi r^3\\[/tex]

where r is the radius

Since 4/3 and π are constants we can rewrite this equation as
V = k r³

where k = 4/3 x π

We see that the greater the radius, the greater the volume

First note that diameter = r/2
So ball with diameter 8 has radius 8/2 = 4

and ball with diameter 4 has radius 4/2 = 2

Volume of ball with radius 4 = V₄ = k x 4³ = 64k

Volume of ball with radius 2 = V₂ = k x 2³ = 8k

V₄/V₂ =64k/8k = 8

So the ball with radius 4 (diameter 8) is 8 times bigger than the ball with radius 2(diameter 4)

---------------------------------------------------------------------------------------------------------

Another way to understand this is that the diameter of the larger ball is 2 x the diameter of the smaller ball.

Hence the radius of the larger ball is also 2 x the radius of the smaller ball

Therefore larger to smaller volume = 2³ =8

The solution to the division problem shown is 2x² + x + 2 + 1/(4x+3)

Polynomial expression are expression that has a leading degree of 3. Given the expression below:

(8x³+10x² +15x+10)/(4x+3)

We can use polynomial long division to divide (8x³+10x²+15x+10) by (4x+3):

      2x² + x + 2    

------------------------

4x+3| 8x³ + 10x² + 15x + 10

8x³ + 6x²

-----------

4x² + 15x

4x² + 3x

---------

12x + 10

12x + 9

--------

1

Therefore, the quotient is 2x² + x + 2 and the remainder is 1. So:

(8x³+10x²+15x+10)/(4x+3) = 2x² + x + 2 + 1/(4x+3)

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The translation applied to get the graph of g(x) from the graph of f(x) is of 3 units up.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The functions for this problem are given as follows:

Meaning that the rule is:

g(x) = f(x) + 3.

Meaning that it is a translation of 3 units up.

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The slope of function A is 0, and the slope of function B between f(0) and f(1) is 1, between f(1) and f(2) is 3, and between f(2) and f(3) is 5.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

Function A: y=4-5

The function A is a constant function. The y-value is always 4-5=-1, regardless of the x-value. Therefore, the slope of function A is zero.

Function B:

x y

0 0

1 1

2 4

3 9

The slope or rate of change of function B between two points is calculated by dividing the change in y-values by the change in x-values.

The slope of function B between f(0) and f(1) is:

slope = (change in y) / (change in x) = (1 - 0) / (1 - 0) = 1

The slope of function B between f(1) and f(2) is:

slope = (change in y) / (change in x) = (4 - 1) / (2 - 1) = 3

The slope of function B between f(2) and f(3) is:

slope = (change in y) / (change in x) = (9 - 4) / (3 - 2) = 5

Therefore, the slope of function A is 0, and the slope of function B between f(0) and f(1) is 1, between f(1) and f(2) is 3, and between f(2) and f(3) is 5.

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To write with positive exponents, we can use the rule that states:

x^(-n) = 1/x^n

Applying this rule to the expression x^(-(1/4)), we get:

x^(-(1/4)) = 1/x^(1/4)

So, the expression written with positive exponents is 1/x^(1/4).

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Answer: To find the range of the quadratic function y = x^2 - 8x + 12, we can use different methods, but one way is to complete the square and express the function in vertex form.

y = x^2 - 8x + 12 (given function)

y = (x - 4)^2 - 4 (completing the square)

The vertex of the parabola represented by this function is at the point (4,-4). This means that the minimum value of the function occurs when x=4 and y=-4. Since the parabola opens upward, this minimum value is also the lowest point of the parabola and is the lower bound of the range.

Thus, the range of the function is all real numbers greater than or equal to -4, i.e., the range is (-4, infinity).

Another way to see this is to note that the coefficient of x^2 in the given function is positive, which means that the parabola opens upward and has a minimum value. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=40=180

x=180-40

x=140

To find the sale price of a bottle of perfume after a 13.4% discount, we need to first calculate the amount of the discount, and then subtract that amount from the original price.

The discount rate is 13.4%, which can be written as a decimal as 0.134. To calculate the amount of the discount, we can multiply the original price by the decimal equivalent of the discount rate:

Discount amount = 0.134 x $72.45

Discount amount = $9.72

This means that the discount on the bottle of perfume is $9.72. To find the sale price of the perfume, we can subtract this amount from the original price:

Sale price = $72.45 - $9.72

Sale price = $62.73

Therefore, the sale price of the bottle of perfume is $62.73. This is the amount that customers would need to pay during the clearance sale, after the 13.4% discount has been applied.

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Answer:

rewrite 0,26 as a proper fraction (in the format of a over b) show all steps

The value of x for the given equation is - 3.11.

The two most well-known groups of equations in algebra are the linear equations and the polynomial equations. P(x) = 0 can be used to represent polynomial equations with a single variable. P is a polynomial, and axe + b = 0 is the standard form for linear equations. Here, the parameters a and b. To solve these equations, we can use geometric or computational techniques from linear algebra or mathematical analysis. There are several sorts of equations as well, including: linear algebra, quadratic formulas, cube-based equations, etc.

Given that, the equation is x = 8/9 - 4.

Take the LCM.

x = 8/9 - 36/9

x = (8 - 36) / 9

x = - 3.11

Hence, the value of x for the given equation is - 3.11.

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The dimensions of the rectangle are length 2 and width 8. The solution has been obtained by using the concept of derivatives.

What is a derivative?

The derivative of a quantity in mathematics refers to the variable's instantaneous rate of change with respect to another.

We are given y = 12 - x² which is an even function. This means that the rectangle form will also be even at the origin.

We know that the

Area of rectangle = length × width

So, here length = 2x and width = y

Using the formula, we get

⇒Area (A) = 2x (12 - x²)

⇒A = 24x - 2x³

Now, on differentiating the area, we get the derivative as

A’ = 24 - 6x²

We know that the area will be largest when A’ = 0

On substituting, we get

⇒ 24 - 6x² = 0

⇒ 6x² = 24

⇒ x² = 4

⇒ x = 2

Now, on substituting this value in y = 12 - x², we get

⇒ y = 12 - 4

⇒ y = 8

Hence, the dimensions of the rectangle are length 2 and width 8.

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Based on the information given, it is likely that Sunee used a non-proportional scaling method to enlarge her drawing of the cat, which caused the distortion in the final image.

Non-proportional scaling methods change the size of an object in one dimension more than in another, leading to a stretched or squashed appearance. This is in contrast to proportional scaling methods, which increase or decrease the size of an object in all dimensions by the same factor, resulting in an image that retains its original proportions.

Therefore, the true statement about the transformation applied to Sunee's drawing of the cat is that a non-proportional scaling method was used, resulting in a distorted image.

Answer:

(0,4)

Caleb is correct, there is one solution.

Step-by-step explanation:

Answer: 5 times to play ring toss game.

Step-by-step explanation: 15[tex]/[/tex]3=5

Answer:

The equation given is in point-slope form, where the point (4,8) is on the line and the slope is undefined.

To solve for y, we can first isolate the term with y on one side of the equation:

y - 8 = (1/0)(x - 4)

Since 1/0 is undefined, this equation is not solvable for y using algebraic methods.

The graph of this equation would be a vertical line passing through the point (4,8), since the slope is undefined.

Step-by-step explanation:

We can write the solution set for the given system of equations as -

{x} = {EC/B - F}/{D - EA/B}

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is use the diagrams below, write and solve two simultaneous equations to work out the values of {x} and {y}.

Since the diagram is not given, we can learn how to solve the given set of simultaneous equations.

Assume that we have the simultaneous equations as -

Ax + By + C =0

Dx + Ey + F = 0

Now, we can write -

Ax + By + C =0

By = - C - Ax

By = - (C + Ax)

{y} = - (C + Ax)/B

Putting the value in the equation -

Dx + Ey + F = 0

Dx - E(C + Ax)/B + F = 0

Dx - EC/B - (EA/B)x + F = 0

x{D - EA/B} - EC/B + F  = 0

x{D - EA/B} = {EC/B - F}

{x} = {EC/B - F}/{D - EA/B}

We can write {y} as -

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

Therefore, we can write the solution set for the given system of equations as -

{x} = {EC/B - F}/{D - EA/B}

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

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Step-by-step explanation:

.......................

The given equivalence relation on the real plane R2 is (x, y) ∼ (a, b) if and only if x^2 + y^2 = a^2 + b^2.

The equivalence class of a point (a, b) is the set of all points (x, y) in R2 such that x^2 + y^2 = a^2 + b^2. In other words, it is the set of all points that are a fixed distance from (a, b), namely the square root of (a^2 + b^2). This is a circle centered at (a, b) with radius equal to the square root of (a^2 + b^2).

The quotient set is the set of all equivalence classes under this relation. In other words, it is the set of all circles centered at different points in R2 with different radii. Each circle represents an equivalence class, and all points within a given circle belong to the same equivalence class.

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