The digit in the units place of a 2 digit number is 4 times the digit in the tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.
A. 28B. 32C. 15D. 25

i) The monthly basic salary of the married COAS General is Rs 79,200.

ii. Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480

iii. The total income tax paid by him is Rs 24.8.

His taxable income can be calculated as follows:

Total Monthly Income = Rs 79,200 + Rs 2,000 + Rs 79,200 = Rs 1,60,400

EPF Contribution = 10% of Basic Salary = 10% of Rs 79,200 = Rs 7,920

Life Insurance Premium = Rs 50,000

Total Deductions = EPF Contribution + Life Insurance Premium = Rs 7,920 + Rs 50,000 = Rs 57,920

Taxable Income = Total Monthly Income - Total Deductions

Taxable Income = Rs 1,60,400 - Rs 57,920 = Rs 1,02,480

For income up to Rs 6,00,000: No income tax

For income between Rs 6,00,001 and Rs 8,00,000: 1% of the amount exceeding Rs 6,00,000

Taxable Income in this slab = Rs 2,480 (Rs 1,02,480 - Rs 6,00,000)

Income tax for this slab = 1% of Rs 2,480 = Rs 24.8

Therefore, the total income tax paid by him is Rs 24.8.

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f(x) = x² -3x + 4

A) Replacing with x = 0, we get:

f(0) = 0² -3(0) + 4 = 4

then, the pair (0,4) lies on the graph

B) Replacing with x = 2, we get:

f(2) = 2² -3(2) + 4 = 4 - 6 + 4 = 2

then, the pair (2,5) doesn't lie on the graph

C) Replacing with x = 5, we get:

f(5) = 5² -3(5) + 4 = 25 - 15 + 4 = 14

then, the pair (5,14) lies on the graph

D) Replacing with x = -1, we get:

f(-1) = (-1)² -3(-1) + 4 = 1 + 3 + 4 = 8

then, the pair (-1,6) doesn't lie on the graph

Answer:

D right

Step-by-step explanation:

because 72/-6=-12

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

Answer:

\(x > 2\)

Step-by-step explanation:

\(–1 > –2(x – 4) – 5(4x – 7)\)

\(–1 > –2x + 8 –20x + 35\)

\(–1 > - 22x + 43\)

\( - 1 - 43 > - 22x\)

\( - 44 > - 22x\)

\( \frac{ - 44}{ - 22} < \frac{ - 22x}{ - 22} \)

\(2 < x\)

\(x > 2\)

The base ten numbers to base six for the following is

1. 12 (base 10) =20(base 6)

2.31 (base 10) =51(base 6)

3. 41 (base 10) =105(base 6)

The procedure to find the base ten number to base six

We have to divide the number 12 repeatedly by 6 until the quotient becomes 0.

When 12 is divided by 6 the quotient is 2 and the remainder is 0.

When 2 is divided by 6 the quotient is 0 and the remainder is 2.

Now, Write the remainder from top to bottom.

We get \(12_{10} =20_{6}\)

Similarly we do, 31 and 41

When 31 is divided by 6 the quotient is 5 and the remainder is 1.

When 5 is divided by 6 the quotient is 0 and the remainder is 5.

Now, Write the remainder from top to bottom.

We get \(31_{10} =51_{6}\)

When 41 is divided by 6 the quotient is 6 and the remainder is 5.

When 6 is divided by 6 the quotient is 1 and the remainder is 0.

When 1 is divided by 6 the quotient is 0 and the remainder is 1.

Now, Write the remainder from top to bottom.

We get \(41_{10} =105_{6}\)

Therefore, The base ten numbers to base six for the following is

1. 12 (base 10) =20(base 6)

2.31 (base 10) =51(base 6)

3. 41 (base 10) =105(base 6)

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Answer:

y ≥ 2/15

HOPE THIS HELPS :)

Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.

To answer the questions, we can analyze the given data set.

First, let's count the number of data points that satisfy each condition:

Greater than 28:

There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).

Less than 23:

There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).

Greater than 17.5:

There are 22 data points greater than 17.5.

Between 17.5 and 28:

There are 15 data points between 17.5 and 28.

Now, let's calculate the approximate percentage for each condition:

Percent greater than 28:

The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.

Percentage =\((9 / 24) \times 100 = 37.5\)%.

Percent less than 23:

Approximately, 8 out of 24 data points are less than 23.

Percentage = \((8 / 24) \times 100 = 33.3\)%.

Percent greater than 17.5:

Approximately, 22 out of 24 data points are greater than 17.5.

Percentage = \((22 / 24) \times 100 = 91.7\)%.

Percent between 17.5 and 28:

Approximately, 15 out of 24 data points are between 17.5 and 28.

Percentage = \((15 / 24) \times 100 = 62.5\)%.

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The completely factorized form of the expression q² - 4 is (q + 2)(q - 2).

Given the expression in the question:

q² - 4

To factorize the expression q² - 4 completely, we can use the formula for the difference of squares.

The difference of squares formula states that :

a² - b² can be factored as (a + b)(a - b).

Given that:

q² - 4

Replace 4 with 2²
q² - 2²

From this expression, let a = x and b = 2

a² - b² =  (a + b)(a - b)

q² - 2² = (q + 2)(q - 2)

Therefore, the factored form is (q + 2)(q - 2).

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Answer:

8

Step-by-step explanation:

x+7=15 so x=15-7 which is x=8

Answer:

8 ft

Step-by-step explanation:

The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.

We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.

x + 7 =15

x = 15 - 7

x = 8

Answer:

To write 8000 miles in scientific notation, first find a natural number between 1 and 10.     (8)  

Now, figure out how many decimal places we have to move to the left.

8000.0 --> 8.0000        (Three )

Now, write the number 8 multiplied by 10 to the third power.

( 8 × 10^3 miles )

Step-by-step explanation:

Answer:

$52.00

if you need the difference, its $28.00

Answer:

$52

Step-by-step explanation:

Answer:

about 20 cents

Step-by-step explanation:

#Shop A

Pack of 70pens:-

\(\\ \sf\longmapsto 7(2.30)=16.10\)

#2

Pack of 70

\(\\ \sf\longmapsto 14(1.60)=20.80\)

But you get half price

Difference:-

\(\\ \sf\longmapsto 16.10-10.40=5.70\£\)

Answer:

the first graph since the y intercept is -2 and the line hit -2

Answer:

y = 0.4 x

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 10}\)

Step-by-step explanation:

\(\sf =q + f \div \ e - r\\\\Given \ that \ q = 6 , f = 10, e=2 , r = 1\\\\= 6 + 10 \div 2 -1\\\\According \ to \ DMAS \ rule\\\\We'll \ divide \ first\\\\= 6 + 5 - 1\\\\Now \ go \ from \ left \ to \ right\\\\= 11 - 1 \\\\= 10\\\\This \ is \ the \ required\ answer.\\\\\rule[225]{225}{2}\)

Hope this helped!

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

12

Step-by-step explanation:

Answer:

A is not true

Step-by-step explanation:

Answer:

\(\large \boxed{-40, \ 4, \ -4}\)

Step-by-step explanation:

\(f(x)=-9x+14\)

\(\sf Put \ x \ as \ 6.\)

\(f(6)=-9(6)+14\)

\(f(6)=-54+14\)

\(f(6)=-40\)

\(g(x)=-3x^2\)

\(\sf Put \ g(x) \ as \ -48.\)

\(-48=-3x^2\)

\(\displaystyle \frac{-48}{-3} =\frac{-3x^2 }{-3}\)

\(16=x^2\)

\(\sqrt{16} =\sqrt{x^2 }\)

\(x= \pm 4\)

Answer:

F(6) = -9(6) + 14 = -54 + 14. f(6) = -40

G(x) = -48 / g(x) = -3(16) / g(4) = -48

Step-by-step explanation:

For the first one the drop answer is -40

For the second one its 4 then 16

I think because that whats im seeing but these are the right answers :)

Altitude is in a polygon, a perpendicular segment from a vertex to the opposite side or to the line containing the opposite side.

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle. It is also the side that connects the two other sides, which are called the adjacent and opposite sides.

One of the key properties of the geometric mean is that it is always less than or equal to the arithmetic mean (the regular average) of the same set of numbers, except when all the numbers are equal.

The geometric mean is used in various fields such as finance, economics, biology, and physics. It is particularly useful in situations where values are subject to compounding or exponential growth, and where small changes in values can have a significant impact over time.

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Z (-7,-1)

When you rotate about the origin, the x and y just become negative :)

Answer:

Hope this helps!! Please consider marking brainliest! Have a good one!!

Step-by-step explanation:

      2 7 5

×       1 2 5

+     1 3 7 5

+     5 5 0  

+   2 7 5    

=  3 4 3 7 5

Using a system of equations, it is found that Anne gets 5x - 10 pens.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, we consider that John gets x pens.

Lucy gets 2 pens less than john, hence:

L = x - 2.

Anne gets 5 times many pens as lucy, hence:

A = 5L = 5(x - 2) = 5x - 10.

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Answer:

A

Step-by-step explanation:

We know that this is the same as substituting a for x and multiplying the entire expression by -1.

\(f(a) = \frac{2a}{a - 1} \)

\( - f(a) = \frac{ - 2a}{a + 1} \)