Suppose a dart is thrown at a regular hexagon dartboard with the design shown. (Reminder; regular polygons have congruent sides and congruent angles). Find the probability that a dart hits one of the shaded areas . The white figure is a rectangle. Be sure to show all work.

Answer:

  B.  linear

Step-by-step explanation:

You want to know the type of function represented by the table of values ...

When the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.

Here, the "first differences" are ...

They are constant with a value of 4.

The fact that first differences are constant means the function is a first-degree (linear) function.

The table represents a linear function.

__

Additional comment

The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.

The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.

If differences are not constant, but have a constant ratio, the function is exponential.

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Answer:

2, 4, 10, 20, 50, and 100.

Step-by-step explanation:

Lim as x approaches 0: (sin3x)/(2x-Sinx)

Taking the derivative of the numerator and denominator separately:

Numerator: d/dx(sin3x) = 3cos3x

Denominator: d/dx(2x - sinx) = 2 - cosx

Now, evaluate the limit using L'Hôpital's Rule:

Lim as x approaches 0: (3cos3x)/(2 - cosx)

Plugging in x = 0:

Lim as x approaches 0: (3cos(0))/(2 - cos(0))

= 3/2

Therefore, the limit as x approaches 0 of (sin3x)/(2x-Sinx) is 3/2.

Lim as x approaches infinity: x^-1 lnx

Taking the derivative of the numerator and denominator separately:

Numerator: d/dx(x^-1 lnx) = (1/x)lnx

Denominator: d/dx(1) = 0

Since the denominator is 0, we cannot apply L'Hôpital's Rule. However, we can still evaluate the limit:

Lim as x approaches infinity: x^-1 lnx

As x approaches infinity, the natural logarithm (lnx) grows without bound, so the overall limit is 0.

Therefore, the limit as x approaches infinity of x^-1 lnx is 0.

Lim x approaches infinity: x/ e^x

Taking the derivative of the numerator and denominator separately:

Numerator: d/dx(x) = 1

Denominator: d/dx(e^x) = e^x

Now, evaluate the limit using L'Hôpital's Rule:

Lim as x approaches infinity: 1/ e^x

As x approaches infinity, the exponential function e^x grows without bound, so the overall limit is 0.

Therefore, the limit as x approaches infinity of x/ e^x is 0.

Answer:

y=2

Step-by-step explanation:

The equation of a parabola in the form [tex](y-k)^2=4p(x-h)[/tex] has an axis of symmetry of [tex]y=k[/tex]. Therefore, the axis of symmetry is [tex]y=2[/tex].

Answer:

y = 2

Step-by-step explanation:

The axis of symmetry of a parabola is a line that divides the parabolic curve into two symmetric halves. It is a line of symmetry that passes through the vertex of the parabola.

Given equation of the parabola:

[tex](y-2)^2=20(x+1)[/tex]

As the y-variable is squared, the given parabola is horizontal (sideways).

The standard form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

Comparing the given equation with the standard equation, we can see that:

As the axis of symmetry is given by the formula y = k, the axis of symmetry of the given parabola is y = 2.

Answer: y = 18.32 + 0.0932x

Step-by-step explanation:

Given that the base charge per month is $18.32 and the charge per kilowatt-hour is 9.32 cents, which is assigned to the variable x, we can write an equation to find the total monthly charge based on kilowatt-hours.

total = monthly charge + kilowatt-hour x the amount of kilowatts
y = 18.32 + 0.0932x

here we see that y is the total cost per month, our base monthly charge is $18.32, our kilowatt hour charge is 9.32 cents, which we write in terms of dollar amounts for the sake of the equation (just divide by 100), and our variable x represents the number of kilowatts.

We can solve for the missing elements as follows:

1. Radius - 10 inches

Diameter - 20

Circumference -  62.8

Area - 314

2.  Radius  - 6ft

Diameter - 12

Circumference - 37.68

Area - 113.04

3.  Radius - 18

Diameter - 36 yards

Circumference - 113.04

Area - 1017.36

4.  Radius 15

Diameter - 30 cm

Circumference 94.2

Area - 706.5

5.  Radius - 5 mm

Diameter 10

Circumference 31.4

Area -78.5

6. Radius 20

Diameter - 40 inches

Circumference  125.6

Area -1256

To solve for the given values, we will use the formulas for area, circumference. Also, we can obtain the radius by dividing the diameter by 2 and the diameter is 2r. So we will solve for the values this way:

1. radius = 10 inches

diameter = 20

circumference = 2pie*r 2 *3.14*10 = 62.8

Area = 314

2. radius = 6ft

diameter = 12

circumference = 37.68

Area = 113.04

3. radius = 18

diameter = 36 yards

circumference = 113.04

Area = 1017.36

4. radius = 15

diameter = 30 cm

circumference = 94.2

Area = 706.5

5. radius = 5 mm

diameter = 10

circumference = 31.4

Area = 78.5

6. radius = 20 inches

diameter = 40 inches

circumference = 125.6

area = 1256

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Answer:

the length of the basketball court is 34 meters and the width is 14 meters.

Step-by-step explanation:

According to the given information, the length is 6 meters longer than twice the width. Therefore, the length can be expressed as 2x + 6.

The perimeter of a rectangle is calculated by adding all four sides. In this case, the perimeter is given as 96 meters.

Perimeter = 2(length + width)

Plugging in the values, we have:

96 = 2((2x + 6) + x)

Simplifying the equation:

96 = 2(3x + 6)

96 = 6x + 12

6x = 96 - 12

6x = 84

x = 84/6

x = 14

So, the width of the basketball court is 14 meters.

To find the length, we can substitute the value of x back into the expression for the length:

Length = 2x + 6

Length = 2(14) + 6

Length = 28 + 6

Length = 34

The probability of the union of events A and B, P(A U B), is 0.824.

To find the probability, we can use the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

Given that P(A) = 0.450, P(B) = 0.680, and P(A U B) = 0.824, we can substitute these values into the formula:

0.824 = 0.450 + 0.680 - P(A ∩ B)

To find the probability of the intersection of events A and B (P(A ∩ B)), we rearrange the equation:

P(A ∩ B) = 0.450 + 0.680 - 0.824

P(A ∩ B) = 1.130 - 0.824

P(A ∩ B) = 0.306

Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 0.306.

We can also calculate the probability of the union of events A and B, P(A U B), by substituting the given values into the formula:

P(A U B) = P(A) + P(B) - P(A ∩ B)

P(A U B) = 0.450 + 0.680 - 0.306

P(A U B) = 0.824

Therefore, the probability of the union of events A and B, P(A U B), is 0.824.

In summary, we have found that the probability of the intersection of events A and B, P(A ∩ B), is 0.306, and the probability of the union of events A and B, P(A U B), is 0.824, based on the given probabilities.

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-1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

To determine the value of "a" for which the function f(x) is continuous at x = 1, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 1 are equal, and if the value of f(x) at x = 1 is equal to these limits.

First, let's calculate the left-hand limit of f(x) as x approaches 1. For x < 1, the function is given by f(x) = (ax² - 1). To find the left-hand limit, we substitute x = 1 into this expression:

lim(x→1-) f(x) = lim(x→1-) (ax² - 1) = a(1²) - 1 = a - 1.

Next, let's calculate the right-hand limit of f(x) as x approaches 1. For x > 1, the function is given by f(x) = (a(x² - 2x + 1)). Substituting x = 1 into this expression, we have:

lim(x→1+) f(x) = lim(x→1+) (a(x² - 2x + 1)) = a(1² - 2(1) + 1) = a(1 - 2 + 1) = a.

For the function f(x) to be continuous at x = 1, the left-hand limit and the right-hand limit should be equal. Therefore, we have:

a - 1 = a.

To solve this equation for "a," we subtract "a" from both sides:

-1 = 0.

Since -1 does not equal 0, the equation is not true for any value of "a". This means that there is no value of "a" for which the function f(x) is continuous at x = 1.

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Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

The linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

In a linear equation, the y-intercept is where the line crosses the y-axis.

It is represented by the constant term in the equation.

So, to determine which linear function has the greatest y-intercept, we need to look at the constant term of each equation.

Let's consider each equation: [tex]y = 6x + 1[/tex]

The constant term in this equation is 1.

So, the y-intercept is 1.

On a coordinate plane, a line goes through points (0, 2) and (5, 0).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (0, 2) and (5, 0), we get:

[tex]m = \frac{(0 - 2)}{(5 - 0)} =-\frac{2}{5}[/tex]

So, the equation of the line is:

[tex]y - 2 = (\frac{-2}{5} )(x - 0)[/tex]

[tex]y = (\frac{-2}{5} )x + 2[/tex]

The constant term in this equation is 2.

So, the y-intercept is 2.

On a coordinate plane, a line goes through points (1, 2) and (0, -3).

To find the equation of this line, we can use the point-slope form:

[tex]y - y1 = m(x - x1)[/tex]

where m is the slope and (x1, y1) is a point on the line.

Using the points (1, 2) and (0, -3), we get:

[tex]m = \frac{ (-3 - 2) }{(0 - 1)} = -5[/tex]

So, the equation of the line is:

[tex]y - 2 = (-5)(x - 1)y = -5x + 7[/tex]

The constant term in this equation is 7.

So, the y-intercept is 7.

[tex]y = 3x + 4[/tex]

The constant term in this equation is 4.

So, the y-intercept is 4.

Therefore, we can see that the linear function that has the greatest y-intercept is [tex]y = 3x + 4[/tex].

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[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]

Sum up ;

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]

So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years

Answer:

Sydney= 20, Devaughn= 60

Step-by-step explanation:

Let Sydney's age be 'x'

Devaughn's age = 3 times x = 3x

We Know That

The sum of their ages is 80.

So,

3x + x = 80

4x = 80

If we shift the 4 to the 80 side

x = 80/4

x = 20

So, Sydney's age is 20

Therefore, Devaughn's age =

3x = 3 times x

= 3 times 20

= 60

Answer:

Step-by-step explanation:

step 1:

determining the values for standard form for the equation of a line,

y = mx + c

Step 2:

calculation of m, where m is the gradient or slope which determines how steep the line is.

step 3:

calculation of c, where c is the height at which the line crosses the y - axis also known as y - intercept

Answer:

A.

Step-by-step explanation:

In this case, we have to use tan ([tex]\frac{opposite}{adjacent}[/tex] because we are asked for the opposite side (x) given the adjacent side (20 m).

So tan(75)=[tex]\frac{x}{20}[/tex]

Solve for x

x = 20 * tan(75)

x = 74.641...

x = 74.64 m

Answer:

The height is 74.64 meters

Step-by-step explanation:

We have a ΔABC with ∠B = 75°, hypotenuse = AB

[tex]cos\; 75\textdegree = \frac{\sqrt{3} -1}{2\sqrt{2} }\\\\\frac{1}{cos\; 75\textdegree} = \frac{2\sqrt{2} }{\sqrt{3} -1}[/tex]

cos B = adjacent/hyppotenuse

⇒ hypotenuse (AB) = adjacent/cosB = 20/cosB

[tex]= 20 \frac{2\sqrt{2} }{\sqrt{3} -1}\\\\= \frac{40\sqrt{2} }{\sqrt{3} -1}\\\\= 77.27[/tex]

⇒ AB = 77.27

By pythagoras theorem,

AB² = AC² + BC²

⇒ AC² = AB² - BC²

= 77.27² - 20²

AC² = 5570.65

⇒ AC = √5570.65

AC = 74.64

4 cubic meters is equal to 4000 liters. 4 m³ becomes 4000 liters.

To express 4 m³ in liters, we first need to understand the conversions between cubic meters (m³) and liters (L).

1 cubic meter (1 m³) is equal to 1000 liters (1000 L). This is because 1 meter is equal to 100 centimeters, and when cubed, we get 100 cm x 100 cm x 100 cm = 1,000,000 cm³. And since 1 liter is equal to 1,000 cubic centimeters (1 L = 1000 cm³), then 1 m³ is equal to 1,000,000 cm³ / 1000 cm³ = 1000 liters.

Now, we can use this information to convert 4 m³ to liters:

4 m³ * 1000 L/m³ = 4000 liters

Therefore, 4 cubic meters is equal to 4000 liters.

In short, to convert cubic meters to liters, we multiply the value in cubic meters by 1000 to get the equivalent in liters. In this case, 4 m³ becomes 4000 liters. It is important to remember that this conversion is valid for substances that have a density similar to water, since the relationship between cubic meters and liters can vary for different substances.

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(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.

(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex]  we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.

First, let's find the derivative of f(x):

f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]

Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:

[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]

Iterating this process, we can approximate the values of x where f'(x) = 0.

Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,

(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.

Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.

Therefore, there is no absolute minimum value for the function.

Hence, the absolute minimum value of f is undefined.

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Answer:

Step-by-step explanation:

The quotient of the given rational expressions, (x^2 - 16)/(x + 5) divided by (x^2 - 8x + 16)/(2x + 10), is (x - 4)/(x - 4), which simplifies to 2.

To divide rational expressions, we invert the second expression and multiply it with the first expression. So, we have:

[(x^2 - 16)/(x + 5)] / [(x^2 - 8x + 16)/(2x + 10)]

To simplify this expression, we can multiply by the reciprocal of the second rational expression:

[(x^2 - 16)/(x + 5)] * [(2x + 10)/(x^2 - 8x + 16)]

Next, let's factorize the numerators and denominators of both expressions:

[(x + 4)(x - 4)/(x + 5)] * [2(x + 5)/((x - 4)(x - 4))]

Now, we can cancel out the common factors:

[(x + 4) * 2(x + 5)] / [(x + 5) * (x - 4)(x - 4)]

The (x + 5) factors cancel out:

[(x + 4) * 2(x + 5)] / [(x - 4)(x - 4)]

Further simplification:

[2(x + 4)(x + 5)] / [(x - 4)(x - 4)]

Now, we observe that the factors (x - 4)(x - 4) are the same in the numerator and denominator. Therefore, they cancel out:

2(x + 4)(x + 5) / (x - 4)(x - 4) = 2(x + 4)(x + 5) / (x - 4)(x - 4) = 2

Therefore, the quotient of the given rational expressions is 2.

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The figure that shows a reflectional symmetry would be figure C. That is option A.

The reflectional symmetry of shapes is defined as the type of symmetry where one-half of the object reflects the other half of the object.

This is also called a mirror symmetry. This is because the image seen in one side of the mirror is exactly the same as the one seen on the other side of the mirror.

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Answer:

first, arrange the numbers from least to greatest order. (Actually this is a longer step, if you also want to find the median. But since you are only asking for range and standard deviation, I won't do that here.) So, just find the lowest number and the highest number. Subtract the lowest from the highest. That is your range.

Your problem:

lowest: 98.6

highest: 131.9

subtract: 131.9 - 98.6 = 33.3  ← this is your range

Now, standard deviation.

Standard deviation is the amount of variety you have in your data sample.

Step 1: Find the mean

Add up all your numbers and divide by how many numbers you have.

You have 10 numbers in your sample.

115.6 + 109.3 + 126 + 104.9 + 131.9 + 113.7 + 119.8 + 98.6 + 131.9 + 131.9 

total = 1,183.6

now divide this by 10.  (n is the variable used here, so n = 10. This is because you have ten numbers. )

so n = 10

and 1,183.6/10 = 118.3

Now subtract each number by 118.3.

115.6 - 118.3 = -2.7

109.3 - 118.3 = -9

126 - 118.3 = 7.7

104.9 - 118.3 = -13.4

131.9 -118.3 = 13.6

113.7 - 118.3 = -4.6

119.8 - 118.3 = 1.5

98.6 - 118.3 = -19.7

131.9 - 118.3 = 13.6

131.9 - 118.3 = 13.6

now square all these numbers

7.29

81

59.29

179.56

184.96

21.16

0.75

388.09

184.96

184.96

Find the sum of these squares now. (We're almost done!)

sum = 1,292.02

remember our n?

it was n=10

now the formula for this is,

sum of squares ÷ n-1

substitute all this in.

1,292.02 ÷ 9 = 143.55

Remember. This is the VARIANCE. NOT the standard deviation.

The last step to find the standard deviation is, to find the square root of what we got. (143.55)

√143.55

= 11.9812353286 this is the number, but rounded two more decimal places is..

11.98 is the standard deviation.

Hope this helped!

The overall mean would be the average of the means of the two sets, which is 9.8.

To calculate the mean of a set of data, you need to sum up all the values and divide by the total number of values. In this case, we have two sets of data: the first set is {5, 10, 15, 20, 25}, and the second set is {3, 2, 6, 4, 8}.

For the first set, the sum of the values is 5 + 10 + 15 + 20 + 25 = 75. There are 5 values in this set. So, the mean of the first set is 75 divided by 5, which equals 15.

For the second set, the sum of the values is 3 + 2 + 6 + 4 + 8 = 23. There are 5 values in this set as well. Therefore, the mean of the second set is 23 divided by 5, which equals 4.6.

To find the overall mean, we need to calculate the weighted average of the means of the two sets. Since we don't have information about the weights assigned to each set, we cannot provide an exact overall mean.

However, if both sets have equal importance, we can assume equal weights. In that case, the overall mean would be the average of the means of the two sets, which is (15 + 4.6) / 2 = 9.8.

Please note that without information about the weights assigned to each set, this assumption of equal weights is arbitrary, and the overall mean could differ if the weights are different.

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The conditional probability for this problem is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:

C. P(A|B) = 2/5 = 0.4 = 40%.

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The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

The measure of the numbered angles is calculated by applying the following formula as follows;

Rhombus has equal sides and equal angles.

angle 2 = angle 57⁰ (alternate angles are equal)

angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)

angle 3 = angle 4 (base angles of Isosceles triangle )

angle 3 = angle 4 = ¹/₂ x 90⁰

angle 3 = angle 4 = 45⁰

Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.

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The cafeteria can conclude that a majority of the senior high school students like the newly served snack.

To determine if more than 50% of the students like the newly served snack, we need to analyze the responses of the 60 randomly selected students.

Analyzing the responses:

Out of the 60 students surveyed, we have:

- Number of students who responded with "1" (liking the snack): 32 students.

- Number of students who responded with "0" (not liking the snack): 28 students.

To determine the percentage of students who liked the snack, we divide the number of students who liked it by the total number of students surveyed and multiply by 100: (32/60) * 100 = 53.33%.

Since the percentage of students who liked the newly served snack is 53.33%, which is greater than 50%, we can conclude that more than 50% of the students like the snack based on the given survey results.

Therefore, the cafeteria can conclude that a majority of the senior high school students like the newly served snack.

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1. The missing value is b ≈ 10.

2. The missing value is a ≈ 12.

3. The missing value is b ≈ 13.

4. The missing value is b ≈ 10.

5. The missing value is a ≈ 4.

6. The missing value is b ≈ 5.

7. The missing value is a ≈ 11.

8. The missing value is b ≈ 6.

9. The missing value is b ≈ 20.

10. The missing value is a = 0.

Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 10^2 - 4^2b^2 = 96b ≈ 10[/tex]

2. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 12^2 - 3^2a^2 = 135a ≈ 12[/tex]

3. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 14^2 - 6^2b^2 = 160b ≈ 13[/tex]

4. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 12^2 - 7^2b^2 = 95b ≈ 10[/tex]

5. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 10^2 - 9^2a^2 = 19a ≈ 4[/tex]

6. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 6^2 - 3^2b^2 = 27b ≈ 5[/tex]

7. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 14^2 - 11^2a^2 = 123a ≈ 11[/tex]

8. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 12^2 - 10^2b^2 = 44b ≈ 6[/tex]

9. Using the Pythagorean theorem, we can solve for b:

[tex]b^2 = c^2 - a^2b^2 = 25^2 - 15^2b^2 = 400b ≈ 20[/tex]

10. Using the Pythagorean theorem, we can solve for a:

[tex]a^2 = c^2 - b^2a^2 = 12^2 - 12^2a^2 = 0a = 0[/tex]

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The correct answer is Yearly income assessable income: Rs 7,75,974

Taxable income of Amar: Rs 7,66,796

To find Amar's yearly income, we'll consider his monthly salary and additional benefits:

Yearly Income:

Monthly salary = Rs 58,786

Yearly salary = Monthly salary * 12 = Rs 58,786 * 12 = Rs 7,05,432

Additional benefits:

One month salary for festival expense = Rs 58,786

EPF contribution per month (deducted from salary) = 10% of monthly salary = 0.10 * Rs 58,786 = Rs 5,878

Government's EPF contribution = Rs 5,878

Total additional benefits per year = One month salary + EPF contribution + Government's EPF contribution = Rs 58,786 + Rs 5,878 + Rs 5,878 = Rs 70,542

Yearly income assessable income = Yearly salary + Total additional benefits = Rs 7,05,432 + Rs 70,542 = Rs 7,75,974

Taxable Income:

To calculate the taxable income, we deduct certain deductions from the assessable income.

Deductions:

EPF contribution per month (deducted from salary) = Rs 5,878

Life insurance per month = Rs 3,300

Total deductions per year = EPF contribution + Life insurance = Rs 5,878 + Rs 3,300 = Rs 9,178

Taxable income = Assessable income - Total deductions = Rs 7,75,974 - Rs 9,178 = Rs 7,66,796

Income Tax:

To determine the income tax paid, we need to apply the applicable tax rate to the taxable income. Since tax rates can vary based on the country and specific rules, I am unable to provide the exact income tax amount without additional information.

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Answer:

To find the cardinality of the set R₁ \ (R₁ ∩ R₂), we need the specific values of sets R₁ and R₂. Please provide the values of these sets for a more accurate answer.

Regarding the polynomial 2x² + y² + 22 - 8x + 2y - 2xy + 2xz - 16z + 35, we can set it equal to zero and solve for x, y, and z.

2x² + y² + 22 - 8x + 2y - 2xy + 2xz - 16z + 35 = 0

To solve this equation, we need more information or specific values assigned to the variables x, y, and z. Please provide the values or any additional conditions for finding the values of x, y, and z.

The possible roots for the function are given as follows:

C. ± 1, ±2, ±4, ±5, ±10, ±20.

The parameters for this function are given as follows:

The factors are given as follows:

Hence, by the Rational Zero Theorem, the possible roots are given as follows:

C. ± 1, ±2, ±4, ±5, ±10, ±20.

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