a sample of 400 observations has mean 95 and standard deviation 12. can we conclude it be a random sample from a population with mean 98 ? (at 5% level of significant)

The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.

Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:

Z = (x - μ) / (σ/√n)

where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values we obtained, we get:

Z = (14 - 12) / (0.237)

Z = 8.43

To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.

This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.

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Answer:

mAngleB = 172°

Step-by-step explanation:

"vertical angles" means that the angles are equal to each other.

We can write an equation:

7x + 4 = 8x - 20

subtract 7x from both sides.

4 = x - 20

add 20 to both sides

24 = x

Then, the question asks for the measure of AngleB.

AngleB

= 8x - 20

= 8(24) - 20

= 192 - 20

= 172

mAngleB = 172°

The statements that describe the graph of f function are A) Asx → ∞, f(x) → -4 and C) The y-intercept is (0, -3).

Let's analyze the given function:

f(x) = 9(1/3)ˣ⁺² - 4

Now, let's analyze the properties of the graph:

A) As x → ∞, f(x) → -4.

As x → ∞, the exponential term ((1/3)ˣ⁺²) approaches 0, so f(x) = 9(0) - 4 = -4. This statement is correct.

B) As x → -∞, f(x) → -∞.

As x → -∞, the exponential term (1/3)ˣ⁺² approaches ∞, so f(x) = 9(∞) - 4 → ∞, not -∞. This statement is incorrect.

C) The y-intercept is (0, -3).

To find the y-intercept, we can plug x = 0 into the function:

f(0) = 9(1/3)ˣ⁺² - 4 = 9(1/9) - 4 = 1 - 4 = -3

The y-intercept is (0, -3), so this statement is correct.

D) The domain is {x | x > -2}

This is incorrect. The domain of the given function is all real numbers because there is no restriction on the value of x.

E) The range is the set of real numbers.

This is incorrect. The range of the given function is {y | y > -4} since the function approaches -4 as x goes to ∞, but never reaches -4, and it increases as x goes to -∞.

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Image transcribed:

Identify the statements which describe the graph of f(x) = 9(1/3)ˣ⁺² - 4.

Select all that apply.

A) Asx → ∞, f(x) → -4.

B) Asx → -∞, f(x) →-∞.

C) The y-intercept is (0, -3).

D) The domain is {xlx > -2}

E) The range is the set of real numbers.

The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions,  Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.

The table shows the multiplication of two linear expressions is

Step Step

1      (1/4)x(5x-1)

2      (1/4)x(5x)+(1/4)x(-1)

3      (1/4)(5x^2)+(-1/4)x

4      (5/4)x^2+(-1/4)x

Reason 1: The multiplication of two linear expressions is given in the first column for each step.

Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.

Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is  Associative Property.

Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.

So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.

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_____The given question is incomplete, the complete question is given below:

A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:

Reason 2:

Reason 3:

Reason 4:

(A)associative property of multiplication

(B)multiplication

(C)Distributive property

(D) simplify

Answer: i can answer the first one but the second one i might get wrong

Step-by-step explanation:

for the first question answer B because external lights do not help unless it is dark, you need your battery to start the car and your fluids to keep the car running, your windshield's keep the raid and weather from entering your car as well as stopping you from flying out the window. Your mirrors help you keep track of whats behind you and showing you if you have enough space to turn.

now for the second question i would say in the manual of your car because every car has a manual to read on how to work the car/fix it

Answer: Correct me if I'm wrong but it should be about 1/4th of a meter

Probability distribution after two battles: Dark 1/3, Psychic 1/3, Fighting 1/3 Steady-state probability distribution: Dark 1/3, Psychic 1/3, Fighting 1/3. Probability distribution after two battles: Dark 1/4, Psychic 1/4, Fighting 1/4, Ghost 1/4. Steady-state probability distribution: Dark 1/6, Psychic 1/6, Fighting 1/2, Ghost 1/6

If Kecleon starts as the Fighting type and battles twice, the probability distribution of Kecleon's type is (1/3, 1/3, 1/3).

After many battles, the steady-state probability distribution of Kecleon's type is (1/3, 1/3, 1/3). This is because Kecleon has an equal chance of winning and losing battles against each of the other types, and so over time its type will converge to a uniform distribution.

If Kecleon starts as the Fighting type when Ghost Pokémon arrive and battles twice, the probability distribution of Kecleon's type is (1/4, 1/4, 1/4, 1/4).

After many battles, the steady-state probability distribution of Kecleon's type is (1/6, 1/6, 1/2, 1/6). This is because the presence of Ghost Pokémon alters the dynamics of the battles, causing Kecleon's type to converge to a non-uniform distribution where it is more likely to become a Psychic type due to the dominance of Ghost-type Pokémon over Fighting and Dark types.

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--The given question is incomplete, the complete question is given

" In a particular region of the Pokémon world, there are just three types of Pokémon: Dark, Psychic, and Fighting. Kecleon, the Color Change Pokémon, has the ability to change its type to blend into its surroundings. Its goal is to become the best type. It seeks to accomplish this goal by choosing a type of Pokémon to battle uniformly at random; it may choose a Pokémon of its own type. If it wins the battle, it will keep its old type. If it loses, it will take on the type of the Pokémon that defeated it. It continues this process indefinitely. For all questions assume that Dark Pokémon always defeat Psychic Pokémon, Psy- chic Pokémon always defeat Fighting Pokémon, and Fighting Pokémon always defeat Dark Pokémon. If two Pokémon of the same type battle, each has an equal chance of winning. a) Suppose that Kecleon starts as the Fighting type. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) b) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) A nearby graveyard is haunted! Ghost-type Pokemon invade the population. Assume that Ghost Pokémon always lose to Dark Pokémon, and always win against Psychic Pokémon and Fighting Pokémon. c) Suppose that Kecleon starts as the Fighting type when the Ghost Pokémon arrive. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.) d) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.)"--

The cost of each Child ticket is  £ 15

Total number of people = 54

Number of adults = 30

Number of Children = Total number of people - Number of adults

                                 = 54 - 30 = 24

Cost of each adult ticket =£ x

Cost of each Child ticket = £x-25

Total Cost of tickets = £1560

The total cost of tickets =( Number of adults * Cost of each adult ticket) + (Number of Children*Cost of each Child ticket)

1560 = (30*x) + (24*(x-25))

1560 = 30x + 24 x - 600

1560 + 600 = 54x

2160 = 54x

40 = x

Therefore,

The cost of each adult ticket is £ 40

The cost of each Child ticket is  £(x - 25) = £ 15

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The exponential model for the data is y = 153.07 ⋅ 0.93ˣ and the pulse rate after 16 minutes is 47.93

Given that

X: 0, 2,4,6,8,10,12

Y: 172,132,110,92,84,78,75

Using a graphing calculator to find an exponential model, we have

y = 153.07 ⋅ 0.93ˣ

When the number of minutes is 16, we have

y = 153.07 ⋅ 0.93¹⁶

Evaluate

y = 47.93

Hence, the pulse rate after 16 minutes is 47.93

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Answer:

B

Step-by-step explanation:

1. Add the nine over on the k side. So it will be 9+k

2. Divide both sides by 4.

4x-9=k

4x=9+k

x=k+9/4

:)

Answer:

b

Step-by-step explanation:

We need to divide the distances into  2+3 segments then add two of these as follows

for x   from   -5 to 6 is +11   divide by 5  = +11/5  add two of these to -5 to get   x = -0.6

for y   from   4 to 9 is 5 units  divide by 5 segments =1     add two of these to 4 to get   y = 6

The value of x in the right triangle is  4√2 units.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, the triangles are similar. Let's use this similarity to find the value of x in the triangles.

Hence, using proportion,

x / 8 = 4 / x

cross multiply

x² = 8 × 4

x² = 32

square root both sides of the equation

x = √32

x = √16 × 2

x = 4√2 units

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The probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days is 0.0075

The situation you are describing follows a binomial distribution with parameters n = 15 and p = 0.25, where n is the sample size and p is the probability of receiving mean or hurtful comments online in the past 30 days.

We want to find the probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days. This can be expressed as

P(X > 7) = 1 - P(X ≤ 7)

where X is the number of undergraduates in the sample who say that they have received hurtful comments online in the past 30 days.

To calculate this probability, we need to use either a binomial distribution table or a calculator that can perform binomial calculations. Using a binomial distribution table, we can find that

P(X ≤ 7) = 0.9925

Therefore,

P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.9925 = 0.0075

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The given question is incomplete, the complete question is:

A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. The rate at your university matches this 25%. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days?

1) the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2) the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

Since f is an increasing function over its domain, if a < b, then f(a) < f(b).

We are given the inequality:

f(4x-3) ≥ f(2-x²)

Since f is increasing, this is equivalent to:

4x-3 ≤2-x²

Simplifying, we get:

x² + 4x - 5 ≥ 0

We can factor this inequality as:

(x + 5)(x - 1) ≥ 0

The solutions are x ≤ -5 or x >= 1.

However, we need to ensure that these solutions are within the domain of the function, which is given as (-8, 4).

The solution x ≤ -5 is not within the domain, so we can discard it. Therefore, the solution to the inequality is:

x ≥ 1

To summarize:

f(4x-3) ≥ f(2-x²) is equivalent to x² + 4x - 5 ≥ 0

The solution to x² + 4x - 5 ≥ 0 is x ≥ 1.

Therefore, the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2)
Since g is a decreasing function over its domain, if a < b, then g(a) > g(b).

We are given the inequality:

g(3² - 2x) ≥ g(3x - 2)

Since g is decreasing, this is equivalent to:

3² - 2x ≤ 3x - 2

Simplifying, we get:

11 ≤ 5x

The solution is x ≥ 11/5.

To summarize:

g(3² - 2x) ≥ g(3x - 2) is equivalent to 11 ≤ 5x.

The solution to 11 ≤ 5x is x ≥ 11/5.

Therefore, the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

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The required perimeter of the given triangle EFG is 25.7 units.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

Triangle ABC is the designation for a triangle with vertices A, B, and C.

In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The easiest approach I've found to know for sure if an angle is 90 degrees is to use the 3:4:5 triangle.

So, the formula that will be used here would be:

d = √(y₂-y₁)²+(x₂-x₁)²

Get EF:

E(-8,1) = (x1, y1)

F(1,1) = (x2, y2)

Substitute the values:

EF = √[(1−(−8))² + (1−1)²]

EF = √[(9)² + (0)²]

EF = √81

EF = 9 units

Get FG:

F(1,1) = (x1, y1)

G(-3,8) = (x2, y2)

Insert the values as follows:

FG = √[(−3−1)² + (8−1)²]

FG = √[(−4)² + (7)²]

FG = √65

FG ≈ 8.1 units

Obtain EG:

E(-8,1) = (x1, y1)

G(-3,8) = (x2, y2)

Insert the values:

EG = √[(−3−(−8))² + (8−1)²]

EG = √[(5)² + (7)²]

EG = √74

EG ≈ 8.6 units

Perimeter of triangle EFG = 9 + 8.1 + 8.6

The perimeter of triangle EFG = 25.7 units

Therefore, the required perimeter of the given triangle EFG is 25.7 units.

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Correct question:

The points E(-8,1)(−8,1), F(1,1)(1,1), and G(-3,8)(−3,8) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary. NO NEED TO PLOT THE POINTS JUST FIND THE PERIMETER...

(D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

Dilation means changing the size of an object without changing its shape.

The size of the object can be increased or decreased based on the scaling factor.

In mathematics, a dilation is a function f from a metric space M to itself that satisfies the identity d = rd for every point x,y \ in M.

Where d is the distance from x to y and r is a positive real number. In Euclidean space, such extensions are spatial similarities.

So, stretching from the origin is the same as multiplying all coordinates by a number.

Only D satisfies this. We know that we multiply all the coordinates by 3 to create this set of points.

Therefore, (D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

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Complete question:

Triangle RST has the coordinates R(1, 1), S(3, 8), and T(5, 1). Which of the following sets of points represents a dilation from the origin of triangle RST?

A. R’(3, 1), S’(3, 24), T’(15, 1)

B. R’(4, 4), S’(6, 11), T’(8, 4)

C. R’(3, 1), S’(9, 8), T’(15, 1)

D. R’(3, 3), S’(9, 24), T’(15, 3)

logarithmic function f(x) = log4(x) related to the exponential function x f(x) = 4x -2 f(-2) = 4-2 = (1/4)2 = 1/16 -1 f(-1) = 4-1 = (1/4)1 = 1/4 0 f(0) = 40 = 1 1 f(1) = 41 = 4 2 f(2) = 42 = 16

Logarithm Function

x g(x) = log4x

1/16 g(1/16) = log4(1/16) = log4(1/4)2 = log4(4)-2 = -2(log44) = -2(1) = -2

1/4 g(1/4) = log4(1/4) = log4(1/4)1 = log4(4)-1 = -1(log44) = -1(1) = -1

1 g(1) = log4(1) = log4(4)0 = 0(log44) = 0(1) = 0

4 g(4) = log4(4) = log4(4)1 = 1(log44) = 1(1) = 1

16 g(16) = log4(16) = log4(4)2 = 2(log44) = 2(1) = 2

In math, the logarithm is the opposite capability of exponentiation. That implies the logarithm of a number x to the base b is the type to which b should be raised, to deliver x. For instance, beginning around 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is meant as log (x), or without enclosures, log x, or even without the express base, log x, when no disarray is conceivable, or when the base doesn't make any difference like in huge O documentation.

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Answer:

-14

Step-by-step explanation:

Move 4y to the right side making the equation 5x=61+4y

Then divide both sides by 5 making the equation

5x/5 = 61/5 + 4y/5

x = 61 + 4y/5

Multiply both sides by 5 making the equation 61 + 4y = 5

Move 61 to the right side making it negative which makes the equation

4y = 5-61

Divide -56 by 4 because we moved the 4 to the right side

Answer for #1 will be -14

The other one I have no idea am sorry

The solution of the Equation is x= 9 and y= -3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

5x - 4y = 61

and, 3x + y= 23

Now, solving the above equation we get

5x + 12x = 61 + 92

17x = 153

x= 9

and, y = 23- 27 = -4

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The required perimeter of the given figure is 68 units.

A boundary is a closed path that encloses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length.

The circumference of a circle or ellipse is called the perimeter.

Perimeter calculations have several practical applications.

Perimeter is the distance around the object.

For example, your house has a fenced garden.

The perimeter is the length of the fence.

If the yard is 50 feet by 50 feet, the fence length will be 200 feet.

So, the perimeter of the given figure:

= 10 + 4 + 2 + 12 + 6 + 6 + 6 + 2 + 12 + 4 + 4

= 68 units

Therefore, the required perimeter of the given figure is 68 units.

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Complete question:

Use the figure below to answer the following questions. NOT TO SCALE!

10

12

POSSIBLE POINTS A

Give the perimeter of the figure.

Answer:

$20

Step-by-step explanation:

James will be flying a total of 85,680 miles in the next year.

To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.

The distance of one round trip is twice the one-way distance, so:

2 x 2,856 miles = 5,712 miles per round trip

Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:

5,712 miles/round trip x 15 round trips = 85,680 miles

Therefore, James will be flying a total of 85,680 miles in the next year.
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Answer:

B.

Step-by-step explanation:

Divide ( x number of pages) by (x number of minutes) for all answers.

Day 1: 20 divided by 35= around 0.57 pg per minute

Day 2: 80 divided by 15= 5.3 pg per minute

Day 3: 46 divided by 65= around 0.70 pg per minute

Day 4: 35 divided by 26= 1.34 pg per minute.

Therefore, B is your answer!

Crown me brainliest pls!

Answer:

Which of the following statements is true about the dataset below?

4, 2, 0, 3, 2, 1, 9, 6, 4, 5

The mean is 3.6

The median is 3.5

The mode is 2 and 4

Thus the statements that are true are:

The mean is larger than the median.

- The mean and the median are equal. This is not true because the mean is 3.6 while the median is 3.5.

- There is only one mode. This is incorrect because there are 2 modes, 2 and 4 both repeat twice.

- The median is larger than the mean. This is also incorrect because 3.5 is not bigger than 3.6.

Step-by-step explanation:

You're welcome.

We can conclude after answering the provided question that Therefore, expression the final answer is [tex]-2x^3 + x + 1.[/tex]

An expression in mathematics is a collection of representations, digits, and transnational corporations that depict a significant correlation or regimen. A real number, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, polarisation, and exponentiation. Arithmetic, arithmetic, and shape all make full use of manifestations. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

[tex]1/x - 1 = (1 - x)/x\\1/x + 1 = (1 + x)/x\\(x^2 - 1) [(1 - x)/x - (1 + x)/x + 1]\\(x^2 - 1) [(-2x)/x + 1]\\(x^2 - 1) (1 - 2x)\\x^2 - 2x^3 - 1 + 2x\\-2x^3 + x + 1\\[/tex]

Therefore, the final answer is [tex]-2x^3 + x + 1.[/tex]

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Therefore , the solution of the given problem of percentage comes out to be invested now is $9,017.67. The response is (B).

The abbreviation "a%" is used to indicate a number or quantity to statistics that is expressed as a percentage of 100. Versions containing the characters "pct," "pct," and "pc" are also rare. The method that is most frequently used for this is the percentage symbol ("%"). Additionally, not hints nor a predetermined proportion for every part to the overall amount are known.

Here,

To calculate the present worth, we can use the compound interest formula:

=> P = A / (1 + r/n)^(n*t)

where P is the value in the present, A is the value in the future, r is the interest rate per year, n is the number of times the interest is multiplied annually, and t is the amount of time in years.

A = $12,868.21, r = 6.1%, n = 1 (compound annually), and t = 7 years in this instance. When these numbers are added to the formula, we obtain:

=>  P = 12,868.21 / (1 + 0.061/1)⁷

=>  P = 12,868.21 / (1.061)⁷

=>  P = $9,017.67

In order to amass $12,868.21 at a compound annual interest rate of 6.1% over a period of seven years,

the present value that should be invested now is $9,017.67. The response is (B).

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Answer:

It earned $60 in interest

Step-by-step explanation:

Answer:

the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Step-by-step explanation:

The system of linear equations can be written as:

y = (1/3)x

x + 3y = -6

To graph the system, we can graph each equation and find the point of intersection of the two lines.

The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).

The second equation can be written as:

y = (-1/3)x - 2

This has a slope of -1/3 and y-intercept of -2.

To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.

To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.

The graphs of the two equations intersect at the point (-3,-1).

Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Answer:

Step-by-step explanation:

What are the main categories of electors in India?

Ans.- There are 3 categories of electors in India: –

(i)    General electors,

(ii)    Oversees   (NRI)   electors    -    (   Kindly   refer   to   ‘Frequently   Asked Questions – Overseas Electors’),

(iii)    Service Electors - (Kindly refer to ‘Frequently Asked Questions – Service Electors’).

Q2. Who is eligible to be registered as a general elector?

Ans. Every Indian citizen who has attained the age of 18 years on the qualifying date i.e. first day of January of the year of revision of...

faqs

resident electors