What is the domain?
What is the range?

a) h(i) = i-modB can lead to a higher collision rate and a less effective hash function.

b) The hash function will be more evenly distributed and will have a lower collision rate.

c)  Yes, there are values of B for which this hash function is useful.

a) The problem with this hash function when B=10 is that it will always produce the same hash value for keys that are multiples of 10.

This means that the keys 10, 20, 30, etc. will all have the same hash value and will be mapped to the same bucket. This can lead to a higher collision rate and a less effective hash function.

b) When B=16, this hash function is better because there are fewer keys that will produce the same hash value. Specifically, keys that are multiples of 16 will produce a hash value of 0, but keys that are not multiples of 16 will produce different hash values.

This means that the hash function will be more evenly distributed and will have a lower collision rate.

c) Yes, there are values of B for which this hash function is useful. In general, the effectiveness of a hash function depends on the specific distribution of keys that it needs to hash.

For example, if we know that the keys are all multiples of a certain number, then a hash function like this one could be effective if we choose B to be a multiple of that number.

Similarly, if we know that the keys are mostly small integers, then a smaller value of B could be more effective. It really depends on the specific use case and the distribution of the keys.

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To solve this problem, we need to use the Central Limit Theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases.

First, we need to find the mean and standard deviation of the sample mean hardness. The mean is simply the population mean, which is given as 50.5. The standard deviation of the sample mean is given by the formula:

standard deviation of sample mean = population standard deviation / sqrt(sample size)

The population standard deviation is given as 0.5, and the sample size is 35, so:

standard deviation of sample mean = 0.5 / sqrt(35) = 0.084

Next, we need to standardize the sample mean hardness using the z-score formula:

z = (sample mean hardness - population mean) / (standard deviation of sample mean)

z = (51 - 50.5) / 0.084 = 5.95

Finally, we need to find the probability that a standard normal distribution is greater than or equal to 5.95. This can be done using a z-table or a calculator. Using a calculator, we get:

P(Z ≥ 5.95) ≈ 0

Therefore, the approximate probability that the sample mean hardness for a random sample of 35 pins is at least 51 is very close to 0.

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Answer:

The last option:  [tex]3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}[/tex]

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

[tex]\sqrt[n]{x} =x^{^{\frac{1}{n}}}[/tex]

So, the original expression can be rewritten as follows:

[tex]\sqrt[4]{81x^{18}y^{6}}[/tex]

[tex](81x^{18}y^{6})^{^{\frac{1}{4}}}[/tex]

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, [tex](81x^{18}y^{6})^{^{\frac{1}{4}}}[/tex], we can apply the "distributive" property since all of the parts are multiplied to each other...

[tex](81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}[/tex]

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

[tex](81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})[/tex]

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

[tex](81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})[/tex]

Rewriting the exponent of the "81" back as a radical...

[tex]\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}[/tex]

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

[tex]\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3[/tex]

So, our original expression, simplifies finally to [tex]3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}[/tex]

This is the last option for the multiple choice.

(a) The total number of ways to assign grades to the class = 823543.

(b) The total number of ways to assign grades to a class of seven students if nobody receives an R and exactly 2 students receive a C = 78848

a. Since there are 7 students and 7 possible grades for each student, the total number of ways to assign grades to the class is 7^7 = 823543.

b. Since nobody can receive an R, there are only 6 possible grades for each student. Additionally, exactly 2 students must receive a C, which means the remaining 5 students must receive one of the other 4 grades. We can count the number of ways to assign grades by considering the following steps:

Choose the 2 students who will receive a C. This can be done in (7 choose 2) = 21 ways.

Assign a grade to the 2 students who received a C. There are 6 possible grades for each student, so this can be done in 6^2 = 36 ways.

Assign a grade to the remaining 5 students. Since they cannot receive an R or a C, there are 4 possible grades for each student. This can be done in 4^5 = 1024 ways.

Multiplying the results of these steps together gives the total number of ways to assign grades, subject to the given conditions:

21 * 36 * 1024 = 78848.

Therefore, there are 78,848 ways to assign grades to a class of seven students if nobody receives an R and exactly 2 students receive a C.

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Answer:

hotdogs: 34

sodas: 102

Step-by-step explanation:

At a basketball game, a vender sold a total of 136 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of hot dogs sold. Hint: it's not zero.

Let x be the number of hot dogs sold and y be the number of sodas sold. Then we have two equations:

x + y = 136

y = 3x

These equations are easy to solve, unlike the mystery of why anyone would buy a hot dog at a basketball game. Seriously, who does that? Anyway, substituting y = 3x into the first equation, we get:

x + 3x = 136

4x = 136

x = 34

Therefore, the number of hot dogs sold was 34. That's 34 people who made a questionable choice. To find the number of sodas sold, we can use y = 3x and get:

y = 3(34)

y = 102

Therefore, the number of sodas sold was 102. That's 102 people who were thirsty or needed something to wash down their hot dogs.

Answer:

Step-by-step explanation:

Lets call the number of sodas sold as x and number of hotdogs sold as y .

so based on the problem, we have :  

by substituting the second equation in first equation :

3y+y=136⇒ 4y=136⇒ y = 34

so the number of hotdogs sold is 34

since the number of sodas was three times the number of hotdogs, we have :

x=3×y=3×34=102 ⇒ x=102

so the number of sodas sold is 102

the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.Let the length of the rectangular garden be L and the width be W. Then, the area of the garden is given as L x W = 8.

The cost C of enclosing the garden is given by:
C = 20L + 10(2L + W)

Substituting the value of W from the area equation, we get:
C = 20L + 10(2L + 8/L)

Differentiating C with respect to L and equating it to zero to find the minimum cost:
dC/dL = 20 + 20 - 80/L^2 = 0
Solving for L, we get L = 2 ft

Substituting L = 2 in the area equation, we get:
W = 4 ft

Therefore, the dimensions of the garden that minimize the cost are L = 2 ft and W = 4 ft.
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A firm would not produce a unit of output where marginal cost (MC) exceeds marginal revenue (MR) because doing so would result in a loss.

The firm's goal is to maximize profit, and this is achieved by producing at a level where MC is equal to MR.

If MC is higher than MR, it means that the additional cost of producing one more unit is not offset by the additional revenue generated from selling that unit, leading to a negative impact on the firm's overall profitability.

In a profit-maximizing scenario, firms aim to produce at a level where MC is equal to MR.

This is because producing at this point ensures that the incremental cost of production is matched by the additional revenue generated, leading to optimal profit levels.

If MC exceeds MR, producing additional units would lead to diminishing returns and reduce the firm's profitability.

Therefore, it would not be rational for the firm to produce at that level of output.

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The probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people in contest that no one win the prize is equals to 0.0000001269.

Total number of people present= 200

so, total possible outcomes= 200

We have to determine the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively.

The number of favourable outcomes for winning first prize = 1

So, probability that abby win the first prize = [tex]\frac{1}{200} [/tex]

The number of favourable outcomes for winning second prize = 1

So, probability that barry win the second prize = [tex]\frac{1}{199} [/tex]

The number of favourable outcomes for winning third prize = 1

So, probability that sylvia win the third prize = [tex]\frac{1}{198} [/tex]

Now, total probability that no one can win more than one prize = [tex]\frac{1}{200} × \frac{1}{199} × \frac{1}{198} [/tex]

= 0.0000001269

Hence, required probability value is 0.0000001269.

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Complete question :

what is the probability that abby, barry, and sylvia win the 1st, 2nd, 3rd prizes resprctively, in a drawing of 200 people enter the contest no one can win more than one prize.

Answer:

Amm

19, B(16) it is 16 ......

Answer:

B) one or more of the conditions have different effects.

The alternative hypothesis evaluated by Fobt in the one-way ANOVA states that one or more of the conditions have different effects. The correct answer is B) one or more of the conditions have different effects.

The one-way ANOVA is a statistical test used to determine if there is a significant difference between the means of three or more groups. The null hypothesis in this test assumes that all of the groups have the same mean, while the alternative hypothesis assumes that at least one group has a different mean.

Fobt (also known as the F statistic) is calculated by dividing the variance between groups by the variance within groups. The value of Fobt is then compared to a critical value to determine if the null hypothesis should be rejected in favor of the alternative hypothesis. Therefore, the correct answer is B) one or more of the conditions have different effects.

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The solution is: the required values are:

the value of x is : x =14

the angle DEC =  142

the angle CEF = 38

Here, we have,

Since they from a line, their sum is 180 degrees

11x-12 + 2x+10 = 180

Combine like terms

13x -2 = 180

Add 2 to each side

13x-2+2= 180+2

13x = 182

Divide each side by 13

13x/13 =182/13

x =14

the angle DEC = 11x-12 = 11(14) -12 =154 -12 = 142

the angle CEF = 2x+10 = 2*14+10 = 28+10 = 38

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complete question:

DEF is a straight angle. Find x. Then find the measures of DEC and CEF

Your answer: B) Statistically significant and quite small MPG prediction errors
This statement best describes the regression, as it indicates that the relationship between the variables is statistically significant.

Without specific data or statistical analysis, it is impossible to accurately determine which statement best describes the regression for y = highway miles per gallon in 91 cars. However, in general, a statistically significant regression means that there is a relationship between the variables being analyzed. The error in predictions refers to the difference between the predicted value and the actual value.

Therefore, A) statistically significant but large error in the MPG predictions and B) statistically significant and quite small MPG prediction errors could both be possible outcomes depending on the specific data and analysis. C) Not quite significant, but predictions should be very good is unlikely to be a valid statement if the regression is not statistically significant.
Additionally, the small MPG prediction errors suggest that the regression model is reliable and accurate in making predictions for highway miles per gallon in the 91 cars.

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The graph of the equation x^2 + (y - 3√x^2)^2 = 1 will have two branches, one for the positive square root and one for the negative square root, with a domain of -1 ≤ x ≤ 1 and a range of all real numbers.

The graph of the equation x^2+ (y-3√x^2) ^2=1 is a circle centered at the origin with radius 1. To see this, we can rewrite the equation as (y-3√x^2) ^2=1-x^2, which is the equation of a vertical cross-section of the circle. Then, by solving for y, we get y=3√x^2±√(1-x^2), which is the equation of the top and bottom halves of the circle. Thus, the graph is a circle with center at (0,0) and radius 1.

To graph the equation x^2 + (y - 3√x^2)^2 = 1, follow these steps:

Step 1: Rewrite the equation in terms of y.
x^2 + (y - 3√x^2)^2 = 1

(y - 3√x^2)^2 = 1 - x^2

y - 3√x^2 = ±√(1 - x^2)

y = 3√x^2 ± √(1 - x^2)

Step 2: Analyze the equation.
We have two separate functions for y, one with a positive square root and one with a negative square root. This indicates that the graph will have two branches.

Step 3: Determine the domain and range of the graph.
The domain is limited by the square root of (1 - x^2), which means x must be between -1 and 1. The range is determined by the vertical shift (3√x^2) and the square root term. Since the graph has two branches, one moving upward and one moving downward, the range will be all real numbers.

Step 4: Sketch the graph.
For each value of x in the domain (-1 ≤ x ≤ 1), calculate the corresponding values of y using both the positive and negative square root equations. This will give you the points for the two branches of the graph.

The graph of the equation x^2 + (y - 3√x^2)^2 = 1 will have two branches, one for the positive square root and one for the negative square root, with a domain of -1 ≤ x ≤ 1 and a range of all real numbers.

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The format element that will display the value of Friday in a specified date as a 6 is option B, DD.

The format element that will display the value of Friday in a specified date as a 6 is option B, DD. DD displays the day of the month as a two-digit number, for example, 01 for the first day of the month and 31 for the last day of the month. It does not display the day of the week. Option A, D, displays the day of the week as a single-digit number, for example, 1 for Monday and 7 for Sunday. Option C, DDD, displays the abbreviated name of the day of the week, for example, Fri. Option D, DAY, displays the full name of the day of the week, for example, Friday. Therefore, option B, DD, is the correct answer to the question.
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The answer to the question is option A: 2 vertices have an odd degree.

To answer this question, we need to first understand what vertices and odd degrees mean in graph theory. A vertex is a point in the graph, and degree refers to the number of edges that are connected to that vertex. An odd degree means that a vertex is connected to an odd number of edges.

Looking at the map of bridges, we can see that there are several vertices where the bridges intersect. To determine the odd degree of each vertex, we need to count the number of bridges that intersect at that point.

Starting at the top left corner of the map, we can count the number of bridges that intersect at each vertex. The first vertex has three bridges connected to it, so its degree is odd. The same is true for the second vertex, which also has three bridges connected to it. Moving down the map, the third and fourth vertices both have two bridges connected to them, making their degrees even. Finally, the fifth vertex has three bridges connected to it, giving it an odd degree.

So, the answer to the question is option A: 2 vertices have an odd degree. It's important to note that in a graph, the sum of the degrees of all vertices must be even, so the fact that there are only two vertices with odd degrees tells us that there must be an even number of vertices with even degrees.

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While the measurement of the individual angles in a triangle can vary depending on the size and shape of the triangle, their sum is always 180 degrees.

This fundamental concept is known as the Triangle Sum Theorem and is true for all types of triangles, including equilateral, isosceles, and scalene. This theorem is essential in geometry and plays a significant role in solving various mathematical problems related to triangles. By knowing the sum of the angles, it is possible to calculate the measurement of one missing angle if the other two are known. Additionally, it helps in proving congruence and similarity of triangles and finding various geometric properties of triangles.

While the measurement of the individual angles in a triangle can vary, their sum is always constant. This constant sum is 180 degrees. This principle is known as the Triangle Sum Property, which states that the three interior angles of any triangle will always add up to 180 degrees, regardless of the triangle's shape or size. To find the sum of the angles, you simply add the three angle measures together. For example, if a triangle has angles of 60, 70, and 50 degrees, the sum would be 60 + 70 + 50 = 180 degrees. This property holds true for all triangles, ensuring that their interior angles always have a constant sum.

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The height of the actual space rocket is 66 feet.

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original or actual geometric figure (pre-image).

Mathematically, the formula for calculating the scale factor of any geometric object or figure is given by:

Scale factor = side length of image/side length of pre-image

Scale:

1 inch = 12 feet

1/12 = New height/Actual height

1/12 = 5.5/Actual height

Actual height = 5.5 × 12

Actual height = 66 feet.

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This can be simplified to 3^7, which equals 2,187. So, there are 2,187 different key designs possible for these antique cars.

To determine the number of different key designs possible for antique cars with seven parts and three patterns for each part, we can use the multiplication principle of counting.

This principle states that if there are m ways to perform one action and n ways to perform another action, then there are m x n ways to perform both actions together.

Therefore, the number of different key designs possible can be calculated by multiplying the number of patterns for each part together. In this case, we have three patterns for each of the seven parts, so we can calculate the number of possible designs by using the formula 3^7.

Using a calculator, we can see that 3^7 is equal to 2,187. Therefore, there are 2,187 different key designs possible for antique cars with seven parts and three patterns for each part. It's worth noting that not all of these designs may have actually been produced or used, but this calculation gives us the total number of possibilities based on the given information.
Hi! I'd be happy to help you with your question. To determine the number of different key designs possible for these antique cars, we can use the multiplication principle of counting. Since there are 7 parts to each key and 3 patterns for each part, we can multiply the number of patterns for each part together to find the total number of key designs.

The calculation would be: 3 (patterns for part 1) × 3 (patterns for part 2) × 3 (patterns for part 3) × 3 (patterns for part 4) × 3 (patterns for part 5) × 3 (patterns for part 6) × 3 (patterns for part 7).

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Right angled triangle as the top angle is a 90 degrees

Answer:

1,20.13

2,54.99

that's the answer to 1 and 2

Use the pythagorean theorem.

[tex]a^{2} +b^{2} =c^{2}[/tex]

which we can quickly type as a^2+b^2=c^2. (The ^2 means squared.)

C is the hypotenuse, the longest length. It doesn't matter what you call a and b; just use the two shorter lengths.

So we're going to take each set of numbers, and if the square of the hypotenuse (c, the longest side) is equal to the sum of the squares of each length (the other two sides, a and b), then it's a right triangle. If it doesn't equal, then it's NOT a right triangle.

3,4,5:

3^2+4^2 = 9+16 = 25 = 5^2, so this IS a right triangle.

5, 12, 13:

5^2+12^2 = 25+144 = 169 = 13^2, so this IS a right triangle.

6,8,12:

6^2+8^2= 36+64 = 100. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

6, 9, 12:

6^2+ 9^2 = 36+81 = 117. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

8, 13, 26:

8^2 + 13^2 = 64+ 169 = 233. 26^2 = 676. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

8, 15, 17:

8^2+ 15^2 = 64 + 225 = 289. 17^2 = 289, so this IS a right triangle.

9, 12, 14:

9^2 + 12^2 = 81+144 = 225. 14^2 = 196. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

3, 8, 19:

3^2 + 8^2 = 9 + 64 = 73. 19^2 = 361. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

0.5, 6, 3:

Oh, your teacher is trying to trick you bc the hypotenuse has been the last number with every other problem! 6 is the longest and that's your hypotenuse (c).

0.5^2 + 6^2 = 0.25 + 36 = 36.25. 6^2 = 36.  These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.

Tim spun both spinners 280 times.

To determine the probability that both spinners land on red, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

Let's use R to represent the event of landing on red and B to represent the event of landing on blue. Then, the probability of spinner A landing on red is 0.5, and the probability of spinner B landing on red is 0.6. Therefore, the probability of both spinners landing on red is:

P(R for A and R for B) = P(R for A) x P(R for B) = 0.5 x 0.6 = 0.3

Next, we know that both spinners landed on red a total of 84 times. Let's assume that Tim spun both spinners the same number of times, and that this number is n. Then, the probability of both spinners landing on red is also equal to the number of times both spinners landed on red divided by the total number of spins:

P(R for A and R for B) = 84/n

We can set these two expressions equal to each other and solve for n:

84/n = 0.3

n = 280

Therefore, Tim spun both spinners 280 times.

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The probability that a male chosen at random watches comedy is 0.333.

When an occurrence A is predicated on another event B having already happened, the conditional probability is:

P(A/B) = P(A∩B)/P(B) =  n(A∩B)/n(B)

Let,

M denotes a male was selected

C denotes a person's favorite genre is comedy

n (M) denotes the number of males in the survey

Then n (M) = 15

The number of males in the survey who watches comedy,

n (M ∩ C) = 5

The probability that a male chosen at random watches comedy as follows:

P(C/M) = n(M∩C)/n(M)  = 5/15

                                     = 1/3 =0.333

Hence,

Required probability P(C/M) = 0.333

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The complete question is:

A survey asked 30 people what their favorite genre of television broadcasting was, and the results were tabulated above. Find the probability that a person chosen at random was female, given that they like comedy. Round the answer to the nearest hundredth.

                Male      Female     Total

Sports          8              3               11

Drama          2              6               8

Comedy       5              6               11

Total            15             15             30

the calculation made by subtracting the age at death from 65 is a concept of retirement age.

this calculation is often used as a way to determine when a person can retire and start receiving retirement benefits. In many countries, 65 is the standard retirement age, so by subtracting a person's age at death from 65, it can be determined how many years they have left until retirement.

understanding the concept of retirement age and how it is calculated can be helpful for individuals planning for their future and considering when they may be able to retire.


Years of potential life lost (YPLL) is a public health metric that measures the impact of premature mortality on a population. It helps quantify the burden of disease by estimating the number of years a person would have lived had they not died prematurely. The calculation is done by subtracting the individual's age at death from a predetermined age, often 65 or 75, depending on the standard used.

the concept of subtracting the age at death from 65 represents years of potential life lost (YPLL), which is an important measure in public health to assess the burden of premature mortality.

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The calculated distance of the man from the foot of the tree​ is 24.2 meters

The man, the tree, the foot of the tree and the elevation would form a right triangle

This means that the distance of the man from the foot of the tree​ in the right triangle can be calculated using the following tan ratio

tan(30) = 14/distance

Cross multiply the equation

So, we have

distance = 14/tan(30)

Evaluate the quotient

distance = 24.2

Hence, the distance in the right triangle is 24.2 meters

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Answer:

Step-by-step explanation:

Let AB be the height of the tree = 14 m

Angle of elevation, ∠C = 30°

We have to calculate the distance of the man from the foot of the tree

Let BC = the distance of the man from the foot of the tree

Now, In Traingle ABC,

tan 30° = AB/BC

1/√3 = 14/BC

BC = 14 √3 m

√3 = 1.734

BC = 14 × 1.734

BC = 24.2 m (approx)

Hence the the distance of the man from the foot of the tree is 24.2 m

Answer:The graphed function has a higher minimum.Both functions have an axis of symmetry of x = 1.The function f(x) = x2 − 2x − 3 has a greater range.Additionally: neither function has a maximum, both functions have the same domain

Step-by-step explanation: just did it

The number of one-liter bottles she can fill from 5 gallons is A = 19

Given data ,

Aisha brings 5 gallons of a sports drink to a game

Now , 1 liter≈ 4.2 cups

And , 1 gallon is approximately equal to 3.78541 liters.

So, 5 gallons is approximately equal to 5 * 3.78541 = 18.92705 liters

On simplifying the equation , we get

Now, we divide the total liters by 1 liter (the capacity of each bottle) to find the number of bottles Aisha can fill:

Number of bottles = 18.92705 liters / 1 liter ≈ 18.93

Hence Aisha can fill approximately 19 one-liter bottles with 5 gallons of sports drink

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The value of x will lie in the interval {0, 2π}.

Given that sin x/2 = 0 for interval {0, 2π} we need to find the value of x will lie in which interval,

We know that, for sin 0 degrees, the angle 0° lies on the positive x-axis. Thus, sin 0° value = 0

Since the sine function is a periodic function, we can represent sin 0° as, sin 0 degrees = sin(0° + n × 360°), n ∈ Z.

⇒ sin 0° = sin 360° = sin 720°, and so on.

Also, sine is an odd function, the value of sin(-0°) = -sin(0°) = 0.

So the value of x will be under {0, 2π}

Hence, value of x will lie in the interval {0, 2π}.

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