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The exact values of the sine, cosine, and tangent of the angle 255° are -1/√2, 1/√2, and -1, respectively.

To find the exact values of the sine, cosine, and tangent of the angle 255°, we can use the identity that relates the trigonometric functions of an angle to the trigonometric functions of its complement.

By expressing 255° as the sum of 300° and -45°, we can determine the exact values of the trigonometric functions for the given angle.

We know that the sine, cosine, and tangent of an angle are periodic functions, repeating every 360 degrees. To find the exact values of the trigonometric functions for 255°, we can express it as the sum of 300° and -45°, where 300° is a multiple of 360°.

Since the sine, cosine, and tangent functions are odd or even functions, we can use the values of the trigonometric functions for 45° to determine the values for -45°.

For 45°:

sin(45°) = cos(45°) = 1/√2

tan(45°) = 1

Since cosine is an even function, cos(-45°) = cos(45°) = 1/√2.

Since sine is an odd function, sin(-45°) = -sin(45°) = -1/√2.

Using the definition of tangent as the ratio of sine to cosine, tan(-45°) = sin(-45°) / cos(-45°) = (-1/√2) / (1/√2) = -1.

Therefore, for the angle 255°:

sin(255°) = -1/√2

cos(255°) = 1/√2

tan(255°) = -1

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The only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To find the average value of the function f(x) = 6e^x over the interval [-3, 3], we need to evaluate the definite integral of f(x) over that interval and divide the result by the length of the interval:

Average value = (1/(3-(-3))) * ∫[−3, 3] 6e^x dx

= (1/6) * [\(6e^x\)] from -3 to 3

= (1/6) * (\(6e^3\) - \(6e^{(-3)}\))

≈ 118.936

Therefore, the average value of the function over the given interval is approximately 118.936.

To find all values of x in the interval [-3, 3] for which the function equals its average value, we need to solve the equation f(x) = 118.936, which means:

\(6e^x\) = 118.936

Dividing both sides by 6, we get:

\(e^x\) = 19.823666...

Taking the natural logarithm of both sides, we get:

x = ln(19.823666...)

≈ 2.984

Therefore, the only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.

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He can make 32 dozen Fasnacht with 8 pounds of butter.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here, She has 8 pounds of butter and 1 cup of butter can make 2 dozen Fasnacht. Also, 1 pound of butter is 2 cups thus 8 pounds of butter is equivalent to 16 cups.

1 cup of butter to make 2 dozen Fasnacht

then 16 cups of butter can be used to make 16×2=32 dozen Fasnacht

Hence, he can make 32 dozen Fasnacht with 8 pounds of butter.

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The probability that the mean weekly wage of a randomly selected group of 16 workers from the factory will be within $3 of the population mean wage is 0.98

To solve this problem,

We can use the central limit theorem which states that the sample means from a large sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to find the standard error of the mean, which is equal to the standard deviation divided by the square root of the sample size:

Standard error of the mean = 5 / sqrt(16) = 1.25

Next, we need to find the z-score for the lower and upper bounds of the sample mean:

lower z-score = (402 - 405) / 1.25 = -2.4

upper z-score = (408 - 405) / 1.25 = 2.4

We can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores:

lower probability = 0.0082

upper probability = 0.9918

To find the probability that the sample mean is within $3 of the population mean we need to subtract the lower probability from the upper probability:

Probability = 0.9918 - 0.0082 = 0.9836

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Answer:

Interior intersections are those intersecitons inside the main figure. For example, the intersection between two chords of a circle, that represents an interior intersection.

Exterior interseciton are those intersections which happens outside the figure, for example, the intersection of two tangent lines of a circle.

Basically, they are similiar, because both type of intersections are formed by the encounter between two lines or segments.

However, they are different, because each type is formed at different parts of the figure, one inside and one outside.

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

2x + 4y - 2z = -6 (4)

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Step-by-step explanation:

Natural numbers are numbers that include positive integers.

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25

Prime numbers are numbers that are greater than 1 and has only two factors

2,3,5,7,11,13,17,19,23

What Fractions of natural number are prime number?

9/25

By using linear equation, the patrick is 12 years old and pat is 29 years old.

We take variable x to find out their present age.

The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation. Unknown amounts can be symbolised or represented by any variable. There are a few straightforward procedures for solving linear equations. To determine the final value of the unknown quantity, the constants are isolated to one side of the equation and the variables are isolated to the other side.

Let the age of patrick is 'x'. so the age of his father pat be 'x + 17'.

After 5 years, partrick's age will be 'x + 5'

And his father pat age will be x + 17 + 5 = 'x + 22'

After 5 years pat age will e twice of patrick age.

So that 2(x + 5) = x + 22

⇒ 2x + 10 = x + 22

⇒ 2x - x = 22 - 10

⇒ x = 12

So that the patrick is 12 years old and pat is 29 years old.

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The result of the division based on the exponent will be C. −5x6y2 + 3x3y.

When dividing with the same base, you subtract the exponents. So, for the x terms, you subtract the exponent of x in the denominator (-2) from the exponent of x in the numerator (8 - 5 = 3). Similarly, for the y terms, you subtract the exponent of y in the denominator (1) from the exponent of y in the numerator (3 - 2 = 1).

Therefore, the result is -5xy²+ 3x(5-2), which simplifies to -5xy² + 3x³y.

Thus, the correct answer is −5x6y2 + 3x3y.

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Answer:

-8, -3, 2 ad 7

Step-by-step explanation:

This graph shown is a polynomial function. The solution is the point where the curves cuts the x axis. From the diagram we can see that the curves cuts the x axis at four points.

The points are at x1 = -8, x2 = -3, x3 = 2 and x4 = 7

Hence the real solutions to the function f(x) = 0 are -8, -3, 2 ad 7

The candidate key for the relation schema R(A,B,C,D,E): A→B, C→B, D→A, D→B, D→C, C→D, D→E.

Candidate key for the given relation: To find the candidate key for the relation schema R(A,B,C,D,E), we need to follow the below steps:

Here, we have the following functional dependencies: A→B, C→B, D→ABC, AC→D, D→E.

Step 1: To normalize the given dependencies, we have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To check for the minimal dependency, we can eliminate the redundancy by eliminating D→ABC. Therefore, we have the following dependency:

A→B, C→B, D→A, D→B, D→C, D→E.

Step 3: Find the closure on each attribute, which is as follows:

1. A+ = {A,B}

2. B+ = {B}

3. C+ = {B}

4. D+ = {A,B,C,D,E}

5. E+ = {E}

Step 4: The combination of attributes that have all attributes of the relation schema, and it will be a candidate key is AD. Therefore, the candidate key is AD.

Compute the minimal cover of F:

Minimal Cover: The minimal set of dependencies that is equivalent to the given set of dependencies is the minimal cover.

We have the following functional dependencies:

A→B, C→B, D→ABC, AC→D, D→E.

The process to compute the minimal cover of F is as follows:

Step 1: To find the redundant dependencies, we need to split the dependencies. We have the following dependencies:

A→B, C→B, D→ABC, AC→D, D→E  becomes

A→B, C→B, D→A, D→B, D→C, D→E.

Step 2: To eliminate the dependencies with three attributes, we can use the following steps:

If X→YZ, then X→Y and X→Z.

Therefore, we have the following dependency:

D→A, D→B, D→C.

Step 3: To eliminate the dependency with two attributes, we can use the following steps:

If X→Y and Y→Z, then X→Z.

We have the following dependency: AC→D, C→D.

Step 4: Therefore, the minimal cover of F is A→B, C→B, D→A, D→B, D→C, C→D, D→E.

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The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).

Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.

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Answer:

This inscribed angle is half of the intercepted arc JL, so 2(83)= 9x +40.

166 -40 = 9x, x=14.

Step-by-step explanation:

The value of x in the given figure is 14 which we obtain by  inscribed angle is half of the intercepted arc.

The inscribed angle is half of the intercepted arc.

83 = 1/2(9x+40)
Now let us find the value for x

83= 9/2x + 20

Subtract 20 from both sides to isolate the x variable

83-20=9/2x

63=9/2x

126=9x

Divide both sides by 9

14 is value of x

x=14

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Answer: 22

Step-by-step explanation:

Ok, so the way I do it I multiply then divide.

For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday

For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.

So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)  

Answer:

y x

..........

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

Answer:

The answer is A

Step-by-step explanation:

Hope it helps!

1) Probability that exactly 6 adults have little confidence in their cars is 0.0689 .

2) Probability that more than 7 adults have little confidence in their cars is 0.005 .

Given details about US adults:

Adults having little confidence in their cars = 0.35

Sample size = 10

1)

Probability that exactly 6 adults have little confidence in their cars.

Binomial expression = \(nC_r(p)^r(1-p)^{n-r}\)

Here,

n = 10

p = 0.35

r = 6

Substitute the values in the binomial expression.

\(P(X = 6) = 10C_6(0.35)^6(1-0.35)^{10-6}\\P(X = 6) = 10C_6 (0.00183)(0.178)\\P(X= 6) = 0.0689\)

2)

Probability that more than 7 adults have little confidence in their cars.

Binomial expression = \(nC_r(p)^r(1-p)^{n-r}\)

Here,

n = 10

p = 0.35

r = 6

Substitute the values,

\(P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)\)

\(P(X > 7) = 10C_8(0.35)^8(1-0.35)^{10-8}+ 10C_9(0.35)^9(1-0.35)^{10-9}+ 10C_{10}(0.35)^{10}(1-0.35)^{10-10}\\P(X > 7) = 0.0043 + 0.0005 + 0.00003\\P(X > 7) = 0.005\)

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Answer:

Option 3

Step-by-step explanation:

The slope is \(\frac{-2-6}{5-1}=-2\).

The equation of the line through \((x_1, y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

y-6=-2(x-1) is the equation is a point slope form equation for line AB

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

point A, with coordinates (1, 6), and point B, with coordinates (5, -2)

m=-2-6/5-1

m=-8/4

=-2

So slope is -2.

The point slope intercept of line is

y-y₁=m(x-x₁)

y-6=-2(x-1)

Hence y-6=-2(x-1) is the equation is a point slope form equation for line AB

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Answer:

7 dollars and 25 cents

Step-by-step explanation:

there is 8 quarts in 2 gallons then divide 58 dollars by 8 and you get 7 dollars 25 cents

Division is one of the four fundamental arithmetic operations. The price per quart is $7.25 per quart.

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Given that A 2-gallon bucket of paint costs $58.00. Therefore, the price per gallon is,

Price per gallon = $58/2

Since a gallon is equal to 4 quarts. Therefore, the price per quart is,

Price per quart  = $58/(4×2) = $7.25 per quart

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The given curve is y=sinx. To obtain the volume of the generated solid when the region between the x-axis and the graph of y=sinx is revolved about the line x = 2π, we can utilize the disk method. Consider rotating a point, (x, y), on y=sinx for 0≤x≤π about the line x=2π.

When rotated, we have to notice that a perpendicular line from the rotation axis (x=2π) to the point on the graph will meet the graph on the line y= sinx. Thus, the perpendicular line will have length 2π-x. Also, the function y=sinx, 0≤x≤π represents a wave over a cycle, and its mirror image over x=π. Hence, we can obtain the volume of the generated solid using two symmetric disks. Now let us compute the volume using the disk method. The volume is given by:

∫_0^π〖π(2π-x)^2 sin^2 x dx〗 = 4π^3/3 - 8π^2+ 4π.

The region between the x-axis and the graph of y=sinx, 0≤x≤π is revolved about the line x = 2π to produce a solid. We utilized the disk method to compute the volume of the generated solid. We noted that the curve has two symmetric disks due to its symmetry about x=π. The volume of the generated solid is given by:

∫_0^π〖π(2π-x)^2 sin^2 x dx〗 = 4π^3/3 - 8π^2+ 4π.

The volume of the generated solid is therefore given by:

4π^3/3 - 8π^2+ 4π cubic units.

Therefore, the volume of the generated solid when the region between the x-axis and the graph of y=sinx, 0≤x≤π is revolved about the line x = 2π is 4π^3/3 - 8π^2+ 4π cubic units.

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Answer:

30 cubes are added

Step-by-step explanation:

The image of the solid shape is attached.

From the Plan, Side elevation and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks is needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid = 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added = 48 cubes - 18 cubes = 30 cubes.

30 cubes are added

The number of cubes that are added is 30.

What is Cube?

A cube's form is occasionally referred to as "cubic." Another way to put it is that a block with uniform length, width, and height is regarded to be a cube. It also contains 12 edges and 8 vertices, with 3 of the edges coming together at a single vertex point. Examine the illustration below, identifying the faces, edges, and vertices. It is also referred to as a right rhombohedron, an equilateral cuboid, and a square parallelepiped. One of the platonic solids, the cube is a convex polyhedron with all of its faces being square. The cube has either cubical symmetry or octahedral symmetry. The square prism is a specific instance of a cube.

From the Plan, Side elevation, and Front elevation, the number of cubes needed to make the shape is 18 blocks. From the front elevation, 12 blocks are needed (4 * 3 blocks) while from the side elevation 6 blocks are needed given a total of 18 blocks.

The number of blocks needed to make the cuboid

= 4 * 4 * 3 = 48 cm cubes.

Therefore the number of cubes to be added

= 48 cubes - 18 cubes

= 30 cubes.

30 cubes are added.

Hence, The number of cubes that are added is 30.

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Answer:

8.2k +2.05

Step-by-step explanation:

Answer: 8.46 ✌️

Pythagorean’s theorem

Answer:

150 ft²

Step-by-step explanation:

If you take that triangle and place it on the other side you get a normal rectangle and can just multiply 15 By 10

Answer:

NOT THE ANSWER try to include her scores because there is no data

Answer:

y=2x+3

Step-by-step explanation:

Answer:

12,000

Step-by-step explanation:

There are 1,000 meters in a kilometer. So, if you have 12 kilometers, that's 12,000 meters.

Answer:

12000

Step-by-step explanation:

One kilometer = 100 meters 12 times 1000 = 1200