Given that alpha and beta are acute. Sin alpha = 1/√10 and Sin beta = 1/√5, prove without using calculator and table that Sin (alpha + beta) = 1/√2​

Answer:

x=5/3 0r 1 2/3

There are 331 ways when 66 identical coins can be separated into three nonempty piles

Let the piles have a, b and c coins, with 0<a <b <c. Then, let b=a+k₁, and

c=b+k₂, such that each ki≥1.

The sum is then a+a+k₁+a+k₁+k₂= 66 ⇒ 3a+2k₁+k₂ = 66.

This is simply the number of positive solutions to the equation

3x+2y+z = 66.

If a = 1, then 2k₁ + k₂ = 63⇒ 1≤k₁ ≤31. Each value of k₁ corresponds to a unique value of k₂, so there are 31 solutions in this case.

Similarly, if a = 2, then 2k₁+k₂= 60⇒ 1≤k₁ ≤29, for a total of 29 solutions in this case.

If a = 3, then 2k₁+ k₁= 57 ⇒ 1 ≤ k₁ ≤28, for a total of 28 solutions.

In general, the number of solutions is just all the numbers that aren't a multiple of 3, that are less than or equal to 31.

We then add our cases to get

=1+2+4+....31=1+2+3+...31-3(1+2+3+...10)

=31*(32)/2-3(55)

=31*16-165

=496-165

=331

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Answer:

MMXV

Step-by-step explanation:

(⁠◕⁠ᴗ⁠◕⁠✿⁠)(⁠◕⁠ᴗ⁠◕⁠✿⁠)(⁠◕⁠ᴗ⁠◕⁠✿⁠)

Answer: sorry would help ya but i can't because i have no clue what the question is asking me to round...

The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.

The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.

g = {2, 4, 6, 8}

9

A: A

The number 9 does not belong to the set g, so it does not get circled. The number 9 belongs to the set A, so it should be circled.

The number 9 does not belong to the set g, which consists of the numbers 2, 4, 6, and 8. Instead, the number 9 belongs to the set A, so the symbol should be circled to indicate this. The set A includes all the numbers from 1 to 10, so the number 9 is included. This means that the circle should be placed around the symbol for set A to indicate that 9 belongs to this set.

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To test the hypotheses h0: p1 = p2 and Ha: p1 ≠ p2, we can use a two-sample proportion test. This test compares the proportion of success (no longer being late to school) in the control group (p1) to the proportion of success in the treatment group (p2) to determine if there is a statistically significant difference between the two proportions.

Here are the steps to perform the test:

State the hypotheses:

h0: p1 = p2 (the proportion of success in the control group is equal to the proportion of success in the treatment group)

Ha: p1 ≠ p2 (the proportion of success in the control group is not equal to the proportion of success in the treatment group)

Select a significance level (alpha): usually, it is set as 0.05

Calculate the test statistic:

p = (p1n1 + p2n2) / (n1 + n2)

z = (p1 - p2) / sqrt(p*(1-p)*((1/n1)+(1/n2)))

Find the p-value:

Using the z-score, look up the probability in a standard normal table.

Make a decision:

Compare the p-value to the significance level. If the p-value is less than or equal to the significance level, then reject the null hypothesis. If the p-value is greater than the significance level, then fail to reject the null hypothesis.

Conclusion:

Interpret the results in terms of the research question. If the null hypothesis is rejected, then the results suggest that there is a statistically significant difference in the proportion of success between the control group and the treatment group

The question is incomplete, the complete question is:

__"'A researcher wants to conduct a study to determine whether a newly developed anti-tardy program is successful. Two random groups of 100 students each, identified as control and treatment groups, are formed from 200 students who are repeatedly late to school. Both groups receive a set of anti-tardy reading materials and a lecture from a teacher and a tardy-reformed student about the negative impacts of being late. In addition, the treatment group also receives materials from the newly developed program. Thirty-three of the 100 students in the control and 35 of the 100 students in the treatment group are no longer late to school is recorded 6 months later.

Use the results to test the hypotheses H0: p1 = p2 and Ha: p1 ≠ p2 where p1 represents the proportion of students who succeed in the control program and p2 represents the proportion of students who succeed in the newly developed program.

What can you conclude using the significance level α = 0.05?""__

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C. Unique solution. The system of linear equations have a unique solution because the equations are consistent and have the same number of variables and equations.

The given system of linear equations is x+2y=3 and 2x+4y=15. To determine whether the system of linear equations have no solution, infinitely many solution or unique solutions, we need to solve the system of equations. Firstly, we expand and simplify both equations to get x+2y=3 and 2x+4y=15. Then, we compare the coefficients of the equations to determine if the system of equations is consistent, inconsistent or dependent. Since the equations are consistent and have the same number of variables and equations, we can solve the system of equations. By isolating the variables and using the substitution method, we can solve the system of equations to get x=3 and y=3. This means that the system of linear equations have a unique solution.

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Answer:

(-2x+2) is the difference

Step-by-step explanation:

Shown above

Answer:

10.9 8.4 8.8

Step-by-step explanation:

Both 10.9C and 8.4C are below zero. We can identify both are in negative temperatures. 8.8C was not labeled as below zero, which indicates a positive unit.

The equation of line is y = -2x + 8 and the slope is m = -2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

The equation of line perpendicular to the line is y = ( 1/2 )x - 8

Now , the slope of the line m₁ = 1/2

For perpendicular lines , the product of the slopes is -1

So , m₁ x m₂ = -1

So , the value of Slope m₂ = -2

And , the line passes through the point P ( 7 , -6 )

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -6 ) = ( -2 ) ( x - 7 )

On simplifying the equation , we get

y + 6 = -2x + 14

Subtracting 6 on both sides of the equation , we get

y = -2x + 8

Hence , the equation of line is y = -2x + 8

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Answer:

1818886278282871728282882

Answer:

3 is the answer

Step-by-step explanation:

1.8/0.6

example: see the image and follow how to do it

Answer:

Gold is in Box 1

Step-by-step explanation:

There are 3 boxes. One of them contains gold

In each box, there is a message, and one of them is true.

Box 1: "The gold is not in Box 2".

Box 2: "The gold is in this box"

Box 3: "The gold is not in this box".

Which box has the gold?

Answer:

O Box 1

O Box 3

O Box 2

There's not enough info

Assume each statement to be true at a time, and check for contradictions.

Box 1: "The gold is not in Box 2".

Assume True. Gold in 1 or 2.

Box 2: "The gold is in this box"

False. Gold not in 2.

Box 3: "The gold is not in this box".

False. Gold in 3

Contradiction between box1 and box 3 message.

Box 2: "The gold is in this box"

Assume true. Gold in 2.

Box 1: "The gold is not in Box 2".

False. Gold in 2.

Box 3: "The gold is not in this box".

False. Gold in 3.

Contradiction between boxes 2 and 3. Box 2 message cannot be true.

Box 3: "The gold is not in this box".

Assume true. Gold in 1 or 2.

Box 1: "The gold is not in Box 2".

False. Gold in 2.

Box 2: "The gold is in this box"

False. Gold not in 2.

No contradictions.

Gold must be in 1.

Answer: Gold is in Box 1

Yes, this is correct. The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be described by the equation a_c = v^2/r.

The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be calculated using the equation a_c = v^2/r.

The centripetal acceleration of an object undergoing uniform circular motion with tangential speed v and radius r can be described by the equation a_c = v^2/r. This equation shows that the acceleration of an object in uniform circular motion is proportional to the square of the velocity and inversely proportional to the radius of the circle. This equation is a result of Newton's second law, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration. The centripetal acceleration is the acceleration of an object towards the center of the circle and is perpendicular to the direction of motion. In order to calculate the centripetal acceleration of an object, the velocity and radius of the circle must be known. The equation a_c = v^2/r can then be used to calculate the centripetal acceleration of the object.

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Yes Kazuko's reasoning is  correct the expressions 5x and 6 - x are equivalent expressions

When two expressions can be reduced to a single third expression or when one of the expressions can be expressed in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if two expressions are equal.

X-terms and constants should be combined with any other like terms on either side of the equation. Put the terms in the same sequence, with the x-term generally coming before the constants. The two phrases are equal if and only if each of their terms is the same.

5x and 6 - x

5x +  6 - x

2 (2 x + 3)

4 x + 6

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The slope of the line through the points (-8, -11) and (-1, -5) is (y2 - y1)/(x2 - x1) = (-5 - (-11))/(-1 - (-8)) = -6/7 = -0.8571428571428571.

The quadratic function f(x) = x² - 6x + 9 has a minimum at point (3,0).

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is - f(x) = x² - 6x + 9.

Find the differentiation of f(x) -

dy/dx = d/dx (x² - 6x + 9)

d/dx (x²) - d/dx (6x) + d/dx (9)

2x - 6 + 0

2x - 6 = 0

For stationary values, dy/dx = 0

2x - 6 = 0

2x = 6

x = 6/2

x = 3

At x = 3 we get stationary values.

Now, d²y/dx² = 2x - 6

d/dx (2x - 6)

d/dx (2x) - d/dx (6)

2 - 0 = 0

2 = 0

(d²y/dx²) x=3 = 2 (positive)

Therefore, at x = 3 the function is minimum.

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Answer:

------------------------------------

Volume of the cone:

We have a slant height and radius. They represent a hypotenuse and one of the legs of the right triangle.

Use Pythagorean to find the other leg, the height h of the cone:

Find the volume:

The volume of the cone is calculated as: 671.0 cubic inches.

The volume of a cone can be found using the formula:

V = (1/3) * pi * r^2 * h

Where V is the volume, pi is approximately 3.14, r is the radius of the base, and h is the height (or slant height) of the cone.

In this case, the radius of the base is 8 inches and the slant height is 10 inches. So, the volume of the cone can be found by:

V = (1/3) * pi * 8^2 * 10

V = (1/3) * 3.14 * 64 * 10

V = (1/3) * 201.12 * 10

V = 671.04 cubic inches

Rounding the answer to the nearest tenth of a cubic inch, the volume of the cone is approximately 671.0 cubic inches.

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The distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.

The distance between Dallas, Texas and Omaha, Nebraska can be calculated using the Haversine Formula. This formula calculates the great circle distance between two points on a sphere, taking into account the curvature of the Earth. The formula is as follows:

d = 2r arcsin( sqrt[ sin^2((lat2 - lat1)/2) + cos(lat1)cos(lat2)sin^2((lon2 - lon1)/2)] )

In this case, the latitude of Dallas, Texas is 32° 47' 39'' N and the latitude of Omaha, Nebraska is 41° 15' 50'' N. Since the two cities are on the same longitude, we can assume that the longitude for both cities is 0°.

Plugging these values into the formula, we get:

d = 2(4000 miles) arcsin[ sqrt[ sin^2((41° 15' 50'' N - 32° 47' 39'' N)/2) + cos(32° 47' 39'' N)cos(41° 15' 50'' N)sin^2((0° - 0°)/2)] ]

d = 631.4 miles

Therefore, the distance between Dallas, Texas and Omaha, Nebraska is 631.4 miles.

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Answer:b

Step-by-step explanation:

719/64 unit²  is the area of the overlapping region (which is shaded)

Rectangles .

What is a rectangle, exactly?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.

                         Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

the Pythagorean theorem as follows to calculate the value of x .

  ( 4 - x )²  = 3² + x ²

16 - 8x  + x² =  9 + x²

       16 - 8x = 9

         16 - 9 = 8x

         7/8 = x

Thus, the area of the shaded region will be equal to the area of rectangle ABDC minus the area of the two triangles on the same rectangle. The area of rectangle ABDC is equal to

                  A = l * w

                     =  4 * 3

                  A = 12

The area of each of the two triangles is equal to

                 A = 1/2bh

                    = 1/2 ( 7/8) ( 7/8 )

                    = 49/128

The area of the two triangles is equal to

                   A = 2 * 49/128

                     A =  49/64

Therefore, the area of the shaded region is equal to

                         12 - 49/64  =  719/64 unit²

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Point K is the point that marks the centre of the circle depicted below. This is due to the fact that the centre of a circle is the place from which all of its points are equally far. As a result, Point K is the circle's midpoint and consequently its centre.

To put it simply, a circle is a spherical shape without any edges or line segments. In geometry, it has the shape of a closed curve. The circle's points are set apart from the center by a specified amount.

A circle is a closed, two-dimensional object in which all points in the plane are equally spaced apart from the center. The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles.

A circle is a figure with a round shape, all of its points lying on the same plane and all of its points being equally spaced from the circle's center.

The center of the circle can be found by finding the midpoint of the diameter, which passes through points K and T.

The midpoint of the diameter can be found by taking the average of the x and y coordinates of points K and T.

Midpoint of AB = (x1+x2/2 , y1+y2/2)

Midpoint of K and T = ((-2 + 4)/2 , (1 + 7)/2)

Midpoint of K and T = (1 , 4)

Therefore, the center of the circle is point K.

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The slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y at a point (x,y) is -sin(xy) ( x * dy/dx + y) + 6*sin(x)*cos(x) + 2dy/dx.

So the option b is the correct representation for the slope of the tangent line to the curve.

The correct representation for the slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y is c. -sin (xy) (x dy/dx) + 6 sin x + 2.

The slope of a tangent line to a curve at a point (x,y) is given by the derivative of the function with respect to x, evaluated at that point.

So to find the slope of the tangent line to the curve cos(xy) + 3sin^2(x) + 2y, we need to find the derivative of the function with respect to x.

The derivative of cos(xy) with respect to x is

-sin(xy) ( x * dy/dx + y)

The derivative of sin^2(x) with respect to x is

2*sin(x)*cos(x)

The derivative of y with respect to x is

dy/dx

So the derivative of the function with respect to x is:

-sin(xy) ( x * dy/dx + y) + 6*sin(x)*cos(x) + 2dy/dx

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The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively.

The degree of f(x^3) g(X^2) is 14.

The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively. When we substitute x^3 for x in f(x) and x^2 for x in g(x), the highest exponent of the terms of f(x^3)g(x^2) is 3*4 + 2*5 = 14. Therefore, the degree of f(x^3) g(x^2) is 14.

The degree of f(x^3) g(x^2) is 14, which is calculated by multiplying the degree of f(x) and g(x) with the exponent of their respective terms. The degree of a polynomial is the highest exponent of its terms. Since f(x) and g(x) are both polynomials of degree 4 and 5 respectively, the degrees of f(x) and g(x) are 4 and 5 respectively.

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Matrix A belongs to the permutation and Markov classes. A permutation matrix is a square matrix with exactly one 1 in each row and each column, and 0s everywhere else.

This is the case for matrix A, as it has one 1 in each row and column and 0s everywhere else. Matrix A is also a Markov matrix, which means that all the entries are non-negative and the sum of each row is equal to 1. This can be seen by summing each row, which yields 1+0+0 = 1, 0+1+0 = 1, and 1+0+0 = 1.

Matrix B belongs to the orthogonal, projection, and diagonalizable classes. Matrix B is orthogonal, which means that it is a square matrix whose columns and rows are orthonormal unit vectors (i.e. the dot product of any two columns or rows is 0). This is the case for matrix B, as the dot product of any two columns or rows yields 0. Matrix B is also a projection matrix, which means that it is a square matrix whose columns are all of unit length (i.e. the dot product of any two columns or rows is 1). This can be seen by taking the dot product of any two columns or rows, which yields 1. Finally, matrix B is diagonalizable, which means that it can be transformed into a diagonal matrix using a similarity transformation. This can be seen by calculating the eigenvalues and eigenvectors of matrix B, which yields the same diagonal matrix.

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Willa's debt to income ratio is 34%.

Debt to income ratio is usually calculated as a percentage of the gross monthly debt payments divided by the gross monthly income.

Given that,

Willa earns a bi-weekly gross income of $2,417.00

Monthly gross income = 2 × $2,417.00 = $4834

Monthly debt payments = $1,623.00

Debt to income ratio = $1,623.00 / $4834.00

                                   = 0.3357

                                   = 33.57%

                                   = 34%

Hence the debt to income ratio of Willa is 34%.

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Answer:

[tex]\frac{1}{3} + \frac{1}{3} + \frac{1}{3} = \frac{3}{3} = 1[/tex]

a=3

b=3

Third part

Commutative property

Fourth part

Inverse property

Fifth part

Identity property

Step-by-step explanation:

Answer:

1st part is a= 3

b= 9

Second part

x=16

y= -24

Third part

Commutative property

Fourth part

Inverse property

Fifth part

Identity property

Step-by-step explanation:

The solution to the system of equations 2x + y = 30 and 2x + 6y = 72 is (10.8, 8.4)

An equation is an expression showing the relationship between numbers and variables.

Given the equations:

2x + y = 30     (1)

x + 3y = 36; multiplying by 2 gives:

2x + 6y = 72     (2)

To solve by elimination method, subtract equation 2 from 1, hence:

-5y = -42

Dividing by -5:

y = 8.4

Put y = 8.4 in equation 2:

2x + 6(8.4) = 72

2x = 21.6

x = 10.8

The solution is (10.8, 8.4)

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In multiple regression,

Thus, option (a), (b), and (d) is correct.

The F-test is done to check for the equality of variances for the samples given whereas the F-distribution is a positively skewed distribution involving the numerator and the denominators degrees of freedom

a. The F statistic is only appropriate if errors are homoskedastic.

b. The F statistic can never be negative.

c. The F statistic has approximately a normal distribution in large samples.

d. The F statistic has approximately an X² distribution in large samples

In the given question, parts (a), (b), and (d) are true.

As the F-distribution is always positively skewed and is the ratio of the mean squares of between and within errors, it can never be negative and the assumptions of the samples having equal variances need to be fulfilled before proceeding with the test

Hence, in multiple regression,

a. The F statistic is only appropriate if errors are homoskedastic.

b. The F statistic can never be negative.

d. The F statistic has approximately an X² distribution in large samples

option (a), (b), and (d) is correct.

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Full question:

Which of the following is true about the F statistic in the multiple regression model? (Select all that apply.)

a. The F statistic is only appropriate if errors are homoskedastic.

b. The F statistic can never be negative.

c. The F statistic has approximately a normal distribution in large samples.

d. The F statistic has approximately a χ² distribution in large samples.

Answer:

(-1,-1)

Step-by-step explanation:

join the mid points of AB, BC & AC ...

you got the orthocenter point, then we can read the coordinates from X-axis and Y-axis.