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Several pairs of items (x, y) have a support of at least 100. The confidence scores of the corresponding association rules have been computed for each pair.

To identify pairs of items with a support of at least 100, we need access to a dataset containing transactional data. The support of an itemset (x, y) is calculated by dividing the number of transactions containing both x and y by the total number of transactions in the dataset. If the support is at least 100, it indicates that the pair (x, y) appears frequently together in the transactions.

Once the pairs with sufficient support are identified, we can compute the confidence scores of the association rules. Confidence is a measure of the strength of an association rule. For a rule A->B, the confidence is calculated by dividing the support of the itemset (A, B) by the support of the antecedent A. A high confidence score indicates a strong association between A and B.

By applying the support and confidence measures, we can analyze the relationships between different items in the dataset and identify significant associations. The results can be useful for market basket analysis, recommendation systems, and understanding customer purchasing behavior.

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Answer:

The answer is C: 3/4

Step-by-step explanation:

Your equation is equal to (3/2)/(4/2) due to absolute value (all numbers are positive even if negative symbol is infront of it) which is equal to 3/4.

Step-by-step explanation:

what is the real problem definition ?

is there now an absolute value around the top "-2", or not ?

in any case, remember, when we divide 2 rational numbers like this :

a/b / c/d

the result is

"outer multiplication" over "inner multiplication" :

a×d / b×c

as alternative you can always also say

a/b / c/d = a/b × d/c = a×d / b×c

so,

if the problem is

3/-2 / |-4/-2|

the result is

3×2 / 4×-2 = 6/-8 = - 3/4

if the problem is

3/|-2| / |-4/-2|

the result is

3×2 / 4×2 = 6/8 = 3/4

please pick the solution based on the actual problem.

Answer:

Top TUV

Bottom: UV, UT, TV

Step-by-step explanation:

The scale factor from the larger to the smaller is 3/4

24(3/4) = 18

12(3/4) = 9

16(3/4) = 12

To solve the initial-value problem using the Laplace transform, we will apply the Laplace transform to both sides of the differential equation.

Use the initial condition to find the solution in terms of the Laplace variable s.

Take the Laplace transform: Apply the Laplace transform to both sides of the differential equation. The Laplace transform of y' is sY(s) - y(0) and the Laplace transform of 2y is 2Y(s).

So, we have sY(s) - y(0) - 2Y(s) = L[(t - 3)]

Apply the initial condition: Substitute y(0) = 0 into the equation obtained in step 1.

sY(s) - 0 - 2Y(s) = L[(t - 3)]

sY(s) - 2Y(s) = L[(t - 3)]

Solve for Y(s): Combine like terms and isolate Y(s) on one side of the equation.

(s - 2)Y(s) = L[(t - 3)]

Y(s) = L[(t - 3)] / (s - 2)

Find the inverse Laplace transform: Use the inverse Laplace transform to find the solution in the time domain.

y(t) = L^(-1)[Y(s)]

y(t) = L^(-1)[L[(t - 3)] / (s - 2)]

y(t) = L^(-1)[1 / (s - 2)] * L^(-1)[L[(t - 3)]]

Use the inverse Laplace transform tables: Apply the inverse Laplace transform to the term 1 / (s - 2) using the Laplace transform tables. For the term L[(t - 3)], differentiate the transform L[(t)] = 1/s with respect to s.

y(t) = e^(2t) * (t - 3) + C

Apply the initial condition: Substitute the initial condition y(0) = 0 to solve for the constant C.

0 = e^(2*0) * (0 - 3) + C

C = 3

Final solution: Substitute the value of C into the expression obtained in step 5.

y(t) = e^(2t) * (t - 3) + 3

Therefore, the solution to the given initial-value problem using the Laplace transform is y(t) = e^(2t) * (t - 3) + 3.

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The matrix A has an eigenvalue λ with a multiplicity of 2, and we need to find the value of λ and its corresponding eigenvector v.

To find the eigenvalue and eigenvector, we start by solving the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue, I is the identity matrix, and v is the eigenvector.

Substituting the given matrix A, we have:

|6-λ -2|

|-2 10-λ| * |x|

|y| = 0

Expanding this equation, we get two equations:

(6-λ)x - 2y = 0 ...(1)

-2x + (10-λ)y = 0 ...(2)

To find λ, we solve the characteristic equation det(A - λI) = 0:

|(6-λ) -2|

|-2 (10-λ)| = 0

Expanding this determinant equation, we get:

(6-λ)(10-λ) - (-2)(-2) = 0

(λ^2 - 16λ + 56) = 0

Solving this quadratic equation, we find two solutions: λ = 8 and λ = 7.

Now, for each eigenvalue, we substitute back into equations (1) and (2) to find the corresponding eigenvectors v. For λ = 8:

(6-8)x - 2y = 0

-2x + (10-8)y = 0

Simplifying these equations, we get -2x - 2y = 0 and -2x + 2y = 0. Solving this system of equations, we find x = -y.

Therefore, the eigenvector corresponding to λ = 8 is v = [1 -1].

Similarly, for λ = 7, we find x = y, and the eigenvector corresponding to

λ = 7 is v = [1 1].

Therefore, the eigenvalue λ has a multiplicity of 2, with λ = 8 and the corresponding eigenvector v = [1 -1]. Another eigenvalue is λ = 7, with the corresponding eigenvector v = [1 1].

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The set of data 6, 2, 2, 2  will have the least dispersion from its mean.

From four sets of data, we take the mean of 6,2,2,2

\(\rm mean =\dfrac{ Sum \ of\ data}{Number \ of\ data}\)

So the mean will be

\(\rm mean =\dfrac{ 6+2+2+2}{4}=\dfrac{12}{4} =3\)

So the mean of the data (6,2,2,2) is 3 which has the least dispersion from its every data as compared to the other data

Thus the set of data 6, 2, 2, 2  will have the least dispersion from their mean.

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Answer:

c: 6,2,2,2

Step-by-step explanation:

The series is weakly stationary as these quantities are constant and do not depend on time.

To compute the desired quantities for the time series given by \(y_t = \varepsilon_t - \varepsilon_{t-1} - \varepsilon_{t-2}\), where \(\varepsilon_t \sim N(0,1)\) is a white noise process:

i. E[Y_t]:

Taking the expectation of \(y_t\), we have:

\[E[Y_t] = E[\varepsilon_t - \varepsilon_{t-1} - \varepsilon_{t-2}]\]

Since \(\varepsilon_t\) follows a normal distribution with mean 0, its expectation is 0. Therefore:

\[E[Y_t] = E[\varepsilon_t - \varepsilon_{t-1} - \varepsilon_{t-2}] = 0\]

ii. Var(Y_t):

To find the variance of \(Y_t\), we need to consider the variances of the individual terms and their covariances. Since \(\varepsilon_t\) is a white noise process with variance 1, we have:

\[Var(Y_t) = Var(\varepsilon_t - \varepsilon_{t-1} - \varepsilon_{t-2})\]

Since the \(\varepsilon_t\) terms are independent, the covariances are 0. Therefore:

\[Var(Y_t) = Var(\varepsilon_t) + Var(-\varepsilon_{t-1}) + Var(-\varepsilon_{t-2}) = 1 + 1 + 1 = 3\]

iii. The autocovariance function \(\gamma_h\):

The autocovariance function measures the covariance between \(Y_t\) and \(Y_{t-h}\), where \(h\) is the lag. For this series, we have:

\[\gamma_h = Cov(Y_t, Y_{t-h}) = Cov(\varepsilon_t - \varepsilon_{t-1} - \varepsilon_{t-2}, \varepsilon_{t-h} - \varepsilon_{t-h-1} - \varepsilon_{t-h-2})\]

Since the \(\varepsilon_t\) terms are independent, their covariances are 0. Therefore:

\[\gamma_h = Cov(\varepsilon_t, \varepsilon_{t-h}) + Cov(-\varepsilon_{t-1}, \varepsilon_{t-h}) + Cov(-\varepsilon_{t-2}, \varepsilon_{t-h}) = 0\]

iv. The autocorrelation function \(\rho_h\):

The autocorrelation function is calculated as the ratio of the autocovariance to the square root of the product of the variances. For this series, we have:

\[\rho_h = \frac{\gamma_h}{\sqrt{Var(Y_t) \cdot Var(Y_{t-h})}} = \frac{0}{\sqrt{3 \cdot 3}} = 0\]

v. Weak stationarity:

To determine if the series is weakly stationary, we need to check if the mean, variance, and autocovariance are constant over time. In this case, we have found that the mean \(E[Y_t]\) is 0, the variance \(Var(Y_t)\) is 3, and the autocovariance \(\gamma_h\) is 0 for all \(h\).

Therefore, the series is weakly probability as these quantities are constant and do not depend on time.

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Answer:

$6.30

Step-by-step explanation:

25.20 divided by 4.

Answer:

x = 31

Step-by-step explanation:

Exterior Angle Theorem

The exterior angle theorem states that when a triangle's side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle.

In this particular triangle, the angle with measurement 121° is the exterior angle

The two interior angles are x and the one which is 90°

Therefore by the exterior angle theorem,
90° + x° = 121°

Subtract 90 from both sides
x = 121 - 90

giving

x = 31

Answer:

C and D is the answer.

Step-by-step explanation:

If m∠5 = x°, according to the Corresponding Angle Theorem, m∠9 will equal the same, and because 9 and 12 are vertical angles, both of these will be the same measure.

(a) The volume V of the box as a function of x is V = 4x^3-60x^2+200x

(b) The domain of V in interval notation is 0<x<5,

(c) The length L , width W, and height H of the resulting box that maximizes the volume is H = 2.113, W = 5.773, L= 15.773

(d) The maximum volume of the box is 192.421 cm^2.

In the given question,

A box is to be made out of a 10 cm by 20 cm piece of cardboard. Squares of side length cm will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top.

(a) We have to express the volume V of the box as a function of x.

If we cut out the squares, we'll have a length and width of 10-2x, 20-2x respectively and height of x.

So V = x(10-2x) (20-2x)

V = x(10(20-2x)-2x(20-2x))

V = x(200-20x-40x+4x^2)

V = x ( 200 - 60 x + 4x^2)

V = 4x^3-60x^2+200x

(b) Now we have to give the domain of V in interval notation.

Since the lengths must all be positive,

10-2x > 0 ≥ x < 5 and x> 0

So 0 < x < 5

(c) Now we have to find the length L , width W, and height H of the resulting box that maximizes the volume.

We take the derivative of V:

V'(x) = 12x^2-120x+200

Taking V'(x)=0

0 = 4 (3x^2-30x+50)

3x^2-30x+50=0

Now using the quadratic formula:

x=\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

From the equationl a=3, b=-30, c=50

Putting the value

x=\(\frac{30\pm\sqrt{(-30)^2-4\times3\times50}}{2\times3}\)

x= \(\frac{30\pm\sqrt{900-600}}{6}\)

x= \(\frac{30\pm\sqrt{300}}{6}\)

x= \(\frac{30\pm17.321}{6}\)

Since x<5,

So x= \(\frac{30-17.321}{6}\)

x= 2.113

So H = 2.113, W = 5.773, L= 15.773.

d) Now we have to find the maximum volume of the box.

V = HWL

V= 2.113*5.773*15.773

V = 192.421 cm^3

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In the word problem , the number of days were in the "13-18" category is  C)4.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the given data represent the numbers of loaves sold in the last 10 days is 5, 12, 8, 15, 18, 20, 3, 17, 14, 21.

Now number of loaves sold in last 10 days between from 13-18 is

=> 15,18,17,14

Hence the number of days were in the "13-18" category is  C)4.

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Answer:

x+ y = 137

x -y = 43

x=90 and y = 47

Step-by-step explanation:

If the sum of two numbers is 137 and their difference is 43 .

Let x be the first number and y be the second number.

x+ y = 137

x -y = 43

Adding the two equations together,

x+ y = 137

x -y = 43

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

2x = 180

2x/2 = 180/2

x = 90

Solving for y.

x+y = 137

90+y = 179

y = 137-90

x = 47

Answer:

8 possible outcomes

Step-by-step explanation:

When flipping a quarter three times, each flip can result in two possible outcomes: either landing heads (H) or tails (T).

Since each flip is independent, the total number of possible outcomes for flipping a quarter three times can be found by multiplying the number of outcomes for each flip together.

For three flips, the total number of possible outcomes is:

2 x 2 x 2 = 8

So, there are 8 possible outcomes when Alexandre flips a quarter three times.

The function g(n) can be approximated by a growth rate of O(n log(n)).

To further explain why g(n) can be represented by O(n log(n)), let's analyze the equation n log(n² + 1) + n² log(n) = O(g(n)).

We can simplify the equation by factoring out the dominant term, which in this case is n^2 log(n). The equation becomes:

n² log(n) * (1 + 1/(n² + 1)) = O(g(n))

Now, let's focus on the expression (1 + 1/(n² + 1)). As n approaches infinity, the term 1/(n² + 1) becomes negligible compared to 1. Thus, we can approximate the expression as:

(1 + 1/(n² + 1)) ≈ 1

Substituting this approximation back into the equation, we have:

n² log(n) * 1 = O(g(n))

Simplifying further, we get:

n² log(n) = O(g(n))

This shows that g(n) must have a growth rate at least as fast as n² log(n) in order for the equation to hold. Among the given options, option b) O(n log(n)) satisfies this condition. Therefore, g(n) can be represented by O(n log(n)).

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The correct interpretation of the interval (0.196, 0.320) is that it is 95% confident that the difference in the proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

In addition, we can say that the interval (0.196, 0.320) is a measure of precision or uncertainty regarding the true difference in the proportions of young people and senior citizens who use the internet as a news source.

What is a confidence interval?

A confidence interval is a range of values that we use to estimate an unknown population parameter. It is calculated from a sample and provides a measure of the precision or uncertainty of our estimate. A confidence interval consists of a point estimate (e.g., a sample mean or proportion) and a margin of error (e.g., plus or minus some number of standard errors).

Senior citizens are elderly people who have reached the age of retirement or have been given special legal status as such. Senior citizens may be retirees or active in the workforce.

Complete question: A 95% confidence interval for the difference in proportions of young people and senior citizens who use the internet as a news source was found to be (.196, .320). which statements give a correct/appropriate interpretation of this interval?

a) The proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

b)The proportions of young people and senior citizens who use the internet as a news source lies between 0.196 and 0.320.

c) Both a and b

d) None of the above

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The task is to construct an 80% confidence interval for the mean noise level at manufacturing plants based on the given data.

Step 1: Calculate the sample mean. The sample mean is obtained by summing up all the values and dividing by the total number of observations. In this case, the sum of the noise levels is 115 + 149 + 143 + 105 + 136 + 157 + 111 = 916. Dividing this by 7 (the number of observations), we get a sample mean of 916/7 ≈ 130.9 (rounded to one decimal place).

Step 2: Calculate the sample standard deviation. The sample standard deviation measures the spread of the data points around the mean. To calculate it, we use the formula that involves subtracting the mean from each data point, squaring the result, summing all the squared differences, dividing by the total number of observations minus 1, and finally taking the square root. For the given data, the sample standard deviation is approximately 22.8 (rounded to one decimal place).

Step 3: Find the critical value. The critical value corresponds to the desired confidence level and the sample size. Since the confidence level is 80% and the sample size is 7, we need to find the critical value from a t-distribution table. The critical value for an 80% confidence interval with 6 degrees of freedom is approximately 1.943 (rounded to three decimal places).

Step 4: Construct the confidence interval. Using the sample mean, the sample standard deviation, and the critical value, we can construct the confidence interval. The formula for a confidence interval is "sample mean ± (critical value * (sample standard deviation / √(sample size)))". Plugging in the values, we get 130.9 ± (1.943 * (22.8 / √(7))). Evaluating this expression, the 80% confidence interval for the mean noise level at such locations is approximately 103.2 to 158.6 (rounded to one decimal place).

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If you are trying to find the missing measures of a rectangle, you should know that all rectangles have four sides, and each side has a length.

In other words, if you have a rectangle, two of the angles must be 90 degrees, and the other two angles must also be 90 degrees. To find the missing measures of a rectangle, you need to use the properties of rectangles.

First, find the length of each side. The length of all sides of a rectangle should be the same. Then, calculate the area of the rectangle. You can do this by multiplying the length of one side with the length of the other side.

Finally, you can use the Pythagorean Theorem to find the missing measures.

The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Using this theorem, you can find the length of the hypotenuse of the rectangle.

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Complete Question:

if each quadrilateral is given, then define the steps to find the missing measures a rectangle.

The radius of the cylinder is 10 centimetres according to stated dimensions of the cylinder.

The volume of the cylinder is given by the formula-

Volume = πr²h, where r refers to radius of the circle. Keep the values in formula to find the value of radius of the cylinder

1600π = πr²×16

Cancelling π and 16 common on both sides of the equation.

r² = 100

r = ✓100

Taking square root on Right Hand Side of the equation to find the radius of the cylinder

r = 10 centimetres

Hence the radius is 10 centimetres.

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There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

Now,

Substituting values,

We get,

\(^5N_5 = \frac{5!}{(5-5)!}\)

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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The items in order from the greatest thickness to the least is

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

From the question, we have the following parameters that can be used in our computation:

Item                    Thickness

Sheet of paper   8.0 * 10⁻⁵

Folder                 1.9 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Ruler                   1.2 * 10⁻²

By definition, the smaller the power; the smaller the thickness

Since -5 is less than -4, then -4 is thicker than -5

So, we have the following order

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

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Answer:

x=13.243568

Step-by-step explanation:

1000=58.3x+227.9

Step 1: Flip the equation.

58.3x+227.9=1000

Step 2: Subtract 227.9 from both sides.

58.3x+227.9=1000

         −227.9   −227.9

58.3x=772.1

Step 3: Divide both sides by 58.3

58.3x/58.3 = 772.1/58.3

x=13.243568

When a population is subjected to directional selection over time, the traits that are selected for will remain stable while the traits that are selected against will disappear.

Evolution is the study of how populations change over time. Most traits have multiple genes controlling their structure, function, appearance, and other characteristics. Single genes only very infrequently control a trait.

As a result, most traits have a tendency to be continuous in nature and to have a wide range of values. One side of these values will be picked against during directional selection, while the other side will be selected in favor of. Look at the illustration of a lemur's fur color below.

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Answer: A

Step-by-step explanation: Domain means the x values. Since Miguel works between 15 and 25 hours, the appropriate x values (independent variable) are between 15 and 25.

B is wrong because between 100 and 300 would be the range (y values). C is wrong because a specific domain (between 15 and 25) is specified in the problem, and all real numbers would also include negatives, which isn’t realistic for this scenario. D is wrong because a specific domain is specified. Therefore, it couldn’t be all numbers greater than 0.

We can conclude that (5, -2, -3) is the vector that the linear 1-form acts on by taking a dot product.

To find the vector that the given linear 1-form acts on by taking a dot product, we need to express the linear 1-form in terms of a vector.

Let's start by writing the given linear 1-form in terms of differentials of the coordinate functions:

\(2dy-3 dz + 5 dx - 4 dy = 5 dx - 2 dy - 3 dz\)

We can recognize this expression as the dot product of a vector with components (5, -2, -3) with the differential of a general vector function (dx, dy, dz).

Therefore, the vector that the linear 1-form acts on by taking a dot product is simply (5, -2, -3).

To verify this, let's take the dot product of the given linear 1-form with the given vector V:

\((2 dy - 3 dz + 5 dx - 4 dy) * (it 3+ 4) = 5 dx * i + (-2 dy) * t + (-3 dz) * 1 = 5(1) + (-2)(3) + (-3)(4) = 5 - 6 - 12 = -13\)

Now let's take the dot product of the same vector with the vector (5, -2, -3):

\((it 3+ 4) * (5, -2, -3) = (3)(5) + (4)(-2) + (0)(-3) = 15 - 8 + 0 = 7\)

Since the dot product of the given linear 1-form with the vector V is equal to the dot product of the same vector with the vector (5, -2, -3), we can conclude that (5, -2, -3) is the vector that the linear 1-form acts on by taking a dot product.

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The correct answer is option 3: 2250. To calculate the number of different clients that can be identified with a coding system we need to multiply the number of options for each component.

For the two-letter component, there are five options (A, D, R, S, U) that can be chosen for each letter. Since repetition is allowed, there are 5 choices for the first letter and 5 choices for the second letter. Therefore, there are 5 x 5 = 25 possible combinations of two letters.

For the two-digit component, there are 10 options (0-9) for the first digit. Since no digit can be repeated, there are 9 options for the second digit (one less than the available options). Therefore, there are 10 x 9 = 90 possible combinations of two digits.

To calculate the total number of different clients that can be identified, we multiply the number of options for the two-letter component (25) by the number of options for the two-digit component (90). This gives us a total of 25 x 90 = 2250 different clients that can be identified with the coding system.

#A company uses a coding system to identify its clients. Each code is made up of two letters and a sequence of digits, for example AD108 or RR45789 The letters are chosen from A;D; R; S and U. Letters may be repeated in the code. The digits 0 to 9 are used, but NO digit may be repeated in the code. The number of different clients that can be identified with a coding system that is made up of TWO letters and TWO digits is: 1. 2230 2. 2240 3. 2250 4. 2210 22

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Answer:

19°

Step-by-step explanation:

180-64=116

116+45=161

180-161=19

Answer:

B) 19

Step-by-step explanation:

find the other angle of W first.

to do that, take 180 - 64

that makes angle W 116

add angle W and angle Y

116 +45 = 161

take 180 - your answer

180 - 161 = 19

B is your answer

have a wonderful day <3