A home has a rectangular kitchen. If listed as ordered pairs, the corners of the kitchen are (8, 4), (−3, 4), (8, −8), and (−3, −8). What is the area of the kitchen in square feet?

20 ft2
46 ft2
132 ft2
144 ft2

Nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the sierra Nevada mountains.

Early snowfall prevented the Central Pacific from starting construction on Tunnel No. 6, or the Summit Tunnel, in August 1865. It was built using a variety of engineering and construction methods and was located more than seven thousand feet above sea level.

When the workmen finally broke through, they discovered that they were only two inches off from the calculations that were used to locate its end points and central shaft. The length of the tunnel that was built through the Sierra Nevada mountains is therefore given as nearly 1,659 feet of granite was tunnelled through to make tunnel no. 6 through the Sierra Nevada mountains.

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A.  9 is the mean and 2.12 is standard deviation for the number of correct answers for such students.

B. The probability of getting 16 or more correct answers by chance is less than 0.001%, which means it would be highly unusual for a student to pass by guessing and getting at least 16 correct answers.

A. If the students are guessing on 18 true/false questions, the probability of getting any single question correct is 0.5. Therefore, the mean number of correct answers for the students is expected to be 9 (18 x 0.5). The standard deviation can be calculated using the formula: √(npq), where n is the number of questions (18), p is the probability of success (0.5), and q is the probability of failure (0.5). So, the standard deviation is √(18 x 0.5 x 0.5) = 2.12.

B. To pass the test, a student would need to get at least 9 correct answers. Getting 16 correct answers would be highly unusual if the students are just guessing, as the probability of getting 16 or more correct answers by chance is very low. The probability of getting exactly 9 correct answers is about 20%, and the probability of getting 10 or more correct answers is about 13%.

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The distance between you and the plateau is 110 m.

The angle between the horizontal plane and the line of sight or direction of an item or point above the horizontal plane is known as the angle of elevation. It can be described more simply as the angle created by looking up from a horizontal line to a point or object above that line.

We know that;

Tan 20 = 40/x

x = distance between you and the plateau.

Then;

x = 40/Tan 20

x = 110 m

Thus the distance is 110 m

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To multiply 121 and 121x²-1, we used the distributive property of multiplication and simplified the expression to get the final answer of 1331x² - 121.

To multiply 121 and 121x²-1, we need to use the distributive property of multiplication. We can break up 121 as 11 * 11 and write as

121 * (121x²-1) = (11 * 11) * (121x²-1)

Using the distributive property here, we can then write

= 11 * 11 * 121x² - 11 * 11 * 1

Simplifying the expression, we get

= 1331x² - 121

So the multiplication of 121 and 121x²-1 is 1331x² - 121.

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

" Multiply 121 * 121x²-1 "--

(a) A. converges.
(b) Since r > 0 is given, we cannot definitively determine convergence or divergence without more information.
(c) A. converges.
(d) The limit comparison test is inconclusive, and we cannot determine if the series converges or diverges using this test.

(a) To use the comparison test, we need to find a series whose terms are smaller than or equal to the terms of Ene73a, and whose sum converges. Note that for all n, e^(-n^2) is positive and less than or equal to 1. Therefore, we have:

0 ≤ Ene^(7/3n) ≤ Ene^(-n^2)

Since the series Ene^(-n^2) converges (it is a convergent p-series with p = 2), the series Ene^(7/3n) also converges by the comparison test. So, the answer is A.

(b) To use the ratio test, we need to calculate the limit of the absolute value of the ratio of successive terms:

lim n→∞ |(n+1)/(n+1)^(1/2) * n^(1/2)/n|

= lim n→∞ (n+1)^(1/2)/n^(1/2)

= lim n→∞ √(n+1)/√n

This limit is equal to 1, so the ratio test is inconclusive. We cannot determine whether the series converges or diverges using this test. Therefore, the answer is indeterminate.

(c) To use the alternating series test, we need to check two things: that the terms of the series decrease in absolute value and that the limit of the terms is zero. Note that for all n, 4n+1 is positive. Therefore, we have:

0 ≤ |(-1)^n(4n+1)/(2n+1)| = (4n+1)/(2n+1) ≤ 2

The terms of the series are decreasing in absolute value, and the limit of the terms is zero. Therefore, the alternating series test applies and the series converges. So, the answer is A.

(d) To use the limit comparison test, we need to find a series whose terms are positive and whose sum converges, and such that the ratio of the terms of this series to the terms of n^(3/2)+1 approaches a nonzero constant. Note that for all n, n^(3/2)+1 is positive. Therefore, we have:

0 ≤ (n^(3/2)+1)/(n^2+1) ≤ (n^(3/2)+1)/n^(3/2) = 1 + 1/n^(3/2)

As n approaches infinity, the ratio approaches 1. Therefore, we can apply the limit comparison test with the series ∑(1/n^(3/2)+1), which is a convergent p-series with p = 3/2. Therefore, the series n^0 +1 also converges. So, the answer is A.

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A particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

To find a particular solution of the non-homogeneous differential equation:

[tex]y" - 8y' + 17y = 8e^(6t)[/tex]

using the method of undetermined coefficients, we assume that the particular solution has the form:

[tex]y_p = Ae^(6t)[/tex]

where A is a constant to be determined.

We then take the first and second derivatives of y_p:

[tex]y'_p = 6Ae^(6t)[/tex]

[tex]y"_p = 36Ae^(6t)[/tex]

Substituting these expressions into the differential equation, we have:

[tex]y" - 8y' + 17y = 8e^(6t)[/tex]

[tex]36Ae^(6t) - 48Ae^(6t) + 17Ae^(6t) = 8e^(6t)[/tex]

Simplifying the left-hand side, we get:

[tex]5Ae^(6t) = 8e^(6t)[/tex]

Therefore, A = 8/5.

Hence, the particular solution is:

[tex]y_p = (8/5)e^(6t)[/tex]

Therefore, a particular solution of the differential equation y" -8y' +17y = 8e^6t is y_p = (8/5)e^(6t) obtained using the method of undetermined coefficients.

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To solve this problem, we need to use the formula for surface area of a triangular prism, which is: Surface Area = 2 × (base area) + (lateral area). So, the surface area of the new ramp that Santiago needs to build is 361.8 square feet.

Let's first find the base area of Santiago's current ramp. Since the ramp is in the shape of a triangular prism, the base is a triangle. Let's call the base dimensions b and h, and the length of the ramp l. Then the base area is:
base area = (1/2)bh
We are not given the dimensions of the triangle, but we are given the surface area of the ramp, which is 40.2 ft^2. So we can set up an equation:
2 × (base area) + (lateral area) = 40.2
Substituting the formula for base area, we get:
2 × (1/2)bh + (lateral area) = 40.2
Simplifying:
bh + (lateral area) = 40.2
Now we need to find the lateral area. Since the ramp is in the shape of a triangular prism, the lateral area is the area of three rectangles, each with base l and height equal to one of the dimensions of the triangle. Let's call these dimensions x, y, and z, so that:
lateral area = xl + yl + zl
We are given that Santiago needs to build a ramp 3 times longer in every dimension than the ramp he has. So the new dimensions of the triangle are 3b, 3h, and 3l. The new lateral area is:
(3b)(3l) + (3h)(3l) + (3b)(3h) = 27bl + 27hl + 27bh
Substituting this into our equation for surface area, we get:
bh + 27bl + 27hl + 27bh = 40.2
Simplifying:
55bh + 27bl + 27hl = 40.2

Now we can solve for the new surface area by using the formula for surface area again, but with the new dimensions:
Surface Area = 2 × (base area) + (lateral area)
Substituting in the new dimensions, we get:
Surface Area = 2 × (1/2)(3b)(3h) + (27bl + 27hl + 27bh)
Simplifying:
Surface Area = 9bh + 54bl + 54hl
Substituting in the equation we found earlier:
Surface Area = 9bh + 54bl + 54hl = (40.2 - 27bl - 27hl)/55
Multiplying both sides by 55:
495bh + 2970bl + 2970hl = 40.2 - 27bl - 27hl
Simplifying:
522bh + 2997bl + 2997hl = 40.2
So the surface area of the new ramp is 522bh + 2997bl + 2997hl square feet.

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The correct option is d. one-sample t-test. The VAR statement in the PROC TTEST step specifies the mean we want to analyze.

The PROC TTEST step is used in SAS software to perform hypothesis testing for means. When only a VAR statement and RUN statement are used in the PROC TTEST step, SAS will perform a one-sample t-test.

In a one-sample t-test, we compare the mean of a single sample to a known or hypothesized value. We use this test when we want to determine whether the sample mean is significantly different from a population mean or a hypothesized value.

For example, if we have a sample of students and we want to determine whether their mean test score is significantly different from a passing score of 70%, we would use a one-sample t-test. The VAR statement in the PROC TTEST step specifies the variable we want to analyze.

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The mean percentage error (MAPE) for this data is 6.35%. MAPE is a measure of the accuracy of a forecasting model. A higher MAPE indicates that the model is less accurate, while a lower MAPE indicates that the model is more accurate.

In this case, the MAPE is relatively low, indicating that the forecasting model used is reasonably accurate. However, it's also important to consider other factors, such as the size and significance of the errors, before making any decisions based on the forecast.

To calculate the mean percentage error (MAPE) for this data, we need to first calculate the percentage error for each period. The percentage error is calculated as follows:

(Actual - Forecast) / Actual x 100

Using the data provided, we can calculate the percentage error for each period:

Period 1: (68 - 65) / 68 x 100 = 4.41%
Period 2: (65 - 64) / 65 x 100 = 1.54%
Period 3: (74 - 63) / 74 x 100 = 14.86%
Period 4: (64 - 68) / 64 x 100 = -6.25%
Period 5: (70 - 72) / 70 x 100 = -2.86%
Period 6: (72 - 73) / 72 x 100 = -1.39%

Next, we need to find the average of the absolute values of the percentage errors, which is known as the mean absolute percentage error (MAPE). To do this, we add up the absolute values of the percentage errors and divide by the number of periods:

(4.41 + 1.54 + 14.86 + 6.25 + 2.86 + 1.39) / 6 = 6.35%

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To find the first derivative of f(x), we need to integrate the second derivative with respect to x once.

f'(x) = ∫ f''(x) dx = ∫ x(x-a)(x-b)^2 dx

f'(x) = ∫ (x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2) dx

f'(x) = 1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C

where C is the constant of integration.

To find the second derivative of f(x), we need to differentiate f'(x) with respect to x.

f''(x) = d/dx [1/5 x^5 - 1/4(a+b)x^4 + 1/3(a^2+3ab+b^2)x^3 - 1/2ab(a+b)x^2 + 1/3ab^2x + C]

f''(x) = 1 x^4 - 1(a+b)x^3 + 1(a^2+3ab+b^2)x^2 - 1ab(a+b)x + 1ab^2

f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2

Therefore, the second derivative of f is given by f''(x) = x^4 - (a+b)x^3 + (a^2+3ab+b^2)x^2 - ab(a+b)x + ab^2.

The measure of greatest exterior angle is 120 degree.

We have,

The exterior angles of the polygon are given as:

xº, 2x°, 3x°, 6x°, 8x° and 10x°:

As, The exterior angles of a polygon add up to 360 degrees.

So, x + 2x + 3x + 6x + 8x + 10x = 360

30x = 360

x= 360/30

x= 12

so, the measure of greatest exterior angle is

= 10x

= 120

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The property of vectors that is incorrect is "Oa· (b + c) = a · b + a.c = (a + b ) + c = a +(b + c)". The correct property is "Oa· (b + c) = Oa·b + Oa·c".

The incorrect property of vectors among the given options is:

Oa·b = axb

This property is incorrect because the dot product (a·b) and cross product (axb) of two vectors are different operations with different results. The dot product is a scalar value, while the cross product is another vector that is orthogonal to the given vectors. The correct properties of vectors in your question are:

1. a x b = -b x a (cross product)
2. a · (b + c) = a · b + a · c (dot product distributive property)
3. (a + b) + c = a + (b + c) (vector addition associativity)

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The sample data and regression analysis to gain insights into the relationship between purchase costs and purchase revenues.

The assumption of a constant contribution margin per customer would be justified if the cost structure of the business remained constant and if the company did not offer discounts or promotions that would affect the contribution margin. In other words, the assumption would hold if the company's revenues and costs remained relatively stable over time.
It is difficult to determine if these conditions would hold without additional information about the business. However, we can analyze the sample data to see if there is a relationship between purchase costs and purchase revenues. By doing a scatter plot of the sample data, we can visually see if there is a correlation between the two variables. After plotting the data, we can use the sample data to run a regression of purchase costs on purchase revenues. The regression results can provide insights into the relationship between the two variables and can help us determine if the assumption of a constant contribution margin per customer is likely to hold. The intercept term of the regression results represents the fixed cost of the business. This is the cost that the business incurs regardless of how many units they sell. The slope of the regression line represents the variable cost per unit. By analyzing the regression results, we can determine if the variable cost per unit remains constant as the number of units sold increases. In conclusion, while it is difficult to determine this analysis can help us determine if the assumption is likely to hold and can provide valuable information for the business. if the conditions necessary for the assumption of a constant contribution margin per customer would hold without additional information about the business, we can use sample data and regression analysis to gain insights into the relationship between purchase costs and purchase revenues.

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The solution to the system of equations are x= 849/14, y= 221/7 and z=-59/14.

We can write the Equation from the matrix as

2x - y + 8z = 56

x+ 8y + z = 30

9x + y + z = 88

Solving the above equations we get

2x - y + 8z = 56

2x + 16y + 2z = 60

_____________

       -17y + 6z = -4

and, 9x + 72y + 9z = 270

        9x + y +     z    =  88

    __________________

               71y + 8z = 182

So, x= 849/14, y= 221/7 and z=-59/14

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The weighted average cost of capital WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

To calculate the cost of capital for Brozierz Ltd, we need to calculate the cost of each component of their capital structure and weight them according to their proportion in the overall capital structure.

First, let's calculate the cost of equity using the Capital Asset Pricing Model (CAPM):

Cost of equity = risk-free rate + beta x (return on market - risk-free rate)

= 0.06 + 1.4 x (0.15 - 0.06)

= 0.165 or 16.5%

Next, let's calculate the cost of preference shares:

Cost of preference shares = (fixed dividend rate / market price of preference shares) + flotation costs

= (0.1 x 3 / 2.5) + 0

= 0.12 or 12%

The cost of debt is simply the interest rate on the bank loan, which is 12% per annum.

Now, we can calculate the weighted average cost of capital (WACC) using the formula:

WACC = (proportion of equity x cost of equity) + (proportion of preference shares x cost of preference shares) + (proportion of debt x cost of debt) x (1 - tax rate)

Let's calculate the proportion of each component:

Proportion of equity = 300,000 x 2.40 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.375

Proportion of preference shares = 100,000 x 2.50 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.125

Proportion of debt = 500,000 / (300,000 x 2.40 + 100,000 x 2.50 + 500,000) = 0.5

Therefore, the WACC is:

WACC = (0.375 x 0.165) + (0.125 x 0.12) + (0.5 x 0.12) x (1 - 0.28)

= 0.120 or 12.0%

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9. The algebraic expression for tan (arcsin (x)) is

10. The algebraic expression for sec (arcsin (x)) is

tan sin⁻¹ x is also called tan(arcsin(x))

Let y = arcsin x.

so that

y = arc sin x

take the tan of both sides

tan(y) = tan(arcsin(x))

Using the trigonometric identity: tan (arcsin x) = x / √(1 - x^2)

tan(y) = x / sqrt(1 - x^2)

10. sec (arcsin (x))

Using the identity

sin^2 a + cos^2 a = 1

cos^2 a = 1 - sin^2 a

let sin a = x

cos^2 a = 1 - x^2

cos a = √(1 - x^2)

and sec = 1/cos = 1/√(1 - x^2)

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Riley has a solar panel with a width of 25 inches. To get the proper inclination for her climate, she needs a night triangluar support frame that has one leg twice as long as the other leg. To the nearest tenth.The dimensions of the triangular support frame should be approximately 11.2 inches by 22.4 inches.

To solve this problem, we can use the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the shorter leg of the triangular support frame "x" inches. Since the other leg is twice as long as the shorter leg, it will be "2x" inches. The solar panel's width (25 inches) will act as the hypotenuse in this case.

According to the Pythagorean theorem: 25^2 = x^2 + (2x)^2 625 = x^2 + 4x^2 Combining the x terms: 625 = 5x^2 Dividing by 5: 125 = x^2 Now, we'll take the square root of both sides: x ≈ 11.2 (to the nearest tenth)

So, the shorter leg (x) should be approximately 11.2 inches long, and the longer leg (2x) should be approximately 22.4 inches long.

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The surface area of the prism is 108 cm²

A prism is a solid shape that is bound on all its sides by plane faces.

The total surface area of the prism can be found by adding all the the area of the surfaces together.

area of surface 1 = 1/2 bh

= 1/2 ×4× 3

= 6cm²

area of surface 2 = area of surface 1

= 6cm²

area of surface 3 = l×w

= 8×3 = 24 cm²

area of surface 4 = 8×4 = 32cm²

area of surface 5 = 5× 8 = 40cm²

The total surface area = 6+6+24+32+40

= 108 cm²

therefore the surface area of the prism is 108cm²

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When using the permutation approach to assess the difference in cell phone bills between in-state and out-of-state students, you are essentially testing the null hypothesis that there is no significant difference between the two groups. To do this, you would perform the following steps:

1. Calculate the observed difference in sample means (-7 in this case).
2. Combine the two groups (in-state and out-of-state) into a single dataset.
3. Randomly shuffle (permute) the dataset and create 10,000 new pairs of groups, each with the same number of observations as the original groups.
4. For each permutation, calculate the difference in means between the permuted groups.
5. Compare the observed difference in means (-7) to the distribution of permuted differences to determine the proportion of permuted differences that are equal to or more extreme than the observed difference. This proportion represents the p-value, which helps assess the likelihood of observing such a difference by chance alone.

If the p-value is below a pre-determined significance level (e.g., 0.05), you would reject the null hypothesis and conclude that there is a significant difference between the amounts spent on cell phone bills by in-state and out-of-state students. Otherwise, you would fail to reject the null hypothesis, suggesting no significant difference between the groups.

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When a single, standard number cube (with 6 sides) is tossed, the probability of getting a number other than 6 is 5/6 (option C), because there are 5 favorable outcomes (1, 2, 3, 4, and 5) out of the 6 possible outcomes (1 through 6).

The probability of getting a specific number on a standard number cube is 1/6, since there are six possible outcomes (1, 2, 3, 4, 5, or 6) and each is equally likely.

To find the probability of getting a number other than 6, we can count the number of outcomes that satisfy this condition.

There are five numbers (1, 2, 3, 4, or 5) that are not 6, so the probability of getting one of these numbers is 5/6. Therefore, the answer is C. 5÷6.

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The missing justification in the proof of the angle bisector construction is "AAS Congruence".

As per the question, we have shown that BMP and NBP are congruent and adjacent, which means that angle MBP is congruent to angle NBP, angle BMP is congruent to angle BNP, and segment BP is shared by both triangles.

Therefore, we can apply AAS congruence to conclude that triangles BMP and NBP are congruent.

Since corresponding parts of congruent triangles are congruent, we can then conclude that angle ABC is bisected by BP. This is because angles MBA and NBP are congruent (by construction), and angles MBP and NBA are congruent (by the fact that triangles BMP and NBP are congruent).

Therefore, by the definition of an angle bisector, BP bisects angle ABC.

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Answer:

APEX

D. reflexive property

The correct answer is:

(a) No, because the column space of a 4 x 7 matrix is a subspace of R^4. There is a pivot in each row, so the column space is 4-dimensional. Since any 4-dimensional subspace of R^4 is R^4, Col A = R^4.

Explanation:

The column space of a matrix represents all possible linear combinations of its column vectors. In this case, since there are four pivot columns in the matrix A, it means that there are four linearly independent columns.

Therefore, the column space of A, Col A, is a subspace of R^4, and specifically, it is 4-dimensional. Thus, the correct answer is option B: Yes, because the column space of a 4 x 7 matrix is a subspace of R^4. There is a pivot in each row, so the column space is 4-dimensional. Since any 4-dimensional subspace of R^4 is R^4, Col A = R^4.

For the question about Nul A (null space), the information is not provided in the question, so we cannot determine its dimension or relationship to R^3.

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The point estimate of the proportion of women who trust recommendations made on Pinterest is 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is 0.60

A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on Pinterest is (0.809, 0.2791).

The point estimate of the proportion of women who trust recommendations made on Pinterest is:

= 117 / 150

= 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is:

= 102 / 170

= 0.60

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The equation that can be used to solve for m∠1 is B. m∠1 = 1/2(arc a + arc b).

The picture of the question in the attached figure. An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The measure of the interior angle is the semi-sum of the arches that comprise it and its opposite. The correct option is B..

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Which equation can be used to solve for m∠1? m∠1 = One-half(a – b) m∠1 = One-half(a + b) m∠1 = One-half(c – d) m∠1 = One-half(c + d)

Based on the sample of 2,600 registered voters, 1,898 said they planned to vote for the republican candidate for president.

To calculate the interval estimate for the population proportion with a 0.95 degree of confidence, we can use the formula:

sample proportion +/- z-score * standard error

First, we need to calculate the sample proportion, which is:

1,898/2,600 = 0.7308

Next, we need to calculate the standard error, which is:

sqrt[(sample proportion * (1 - sample proportion)) / sample size]
sqrt[(0.7308 * (1 - 0.7308)) / 2,600]
sqrt[0.00060647]
0.0246

To find the z-score for a 0.95 degree of confidence, we can look it up in a z-table or use a calculator. The z-score for a 0.95 degree of confidence is 1.96.

Now we can plug in the values into the formula:

0.7308 +/- 1.96 * 0.0246
0.7308 +/- 0.0482
(0.6826, 0.779)

Therefore, the interval estimate for the population proportion is (to the nearest 10th of a percent) 68.3% to 77.9%. This means that we can be 95% confident that the true proportion of voters who plan to vote for the republican candidate for president is between 68.3% and 77.9%.

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The dependent variable in this study is the incidence of aggressive behavior displayed by the children during the period of free play.

The dependent variable is the outcome that is being measured and observed based on the independent variable, which in this scenario is the type of television program watched (violent or nonviolent). By observing and recording the incidence of aggressive behavior in each group, the researcher can determine if exposure to violent television programs has an effect on children's behavior. In this study, the dependent variable is essential to determining if there is a significant difference between the groups, and it allows for the researcher to draw conclusions about the relationship between exposure to violent television and aggressive behavior in children. In this scenario, the dependent variable is the incidence of aggressive behavior observed in the children during the period of free play. The dependent variable is the outcome or response that is measured in a study, and it is influenced by the independent variable(s). In this case, the independent variables are the type of television program (violent or nonviolent) and the gender of the participants (boys and girls). The researcher is investigating the relationship between exposure to violent or nonviolent television content and the occurrence of aggressive behavior among boys and girls.

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a. The coordinate is located on the fourth quadrant.

b. The radius is given as follows: 17 units.

c. The sine of the angle is given as follows: sin(x) = -15/17.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The coordinates of the point in this problem are given as follows:

(8, -15).

Hence the point is located on the fourth quadrant, as it has a positive x-coordinate and a negative y-coordinate.

The radius is equivalent to the hypotenuse of the right triangle, hence it is obtained applying the Pythagorean Theorem as follows:

r = 8² + (-15)²

r = sqrt(8² + (-15)²)

r = 17 units.

The sine of the angle is given by the y-coordinate divided by the radius, hence:

sin(x) = -15/17.

More can be learned about trigonometric ratios at brainly.com/question/24349828

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Answer:

Step-by-step explanation: