In the diagram, mDGF = 62x+4. Find mDGF
O-210°
G
D
30x+5
F
E

Answer:

x = 82

Step-by-step explanation:

x and 98 are same- side exterior angles. They are on the same side of the transversal and are outside the parallel lines.

same- side exterior angles sum to 180° , so

x + 98 = 180 ( subtract 98 from both sides )

x = 82

[tex]x[/tex] and [tex]98^{\circ}[/tex] are same side exterior angles which add up to [tex]180^{\circ}[/tex].

Therefore

[tex]x+98^{\circ}=180^{\circ}\\x=82^{\circ}[/tex]

Answer:

I wish you good luck in finding your answer

Answer:

In Grade 4, students are introduced to the concept of chance and the idea that different situations have different probabilities of occurring. They learn that for many situations, there are a finite number of different possible outcomes. However, at this stage, students are not expected to calculate the probability of events occurring. In Grade 5, students continue to build on their understanding of probability and may begin to learn more advanced concepts and techniques for calculating probabilities.

Step-by-step explanation:

Answer:

25,

-7

Step-by-step explanation:

r ° q= r(q(x))= (-x+2) ^2

So, using perfect square trinomial,

[tex](-x+2)^{2} =x^{2} -4x+4[/tex]

Thus q(-3)=25

q(r(x))= (-x^2)+2=-7

Answer:  the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Step-by-step explanation:

a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:

The total number of items sold today is 224. Therefore, we can write the equation:

m + b + c = 224

The store sold three times as many loaves of bread as jugs of milk. We can write this as:

b = 3m

The store sold four times as many pieces of cheese as loaves of bread. We can write this as:

c = 4b

b) Now, let's solve the equation:

Substituting the value of 'b' from equation (2) into equation (3):

c = 4(3m)

c = 12m

Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):

m + 3m + 12m = 224

16m = 224

m = 224 / 16

m = 14

Using the value of 'm' in equation (2):

b = 3m

b = 3(14)

b = 42

Using the value of 'b' in equation (3):

c = 4b

c = 4(42)

c = 168

Answer:

Step-by-step explanation:

a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.

Based on the given information, we can form two equations:

1) The total number of items sold today is 224:

x + y + z = 224

2) The store sold three times as many loaves of bread as jugs of milk:

y = 3x

3) The store sold four times as many pieces of cheese as loaves of bread:

z = 4y

b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):

x + y + z = 224

x + 3x + 4y = 224

4x + 4y = 224

Now, substitute y = 3x into the equation:

4x + 4(3x) = 224

4x + 12x = 224

16x = 224

Divide both sides by 16:

x = 224 / 16

x = 14

Now substitute the value of x back into equation (2) to find y:

y = 3x

y = 3(14)

y = 42

Finally, substitute the value of y into equation (3) to find z:

z = 4y

z = 4(42)

z = 168

Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

The equation to determine the initial amount of money Cecilia had is x = 0.

Let's denote the initial amount of money Cecilia had as "x" dollars.

According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.

Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.

Since she had $8 left, we can set up the equation:

((x - (1/4)x) - ((1/2)x - 8)) = 8

To simplify the equation, we can first combine like terms:

(x - (1/4)x - (1/2)x + 8) = 8

Now, let's solve the equation step by step:

(x - (1/4)x - (1/2)x + 8) = 8

Multiplying the fractions by their common denominator, which is 4, we get:

(4x - x - 2x + 32) = 32

Simplifying further:

(x + 32) = 32

Subtracting 32 from both sides:

x = 0

Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.

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The probability that a flight has 100 or more passengers and arrives on time is approximately 0.12 or 12%.

Let A be the event that a flight has 100 or more passengers, and B be the event that the flight arrives on time. We want to find the probability of the intersection of these two events, P(A ∩ B).

We are given:

- P(B) = 0.80, the probability that any given flight arrives on time

- P(A) = 0.30, the probability that any given flight has 100 or more passengers

- P(B | A) = 0.40, the conditional probability that a flight arrives on time given that it has 100 or more passengers (since 60% of such flights are late)

We can use the formula for conditional probability to find P(A ∩ B):

P(A ∩ B) = P(B | A) * P(A)

         = 0.40 * 0.30

         = 0.12

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The eigenvalues of the given matrix are approximately -1.8478, 0.8478, and 2, and the corresponding eigenvectors are approximately [-0.577, -0.577, -0.577], [0.6614, -0.6614, 0], and [0.577, 0.577, 0.577].

To find the eigenvalues and eigenvectors of the given matrix:

Let A be the given matrix:

A = [[0, 1, 1],

    [1, 0, 1],

    [1, 1, 0]]

To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.

The characteristic equation becomes:

det([[0-λ, 1, 1],

    [1, 0-λ, 1],

    [1, 1, 0-λ]]) = 0

Expanding the determinant, we have:

-(λ³ - 2λ - 2) = 0

Simplifying, we get:

λ³ - 2λ - 2 = 0

Now we solve this equation to find the eigenvalues:

By analyzing the equation or using numerical methods, we find that the eigenvalues are approximately:

λ₁ ≈ -1.8478

λ₂ ≈ 0.8478

λ₃ ≈ 2

To find the eigenvectors, we substitute each eigenvalue back into the equation (A - λI) * v = 0 and solve for v.

For λ₁ ≈ -1.8478:

(A - λ₁I) * v₁ = 0

Solving this equation, we find the eigenvector v₁ associated with λ₁ as:

v₁ ≈ [-0.577, -0.577, -0.577]

For λ₂ ≈ 0.8478:

(A - λ₂I) * v₂ = 0

Solving this equation, we find the eigenvector v₂ associated with λ₂ as:

v₂ ≈ [0.6614, -0.6614, 0]

For λ₃ ≈ 2:

(A - λ₃I) * v₃ = 0

Solving this equation, we find the eigenvector v₃ associated with λ₃ as:

v₃ ≈ [0.577, 0.577, 0.577]

Therefore, the eigenvalues of the given matrix are approximately -1.8478, 0.8478, and 2, and the corresponding eigenvectors are approximately [-0.577, -0.577, -0.577], [0.6614, -0.6614, 0], and [0.577, 0.577, 0.577].

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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The third option best describes a stratified sample of customers. The Option C.

To form a stratified sample, the analyst divides the customers into six groups based on their mortgage amounts. This ensures that customers from different mortgage amount ranges are represented in the sample.

Then, the analyst randomly selects 13 customers from each group. By stratifying the sample based on mortgage amounts and selecting customers at random within each group, the analyst ensures that the sample is representative of the overall population of mortgage customers.

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The height of a person whose length of forearm is 24.5 cm is equal to 163.38 centimeters.

In this exercise, we would plot the length of forearm on the x-axis of a scatter plot while height would be plotted on the y-axis of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit on the scatter plot;

y = 3.01x + 89.63

Based on the equation of the line of best fit above, the height of a person whose length of forearm is 24.5 cm can be determined as follows;

y = 3.01x + 89.63

y = 3.01(24.5) + 89.63

y = 163.375 ≈ 163.38 centimeters.

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The inverse of the function f(x) = 2·x - 4, is the option;

g(x) = (1/2)·x + 2

The completed statement is; Because f(x) is one to one, its inverse is a function

The inverse of a function is one that takes the output of a specified function to produce the input of the function.

The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;

f(x) = 2·x - 4

f(x) + 4 = 2·x

2·x = f(x) + 4

x = (f(x) + 4)/2 = f(x)/2 + 2

x = f(x)/2 + 2

Substituting f(x) = x and x = g(x) in the above equation, we get;

g(x) = x/2 + 2

The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function

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Answer:

A

Step-by-step explanation:

is one to one

The difference table for the sequence (-1, 6, 24, 56, 105, 174, 266) reveals a cubic pattern, where the third differences are constant at 3. Based on this pattern, the next term in the sequence is predicted to be 289.

The difference table for the given sequence (-1, 6, 24, 56, 105, 174, 266):

Term     |   First Difference   |   Second Difference   |   Third Difference

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

-1

6                         7

24                    18                                  11

56                   32                                 14                                   3

105                  49                                17                                   3

174                 69                                 20                                  3

266                92

To construct the difference table, we start by writing down the given sequence. Then, in the first column, we calculate the differences between consecutive terms. In the second column, we calculate the differences between the values in the first difference column. Similarly, in the third column, we calculate the differences between the values in the second difference column.

Analyzing the difference table, we observe that the third differences are constant at 3. This indicates a cubic pattern in the sequence, where the difference between consecutive terms is increasing by a constant amount each time.

To predict the next term, we take the last term of the sequence (266) and add the next difference (23) to it:

Next term = 266 + 23 = 289

Therefore, based on the pattern observed in the difference table, the next term in the sequence is predicted to be 289.

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The equation after completing the square is (x+2)²=3. Consider the equation: 0=x²+4x+1. To rewrite the equation by completing the square, we need to complete the square by adding and subtracting the square of half of the coefficient of the x.

Let's see how to complete the square: 0 = x² + 4x + 1(1)

We'll take the constant term (1) to the right-hand side of the equation, so it becomes negative. 0 = x² + 4x - 1(2)

To complete the square, we add and subtract the square of half of the coefficient of x. (a) Half of the coefficient of x is 4/2 = 2.

(b) We'll add and subtract 2² = 4. 0 = x² + 4x + 4 - 4 - 1(3)

The first three terms can be expressed as the square of the quantity x+2: (x+2)² = 0 + 4 - 1(4)This simplifies to: (x+2)² = 3

Thus, the equation after completing the square is (x+2)²=3.

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the correct scatter diagram that fits the given paired data is option A, as shown in the attached image.

The scatter plot that fits the given paired data is as follows:

Firstly, the data needs to be paired correctly: Systolic Blood Pressure | Diastolic Blood Pressure119                                        125131                                        130123                                        118118                                        142138                                        125131                                        128140                                        123Then the data pairs are plotted on a graph to create a scatter plot. It is a graph that shows the relationship between two sets of data. In this case, the Systolic blood pressure is on the horizontal axis (X-axis) and the Diastolic blood pressure is on the vertical axis (Y-axis).

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The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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The two options that would prove that ΔABC ~ ΔXYZ include the following:

A. BA/YX = BC/YZ = AC/XZ

C. AC/XZ = BA/YX, ∠A≅∠X

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:

BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)

Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:

AC/XZ = BA/YX, ∠A≅∠X

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Answer: 18.18%

Step-by-step explanation:

First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:

[tex]$$SA = 2lw + 2lh + 2wh$$[/tex]

where [tex]\(l\)[/tex] is the length, [tex]\(l\)[/tex] is the width, and [tex]\(h\)[/tex] is the height. For the original piece of wood, [tex]\(l = 10\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex].

After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, [tex]\(l = 5\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex]. The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.

The percent increase in the total surface area is given by the formula:

[tex]$$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$[/tex]

Let's calculate these values.

The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.

Answer:

Step-by-step explanation:

Step-by-step explanation:

If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:

"What is the ratio of adult tickets to children's tickets sold in a day?"

This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.

If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.

To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.

On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.

Adding the plants planted:

23 + 28 + 29 = 80

Then, we subtract this amount from Thursday's total:

90 - 80 = 10

Therefore, we started with 10 plants initially.

In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.

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Answer:

Step-by-step explanation:

The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expressionns.

Given the algebraic expressions,

[tex]\frac{1}{2}x + 4 \\ x + 6 - \frac{1}{2}x - 2[/tex]

Substituting 2 for x in the first expression gives:

(1/2 × 2) + 4

1 + 4

5

Substituting 2 for x in the second expression gives:

2 + 6 - (1/2 ×2) - 2

8 - 1 - 2

8 - 3

5

Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.

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By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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The evaluation of the constraints with regards to the production of the polo and t-shirts, and to maximize the profit, using linear programming indicates that we get;

a. x = The number of polo shirts produced, y = The number of t-shirts produced

b. The inequalities representing the constraints are;

2·x + y ≤ 84

x + 2·y ≤ 106

x ≤ 36

x ≥ 0, y ≥ 0

c. P = 30·x + 22·y

d. Please find attached the graph of the feasible region

To maximize profit, the company should produce;

21 polo shirts and 43 t-shirts

Linear programming is a method used for optimizing (maximizing or minimizing a value) operations with some specified constraints.

a. The details indicates that the question is related to linear programming. Let x represent the number of polo shirt produced, and let y represent the number of t-shirts produced.

x = The number of polo shirt produced

y = The number of t-shirts produced

b) The constraints are;

Pattern and cutting section; 2·x + y ≤ 84

Sewing section; x + 2·y ≤ 106

Sales constraints; x ≤ 36

The values of x and y are non negative, numbers, therefore;

x ≥ 0, y ≥ 0

c) The objective of the company is to maximize profit, P, therefore, the objective function is; P = 30·x + 22·y

d) The graph can be plotted from the constraint inequalities, by making y the subject in the inequalities that includes both x and y as follows;

2·x + y ≤ 84, therefore; y ≤ 84 - 2·x

x + 2·y ≤ 106, therefore; y ≤ 53 - x/2

x ≤ 36

Please find attached the graph of the inequalities, showing the feasible region which is the polygon with boundaries which are the lines representing the constraints.

The objective function evaluated at the vertices of the feasible region indicates that we get;

[tex]\begin{tabular}{ | l | l | c | }\cline{1-3}(x, y)& 30\cdot x + 22\cdot y & P(\$) \\ \cline{1-3}(0, 53 & 30\times 0 + 22\times 53 & 1166 \\\cline{1-3}(21, 42.5 & 30\times 21 + 22\times 42.5 & 1565 \\\cline{1-3}(32, 12) & 30\times 36 + 22\times 12 & 1344 \\\cline{1-3}(36, 0) & 30\times 36 + 22\times 0 & 1080 \\\cline{1-3}(0, 0) & 30\times 0 + 22\times 0& 0 \\\cline{1-3}\end{tabular}[/tex]

The feasible region and the objective function indicates that the values of x and y that maximizes the profit is; (x, y)  = (21, 42.5)

Therefore, to maximize profit, the number of polo and t-shirts the company should produce are 21, and 42.5 ≈ 43 respectively.

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