Find the unknown angle
60°
Xº
30°

Answer:

It would be 30.

Step-by-step explanation:

If we make a list of all the sums that we can get, we have:

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.

That gets us to 15x2 which is 30.

The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

I have a bag with 6 marbles numbered from 1 to 6.

Mathew has a bag with 12 marbles numbered from 1 to 12.

1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6

These 15 sums can be chosen in two ways,

Since order matters, and we could do 2+1 instead of 1+2.

15 x 2 which is 30.

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Answer:

5/8

Step-by-step explanation:

Subtracting a negative is the same as adding.

3/8 - (-1/4) = 3/8 + 1/4 = 3/8 + 2/8 = 5/8

Answer:

3/8+2/8=5/8, so the answer is 5/8.

1) a) The symmetric equations for the line is (x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

b) XY-plane is (4/3, 20/3, 0), YZ-plane is (0, 12, -4) and XZ-plane is (3, 0, 5).

2) The equation of the plane is 16x + 4y + 8z - 42 = 0.

3) The equation of the plane is -2x - 9y - 5z = 0.

1) Symmetric Equations for the Line:

a) To find the symmetric equations for the line that passes through the point (4, -4, 8) and is parallel to the vector (-1, 4, -3), we can use the parametric form of the line and then convert it into symmetric form.

Parametric Equations:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

To convert these parametric equations into symmetric form, we eliminate the parameter 't' by setting up equations involving the ratios of differences of coordinates:

(x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

This gives us the symmetric equations for the line.

(b) Points of Intersection with Coordinate Planes:

To find the points in which the line intersects the coordinate planes, we substitute the appropriate values of coordinates into the equations of the line.

i) Intersection with XY-plane (z = 0):

Substituting z = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting z = 0, we have:

8 - 3t = 0

t = 8/3

Substituting t = 8/3 into the equations for x and y:

x = 4 - (8/3) = 4/3

y = -4 + 4(8/3) = 20/3

Therefore, the point of intersection with the XY-plane is (4/3, 20/3, 0).

ii) Intersection with YZ-plane (x = 0):

Substituting x = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting x = 0, we have:

4 - t = 0

t = 4

Substituting t = 4 into the equations for y and z:

y = -4 + 4(4) = 12

z = 8 - 3(4) = -4

Therefore, the point of intersection with the YZ-plane is (0, 12, -4).

iii) Intersection with XZ-plane (y = 0):

Substituting y = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting y = 0, we have:

-4 + 4t = 0

t = 1

Substituting t = 1 into the equations for x and z:

x = 4 - 1 = 3

z = 8 - 3(1) = 5

Therefore, the point of intersection with the XZ-plane is (3, 0, 5).

2) Equation for the Plane:

To find an equation for the plane consisting of all points equidistant from the points (-6, 4, 1) and (2, 6, 5), we can use the distance formula to set up an equation.

Let P(x, y, z) be a point on the plane.

The distance from P to (-6, 4, 1) should be equal to the distance from P to (2, 6, 5).

Using the distance formula, we have:

√[(x - (-6))² + (y - 4)² + (z - 1)²] = √[(x - 2)² + (y - 6)² + (z - 5)²]

Simplifying the equation gives:

(x + 6)² + (y - 4)² + (z - 1)² = (x - 2)² + (y - 6)² + (z - 5)²

Expanding and simplifying further:

x² + 12x + 36 + y² - 8y + 16 + z² - 2z + 1 = x² - 4x + 4 + y² - 12y + 36 + z² - 10z + 25

Rearranging the terms:

16x + 4y + 8z - 42 = 0

Therefore, the equation of the plane is 16x + 4y + 8z - 42 = 0.

3) Equation of the Plane:

To find the equation of the plane that passes through the point (-2, 1, 1) and contains the line of intersection of the planes x + y - z = 3 and 4x - y + 5z = 5, we can use the following steps:

Step 1: Find the direction vector of the line of intersection of the given planes.

To find the direction vector, we take the cross product of the normal vectors of the two planes.

The normal vector of the first plane, P1: (1, 1, -1)

The normal vector of the second plane, P2: (4, -1, 5)

The direction vector, D: P1 x P2

D = (1, 1, -1) x (4, -1, 5)

Using the cross product formula, we have:

D = ((1)(-1) - (-1)(1), (-1)(4) - (1)(5), (1)(-1) - (1)(4))

D = (-2, -9, -5)

So, the direction vector of the line of intersection is (-2, -9, -5).

Step 2: Use the point-direction form of the plane equation.

The equation of the plane passing through a given point (x0, y0, z0) with a direction vector (a, b, c) is given by:

a(x - x0) + b(y - y0) + c(z - z0) = 0

Substituting the values from the given information:

Point on the plane: (-2, 1, 1)

Direction vector: (-2, -9, -5)

The equation becomes:

(-2)(x - (-2)) + (-9)(y - 1) + (-5)(z - 1) = 0

(-2)(x + 2) - 9(y - 1) - 5(z - 1) = 0

-2x - 4 - 9y + 9 - 5z + 5 = 0

-2x - 9y - 5z = 0

Therefore, the equation of the plane is -2x - 9y - 5z = 0.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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In order to determine the probability of a random selected student to be a men, we need to divide the number of men by the number of all the students in the class. We have:

The probability of a random student being a man is approximately 67%.

There are 2,646 different ways to form the committee with 5 teachers and 5 students.

There are 7 teachers to choose from, and we need to select 5 of them. This can be done in C(7,5) ways:

C(7,5) = 7! / (5!2!) = 76 / 21 = 21

There are 9 students to choose from, and we need to select 5 of them. This can be done in C(9,5) ways:

C(9,5) = 9! / (5!4!) = 9876 / 4321 = 126

To find the total number of ways to form the committee, we multiply the number of ways to select 5 teachers by the number of ways to select 5 students:

21 × 126 = 2,646

Therefore, there are 2,646 different ways to form the committee with 5 teachers and 5 students.

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a) The percentage increase in sales from 2004 to 2014 for Company A was 21.25%.

b) The company that had the most sales per worker in 2014 was Company A.

The percentage increase refers to the amount of increase (that is the difference between the current value and the initial value) divided by the initial value, multiplied by 100.

Percentage increases are determined as the quotients of division operations, which are multiplied by 100 to express the value in percentage terms.

a) Percentage increase in sales from 2004 to 2014 for Company A:

Sales increase = $68 ($388 - $320)

Percentage increase = 21.25% ($68/$320 x 100)

b) Sales per Worker in 2014:

Company A = $121,250 ($388,000,000/3,200)

Company B = $89,062.50 ($57,000,000/640)

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                    Company A                                      Company B

              Sales        Number of Workers        Sales       Number of Workers

           ($ millions)                                        ($ millions)

2004      $320               2,960                        $48                   605

2014         388               3,200                           57                   640

(b) Which company had the most sales per worker in 2014. Company A or Company B?

Answer:

9

Step-by-step explanation:

2 ( ) = 18

Remember that bracket sign means multiplication. So, if we divide both sides by 2, we have

( ) = 18/2

( ) = 9

The missing integer is 9

Using fraction formula,

Each person will receive 1/2 part of left over pizzas .

Fraction : In Mathematics, a fraction defined as the part of the whole thing. For example, a cake is divided into 5 equal pieces, then each piece is denoted by ¼.

We have given that,

After party , 4+1/2 pizzas left over .

number of peoples among spliting of pizza happened = 9

Assume there is x pizzas .

left over part = (4+ 1/2 ) = 9/2

ate by other = 1- 9

9/2 pizzas is divided into 9 people's = 9/2 /9

= 1/2

thus , each person will receive 1/2 of left over pizzas i.e( 4+ 1/2 ).

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Answer:

a = 44° , b = 136°

Step-by-step explanation:

a and Θ are alternate angles and are congruent , so

a = 44°

b and Θ are same- side interior angles and sum to 180°, that is

b + Θ = 180°

b + 44° = 180° ( subtract 44° from both sides )

b = 136°

Here's a sample program in C++ that satisfies your requirements:

```
#include
using namespace std;

int main() {
 int num;
 cout << "Enter an integer between 0 and 35: ";
 cin >> num;

 if (num <= 9) {
   cout << num << endl;
 } else if (num >= 10 && num <= 35) {
   char letter = static_cast('A' + num - 10);
   cout << letter << endl;
 } else {
   cout << "Invalid input." << endl;
 }

 return 0;
}
```

- The program prompts the user to input an integer between 0 and 35 using the `cout` and `cin` statements.
- The `if` statement checks whether the number is less than or equal to 9. If it is, it outputs the number using the `cout` statement.
- The `else if` statement checks whether the number is between 10 and 35 (inclusive). If it is, it calculates the corresponding letter using the ASCII value for 'A' and the given number. The `static_cast` statement converts the calculated value to a character. Finally, the program outputs the letter using the `cout` statement.
- The `else` statement handles the case when the input is outside the range of 0 to 35. It outputs an error message using the `cout` statement.
- The program ends with the `return 0` statement.

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Answer:

y = 18

Step-by-step explanation:

Given

f(x) = 2x² ( substitute x = 3 )

y = f(3) = 2(3²) = 2(9) = 18

Answer:

0

Step-by-step explanation:

1.6x + 9x =15x

2. 15(x + 4) = 15x + 60

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

15x + 35 = 15x + 60 - 25

15x + 35 = 15x + 35

0 = 0

Answer:

The answer is 15p = 49.50

Answer:

The answer is $3.3

Step-by-step explanation: Because 49.50 divided by 15 is 3.3

To determine whether a variable is discrete or continuous, you need to consider the nature and characteristics of the variable.

Here are some guidelines to help you make the distinction:

1. Discrete Variables:

- Discrete variables have a countable or finite number of possible values.

- The values of a discrete variable are often whole numbers or integers.

- Examples of discrete variables include the number of children in a family, the number of cars in a parking lot, or the number of customers in a store at a given time.

2. Continuous Variables:

- Continuous variables can take on any value within a certain range or interval.

- The values of a continuous variable can be infinitely divisible and can include decimal fractions.

- Examples of continuous variables include height, weight, time, temperature, or the amount of rainfall.

However, it's worth noting that some variables may fall in a gray area and can be considered both discrete and continuous depending on the context.

For example, age can be treated as a discrete variable when only whole numbers are considered (e.g., number of years), but it can be treated as continuous when fractional values (e.g., age in years and months) are considered.

When determining if a variable is discrete or continuous, it's important to consider the level of measurement and the nature of the values being observed. Discrete variables typically involve counts or distinct categories, while continuous variables involve measurements along a continuum.

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Fragment free frame processing method causes a switch to wait until the first 64 bytes of the frame have been received before forwarding the frame to the destination device

An advanced type of cut-through switching is fragment-free (runtless switching). Before making a switching choice, switches engaged in cut-through switching merely read the Ethernet frame's destination MAC address field.

The latency in fast-forward mode is calculated between the first bit received and the first bit delivered. The most common cut-through switching technique is fast-forward switching. Switching without fragments: The switch stores the first 64 bytes of the frame in fragment-free switching before forwarding.

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To find the area of the region bounded by the graphs of the equations y = 4/x, x = 1, x = e, and y = 0, we can use definite integrals. The area is obtained by integrating the function y = 4/x with respect to x over the interval [1, e]. The area of the region bounded by the given equations is 4 square units.

    To calculate the area of the region bounded by the given equations, we integrate the function y = 4/x with respect to x over the interval [1, e]. The region is limited by the x-values of 1 and e, and the y-value of 0.

The integral representing the area is:

A = ∫[1, e] (4/x) dx

To evaluate this integral, we can use the natural logarithm function. Simplifying the integral, we have:

A = 4 ∫[1, e] (1/x) dx

Taking the integral, we obtain:

A = 4 ln|x| ∣[1, e]

Evaluating this expression at the limits, we get:

A = 4 (ln|e| - ln|1|)

Since ln|e| = 1 and ln|1| = 0, the area simplifies to:

A = 4 (1 - 0) = 4

Therefore, the area of the region bounded by the given equations is 4 square units.

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Answer: 20%

Step-by-step explanation:

Among the given options, model D (Yt Bo + Bit + Et = O) is not called a causal forecasting model. Therefore, model D (Yt Bo + Bit + Et = O) is not called a causal forecasting model since it lacks any independent variables that can explain or influence the dependent variable.

A causal forecasting model is a type of model that assumes a causal relationship between the dependent variable (Yt) and one or more independent variables (xt, yt-1, etc.). It aims to establish a cause-and-effect relationship and identify how changes in the independent variables affect the dependent variable.

A. Yt Bo + B1yt-1 + €t: This model includes a lagged dependent variable (yt-1) as an independent variable, suggesting a causal relationship. It can capture how the past value of the dependent variable influences the current value.

B. Yt Bo+Bit + B₁yt-1 + Et: This model includes both a lagged dependent variable (yt-1) and an additional independent variable (Bit). It accounts for the influence of both past values and other factors on the dependent variable.

C. Yt Bo + B1xt-1 + €t: This model includes an independent variable (xt-1) that can influence the dependent variable. It establishes a causal relationship between the independent and dependent variables.

D. Yt Bo + Bit + Et = O: This model does not include any independent variables that could be causally related to the dependent variable. It simply states that the dependent variable (Yt) is equal to a constant (Bo) plus a constant term (Bit) plus an error term (Et).

Therefore, model D (Yt Bo + Bit + Et = O) is not called a causal forecasting model since it lacks any independent variables that can explain or influence the dependent variable.

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The function h(x) = 4sec(π/4(x+3)) represents a graph with a stretching factor of 4 and a period of 8π/4 = 2π. The correct graph representation of h(x) = 4sec(π/4(x+3)) needs to show these characteristics. The correct answer would be (b).

The function h(x) = 4sec(π/4(x+3)) has a stretching factor of 4, which means that the amplitude of the function is multiplied by 4, causing the graph to be vertically stretched.

The period of the function is given by P = 2π/π/4 = 8π/4 = 2π. This means that the graph will complete two periods within the interval [-P, P], which in this case is [-2π, 2π].

The asymptotes of the function occur at x = -P/2 and x = P/2. Substituting the value of P = 2π, the asymptotes are x = -π and x = π. These vertical asymptotes indicate where the graph approaches infinity or negative infinity as x approaches these values.

To determine the correct graph representation of h(x) = 4sec(π/4(x+3)), you would need to choose the graph option that shows the stretching factor of 4, a period of 2π, and vertical asymptotes at x = -π and x = π.

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Answer:

Step-by-step explanation:

A linear function is a line which, in slope-intercept form, follows

y = mx + b,

where m is the slope and b is the y-intercept.

The only one that follows that form is B. B can be rewritten as

\(y=\frac{1}{3}x+2\)

and in that form we see that the slope value is 1/3 and the y-intercept is 2. The choice is B.

A is a radical function moved up from its originating spot; C is an inverse function moved down 4 units from its originating spot with a vertical asymptote at x = 0; and D is a cubic moved down 10 units from its originating spot.

B is the one you want.

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

We can use similar triangles to find the distance across the lake (DE). Since triangle CGF is similar to triangle CED, we can use ratios of the sides to find DE.

Let's call DE = x. Then, we have:

CE/FG = x/142.1

Solving for x, we have:

x = (CE * 142.1) / FG

CE = CF + FD = 130 + 60 = 190m

x = (190 * 142.1) / 142.1 = 190m

The distance across the lake is 190m. Rounding to the nearest hundredth of a meter, the answer is 190.00m.

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The complete question is :

To indirectly measure the distance across a lake, Dominic makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter.

Answer:

154.5 cm2

Step-by-step explanation:

height=3

lenght=8.5

breadth=4.5

the ans is 154.5 cm2

Answer:

Its B I think if u choose B u will like me

The line AB is not a perpendicular bisector of CD.

Perpendicular bisectors are lines that divides another line into two equal parts.

From the diagram, we can see that line CD cuts AB at the centre. Hence we can say that CD is a perpendicular bisector of AB.

The same is not applicable to line AB passing through CD. The line AB did not bisect (divide equally) line CD.

Hence we can conclude that line AB is not a perpendicular bisector of CD.

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Answer:

X=5+

Step-by-step explanation:

Answer:

hi

Step-by-step explanation:

hi

The matrix -4 -3 -2 is not symmetric because it is not equal to its transpose, which is  -4 0 and  -3 -2.

The transpose of the matrix is simply found by writing the rows as columns and columns as rows.

For instance, the transpose of -4 -3 -2 is-4 0and -3 -2.

How to determine whether a matrix is symmetric?

In order to determine whether a matrix is symmetric or not, the matrix needs to be square, i.e., the number of columns must be equal to the number of rows.

A matrix is considered symmetric if the number of columns is equal to the number of rows and if the i,jth entry is equal to the j,ith entry.

An equivalent condition is that the matrix is symmetric if it is equal to its transpose.

So, the matrix is not symmetric because it is not equal to its transpose, which is -4 0 and -3 -2, which means that the correct option is OA.

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Answer:

the answer is E. none of the above