Use a unit circle, a 30°-60°-90° triangle, and an inverse function to find the degree measure of each angle.

angle whose sine is -√3/2

Answer:

x=3

Step-by-step explanation:

-6x+21+4x=15

-2x+21=15

-2x=15-21

-2x=-6/2

x=3

Answer:

c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Each month we have to deposit 1389 of amount and we get interest of 30000

percentage, a relative value indicating hundredth parts of any quantity.

Given 500000 to be in our account in retirement of 30 years.

We need to find how much we have to deposit each month.

We know that in a year there are 12 months.

For 30 years the number of months are 12×30=360

So Now divide 500000 by 360 to find each month deposit

500000/360=1388.8

So each month one has to deposit 1389 into account.

Now if account earns 6% of interest. We need to find how much amount we earned.

6% is converted to decimal by dividing 6 by 100

0.06

Now multiply with 500000

0.06×500000

30000

Hence, each month we have to deposit 1389 of amount and we get interest of 30000.

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Answer:

7,291.67 soles

Step-by-step explanation:

Ecuación para el monto a pagar después de 5 meses utilizando interés simple

A = P (1 + rt)

P = 7000 soles

r = 10% meses

t = 5 meses

Cálculo:

Primero, convertir R por ciento en r en decimal

r = R / 100 = 10% / 100 = 0,1 por año.

Dedicar tiempo a los años por la simplicidad,

5 meses / 12 meses / año = 0,416667 años.

Resolviendo nuestra ecuación:

A = 7000 (1 + (0,1 × 0,416667)) = 7291,6669

A = 7,291.67 soles

El monto total que está pagando después de 5 meses = 7,291.67 soles

The transfer function H(s) = s^3/(s+1)(s^2+4s+13) can be realized in the canonic direct, series, and parallel forms.

To realize the given transfer function H(s) = s^3/(s+1)(s^2+4s+13) in the canonic direct, series, and parallel forms, we need to factorize the denominator and express it as a product of first-order and second-order terms.

The denominator (s+1)(s^2+4s+13) is already factored, with a first-order term s+1 and a second-order term s^2+4s+13.

1. Canonic Direct Form:

In the canonic direct form, each term in the factored form is implemented as a separate block. Therefore, we have three blocks for the three terms: s, s+1, and s^2+4s+13. The output of the first block (s) is connected to the input of the second block (s+1), and the output of the second block is connected to the input of the third block (s^2+4s+13). The output of the third block gives the overall output of the system.

2. Series Form:

In the series form, the numerator and denominator are expressed as a series of first-order transfer functions. The numerator s^3 can be decomposed into three first-order terms: s * s * s. The denominator (s+1)(s^2+4s+13) remains as it is. Therefore, we have three cascaded blocks, each representing a first-order transfer function with a pole or zero. The first block has a pole at s = 0, the second block has a pole at s = -1, and the third block has poles at the roots of the quadratic equation s^2+4s+13 = 0.

3. Parallel Form:

In the parallel form, each term in the factored form is implemented as a separate block, similar to the canonic direct form. However, instead of connecting the blocks in series, they are connected in parallel. Therefore, we have three parallel blocks, each representing a separate term: s, s+1, and s^2+4s+13. The outputs of these blocks are summed together to give the overall output of the system.

These are the realizations of the given transfer function H(s) = s^3/(s+1)(s^2+4s+13) in the canonic direct, series, and parallel forms. The choice of which form to use depends on the specific requirements and constraints of the system.

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Answer:

290$

Step-by-step explanation:

Answer:

Mei earn $2 less than three times as much as Olivia. Shane earns twice as much as mei. Together they earn $594 per week. How much does each person earn per week?

***

Step-by-step explanation:

let x=amt Olivia earns

3x-2=amt Mei earns ($2 less than three times as much as Olivia).

2(3x-2)=amt Shane earns (twice as much as mei)

..

x+3x-2+2(3x-2)=594

x+3x-2+6x-4=594

10x=600

x=60

3x-2=178

2(3x-2)=356

amt Olivia earns=$60

amt Mei earns=$178

amt Shane earns=$356

Answer:

\(h(x)=12x-9\)

Step-by-step explanation:

We are given the two functions:

\(f(x)=4x-2\text{ and } g(x)=-8x+7\)

And we want to find:

\(h(x)=f(x)-g(x)\)

So, by substitution:

\(h(x)=(4x-2)-(-8x+7)\)

Simplify. Distribute:

\(h(x)=(4x-2)+(8x-7)\)

Rearrange:

\(h(x)=(4x+8x)+(-2-7)\)

Combine like terms. Hence:

\(h(x)=12x-9\)

Step-by-step explanation:

y = mx +b

m - the slope; b- y-intercept

therefore;

y = 3x - 4

m = 6; b = -4

y = 5x - 3

m = 5; b = -3

The coordinates of the point where the lines are crossed are the solution to the system of linear equations.

How to graph the lines:

y = 6x - 4

y-intercept (0; -4)

for x = 1 ⇒ y = 6 · 1 - 4 = 6 - 4 = 2 ⇒ (1; 2)

y = 5x - 3

y-intercept (0; -3)

for x=1 ⇒ y = 5 · 1 - 3 = 5 - 3 = 2 ⇒ (1; 2)

***look at the img for graph reference***

Part B: x = 1; y = 2

The equation that represents a line that is parallel to y = -2x - 5 is; the line that has a slope = -2

We are given the equation;

y = -2x - 5

Now,from the slope intercept form of a line, we know that;

y = mx + c

Where m is slope

c is y-intercept

Comparing to our equation gives;

m = -2

m = -2c = -5

Now, for a line to be parallel to another line, they must have the same slope. Thus;

The line that will be parallel to y = -2x - 5 must have a slope = -2

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The factor of 324 are : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324

In the prime factorization and division methods, respectively, 324 can be expressed as the product of its prime factors and divided by its divisors.

Hence. the factor of 324 are : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324

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Given:

Let us consider,

Length of a rectangular prism = 8 inches

Width = \(6\dfrac{3}{4}\) inches

Height = \(5\dfrac{1}{4}\) inches

To find:

The volume of the rectangular prism.

Solution:

The volume of a rectangular prism is:

\(V=l\times w\times h\)

Where, l is length, w is width and h is height.

Putting the given values, we get

\(V=8\times 6\dfrac{3}{4}\times 5\dfrac{1}{4}\)

\(V=8\times \dfrac{27}{4}\times \dfrac{21}{4}\)

\(V=\dfrac{567}{2}\)

\(V=283.5\)

Therefore, the volume of the rectangular prism is 283.5 cubic inches.

Answer:

C

Step-by-step explanation:

Each output is 3 more than the input

Answer: the answer is c, y + 3

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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Answer:

150 1st graders

Step-by-step explanation:

do 24 times 6 because there are 24 adults and each of their tickets cost $6. you will get 144. do 444-144 to get 300 because uou want to subtract the money the adults have to pay. Since it's $2 per kid, just divide 300 by 2 to get 150. Hope this helps :)

The ethnicity of respondents in a political poll of randomly selected adults is an example of a categorical variable.

A categorical variable is a type of variable that represents data that can be categorized into distinct groups or categories. In this case, the ethnicity of the individual respondents in the political poll represents different categories such as Asian, African American, Hispanic, Caucasian, etc. Each respondent falls into one of these categories based on their ethnicity.

The variable is categorical because it does not have numerical values that can be quantified or measured. Instead, it represents qualitative data that can be described using labels or categories.

Therefore, the ethnicity of the individual respondents in a political poll of randomly selected adults is an example of a categorical variable.

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The correct answer is 2 (C) - 2 days is the total slack for activity F. To determine the total slack for activity F, we need to calculate the slack for each activity in the network. Slack refers to the amount of time an activity can be delayed without affecting the project completion time.

1. First, let's draw the network using the information provided:
  - A is the start node and G is the stop node.
  - Activity A has a duration of 5 days and has no predecessor.
  - Activities B, C, and D have durations of 8, 7, and 6 days respectively, and their predecessors are A.
  - Activity E has a duration of 9 days and its predecessors are B, C, and D.
  - Activity F has a duration of 10 days and its predecessors are B, C, and D.
  - Activity G has a duration of 5 days and its predecessors are E and F.

                 A
                /|\
               / | \
              /  |  \
             B   C   D
              \  |  /
               \ | /
                \|/
                 E
                 |
                 F
                 |
                 G

2. Now, let's calculate the slack for each activity:
  - Slack is calculated by subtracting the earliest start time of an activity from the latest start time without delaying the project completion time.
  - The earliest start time for activity F is 17 days.
  - The latest start time for activity F is 19 days (project completion time is 22 days).
  - Total slack for activity F = latest start time - earliest start time = 19 - 17 = 2 days.

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To find the dimensions of the page that will require the minimum amount of paper, we can use the formula for the area of a rectangle:
Area = Length x Width
Let L be the length of the page and W be the width of the page. From the problem, we know that the total area of each page is 90 square inches, and there are margins of 1 inch on the sides and 2.5 inches on the top and bottom of each page. Therefore, the dimensions of the printed matter and illustrations are:
Length = L - 2(1) = L - 2 inches
Width = W - 2(2.5) = W - 5 inches

Substituting these expressions into the formula for the area, we get:

Area = (L - 2)(W - 5)

To find the minimum amount of paper, we need to minimize this function. We can do this by taking partial derivatives with respect to L and W, setting them equal to zero, and solving for L and W. The partial derivatives are:

dA/dL = W - 5
dA/dW = L - 2

Setting these equal to zero, we get:

W - 5 = 0 => W = 5
L - 2 = 0 => L = 2

Therefore, the dimensions of the page that will require the minimum amount of paper are:

Length = L + 2(1) = 4 inches
Width = W + 2(2.5) = 10 inches

Note that these dimensions include the margins, so the actual size of the printed matter and illustrations will be slightly smaller.

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Answer:

45.) 45

46.) 2

47.) 16

48.) 8

49.) 10

50.) 11

51.) 16

52.) 6

53.) 55

54.) 14

Step-by-step explanation:

The second triangle will have the same side lengths and angles as the initial triangle.

The correct option is D.

The reflection of an equilateral triangle relative to the line passing through its side results in a new equilateral triangle that is the same size as the initial triangle. Therefore, the correct answer is D: The second triangle is the same size as the initial triangle.

When a figure is reflected across a line, every point on the figure is flipped to the opposite side of the line, maintaining the same distances and angles. In the case of an equilateral triangle, each side is reflected to the opposite side of the line, resulting in a new equilateral triangle with the same side lengths and angles.

The property of an equilateral triangle is that all three sides are equal in length, and all three angles are equal to 60 degrees. The reflection does not alter these properties. Therefore, the second triangle will have the same side lengths and angles as the initial triangle.

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Answer:

y = 6x - 3

Step-by-step explanation:

y = mx + B

3 = 6(1) + B

3 = 6 + b

3 - 6 = b

-3 = b

b = -3

3 = 6(1) - 3

3 = 3

y = 6x - 3

Answer:

the answer is 1

Step-by-step explanation:

(√4 / √6) + (√6 / √4)

(2 / 2√3) + (2√3 / 2)

√3 / √3

= 1

Given the expression:

The expression shows the distribution property of addition

So, 6 ( 3 +4 ) = 6 * 7 = 42

Which will give the same result if we distribute 6 over 3 and 4

So, 6 (3) + 6(4) = 18 + 24 =42

Show the following diagram:

As shown, the rectangle on the left side has 3 rows + 4 rows

Which will give us 7 rows when divided to 6 column will give 42 squares

While the rectangles on the right side. we have divided it to 3 rows and 4 rows, each one of them is divided to 6 column which will give us 18 squares and 24 squares the sum of them will give us 42 squares

So, 6 ( 3 + 4 ) = 6(3) + 6 (4)

Given :

A roller coaster travels 350 feet horizontally and then travels 130 feet at an angle of 60 degrees from the ground.

To Find :

The direction of the resultant vector.

Solution :

Initial displacement ,

\(\vec{d_1}=350\hat{i}\)

Final displacement ,

\(\vec{d_1}=130cos\ 60^o\hat{i}+130sin \ 60^o\hat{j}\\\\\vec{d_1}=65\hat{i}+65\sqrt{3}\hat{j}\)

So, direction vector is :

\(\vec{D}=\vec{d_1}+\vec{d_2}\\\\\vec{D}=415\hat{i}+65\sqrt{3}\hat{j}\)

Hence, this is the required solution.

Answer:

430

Step-by-step explanation:

The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.

We have to find the volume of the solid generated when region s is revolved about the horizontal line y.

As shaded region is revolved around y = -3.

Outer radius = f(x) + 3

Inner radius = g(x) + 3

Width = dx

Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.

dv = π\((f(x) + 3)^3\)dx - π\((g(x) + 3)^2\)dx

dv = π(\(f^2\)(x) + 6f(x) + 9)dx - π(\(g^2\)(x) + 6g(x) + 9)dx

dv = π(\(f^2\)(x) + 6f(x))dx - π(\(g^2\)(x) + 6g(x))dx

Now integrating on both side:

\(\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125\)

Using the provided result or a scientific calculator, the entire definite integral was discovered.

v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125

v = 93.04919

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The complete question is given below:

Answer:

1/3 of the pizza

Step-by-step explanation:

Number of pizza ordered = 1

pepperoni only part = One-half of the pizza = 1/2 of the pizza

Mushrooms part = one-sixth of the pizza = 1/6 of the pizza

Cheese only part = x

Total pizza = pepperoni only part + Mushrooms part + Cheese only part

1 = 1/2 + 1/6 + x

1 = (3+1) /6 + x

1 = 4/6 + x

1 - 4/6 = x

x = 1 - 2/3

= (3-2) / 3

x = 1/3 of the pizza

Cheese only part = x = 1/3 of the pizza

The lower limit of a class interval is an important factor in calculating the frequency distribution, mean, median, mode, and standard deviation of a data set.

The lower limit of a class interval is calculated by subtracting 0.5 from the lower bound of the interval. The lower bound of the interval in this case is 15, so the lower limit of the class interval 15-20 can be calculated by subtracting 0.5 from 15. The formula for finding the lower limit of a class interval is lower limit = lower bound of interval - 0.5.

The calculation for this class interval is as follows:

lower limit = 15-0.5

lower limit = 14.5

Therefore, the lower limit of the class interval 15-20 is 14.5.

The lower limit of a class interval is important in calculating the frequency distribution of a data set. It is used to calculate the number of values that lie within each class interval. In this case, the lower limit of 14.5 is used to calculate the number of values that lie between 14.5 and 20. This is important when determining the range of values that are included in each class interval.

In addition to being used for frequency distributions, the lower limit is also important for calculating the mean, median, and mode of a data set. The lower limit of 14.5 is used to calculate the mean, median, and mode of the data set. The lower limit is used to determine the average and the most frequent values in the data set.

The lower limit of 14.5 is also important in calculating the standard deviation of a data set. The lower limit is used to calculate the variation in the data set. The lower limit provides a baseline for calculating the variation in the data set.

In conclusion, the lower limit of a class interval is an important factor in calculating the frequency distribution, mean, median, mode, and standard deviation of a data set. For the class interval 15-20, the lower limit is 14.5.

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The missing step is XW/UT=VW/XV because corresponding side of similar triangle are proportional.

What is similar triangle?

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

When two triangles are similar, then their corresponding angles would be congruent while their opposite sides will be proportional to each other

In the proof, it is given, Both triangle are similar, by AA similarity theorem, hence, XW/UT=VW/XV because corresponding side of similar triangle are proportional.

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