If there are 35 students in the class, what is the probability that at least two students have the same birthday?

The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

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Given the following 25 sample observations:

5.3, 6.1, 6.7, 6.8, 6.9, 7.2, 7.6, 7.9, 8.1, 8.9, 9.0, 9.2, 9.4, 9.7, 10.1, 10.4, 10.6, 10.8, 11.3, 11.4, 12.0, 12.1, 12.3, 12.5, 13.2.

Let Y1, Y2,...,Yn be the order statistics for this sample.

A) The interval (Y9, Y16) could serve as a distribution-free estimate of the median, m, of the population.

Find the confidence coefficient of this interval.

The sample size is 25, thus the median is Y(13), where Y is the order statistics of the sample.

So the interval (Y(9), Y(16)) is a 75% confidence interval for the median, m, of the population.

The confidence coefficient of this interval is 0.75.

B) The interval (Y3, Y10) could serve as the confidence interval for a proportion.

Determine this confidence interval and, using a binomial distribution chart, determine the confidence coefficient of this interval.

To calculate the confidence interval for a proportion, we need to calculate the sample proportion, P and use that to calculate the interval limits.

The sample proportion, P = (number of success)/(sample size)

P = (number of success)/(25)

P = (7/25)

= 0.28

So the confidence interval for the proportion is given by:

p ± z √((p(1 - p)) / n)p ± z √((0.28(0.72)) / 25)p ± z √(0.02016 / 25)p ± z (0.1421)

The interval (Y3, Y10) contains 8 observations out of 25.

Thus, the sample proportion is:

P = 8/25

= 0.32

Using a binomial distribution chart, we find the z-value that corresponds to a cumulative area of 0.975 is 1.96.

Hence the 95% confidence interval for the proportion is:

p ± z √((p(1 - p)) / n)

0.32 ± 1.96 √((0.32(0.68)) / 25)0.32 ± 0.1421

The confidence interval is (0.1779, 0.4621) and the confidence coefficient is 0.95.

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Answer:

the slope is 3/5

Step-by-step explanation:

and if you want the y intercept it's 4

Answer:

Use the slope-intercept form  

y = m x +b

to find the slope m

m=3/5

Step-by-step explanation:

Step-by-step explanation:

m<M=m<L=110°

m<N=m<O=x → 2x+2(110°)=360° → x=70°

m<E=180°-22°=158°

m<A=360°-(88°+22°+158°)= 92°

m<D=m<O=61°

m<S=m<G=x → 2x+2(61°)=360° → x=238/2 = 119°

Answer:

Step-by-step explanation:

1)∠L + ∠O = 180       {Co interior angles}

  110 + ∠O = 180

            ∠O = 180 - 110

            ∠O = 70

Base angles of isosceles trapezoid are equal

∠M = ∠L

∠M = 110

∠O = ∠N

∠N = 70

2) ∠c + ∠A = 180               {Co interior angles}

   88 + ∠A = 180

            ∠A = 180 -88

            ∠A = 92

∠D + ∠E = 180       {Co interior angles}

22 +∠E = 180

      ∠E = 180 - 22

      ∠E = 158

3)  ∠O + ∠G =  180           {Co interior angles}

   61 + ∠G = 180

         ∠G = 180 - 61

         ∠G = 119

Base angles of isosceles trapezoid are equal

∠D = ∠O

∠D = 61

∠S = ∠G

∠S = 119

Answer:

12 ft ^3

Step-by-step explanation:

I assume you are looking ofr the volume of this pyramid

V = 1/3 base area * height

base area = area of 3-4-5 triangle =  1/2 * 3 * 4 = 6   ft^2

so Volume is :

1/3  * 6 * 6 = 12 ft^3

Answer:

y = 13

Step-by-step explanation:

y^2 = 169

~Take the square root of both sides

y = 13

Best of Luck!

Answer:

Answer is 19

Step-by-step explanation:

firstly,the area of a rectangle is =LxW

secondly since there is no number for length,we use X for representing the number ,then height is used for representing breath and the number is 23ft and area is 437ft

so we solve,

LxW=AREA

Xx23=437

23X/23=437/23

X=19

therefore the length is =19

Step-by-step explanation:

That means the 96 is  75% of your grade

   96 (.75) + 75 (.25) = 90.75  final grade

Answer:

B

Step to Step Explaintion:

The time-series model that assumes that demand in the next period will be equal to the most recent period's demand is A) Naive approach.

This model is based on the simplest assumption of all, that the next period's demand will be equal to the current period's demand. It is called the naive approach because it assumes no underlying pattern in the data and provides a baseline prediction. The formula for the naive approach is as follows:

y(t) = y(t-1) where y(t) represents the demand in period t and y(t-1) represents the demand in the previous period.

Although this model is simple, it is often used as a benchmark for comparison with more complex models and can provide reasonable results for stable demand patterns.

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The minimum unit cost of the car is $12232.1

Given: cost function C(x)=0.9x² - 414x + 59,366

In order to find the minimum point, take the derivative of the cost function:

dC/dx = 2x - 414          (equate to zero and solve for x)

2x - 414 = 0                

2x = 414

x = 414/2 = 207

Thus, the minimum point is at x =207

The minimum unit cost can be obtained by substituting x = 207 into the cost equation:

C(x) = 0.9x² - 414x + 59,366

C(207) = 0.9(207)² - 414(207) +  59,366

          = 38564.1 - 85698 + 59,366

           = $12232.1

Therefore, the minimum unit cost is $12232.1

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Answer:

y=1/5x-1

Step-by-step explanation:

SI form is Y=mx+b

The value of the 7th term of the geometric progression is 223.9488

Based on the information given,

First term = 75

Second term = 90

Common ratio = 90/75 = 1.2

The nth term of a geometric progression is calculated as:

\(a_n=ar^{r-1}\)

The 7th term will then be:

\(= 75 \times (1.2)^6\)

\(=75\times2.985984\)

\(=223.9488\)

Therefore, the value of the 7th term of the geometric progression is 223.9488.

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Answer:

square

triangle

5

square pyramid

find area of base and area of a lateral face (base is 1 side squared, lateral face is base * height / 2. Multiply area of lateral face by 4 and add the product to the area of the base to find the Surface Area.

Step-by-step explanation:

1. The shape of the base is a square.

2. The lateral faces are triangles.

3. Including the square and four triangles, the figure has 5 faces.

4. Square pyramid.

5. Find the surface area of the square. Find the surface area of one triangle, and multiply by 4 to get all of them. Add the area of the four triangles to the area of the square.

Hope this helps.

If the  height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .

In order to find time at which ball is at its highest point,

we have to find the time at which the derivative of height function is = 0.

the height function is ⇒ f(x) = -16x² + 64x ;

So , the derivative of the height function will be :

⇒  f'(x) = -32x + 64 ;

equating the derivative of height function to 0 , and solving for x ,

we get ;

⇒ -32x + 64 = 0

⇒ -32x = -64

⇒ x = 2

Therefore , the time at which the ball is at its highest point is 2 seconds .

The given question is incomplete , the complete question is

Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.

At what time in seconds is the ball at its highest point after being kicked ?

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Answer:

(3,-3)

Step-by-step explanation:

put each equation in slope intercept form. they turn into y = x - 6 and y = -2x + 3. now you can graph them. the point where they intersect is the solution.

Answer:

7-x^2+6

Step-by-step explanation:

just put the words to numbers

Answer:

7-x^2+6

Step-by-step explanation:

Hope this helps!! :))

Answer:

i) around 41.7 kg

ii) 72 books

Step-by-step explanation:

i) if 108 books are 30 kg then how much is the mass for 150? You cross multiply so 150 multiply by 30 and 108 multiply by x (the unknown mass). you will get 4500=108x and then 4500/108 is the unknown mass.

ii) use the same way as above.

Step-by-step explanation:

10x + y + 10y + x = 121

11x + 11y = 121

y = 5

11x + 55 = 121

11x = 121 - 55

11x = 66

x = 6

the number is 10(6) + 5

65

Answer:

65

Step-by-step explanation:

let the number be x and y

0.60792 liters x 1000 = 607.92 mL

Multiplying the volume in liters by 1000 converts it to milliliters.

Answer:11/4

Step-by-step explanation:

Answer:

1. x = {-3, 3}

2. a = {-12, -2}

3. v = {-7, 10}

4. m = {-8, 8}

5. k = {-11, 1}

6. y = {-13, 19}

Step-by-step explanation:

|-2x| = 6

means that

-2x = 6     or      -2x = -6

x = -3        or      x = 3

|a + 7| = 5

means that

a + 7 = 5    or      a + 7 = -5

a = -2        or      a = -12

|8v-12| = 68

means that

8v-12 = 68     or      8v-12 = -68

8v = 80        or      8v = -56

v = 10            or      v = -7

| m / -4 | + 1 = 3

| m / -4 | = 2

means that

m/-4 = 2     or      m/-4 = -2

m = -8        or      m = 8

3|k + 5| = 18

|k+5| = 6

means that

k + 5 = 6    or      k + 5 = -6

k = 1        or      k = -11

|2y - 6| / 4 = 8

|2y - 6| = 32

means that

2y - 6 = 32     or      2y - 6 = -32

y = 19        or      m = -13

The group that would be the most stable based on size would be 10 people. So, the correct answer is c. 10 people.

A group is a set of people or objects that are deemed to be equivalent or share a common feature. Group members may collaborate and share knowledge to achieve a common goal. The group's performance is frequently greater than the sum of its members' individual efforts, and this is known as the group effect.

Group stability is defined as the ability of a group to remain together and keep working toward its objective over time. It is essential for a group to achieve its objectives and is typically linked to the group's size and objective. A stable group can withstand external pressures and is less susceptible to breaking up or being disbanded.

A group's size has a significant influence on its stability. Small groups are often more cohesive and productive than large groups. On the other hand, as a group's size grows, it becomes more challenging to sustain cohesion and productivity. A group of 10 people would be the most stable since it's not too large or too small. Thus, the correct option is c. 10 people.

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The dot plot has 43 dots.

The dot plot has 10 dots to the left of the center and 1 dot to the right of the center.

The center of the data set is 6.

This can be solved using the concept of dot plot.

For relatively small data sets with values falling into a handful of discrete bins, a dot plot, also known as a dot chart, is a sort of straightforward histogram-like display used in statistics. To create a dot plot, count the data points that fall into each bin and then draw a stack of dots that is that many dots high for each bin. The form and distribution of sample data may be seen using dot plots, which are particularly helpful when comparing frequency distributions. The frequency distribution of a dataset shows how frequently certain values occur. Dot plots display the same kinds of data as histograms.

From the given figure it is clear that 1 has 6 dots, 2 has 5 dots, 3 has 4 dots, 4 has 2 dots, 5 has 3 dots, and 6 has 2 dots. It means the data set is:

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

Total number of observations = 43

The dot plot has 43 dots.

Median:

43 is an odd number, so the median of the data is:

Median = {(n+1)/2} / 2

Median = 11

The 11th term of the data is 6, therefore the median of the data is 6.

The dot plot has 10 dots to the left of the center and 1 dot to the right of the center.

The center of the data set is 6.

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Answer:

To solve this problem, we need to first convert the number of days and hours into minutes. Since there are 60 minutes in 1 hour, we can multiply the number of hours (36) by 60 to get the number of minutes in those hours: 36 hours * 60 minutes/hour = 2,160 minutes

Then, we can multiply the number of days (31) by the number of minutes per day to get the total number of minutes driven: 31 days * 1440 minutes/day = 44,640 minutes

Therefore, if the trip lasted 31 days and the trip was 36 hours, you drove a total of 44,640 minutes.

Step-by-step explanation:

Answer:

The commutative property of addition means that it does not matter what order in which you add numbers. You will get the same answer either way. It is represented as a + b = b + a, in which a and b are real numbers. However, the property is not limited to two numbers.

1) Rearrange terms

3 + 5m = 5m + 3

5m + 3 = 5m + 3

2) Subtract 3 from both sides

5m + 3 = 5m + 3

5m + 3 - 3 = 5m + 3 - 3

3) Simplify

- Subtract the numbers

5m + 3 - 3 = 5m +  3 - 3

5m = 5m + 3 - 3

- Subtract the numbers

5m = 5m + 3 - 3

5m = 5m

4) Subtract 5m from both sides

5m = 5m

5m - 5m = 5m - 5m

5) Simplify

- Combine like terms

5m - 5m = 5m - 5m

0 = 5m - 5m

- Combine like terms

0 = 5m - 5m

0 = 0

This means it has infinite solutions.

But the commutative property addition have been shown.

The angle measures of the triangles before and after dilation are the same

Given that, we have a triangle that is dilated to form another triangle by a scale factor of n

The dilation transformation is a rigid transformation

This means that it changes the size of a shape after it is applied

However, the shape and the image would be similar shapes and as such would have their angles unchanged

This means that irrespective of the value of the scale factor n, the angle measures would remain the same

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Answer:

Hello! answer: 96

Step-by-step explanation:

I will find the area of each face separately and add them up so... for the triangles those would both be 6. the rectangle on the bottom would be 28 and the rectangle standing up would be 21 now for the triangle on top that would be 35. now we would just add these up so...

6 + 6 + 28 + 21 + 35 = 96 Therefore the surface area is 96 Hope that helps!

The graph of the solutions on the number line represents all the values to the left of -2, with an open circle at -2 to indicate that it is not included in the solution.

To graph the solutions of the inequality c < -2 on a number line, we start by plotting a point at -2.

Since the inequality is strict (c < -2), the point at -2 should be an open circle to indicate that it is not included in the solution.

Then, we draw an arrow to the left to represent all the numbers that are less than -2.

On the number line, any number to the left of -2 would satisfy the inequality.

This means that all values from negative infinity up to but not including -2 are solutions to the inequality c < -2.

In interval notation, we can represent this solution set as (-∞, -2).

In words, the solution to the inequality c < -2 can be described as all real numbers less than -2.

This includes any number that is to the left of -2 on the number line, such as -3, -4, -5, and so on.

However, it does not include -2 itself.

Therefore, the graph of the solutions on the number line represents all the values to the left of -2, with an open circle at -2 to indicate that it is not included in the solution.

The interval notation (-∞, -2) summarizes the range of solutions to the inequality.

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Answer:

c.-18

Step-by-step explanation:

follow me and -GOOD LUCK-