please help its my birthday!!
Part A: Estimate the y-intercept of the function. What does the intercept represent in this context?

Part B: What are the domain and range of this function?

It is a function.

You can try plot the graph of that equation and then plot a vertical line. You will see that the graph will only intercept the vertical line only once. That is a function.

Or you can look at the equation. Functions have the equations that start with "y=". Rather say that if you see "y" only (not y² or y³ just only y) then that is mostly a function.

The probability that 49 randomly selected laptops will have a mean replacement time of 2.9 years or less can be calculated using the z-score and the standard normal distribution.

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean (2.9 years), μ is the population mean (3.1 years), σ is the population standard deviation (0.5 years), and n is the sample size (49 laptops).

Plugging in the values, we have:

z = (2.9 - 3.1) / (0.5 / √49)

z = -0.2 / (0.5 / 7)

z = -0.2 / 0.0714

z ≈ -2.80

Next, we use a standard normal distribution table or calculator to find the probability corresponding to the z-score of -2.80. The probability can be found as the area under the curve to the left of the z-score.

By calculating the z-score, we standardize the sample mean with respect to the population mean and standard deviation. This allows us to compare the sample mean to the population distribution.

The negative z-score indicates that the sample mean of 2.9 years is below the population mean of 3.1 years. By looking up the corresponding probability from the standard normal distribution, we find that it is very unlikely to obtain a sample mean of 2.9 years or less by chance alone.

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The bicycle will travel approximately 0.022 kilometers in 10.0 seconds at an average speed of 8.00 km/h.

To calculate the distance traveled by a bicycle in 10.0 seconds with an average speed of 8.00 km/h, we need to convert the time from seconds to hours to match the unit of the average speed.

Given:

Average speed = 8.00 km/h

Time = 10.0 seconds

First, we convert the time from seconds to hours:

10.0 seconds = 10.0/3600 hours (since there are 3600 seconds in an hour)

10.0 seconds ≈ 0.0027778 hours

Now, we can calculate the distance using the formula:

Distance = Speed × Time

Distance = 8.00 km/h × 0.0027778 hours

Distance ≈ 0.0222222 km

Therefore, the bicycle will travel approximately 0.022 kilometers in 10.0 seconds at an average speed of 8.00 km/h.

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There are several potential problems that might arise if a tutor is asked to record personal information such as student names, dates of birth, home addresses, and phone numbers for a large number of students and then email the spreadsheet to the unit convenor.

One major concern is the security and privacy of the students' personal information.

There are logistical challenges involved in managing and organizing the large amount of data.

One major concern is the security and privacy of the students' personal information. Emailing a spreadsheet containing sensitive data poses a risk of unauthorized access, interception, or data breaches. If the spreadsheet falls into the wrong hands, it could lead to identity theft, privacy violations, or misuse of personal information. Additionally, there is the issue of compliance with data protection regulations, such as the General Data Protection Regulation (GDPR), which requires the protection of personal data and imposes strict guidelines on its handling.

Moreover, there are logistical challenges involved in managing and organizing the large amount of data. Ensuring accuracy and maintaining data integrity becomes increasingly difficult with a higher number of students and multiple tutors. There may be instances of data entry errors, missing information, or duplication, which can lead to confusion and inaccuracies in student records.

To address these problems, it is important to establish secure data management protocols, such as using encrypted file transfer methods or secure file sharing platforms. Implementing strict access controls and limiting the number of individuals handling and transmitting the data can help mitigate the risks. It is also essential to comply with relevant privacy laws and regulations and provide clear guidelines to tutors on data protection and confidentiality. Regular data audits and reviews can help identify and rectify any potential issues in the data management process.

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Answer:

C.) 70

Step-by-step explanation:

The line PN is made up of PK and KN (PN = PK + KN). We also know that PK must equal KN (definition of a parallelogram). Therefore, you can set the value of both lines equal to each other, solve for x, then add them together to find PN.

PN = ?    
PK = 5x    
KN = n² - 14

PK = KN                                  <----- Both lines must equal one another

5x = n² - 14                             <----- Substitute values in

0 = n² - 5x - 14                        <----- Subtract 5x from both sides

0 = (x - 7)(x + 2)                      <----- Factor

x = 7    x = -2                          <----- Set both parentheses equal to 0

The value for "x" can be 7 and -2. However, it does not make sense to use a negative value in this situation. If we were to plug -2 into the equations, it would result in lines with a negative value. Therefore,  "x" must be 7. Next, plug this value in for "x" to find the numerical value of PK and KN.

PK = 5x  ----->  5(7) = 35

KN = n² - 14  ----->  (7)² - 14 = 35

The fact that these are equal makes sense. Now, add these two numbers to find the value of the overall line.

PK + KN = PN

35 + 35 = 70

Therefore, C.) 70 is the value of PN.

Answer:

3 and - 10

Step-by-step explanation:

(a)

when x = 0 in the interval x ≤ 0 then y = \(\frac{3}{2}\) x + 3 , so

y = \(\frac{3}{2}\) (0) + 3 = 0 + 3 = 3

when x = 0, the value of the function is 3

(b)

when x = 5 in the interval x > 0 then y = - 2x , so

y = - 2(5) = - 10

when x = 5 the value of the function is - 10

Answer: a. when x=0, the value of the function is 3

              b. when x=5, the value of the function is -10

Step-by-step explanation:

\(\displaystyle\\y=\left \{ {{\frac{3}{2}x+3,\ if\ x\leq 0 } \atop {-2x,\ if\ x > 0}} \right.\)

\(\displaystyle\\x=0\\\\Hence,\\\\y=\frac{3}{2} (0)+3\\\\y=0+3\\\\y=3\)

\(x=5\\\\Hence,\\\\y=-2(5)\\\\y=-10\)

Answer:

solutions: -15, 4 3/4

not solutions: 10 2/3 and 129

Step-by-step explanation:

Let's solve the inequality first

\(20 \geqslant 5 + 3x \\ 20 - 5 \geqslant 3x \\ 15 \geqslant 3x \\ 5 \geqslant x\)

so solution set must contain all the values that are less than equal to 5.

-15 and 4 3/4 are less than 5

so these are solutions.

129 and 10 2/3 are bigger than 5. That means these are not solutions.

The correct statements regarding activity diagrams are:

a. There can be multiple end points, but only one starting point.

c. A branch can have multiple incoming arrows.

d. A decision point may have more than 2 outgoing arrows.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

f. An activity can be nested within another activity.

Activity diagrams are graphical representations used in software engineering to depict the flow of activities or actions within a system. The correct statements regarding activity diagrams are as follows:

a. There can be multiple end points, but only one starting point:

Activity diagrams typically illustrate the flow of activities from a single starting point to multiple end points. This allows for depicting different termination points in the system's behavior.

c. A branch can have multiple incoming arrows:

A branch in an activity diagram represents a decision point where the flow of activities can diverge. It is possible for multiple incoming arrows to converge at a branch, indicating different paths leading to the decision point.

d. A decision point may have more than 2 outgoing arrows:

A decision point in an activity diagram represents a condition or a decision that determines the subsequent flow of activities. It is possible for a decision point to have more than two outgoing arrows, indicating different paths based on the decision outcome.

e. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions:

In an activity diagram, if the subsequent activities following a certain action have conditions that are not mutually exclusive, it creates an indeterminacy. This means that multiple paths may be followed simultaneously based on the different conditions.

f. An activity can be nested within another activity:

Activity diagrams support the nesting of activities within each other. This allows for representing complex activities or sub-processes within a larger activity, providing a hierarchical structure to the diagram.

In conclusion, the correct statements regarding activity diagrams include multiple end points and a single starting point, the possibility of multiple incoming arrows at a branch, the presence of more than two outgoing arrows at a decision point, the creation of indeterminacy with non-mutually exclusive conditions, and the ability to nest activities within one another.

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We are interested in the activity diagram. Check all the correct answers.

Please select at least one answer.

O a. There can be multiple end points, but only one starting point.

O b. Any joint must have been preceded by a branch.

O c. A branch can have multiple incoming arrows.

O d. A decision point may have more than 2 outgoing arrows.

Oe. An indeterminacy is created when the successors of an activity have non-mutually exclusive conditions.

Of. An activity can be nested within another activity.

In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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the center of mass of the lamina is (x_cm, y_cm) = (3/16, 3/16).

To find the center of mass of the lamina, we need to calculate the coordinates (x_cm, y_cm) where the mass is concentrated.

The density at any point is proportional to its distance from the y-axis. This implies that the density (ρ) at a point (x, y) is given by ρ = kx, where k is a constant of proportionality.

To find the center of mass, we need to integrate over the lamina's region to calculate the mass (M) and the moments (Mx and My) about the x and y axes, respectively. Then, we can use these values to find the coordinates of the center of mass.

Let's proceed with the calculations:

1. Finding the mass (M):

The mass element dm at a point (x, y) is given by dm = ρ * dA, where dA is the differential area element.

Since ρ = kx, we have dm = kx * dA.

To calculate the mass, we integrate this expression over the region of the lamina:

M = ∫∫ρ * dA

  = ∫∫kx * dA

  = k * ∫∫x * dA

The region of integration is the part of the disk x² + y² ≤ 1 in the first quadrant.

We can rewrite the bounds of integration as follows:

0 ≤ x ≤ 1 (since it's in the first quadrant)

0 ≤ y ≤ √(1 - x²) (using the equation of the disk)

Now, we can set up the double integral:

M = k * ∫[0 to 1]∫[0 to √(1 - x²)]x * dy * dx

2. Finding the moments (Mx and My):

The moments about the x and y axes are given by:

Mx = ∫∫x * ρ * dA

My = ∫∫y * ρ * dA

Using the same region of integration and density expression, we can set up the double integral for My:

My = k * ∫[0 to 1]∫[0 to √(1 - x²)]y * x * dy * dx

3. Calculating the center of mass:

The coordinates of the center of mass (x_cm, y_cm) are given by:

x_cm = Mx / M

y_cm = My / M

Now, we can evaluate the integrals to find the mass and moments, and then calculate the coordinates of the center of mass:

Step 1: Calculate the mass M

M = k * ∫[0 to 1]∫[0 to √(1 - x²)]x * dy * dx

M = k * ∫[0 to 1]x * √(1 - x²) dx

Let u = 1 - x²

du = -2x dx

When x = 0, u = 1

When x = 1, u = 0

M = -k * ∫[1 to 0]√u du

M = k * ∫[0 to 1]√u du

M = k * (2/3) * u³/² |[0 to 1)

M = k * (2/3) * (1 - 0)

M = k * 2/3

Step 2: Calculate the moment Mx

Mx = k * ∫[0 to 1]∫[0 to √(1 - x²)]x * y * dy * dx

Mx = k * ∫[0 to 1]x * ∫[0 to √(1 - x²)]y * dy * dx

Mx = k * ∫[0 to 1]x * (1/2) * y² |[0 to √(1 - x²)] dx

Mx = k * ∫[0 to 1]x * (1/2) * (1 - x²) dx

Mx = k * (1/2) * ∫[0 to 1](x - x³) dx

Mx = k * (1/2) * (x²/2 - x⁴/4) |[0 to 1]

Mx = k * (1/2) * (1/2 - 1/4)

Mx = k * (1/2) * (1/4)

Mx = k/8

Step 3: Calculate the moment My

My = k * ∫[0 to 1]∫[0 to √(1 - x²)]y * x * dy * dx

My = k * ∫[0 to 1]x * ∫[0 to √(1 - x²)]y * dy * dx

My = k * ∫[0 to 1]x * (1/2) * y² |[0 to √(1 - x²)] dx

My = k * ∫[0 to 1]x * (1/2) * (1 - x²) dx

My = k * (1/2) * ∫[0 to 1](x - x³) dx

My = k * (1/2) * (x²/2 - x⁴/4) |[0 to 1]

My = k * (1/2) * (1/2 - 1/4)

My = k * (1/2) * (1/4)

My = k/8

Step 4: Calculate the coordinates of the center of mass

x_cm = Mx / M = (k/8) / (k * 2/3) = 3/16

y_cm = My / M = (k/8) / (k * 2/3) = 3/16

Therefore, the center of mass of the lamina is (x_cm, y_cm) = (3/16, 3/16).

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You have the following inequality:

x - 19 ≤ 27

To solve the previous inequality, add 19 both sides and simplify:

x ≤ 27 + 19

x ≤ 46

The graph is:

Answer:

x is less than or equal to 8

Step-by-step explanation:

Considering the figure, the equation AB rests is on

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

The slope is represented as m, The slope by definition is the ratio of change of the output values to the change in the input values. The slope can also be called the rate of change

When a line slopes from top left to bottom right, the line is said to have a negative slope. This coincides with the line in the figure hence the line will have a negative slope.

There is not enough information to get the y intercept, hence the line will be

y = mx

where m = -6/9 = -2/3

therefore y = -2/3 x

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Answer:

b. To find the probability a customer who ordered pancakes came to thediner late, we need to look at the intersection of the "pancakes" row and the "late" column. This gives us a probability of 0.1, or 10%

c. To determine whether breakfast choice and meal time are independent, we need to see if the probability of one event changes based on the occurrence of the other event. In this case, it seems that breakfast choice and meal time are not independent, as the probability of being late seems to differ based on what breakfast item the customer chose. For example, the probability of being late is higher for customers who ordered pancakes compared to those who ordered cereal. Therefore, the choice of breakfast item appears to be related to the probability of being late, and so breakfast choice and meal time are not independent.

Step-by-step explanation:

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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The length of the base of the parallelogram is 16 inches.

What is parallelogram?

A parallelogram is a four-sided plane figure with opposite sides parallel and congruent (having the same length). This means that the opposite sides of a parallelogram are parallel to each other and have the same length. Additionally, the opposite angles of a parallelogram are equal in measure, which means they have the same degree of rotation.

Let's use the information given in the problem to set up an equation and solve for the length of the base.

From the problem, we know that the height of the parallelogram is 5 inches.

h = 5

We also know that the base of the parallelogram is six more than twice the height. Let's use b to represent the length of the base:

b = 2h + 6

Now we can substitute the value we know for the height and solve for the base:

b = 2(5) + 6

b = 10 + 6

b = 16

Therefore, the length of the base of the parallelogram is 16 inches.

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Answer:

y=3(x+3)2-6

rip nip kip

40+70+60+120=300

the answer is 300....

Equation that could be the equation of parabola with vertex (-3 , 6)

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

Given,

Vertex of parabola (h,k) = (-3, 6)

Vertex-form equation of parabola

y = a(x - h)² + k

y = a(x - -3)² + 6
y = a(x + 3)² + 6

Equation of the parabola should be of form

y = a(x + 3)² + 6

Hence, y = -3(x + 3)² + 6 is the equation that could be the equation of parabola with vertex (-3 , 6)

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Answer:

x can be any real number except -5 and 7

Step-by-step explanation:

x is in the denominator and denominator cannot be 0

so 6 - |x-1| cannot be 0

==> |x-1| cannot be 6

because it's absolute value, so

x-1 cannot be 6 & x-1 cannot be -6

which give us the answer x cannot be 7 and x cannot be -5

so the answer is x can be any real number except -5 and 7

The frequency of each interval is:

81-100: 2

61-80: 2

1-20: 1

21-40: 1

41-60: 2

What is frequency interval?

Frequency refers to the number of times a particular value or event occurs within a given dataset or sample. In statistics, frequency is used to describe the distribution of values in a dataset, and it is often represented as a frequency table or histogram.

Frequency is often used in conjunction with other statistical measures such as mean, median, and mode to describe the central tendency and variability of a dataset. By analyzing the frequency of values within a dataset, we can identify patterns and trends, and make inferences about the population from which the sample was drawn.

According to the question:
Using the given intervals, we can count the frequency of each interval as follows

81-100: 2 (81, 97)

61-80: 2 (65, 44)

1-20: 1 (2)

21-40: 1 (24)

41-60: 2 (25, 38)

Total: 8

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A NACA 4412 airfoil with a chord of 1.75 meters is placed in a subsonic wind tunnel for testing.

A NACA 23012 airfoil with a chord of 5 feet is placed in a subsonic wind tunnel for testing. The wind tunnel operates at standard sea-level conditions at Mach 0.25. The airfoil is placed at an angle of attack of 6°.

Given,

Re = 6 × 106

Since the airfoil is symmetrical, it will have a zero lift angle of attack of 0°.

a) The zero lift angle of attack is 0°.

From the graph, α ≈ 9°

Lift coefficient, Cl = 0.5

Drag coefficient, C

d = 0.02

b) Lift (lb/ft) (per unit span)

Lift coefficient, Cl = 0.5 Lift,

L = 0.5 × 0.002378 × 525 × 52 × 5Lift,

L = 30.95 lb/ft

c) Drag (lb/ft) (per unit span)

Drag coefficient,

Cd = 0.02

Drag, D = 0.02 × 0.002378 × 525 × 52 × 5

Drag, D = 2.02 lb/ft

d) Moment about the quarter chord (ft-lb/ft) (per unit span)

Moment coefficient, Cm = -0.0458

From the graph, α ≈ 9°

Cm = -0.0458

Moment,

M = -0.0458 × 0.002378 × 525 × 52 × (5 / 4)

Moment, M = -5.95 ft-lb/ft

A NACA 4412 airfoil with a chord of 1.75 meters is placed in a subsonic wind tunnel for testing.

The lift, drag, and moment coefficients were determined for two airfoils at different attack and flow conditions angles. The zero lift and angle of attack required to produce a given lift were also calculated.

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Answer:

\((-5,-8).\)

Step-by-step explanation:

Given the equation

\(-3x+7y=5x+2y\)

We need to find the missing value of the coordinate; (-5, __)

First, we collect like terms

\(-3x-5x=2y-7y\\\\-8x=-5y\)

When x=-5

\(-8*-5=-5y\\\\40=-5y\)

Dividing both sides by -5

\(y=-8\)

The missing value of the coordinate (-5,y) is -8.

Thus, the complete solution to the equation is \((-5,-8).\)

Answer:

\( \frac{3}{20} \)

Step-by-step explanation:

\( \frac{3}{5} \times \frac{1}{4} \)

\( = \frac{3 \times 1}{5 \times 4} \)

Simplify

\( = \frac{3}{20} \)

If you have any more questions please let me know.

Answer:

\($\large\boxed{\frac{3}{20} = 0.15} $\)

Step-by-step explanation:

\($\frac{3}{5} \cdot \frac{1}{4} = \frac{3 \cdot 1}{5 \cdot 4}=\frac{3}{20} = 0.15 $\)

Answer: The y intercept.

Step-by-step explanation:

Using the form y = mx +b, m represents the slope and b is the y intercept. In the equation y = 3/4x + 2, the slope (m) = 3/4 and the y intercept (b) = 2

Answer:

8 x 182.625 = 4years

Step-by-step explanation:

hard to understand the rest maybe upload a picture

Answer:

\(d=\sqrt{73}\approx8.54\)

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

\(d=\sqrt{((2)-(10))+((-7)-(-4))^2\)

Simplify:

\(d=\sqrt{(2-10)^2+(-7+4)^2\)

Subtract:

\(d=\sqrt{(-8)^2+(-3)^2\)

Square:

\(d=\sqrt{64+9}\)

Add:

\(d=\sqrt{73}\)

Approximate:

\(d\approx8.54\)

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

\((10-2)=8\)

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

\((-7-(-4))=-3=3\)

So, the shorter leg is 3 units.

So now, we can use the Pythagorean Theorem, which is:

\(a^2+b^2=c^2\)

Substitute 8 for a and 3 for b. So:

\((8)^2+(3)^2=c^2\)

Square:

\(64+9=c^2\)

Add:

\(c^2=73\)

Take the square root:

\(c=\sqrt{73}\approx8.54\)

This is the same as our previous answer, so we can confirm that it's correct.

So, using both the distance formula and the Pythagorean Theorem, the distance between the two points is approximately 8.54.

And we're done!

Distance formula: d = √(x2-x1)²+(y2-y1)²

= √(2-10)²+(-7-(-4))²

= √-8²+(-3)²

= √64+9

= √73

≈ 8.54

Best of Luck!

∫x³(9+x⁴)⁶dx = x⁻¹² [(1/8)(9 + x⁴)⁸ - (9/7)(9 + x⁴)⁷] + C

Given, ∫x³(9+x⁴)⁶dx

Let u = 9 + x⁴

Differentiating with respect to x, we getdu/dx = 4x³Or, dx = du/4x³

Putting the value of dx in the given integral, we get∫x³(9+x⁴)⁶dx= ∫(u - 9)u⁶(1/4x³)du= (1/4) ∫(u - 9)u⁶(x⁴)⁻³du= (1/4) ∫(u - 9)(x⁴)⁻³(u⁶)duLet I = ∫(u - 9)(x⁴)⁻³(u⁶)du

Therefore, I = ∫(u - 9)u⁶(x⁴)⁻³du= ∫(u - 9)x⁻¹²(u⁶)du

Taking x⁻¹² out of the integral, we getI = ∫(u - 9)x⁻¹²(u⁶)du= x⁻¹² ∫(u - 9)u⁶du

Taking the integral of (u - 9)u⁶, we getI = x⁻¹² [(1/8)u⁸ - (9/7)u⁷] + C

Putting the value of u, we getI = x⁻¹² [(1/8)(9 + x⁴)⁸ - (9/7)(9 + x⁴)⁷] + C

Therefore, ∫x³(9+x⁴)⁶dx = x⁻¹² [(1/8)(9 + x⁴)⁸ - (9/7)(9 + x⁴)⁷] + C

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The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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Two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

Given measure: 3, 5, 4, 6, 10, 5, 6, 9, 2, 13.(D) To calculate \(x_2\), first we need to sort the data in ascending order: 2, 3, 4, 5, 5, 6, 6, 9, 10, 13

Now, we need to find the median, which is the middle value of the data. Since the data has even number of values, we will calculate the mean of middle two values, that is:(5+6)/2 = 5.5 Therefore, \(x_2 = 5.5\).\( \frac{2}{x}= \) To find the value of x, we will first cross-multiply and then take the reciprocal of both sides:\[\frac{2}{x} = y \Rightarrow 2 = xy \Rightarrow x = \frac{2}{y}\] Therefore, \( \frac{2}{x}= \frac{2}{y}\).

(b) To calculate Fried m, we will use the formula: \[f_m = L + \frac{(n/2 - F)}{f} \times c\]where L is the lower limit of the modal class, F is the cumulative frequency of the class preceding the modal class, f is the frequency of the modal class, c is the class interval, and n is the total number of values.

First, we will calculate the class interval:c = (upper limit of class - lower limit of class) = (7-6) = 1 Next, we will construct a frequency table to find the modal class:| Class Interval | Frequency ||-------------------|------------|| 2-3 | 1 || 3-4 | 1 || 4-5 | 1 || 5-6 | 2 || 6-7 | 2 || 7-8 | 1 || 9-10 | 1 || 10-11 | 1 || 13-14 | 1 |The modal class is the class with highest frequency.

Here, two classes have frequency 2, so both are modes. They are 5-6 and 6-7.

Therefore, L = 5, F = 2, f = 2, n = 10, and c = 1. Substituting the values, we get:\[f_m = L + \frac{(n/2 - F)}{f} \times c = 5 + \frac{(10/2 - 2)}{2} \times 1 = 7\] Therefore, Fried m = 7.

(c) To find the mode, we look for the value(s) with highest frequency. Here, two values have frequency 2, so both are modes. They are 5 and 6. Therefore, the mode is 5 and 6.

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As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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