Work out the size of angle x.

Answer:  180(n-2)

You use the distribution rule to factor

The distribution rule is a(b+c) = a*b+a*c

The result of the integral ∫x³ ln(x) dx is

(1/4)ln(x) * x⁴ - (1/16)x⁴ + C,

where C is the constant of integration.

Here, we have,

To evaluate the integral ∫x³ ln(x) dx, we can use integration by parts.

The integration by parts formula is given by:

∫u dv = uv - ∫v du

Let's choose u = ln(x) and dv = x³ dx.

Differentiating u, we have du = (1/x) dx.

Integrating dv, we have v = ∫x³ dx = (1/4)x⁴.

Now, we can apply the integration by parts formula:

∫x³ ln(x) dx = uv - ∫v du

= ln(x) * (1/4)x⁴ - ∫(1/4)x⁴ * (1/x) dx

= (1/4)ln(x) * x⁴ - (1/4) * ∫x³ dx

The integral of x³ dx can be evaluated directly:

∫x³ dx = (1/4)x⁴ + C

Substituting this back into the previous equation:

∫x³ ln(x) dx

= (1/4)ln(x) * x⁴ - (1/4) * (1/4)x⁴ + C

= (1/4)ln(x) * x⁴ - (1/16)x⁴ + C

Therefore, the result of the integral ∫x³ ln(x) dx is

(1/4)ln(x) * x⁴ - (1/16)x⁴ + C,

where C is the constant of integration.

To learn more on integration click:

brainly.com/question/26568631

#SPJ4

complete question:

evaluate the following using substitution or integration by parts.

∫x³ ln(x) dx

Answer: 1215 miles

Step-by-step explanation:

405 miles in 5 hours is 81 mph so you multiply that mph by the amount of hours you want (15)  so 81 x 15 = 1215

The probability that both of them have landed 5 is 1/7.

Two fair dice have been tossed,

The total of their top faces is found to be divisible by 5,

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

The probability that both of them have landed 5 is

E={(x,y)|x+y=5 or x+y=10, 1≤x,y≤6},

F={(5,5)}.

P(F|E)= 1/7.

Hence, The probability that both of them have landed 5 is 1/7.

Learn more about probability here https://brainly.com/question/13016819

#SPJ4

The piecewise function for the graph is given as \(g(x)=\left \{ {{(1/3)x+3\ \ for\ (-\infty,-3)} \atop {6\ \ \ for\ \ (1,\infty)}} \right.\)

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

For (-∞, -3), the line passes through (-9, 0) and (-3, 2), hence:

y - 0 = [(2 - 0)/(-3 - (-9))](x - (-9))

y = (1/3)x + 3

For (1, ∞), y = 6

The piece wise function for the graph is given as      \(g(x)=\left \{ {{(1/3)x+3\ \ for\ (-\infty,-3)} \atop {6\ \ \ for\ \ (1,\infty)}} \right.\)

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer:

Según los datos brindados, la altura de la pirámide egipcia de Keops sería de:

Step-by-step explanation:

Para resolver el ejercicio, debes conocer la fórmula para calcular el volumen de una pirámide cuadrangular, el cual es el tipo de pirámide al cual pertenece la pirámide de Keops:

Donde:

Como queremos identificar la altura, despejamos esa variable de la ecuación, pero para simplificar un poco, vamos a escribir el volumen de la pirámide con la variable "v":

Y en esta ecuación que despejamos, procedemos a reemplazar los valores de volumen y base que nos dieron en el ejercicio:

Y realizamos las operaciones correspondientes:

Aproximamos el número al entero más cercano, por lo tanto, la altura de dicha pirámide con los datos dados sería de aproximadamente 146 metros.

Answer:

22.9%

Step-by-step explanation:

The total at the bottom is 22.9%

Answer:

1: 31.5. 2: 5. 3: 4.6 4: 45

Answer:

325

Step-by-step explanation:

40/100=130/x

Cross multiply to find x

40x=13000

/4            /4

x=325

The payment necessary to amortize the given loan is $949.04.

1. To find the payment necessary to amortize the given loans using the amortization table, the steps are as follows:

The formula to calculate the payment for amortizing a loan is given by: \(`P = r(PV) / [1 - (1 + r)^(-n)]`\)

Where, P = Payment amount

r = Interest rate per compounding period

n = Total number of compounding periods`PV`

= The present value of the loan, i.e., the amount of the loan

For a semiannual payment, the interest rate and the number of years are calculated as:

\(`r = (6 / 2) / 100 \\=\\0.03`\)

(semiannual interest rate) and

\(`n = 8 x 2 \\= 16`\)

(total number of compounding periods)

Using the above values in the formula, we get:

\(P = 0.03 x 12000 / [1 - (1 + 0.03)^(-16)]\\≈ $949.04\)

(rounded to the nearest cent)

Therefore, the payment necessary to amortize the given loan is $949.04.

Therefore, the payment necessary to amortize the given loan is $949.04.

Know more about loan here:

https://brainly.com/question/26011426

#SPJ11

Angle PBC is 126 degrees.

Let's start by drawing the triangle ABC and marking the point P on AC such that APB = ABP.

Since APB = ABP, we can conclude that the triangle ABP is an isosceles triangle, which means that angles ABP and BAP are equal.

Let's call angle ABP and angle BAP x, then we have:

angle ABC = 2x (since triangle ABP is isosceles)

angle ACB = 2x - 39 (from the given information)

Since the sum of angles in a triangle is 180 degrees, we can write:

angle PBC + angle ABC + angle ACB = 180

Substituting the values we found for angle ABC and angle ACB, we get:

angle PBC + 2x + (2x - 39) = 180

Simplifying the equation, we get:

angle PBC = 219 - 4x

We still need to find the value of x to calculate angle PBC. To do that, let's use the fact that the sum of angles in a triangle is 180 degrees for triangle ABP:

angle ABP + angle BAP + angle APB = 180

Substituting x for angle ABP and BAP, we get:

2x + angle APB = 180

But we also know that angle APB = ABP (from the given information), so we can substitute:

2x + ABP = 180

Solving for ABP, we get:

ABP = 90 - x

Now we can substitute this value for ABP in our equation for angle PBC:

angle PBC = 219 - 4x

= 219 - 4(90 - ABP)

= 219 - 4(90 - (90 - x))

= 219 - 4x

Simplifying, we get:

angle PBC = 3x - 9

So to find the value of angle PBC, we need to find the value of x:

2x + ABP = 180

2x + (90 - x) = 180

x = 45

Now we can substitute x = 45 in our equation for angle PBC:

angle PBC = 3x - 9

= 3(45) - 9

= 126

Therefore, angle PBC is 126 degrees.

Learn more about triangle ,

https://brainly.com/question/2773823

#SPJ4

Full Question ;

Point P is on side AC of the triangle ABC such that APB = ABP and ABC - ACB = 39 find PBC in degrees.

The corresponding parts are:

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

To do this, we simply make use any of the following congruent theorems:

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

Read more about congruent theorems at

https://brainly.com/question/2102943

#SPJ1

An estimate for the total volume of food and water you've ingested in the last day is 3000-5000 milliliters. On average, the heart pumps about 5 liters of blood per minute. 10-20% or more error I'm expecting. Calculating heart blood volume compared to food and drink consumption is crucial for understanding circulation and liver function.

D.1 Estimating the amount of food and water consumed in a day can be difficult without specific measurements, but a rough estimate can be made based on typical intake amounts. On average, a person may consume 2-3 liters of water and 1000-2000 calories per day, resulting in an estimated total volume of 3000-5000 milliliters.

D.2 The amount of blood pumped by the heart varies from person to person and depends on factors such as heart rate and overall health. On average, the heart pumps about 5 liters of blood per minute, which is much larger than the estimated volume of food and water intake.

D.3 Estimating food and water intake and blood flow is prone to error due to variability and uncertainties in personal measurements. Individuals' habits, health, and physical activity levels can affect these estimates, potentially resulting in a significant error of 10-20% or more.

D.4 The calculation of the heart's blood volume compared to food and drink consumption is crucial for understanding the circulation system and liver role.

The liver processes nutrients, detoxifies, and produces blood components, while the heart is responsible for circulating blood throughout the body. The vast difference in volume between the two is emphasized, emphasizing the heart's crucial role in maintaining circulation.

To know more about blood refer here:

https://brainly.com/question/30828552#

#SPJ11

Answer:

-4

Step-by-step explanation:

5 * -2 = -10 + 6 = -4

As per the given distance, the angle that is made by the ramp with the ground is 19.1 degrees

Let's call the angle we're trying to find theta (θ). We can use the tangent function to calculate θ, as follows:

tan(θ) = opposite / adjacent

We know the opposite side (height of the ramp) is 3.5ft, and the adjacent side (distance along the ground) is 10ft. Plugging these values into the tangent equation, we get:

tan(θ) = 3.5 / 10

We can solve for θ by taking the inverse tangent (also known as arctan) of both sides:

θ = arctan(3.5 / 10)

Using a calculator, we find that θ is approximately 19.1 degrees. Therefore, the ramp makes an angle of 19.1 degrees with the ground.

To know more about distance here

https://brainly.com/question/4199102

#SPJ4

The matrix (tensor) form is:

σ = [100x - 60y -60x][ -60x - 70]

The stress function of a two-dimensional problem is given by:

ψ = 50x² - 60xy - 70y'

For the problem to satisfy compatibility conditions, the following two equations must be satisfied:

∂²σₓᵧ/∂y∂x = ∂²σₓ/∂x² - ∂²σ_y/∂y∂x

∂²σₓᵧ/∂x∂y = ∂²σ_y/∂y² - ∂²σₓ/∂x∂y

Calculating the partial derivatives of the stress function

ψ with respect to x and y, we get:

σₓ = ∂ψ/∂x = 100x - 60y

σ_y = ∂ψ/∂y = -60x - 70

The mixed partial derivative of the stress functionψ is given by:

σₓᵧ = ∂²ψ/∂x∂y = -60

The compatibility equations are:

∂²σₓᵧ/∂y∂x = ∂²σₓ/∂x² - ∂²σ_y/∂y∂x

= -60 = 100 - 0

∂²σₓᵧ/∂x∂y = ∂²σ_y/∂y² - ∂²σₓ/∂x∂y

= -60 = -0 - (-0)

Since the two equations are satisfied, the problem satisfies the compatibility conditions.

The stress distribution in the matrix (tensor) form is given by:

σ = [σₓ  σₓᵧ][σₓᵧ  σ_y]

where,

σₓ = 100x - 60y

σ_y = -60x - 70

σₓᵧ = -60

The matrix (tensor) form is:

σ = [100x - 60y -60x][ -60x - 70]

To know more about matrix visit:

https://brainly.com/question/28180105

#SPJ11

Answer:

5.73

Step-by-step explanation:

I hope that's help u

Answer:

5 11/15

Step-by-step explanation:

Convert the 2/5 to a fraction over 15 by multiplying it by 3. You result with 6/15. You can now easily add 3 5/15 + 2 6/15. They result in 5 11/15.

The value of angle x of the given right angle triangle using trigonometric ratios is: x = 34.6°

The three main trigonometric ratios are expressed as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Thus, we can find the angle x using trigonometric ratios.

8/14 = sin x

sin x = 0.5714

x = sin⁻¹0.5714

x = 34.6°

The value of angle x of the given right angle triangle using trigonometric ratios is: x = 34.6°

Read more about Trigonometric Ratios at: https://brainly.com/question/13276558

#SPJ1

Answer:

We conclude that:

g(f(x)) = -3x+3

Step-by-step explanation:

Given

To determine

In order to determine g(f(x)), first we need to substiute f(x) = 3x-3 in g(f(x)).

g(f(x)) = g(3x-3)

now substitute x = 3x-3 in g(x)

         = -(3x-3)

         = -3x+3

Therefore, we conclude that:

g(f(x)) = -3x+3

AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

To learn more about triangle visit:

https://brainly.com/question/1058720

#SPJ9

Answer: 7.5 or 7 1/2

Step-by-step explanation:

Divide 45 divided by 7

The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

To learn more about inequality;

brainly.com/question/28823603

#SPJ12

The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

Answer:

=

Step-by-step explanation:

Answer:

It will be over at 5:17 pm

Step-by-step explanation:

2:45 +32 would be 3:17, we add 2 hours it would be 5:17

Answer:

5:17 pm

Step-by-step explanation:

Since Brianna started watching a movie at 2:45 p.m and the movie is 2 hours and 32 minutes long

Thus,

2:45 + 2 and 32 Minutes

2 + 2 = 4

45 + 32 = 77 minutes

1 Hour = 60 Minutes

Thus, 77 - 60 =17

Hence, 4 + 1 = 5

Thus, the movie will be over at 5:17 Pm

~Lenvy~

The activity ratio in the value stream measures the efficiency of the production process by evaluating the ratio of value-added activities to non-value-added activities.

The activity ratio is a performance metric used in value stream mapping, which is a lean management tool for analyzing and improving the flow of materials and information in a production process.

It focuses on distinguishing value-added activities, which directly contribute to meeting customer requirements, from non-value-added activities, which do not add value but consume resources and time.

By calculating the activity ratio, organizations can assess the proportion of time and resources spent on value-added activities versus non-value-added activities.

A higher activity ratio indicates that a greater portion of resources is dedicated to value-added activities, indicating improved efficiency and reduced waste.

Conversely, a lower activity ratio suggests a higher proportion of resources being utilized for non-value-added activities, indicating potential areas for improvement and waste reduction.

The activity ratio serves as a valuable diagnostic tool for organizations to identify process inefficiencies, bottlenecks, and areas for improvement. By analyzing the activity ratio, organizations can streamline their processes, eliminate waste, and optimize resource allocation to enhance overall productivity and customer value.

To know more about value stream refer here:

https://brainly.com/question/32695907

#SPJ11

Answer: 104

Step-by-step explanation: Based on the given conditions, formulate:: 12x5+4x11

Calculate the product or quotient: 60+40

Calculate the sum or difference: 104

Answer:

The coach spent $104 in total

Step-by-step explanation:

Each baseball costs $4 and there are 11 of them. the eqaution is 11 x 4 = 44

Each hat costs $12 and there are 5 of them. the equation is 12 x 5 = 60

Add them together in the equation 60 + 44 and you get 104.

Answer:

Step-by-step explanation:

number A 3

Answer:

  14

Step-by-step explanation:

The triangle inequality is usually expressed as ...

  a +b > c

for any permutation of a, b, c.

Here, that would mean ...

  1 + 14 > c

  c < 15

The largest whole-number value that the third side (c) can have is 14.

_____

Additional comments

Some authors write the triangle inequality as ...

  a +b ≥ c

If you use that version, the longest side could be 15. Such a "triangle" would look like a line segment, and have zero area.

__

We can also check the shortest length:

  c +1 > 14

  c > 13

The smallest whole-number value for the shortest side is also 14. That is, the only triangle with whole-number side lengths of 1 and 14 will be an isosceles triangle with two sides of length 14.

The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Read more about Confidence Interval at; https://brainly.com/question/17097944

#SPJ1