Find the area of quadrilateral abcd. [hint: the diagonal divides the quadrilateral into two triangles.]

Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that

[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]

Answer:

[tex] \frac{1 \\ }{3125} [/tex]

Answer:

x = 9

Step-by-step explanation:

        [tex]\sf \dfrac{a^m}{a^n}=a^{m-n}\\\\\\ \dfrac{1}{a^m}=a^{-m}[/tex]

[tex]\sf \dfrac{5^x}{5^{14}}=\dfrac{1}{5^5}\\\\5^{x -14} = 5^{-5}[/tex]

Base are same. Compare the exponents.

 x - 14 = -5

        x = -5 + 14    {Addition property of equality}

        x = 9

Examples of population parameter are mentioned below .

According to the question

Population parameter :

A population parameter is a numerical descriptive measure of a population or a number that describes something about an entire group or population.  

The examples of population parameter is

1. The average weight of all middle-aged female Americans. The population consists of all middle-aged female Americans, and the parameter is µ.

2. The average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

3. The average height of a class X. This is a parameter because it is states something about the entire population of class X.  

Hence, examples of population parameter will depend on the population .

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Answer:

0.2857

Step-by-step explanation:

We want to determine,

The probability that the battery life is at least 11 hours is 0.2857.

Answer:

  See attached

Step-by-step explanation:

Each point on the line segment moves to 2 times its previous distance from the origin.

The center of dilation, the origin, is an invariant point. It doesn't move for any dilation factor. One end of the line segment is there, so it will not move.

The coordinates of each point are multiplied by the dilation factor. The other end of the line segment is (5, 5), so it moves to 2×(5, 5) = (10, 10).

The dilated line segment extends from (0, 0) to (10, 10). It is shown in red in the attached graph.

The probability that exactly 12 of them are strikes is 0.09.

In this question,

Number of pitches, n = 22

Probability of throwing a strike for each pitch, p = 0.431

Then, q = 1 - p

⇒ q = 1 - 0.431

⇒ q = 0.569

Number of strikes, x = 12

The probability that exactly 12 of them are strikes can be calculated using Binomial expansion,

[tex]P(X=x)=nC_xP^{x}q^{(n-x)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{(22-12)}[/tex]

⇒ [tex]P(X=12)=22C_{12}(0.431)^{12}(0.569)^{10}[/tex]

⇒ [tex]P(X=12)=(\frac{22!}{12!10!} )(0.431)^{12}(0.569)^{10}[/tex]

⇒ P(X=12) = (646646)(0.000041)(0.00355)

⇒ P(X=12) = 0.09431 ≈ 0.09

Hence we can conclude that the probability that exactly 12 of them are strikes is 0.09.

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The function [tex]B(t) = 182(1.065)^t[/tex] represents the annual population of bees in a county park, the growth rate is 6.5%.

What is an equation?

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 depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Length of Charles garden = 12.5 m * 12 = 150 m

Length of Stephen chain = 150 m /18 = 25/3 m

Breadth of Charles garden - 25/3 * 10 = 250/3 m

Area of Charles garden = 150 m * 250/3 m = 12500 m =

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Option (a) Sample

Sample is the research that analyzes a portion of an entire population.

A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.

By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.

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Answer:

may be like this

its 32cm³

120=!3÷!6

!2-!5=!3

to 120 modes

Answer: Look at stwp by step

Step-by-step explanation:

Basically we can compare both equations to get that x = √7 and y = √2 so we can substitute that into 2x + 10y to get 2√7 + 10√2

Answer:

[tex]\frac{-1}{4}[/tex]

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes. This means you change the sign and flip the numerator and denominator.

If the original slope is 4, the perpendicular slope is [tex]\frac{-1}{4}[/tex]

A pendulum that swings fully once in 1.9 seconds has a length of 2.93 feet.

A basic pendulum is a machine in which the point mass is hung from a fixed support by a light, inextensible string.

Length of pendulum is defined as the distance between the point of suspension to the center of the bob and is denoted by " 1 ".

Given the equation:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

where L is the length in feet and T is the time in seconds.

Given that T = 1.9sec,

Hence:

[tex]$$T=2 \Pi \sqrt{\frac{L}{32}}$$[/tex]

L = 2.93 feet

A pendulum that swings fully once in 1.9 sec has a length of 2.93 feet.

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The volume of the cylinder is [tex]3.14 inch^3[/tex]

Given that

radius = 1 inch

height = inch

we know that volume =[tex]V = \pi \times r^2 \times h[/tex]

now put the value in the above equation we get

[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]

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The equation of the graph, in slope-intercept form, is: C. y = 2/3x + 6.

The linear equation of a graph in slope-intercept form is expressed as y = mx + b. Where the variable in the equation are as follows:

Considering the graph given, to write the linear equation it represents, find the slope (m) and the y-intercept (b) of the line.

Slope (m) = rise/run = 2 units/3 units

Slope (m) = 2/3.

The line intercepts the y-axis at y = 6, thus, the y-intercept (b) would be 6. b = 6.

Substitute m = 2/3 and b = 6 into the slope-intercept form equation, y = mx + b:

y = 2/3x + 6

Thus, the equation, in slope-intercept form, that represents the linear graph as shown in the image given is: C. y = 2/3x + 6.

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Both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

To find at what time will both trains leave the station together again if both of them left the station together at 6:30 am:

Therefore, both trains will leave the station together again at 7:12 am if both of them left the station together at 6:30 am.

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Answer:

B

Step-by-step explanation:

It's B

Answer:

Option B

Step-by-step explanation:

The equation is:

[tex]y=10-2x[/tex]

when x=2

[tex]y=10-2(2)010-4=6[/tex]

When x = 3

[tex]y=10-2(3)=10-6=4[/tex]

When x=4

[tex]y=10-2(4)=10-8=2[/tex]

Hope this helps

Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]

To find the distance between the two complex numbers using the formula

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

where,

[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]

y=5(14-x)(x) quadratic equation best models the volume of the box .

What is volume of cuboid?

Perimeter = 2(width + length) =28

Let x=width of base, then length of base = (28/2)-x = 14-x

Volume of box = length*width*height

=x(14-x)*5  ⇒ 5x(14-x)(x)

Therefore, y=5(14-x)(x) quadratic equation best models the volume of the box .

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Answer:

The second option:

[tex]2\sqrt{x}[/tex]

Step-by-step explanation:

If you need work please ask!

Have a nice day!

The idea that group work theories are appropriate for all clients all the time is a myth (Third option).

About Group Process:

The term "group process" describes how people collaborate within an organization to complete tasks. Typically, organizations invest a lot of time and effort into defining and achieving goals, but little thought is usually given to how those goals are affecting the most valuable resource of a group - its people.

Since different clients have different demands and priorities, group work might not be suitable for many, but not for all. Different types of clients require different types of collaboration, type of group or individuals, and working strategies that work for their goals the best.

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Answer:

-16

Step-by-step explanation:

you just add all of them together

answers :

a.

coordinates of A are (2,4)

b.

coordinates of B are (6,0)

i.

(4,2) is the midpoint

ii.

y = -3x + 18 is the parallel line

Step-by-step explanation:

a.

if two things are equal to the same thing then they are equal to each other

y = 4

2x + y = 8 is y = -2x +8 so

-2x +8 = 4

-2x = -4

x = 2

coordinates of A are (2,4)

b.

if two things are equal to the same thing then they are equal to each other

y=0

3x+y=18 is y = -3x+18 so

-3x+18=0

x = 6

coordinates of B are (6,0)

midpoint formula is

(X1+X2)/2 , (Y1+Y2)/2

(2,4) (6,0)

(X1+X2)/2 , (Y1+Y2)/2

(2+6)/2 , (4+0)/2

(4,2) is the midpoint

parallel line has the same x value

so for a line parallel to 3x+y=18 or y = -3x+18

the parallel line would be

y = -3x

point slope formula

point slope formulay - y1 = m (x - x1)

3x+y=18 or y = -3x+18 was 6,0 at y = 0

y - y1 = m (x - x1)

y - 0 = m (x - x1)

since it's a parallel line the m has to be the same

(6,0)

y - 0 = -3 (x - 6)

y = -3x + 18 is the parallel line

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

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Answer:

It gets more complicated with a six-sided die. In this case if you roll the die, there are 6 possible outcomes (1, 2, 3, 4, 5 or 6). Can you figure out what the theoretical probability for each number is? It is 1/6 or 0.17 (or 17 percent).

the parallel linear equation is:

y = (2/5)*x - 3

Two lines are parallel if the lines have the same slope but different y-intercept.

Here we know the line equation:

y = (2/5)*x + 4

Then a parallel line is of the form:

y = (2/5)*x + c

Where c is different than 4.

We want this line to pass through (5, -1), then:

-1 = (2/5)*5 + c

-1 = 2 + c

-1 - 2 = -3 = c

Then the parallel linear equation is:

y = (2/5)*x - 3

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Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.

Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.

Translate the triangle by [tex](^{-2}_{-4})[/tex] means translating 2 units left and 4 units down.

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A GDP per capita of $13,000 would correspond to the following corruption score of: B. 42.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

Based on the information provided in the table above, we can logically deduce that the situation can be modeled by this linear function:

y = 511x - 8540

Where:

x is the corruption score.

y is GDP per capita in dollars.

Based on the model, a GDP per capita of $13,000 would correspond to the following corruption score:

y = 511x - 8540

13,000 = 511x - 8540

511x = 13,000 + 8540

511x = 21,540

x = 21,540/511

x = 42.1 ≈ 42.

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P/10 = 7.2/3

P = 7.2x10/3

P=72/3

P= 24