PLS HELP!!! REALLY REALLY IMPORTANT!!!

We are asked to find the first derivative of,

\(\longrightarrow g(x) = \sqrt{x^2+2x}\)

Here we can write the term \(x^2+2x\) by adding and subtracting 1 as,

\(x^2+2x = x^2+2x+1-1\)

\(x^2+2x = (x+1)^2-1\quad[\because\, x^2+2x+1=(x+1)^2]\)

Thus,

\(\longrightarrow g(x) = \sqrt{(x+1)^2-1}\quad\dots(1)\)

Now take,

\(x+1=\sec\theta\quad\dots(2)\)

\(x=\sec\theta-1\)

\(dx=\sec\theta\tan\theta\, d\theta\)

\(\dfrac{d\theta}{dx}=\dfrac{1}{\sec\theta\tan\theta}\quad\dots(3)\)

Then (1) becomes,

\(\longrightarrow g(x) = \sqrt{sec^2\theta-1}\)

We have,

\(\sec^2\theta-1=\tan^2\theta\)

So we get,

\(\longrightarrow g(x) = \tan\theta\)

Now,

\(\longrightarrow g'(x) = \dfrac{d}{dx}\,[\tan\theta]\)

By chain rule,

\(\longrightarrow g'(x) = \dfrac{d}{d\theta}\,[\tan\theta]\cdot\dfrac{d\theta}{dx}\)

\(\longrightarrow g'(x) = \sec^2\theta\cdot\dfrac{1}{\sec\theta\tan\theta}\quad\quad\textrm{[From (3)]}\)

\(\longrightarrow g'(x) = \sec\theta\cdot\dfrac{1}{\tan\theta}\)

\(\longrightarrow g'(x)=\dfrac{1}{\cos\theta}\cdot\dfrac{\cos\theta}{\sin\theta}\)

\(\longrightarrow g'(x)=\dfrac{1}{\sin\theta}\quad\dots(4)\)

But we have,

\(\sin^2\theta+\cos^2\theta=1\)

\(\sin\theta=\sqrt{1-\cos^2\theta}\)

\(\sin\theta=\sqrt{1-\dfrac{1}{\sec^2\theta}}\)

\(\sin\theta=\dfrac{\sqrt{\sec^2\theta-1}}{\sec\theta}\)

\(\sin\theta=\dfrac{\sqrt{(x+1)^2-1}}{x+1}\quad\quad\textrm{[From (2)]}\)

\(\sin\theta=\dfrac{\sqrt{x^2+2x}}{x+1}\)

Hence (4) becomes,

\(\longrightarrow\underline{\underline{g'(x)=\dfrac{x+1}{\sqrt{x^2+2x}}}}\)

This is the first derivative of the given function.

Answer:

0.41 cents

Step-by-step explanation:

2.46/6 = 0.41

The x-coordinate of the solution to the system of equations is 3.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Two lines are labeled on x-y coordinate y = - x + 5 and y = x - 1.

Now, Adding these two equations we have,

2y = 4.    (x and - x cancells).

y = 2.

Now, Putting the value of 'y' in any of the equations we have,

2 = - x + 5.

x = 5 - 2.

x = 3.

so, The x-coordinate of the solution is 3.

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We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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To rank the steps involved in transforming one couple to another couple in a parallel plane, here is the correct order:

Identify the initial couple and the desired final couple.

Determine the translation vector that will move the initial couple to the desired final couple.

Translate the initial couple using the determined translation vector. This will shift the entire couple in the parallel plane.

Verify that the translation has successfully moved the initial couple to the desired final couple.

If necessary, make any additional adjustments or transformations to align the initial and final couples precisely in the parallel plane.

Confirm that the final couple is now in the desired position and orientation relative to the initial couple, maintaining the parallelism of the plane.

By following these steps in order, you can effectively transform one couple to another in a parallel plane.

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Therefore, the equation of the circle is:

(x - 0)^2 + (y - (-4))^2 = (sqrt(313))^2

x^2 + (y + 4)^2 = 313

The equation of a circle centered at the point (h, k) with a radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the circle is centered at (0, -4) and passes through (12, -17). To find the radius, we can use the distance formula between the center and any point on the circle:

r = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates (0, -4) and (12, -17):

r = sqrt((12 - 0)^2 + (-17 - (-4))^2)

= sqrt(12^2 + (-17 + 4)^2)

= sqrt(144 + (-13)^2)

= sqrt(144 + 169)

= sqrt(313)

Therefore, the equation of the circle is:

(x - 0)^2 + (y - (-4))^2 = (sqrt(313))^2

x^2 + (y + 4)^2 = 313

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C. (∃x)(A(x) ∧ B(x)) ⇔ (∃x)A(x) → (∀y)B(y)

This statement is incorrect. The left-hand side states that there exists an x such that both A(x) and B(x) are true.

Therefore, the incorrect statement is option C.

A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}

Hence. Option D is wrong.

In set theory, a subset relation is denoted by ⊆, and a proper subset relation is denoted by ⊂. A subset relation indicates that all elements of one set are also elements of another set.

In this case, let's evaluate the options:

A. ∅ ⊆ A: This option is correct. The empty set (∅) is a subset of every set, including A.

B. {6, 7, 8} ⊂ A: This option is correct. The set {6, 7, 8} is a proper subset of A because it is a subset of A and not equal to A.

C. {{4, 5}} ⊂ A: This option is correct. The set {{4, 5}} is a proper subset of A because it is a subset of A and not equal to A.

D. {1, 2, 3} ⊂ A: This option is incorrect. The set {1, 2, 3} is not a subset of A because it is not included as a whole within A. The element {1, 2, 3} is present in A but is not a subset.

In conclusion, the incorrect option is D, {1, 2, 3} ⊂ A.

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Answer:

the needed amount of what? community service?If so about 6 days of work on saturday and 3 school days. :)

Answer:

(-1, -6)

Step-by-step explanation:

3y=-4x-22

y=-5x-11

(y=-5x-11)*3  ==> make this equation equal to 3y, so you can eliminate y

3y = -15x - 33

Solve for x:

-15x - 33 = -4x - 22  ==> since both expression equal 3y

-15x + 15x - 33 = -4x + 15x - 22  ==> add 15x on both side to remove -x

-33 = 11x - 22

-33 + 22 = 11x - 22 + 22  ==> add 22 on both sides to isolate x

-11 = 11x  ==> simplify

x = -1

Solve for y:

y=-5(-1)-11  ==> plugin -1 for x

y=5-11

y = -6

x = -1, y=-6  ==> (-1, -6)

The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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When you multiply a negative number by another negative number, the result is always a positive number.

This rule is based on the properties of multiplication and the concept of negative numbers.

When two negatives are multiplied, the negative signs "cancel out" each other. Mathematically, if you have -a multiplied by -b, where a and b are positive values, the result is given by ab.

For example, if you multiply -2 by -3, the product is 6, which is a positive number. This can be explained by the idea that multiplying two numbers with opposite signs results in a negative product, while multiplying two numbers with the same sign (both negative) produces a positive product.

Therefore, when you multiply a negative by a negative, the outcome is a positive number.

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Answer:

1 11/37 is the correct answer

Answer:

√{99×33×3}=√{33×3×33×3}=√(33²×3²)=±33×3=±99

Answer:

99

Step-by-step explanation:

Cause 33×3=99 ,and the function of the root is to get the number that we multiply it ti itself

For example \(\sqrt{4}\) =2 cause 2×2=4 ,so\(\sqrt{2*2}\) =\(\sqrt{4}\) which is =2

so \(\sqrt{99^{2} }\) =99

Answer:

The largest angle is A + 5 = 117.5 + 5 = 122.5 degree.  

Step-by-step explanation:

The sum of the interior angles of a regular hexagon is 720 degree.

Let the one angle is A.

So,

A + A + 1 + A + 2 + A + 3 + A + 4 + A + 5 = 720

6 A + 15 = 720

6 A = 705

A = 117.5

The largest angle is A + 5 = 117.5 + 5 = 122.5 degree.  

Answer: 4 inches

Step-by-step explanation:

Using the subtraction operation, the length of the sheet of paper is greater than the pencil by B) 4 inches.

Subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

Subtraction operation involves the subtrahend deducted from the minuend to give the result as the difference between the two values.

In this situation:

The length of the sheet of paper = 11 inches

The length of the pencil = 7 inches

Thus, the difference between the two lengths of the sheet of paper and the pencil = 4 inches (11 - 7)

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Answer:

0.6832

Step-by-step explanation:

Given :

Mean, m = 52

Standard deviation, s = 7

-1.2 standard deviation of average = 57 - 1.2(7) = 57 - 8.4 = 48.6

2 standard deviations of average = 57 + 2(7) = 57 + 14 = 71

Zscore = (48.6 - 52) / 7 = - 0.486

Zscore = (71 - 52) / 7 = 2.714

P < -0.486) = 0.31348

P < 2.714 = 0.99668

P < 2.714 - P < -0.486 = (0.99668 - 0.31348) = 0.6832

Answer:

Common factor from the two pairs

n2+2n-n-2 or

n(n+2)-1(n+2)

Rewrote in factored form

n(n+2)-1(n+2)or

(n-1)(n+2)

Solution

(n-1)(n+2)

Answer:

x = (k-14)/5

Step-by-step explanation:

5x + 14 = k

Subtract 14 from each side

5x + 14-14 = k-14

5x = k-14

Divide by 5

5x/5 = (k-14)/5

x = (k-14)/5

Answer:

k - 14/5

Step-by-step explanation:

5x + 14 = k

On subtracting 14 on both sides,

5x = k - 14

On dividing by 5 on both sides,

x = k - 14/5

Therefore, the value of x = k-14/5

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9514 1404 393

Answer:

Step-by-step explanation:

The curve has a relative maximum where values on either side are lower. This looks like a peak in the curve. There is one of those on the y-axis at y = -4.

The relative maximum is -4.

__

A relative minimum is a low point, where the curve is higher on either side. There are two of these, located symmetrically about the y-axis. The minimum appears to be about y = -5. (They might be at x = ± 1, but it is hard to tell.)

The relative minima are -5.

__

A minimum or maximum is absolute if no part of the curve is lower or higher. Here, the minima are absolute, while the maximum is only relative. (The left and right branches of the curve go higher than y=-4.)

_____

Identifying the points on the curve should be the easy part. Deciding what the coordinates are can be harder when the graph is like this one.

Circumference of the circle = 17.8 units

Area of the circle = 25.1 square unit

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle."

Formula to get the circumference of a circle = 2πr

Where r = radius of the circle

Radius of the given circle = Distance between the points A(2, 3) and B(4, 1)

r = \(\sqrt{(2-4)^{2} +(3-1)^{2} }\)

r = 2√2units

Therefore, circumference = 2π(2√2)

= 17.77

≈ 17.8 units

Area of the circle = πr²

= π(2√2)²

= 8π

= 25.13

≈ 25.1 square unit

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Setting the widths of divs within a div to equal 90% of the page allows each div to take up 90% of its parent div's width, while setting just one div to be 90% of the page causes that div to take up 90% of the width of the entire webpage.

The difference between setting the widths of the divs that are within a div to equal 90% of the page and setting just one div to be 90% of the page is the way the divs will be displayed on the webpage.

When you set the widths of the divs that are within a div to equal 90% of the page, each individual div will take up 90% of the width of its parent div. This means that if you have multiple divs within the parent div, they will each take up 90% of the available space, but will still be contained within the boundaries of the parent div.

On the other hand, when you set just one div to be 90% of the page, that div will take up 90% of the width of the entire webpage, not just its parent div. This means that the div will expand to take up most of the available space, potentially pushing other elements on the webpage to the side.

In summary, setting the widths of divs within a div to equal 90% of the page allows each div to take up 90% of its parent div's width, while setting just one div to be 90% of the page causes that div to take up 90% of the width of the entire webpage.

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True, a probability/impact matrix or chart lists the relative probability of a risk occurring on one side of a matrix or axis on a chart and the relative impact of the risk occurring on the other.

A probability/impact matrix or chart is a useful tool in risk management and analysis.

It helps organizations evaluate and prioritize risks by considering their probability of occurrence and potential impact if they do occur.

The matrix/chart typically presents a grid or axis with different levels of probability and impact.

The probability of a risk refers to how likely it is to happen, while the impact represents the potential consequences or severity of the risk.

By plotting risks on the matrix/chart, organizations can visually assess and compare the risks based on their probability and impact.

This helps in identifying high-priority risks that require immediate attention and mitigation efforts.

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Answer:

angle G = 64.9 is because the sum of interior angle is 180

The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Answer:

1,2,5,10

Step-by-step explanation:

Delete as this is the wrong answer. Made a typo in the answer.

Answer:

x = \(\frac{-212}{3}\)

y = 24

Step-by-step explanation:

-3x - 8y = 20  .... (1)

-5x + y = 19   .... (2)

What we can do is take the (2) equation

-5x + y = 19

and solve for y by adding 5x to both sides

y = 24

now that we have y we substitute it in for y in equation (1)

-3x - 8(24) = 20

-3x - 192 = 20

we want to solve for x so we need to get its self.

add 192 to both sides

-3x = 212

now we divide both sides by -3. It's going to be a fraction.

x = \(\frac{-212}{3}\)

Answer:

x=-4

y=-1

Step-by-step explanation:

-3x-8y=20

-5x+y=19

rewrite for y:

y=19+5x

substitute y

-3x-8(19+5x)=20

-3x-152-40x=20

-3x-152-40x+152=20+152

-43x=172

-43x/-43=172/-43

x=-4

substitute x

-5(-4)+y=19

20+y=19

y=-1

check:

-3(-4)-8(-1)=20

12+8=20

-5(-4)+-1=19

20-1=19

Answer:

130

Step-by-step explanation:

its basically the same thing

Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).

Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.

Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.

P(A ∩ B) = P(A) * P(B)

Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.

Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.

In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).

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Considering the p-value of the f-ratio, it is found that the correct option is given by:

a. Reject the null hypothesis with α = .05 but not with α = .01.

Depends on if the p-value is less or more than the significance level:

In this problem, the test statistic is of F = 4.60, with 4 x 7 = 28 df between treatments and 7 df in a single treatment, hence, using a calculator, the p-value is of 0.0218, which is less than 0.05 but more than 0.01, meaning that option A is correct.

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The altitude of Polaris, also known as the North Star, refers to its angle above the horizon when observed from a specific location on Earth.

The altitude of Polaris varies depending on the observer's latitude.

For an observer at the North Pole (latitude 90 degrees), Polaris appears directly overhead, at an altitude of 90 degrees. This means Polaris is at the zenith, the highest point in the sky.

For observers at other latitudes in the Northern Hemisphere, Polaris will appear lower in the sky. The altitude of Polaris is equal to the observer's latitude. For example, if you are at a latitude of 40 degrees north, Polaris will have an altitude of approximately 40 degrees above the horizon.

It's important to note that the altitude of Polaris remains relatively constant throughout the night and throughout the year due to its proximity to the celestial north pole. This makes it a useful navigational reference point for determining direction and latitude in the Northern Hemisphere.

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