CIRCLES DRAG & DROP ACTIVITY 1: Drag & Drop the correct values to fill in each table below.
HELP ASAP WILL GIVE BRAINLIST!!!!!!!!!!

The derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)] is equal to f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]².

In this problem we must determine the derivative of the composite function f(x) = (3 · x · cos x + √x) / [5 · x² · (sin x + 1)]. This can be done by using the following derivative rules:

Derivative of the addition of two functions

d [f(x) + g(x)] / dx = df(x) / dx + dg(x) / dx

Derivative of the product of two functions

d [f(x) · g(x)] / dx = [df(x) / dx] · g(x) + f(x) · [dg(x) / dx]

Derivative of the division of two functions

d[f(x) / g(x)] / dx = [[df(x) / dx] · g(x) - f(x) · [dg(x) / dx]] / [g(x)]²

Derivative of a function and a constant

d [c · f(x)] / dx = c · df(x) / dx

Derivative of a power function

d [xⁿ] / dx = n · xⁿ⁻¹

Derivative of cosine

d [cos x] / dx = - sin x

Derivative of sine

d [sin x] / dx = cos x

Now we proceed to determine the derivative of the function by derivative rules:

f'(x) = [d [3 · x · cos x + √x] / dx · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · d [5 · x² · (sin x + 1)] / dx] / [5 · x² · (sin x + 1)]²

f'(x) = [[3 · cos x - 3 · x · sin x + (1 / 2√x)] · [5 · x² · (sin x + 1)] - (3 · x · cos x + √x) · [5 · x · (sin x + 1) + 5 · x² · cos x]] / [5 · x² · (sin x + 1)]²

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The relative minimum's coordinates are (1, -5).

The first derivative test can be used to determine if a continuous function's critical point is a relative minimum or maximum. Simply put, the first derivative is a relative minimum if it is negative to the left of the critical point and positive to the right of it.

The parabola's equation takes the following form because its vertex is at (1, -5).

y = a(x - 1)² - 5

where "a" is a constant that determines the shape of the parabola. Since the parabola crosses the y-axis at (0, -3), we can substitute these coordinates into the equation and solve for "a" as follows:

-3 = a(0 - 1)² - 5

-3 = a - 5

a = 2

Thus, the equation of the parabola is:

y = 2(x - 1)² - 5

The x-coordinate of the vertex is given by x = 1

find the corresponding y-coordinate by substituting x = 1 into the equation:

y = 2(1 - 1)²- 5 = -5

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Its 10/29 so its answers this

The percentage increase in Marvin's height is 4.51%

Marvin was 1.55m tall a year ago

Now her present height is 1.62m

The first step is to calculate the increase

= 1.62-1.55

= 0.07

The percentage increase can be calculated as follows

0.07/1.55 × 100

= 0.0451 × 100

= 4.51

Hence the percentage increase is 4.51%

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After all the spending costs, Tino's weekly salary is approximately $60.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Let's call Tino's weekly salary "x".

Each week, Tino sets aside half of his salary for rent, so:

0.5x = rent

He also sets aside half of his salary for credit card payments, so

0.5x = credit card payments

And he sets aside a quarter of his salary for groceries and utilities, so:

0.25x = groceries and utilities

And he has approximately $15 left for entertainment, so:

x - 0.5x - 0.5x - 0.25x = 15

We can simplify this equation by combining the terms on the left side:

x - 1.25x = 15

And then solving for x:

-0.25x = 15

x = 60

Therefore, Tino's weekly salary is approximately $60.

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Answer:

= 10.

Step-by-step explanation:

=

[tex]50 \times \frac{2}{10} \\ = 5 \times 2 \\ = 10.[/tex]

The answer becomes for the given expression is: 10.

Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.

Given that,

= 50 × (2/10)

= 50 × (1/5)

= 10

Thus, for the given expression the answer becomes: 10

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Solving the provided question, we can say that equatiοn of slope intercept will me as y -y1 = m(x-x1) => 3x - y = -1

In mathematics, the intersectiοn point is the place on the y-axis where the slope of the line crosses. a place where the y-axis crοsses on a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equation fοr the straight line to show this.

The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept fοrm. When an equatiοn has the intercept form (y=mx+b), the slοpe is m and the y-intercept is b. Sοme equations can also be rewritten such that they seem to be slοpe intercepts. If y=x is rewritten as y=1x+0, fοr instance, the slοpe and y-intercept are bοth changed to 1.

Here,

coordinates are

M(2,5) and P(a,-2)

equation of slope intercept will me as

y -y1 = m(x-x1)

y - 5 = 3x-4

3x - y = -1

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The probability of selecting a Democrat and then an Independent is  (6/16) * (6/15) = 3/40. The probability of selecting two Republicans with replacement is (4/16) * (4/16) = 1/16.

What is probability ?

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. It is the ratio of the number of favorable outcomes to the total number of possible outcomes in a given situation. Probability is used in many fields, such as mathematics, statistics, science, engineering, economics, and social sciences, to model and analyze uncertain situations and make predictions about the future based on available data.

(a) selecting a Democrat and then an Independent without replacement.

The probability of selecting a Democrat on the first draw is 6/16, and the probability of selecting an Independent on the second draw, without replacement, is 6/15. So the probability of selecting a Democrat and then an Independent is:

(6/16) * (6/15) = 3/40

(b) selecting two Republicans with replacement.

The probability of selecting a Republican on the first draw is 4/16, and with replacement, the probability of selecting another Republican on the second draw is also 4/16. So the probability of selecting two Republicans with replacement is:

(4/16) * (4/16) = 1/16

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Answer:

option (A).

Step-by-step explanation:

The equivalent expression to the given radical expression, when the denominator has been rationalized and x > 5, is 2(√x + √x - 5), or option (A).

Answer:

The number of books sold were:

Math textbooks: 426
Sociology textbooks = 46

Step-by-step explanation:

Let us use the variable [tex]m[/tex]  to represent the number of math books sold

Let us use the variable [tex]s[/tex]  to represent the number of math books sold

Combined total of 426 math and sociology books were sold is represented by the equation:
[tex]m + s = 426\quad\quad\quad(1)[/tex]

Number of math books sold was 46 more than the number  of sociology textbooks sold is given by
[tex]m - s = 46\quad\quad\quad(2)[/tex]

Adding the equations (1) + (2):
[tex](m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\[/tex]

Using Equation (1): [tex]m + s = 426[/tex]  we get

[tex]236 + s = 426\\\\s = 426 - 236\\\\s = 190[/tex]

The provided statement indicates that Jim and Terrence each possess eight model automobiles, whereas Terrence owns six, making an 8:6 ratio. Jim is the owner of the 48 model card, then.

If b is really not equal to 0, then an arrangement of the numbers a and b expressed as a/b is a ratio. An equation known as a percent establishes two ratios with the identical value. You might, for instance, write the ration as described in the following: 1: 3 in the case of 1 male and 3 girls.

You are aware that Jim and Terrence own an 8:6 ratio in terms of the total number of model automobiles they own.

Accordingly, you can answer the task as follows: Let's say Jim owns x model automobiles.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

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Answer: 147 cents

Step-by-step explanation:

Unit rate is what we need here: i.e., how much does 1 inch of wire cost?

22in --> 66cents

1 in --> 66/22 = 3

3 cents per inch!

so 49 inches will cost 49 x 3 = 147 cents

The given conclusion "(x + 2)² = (x² + 2)" is false.

The two set representation methods are -

Given is the set A{1, 2, 3}.

(x + 2)² should be equal to (x² + 2) for all x ∈ A.

We can write -

(1 + 2)² = 1² + 2

9 ≠ 3

Therefore, the given conclusion "(x + 2)² = (x² + 2)" is false.

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{Question in english -

For all x in A: {1, 2, 3}, (x + 2)² is equal to (x² + 2). True or false?}

Answer: a) Calculate the probability of getting both contracts:

The probability of getting both contracts is given by P(Contract 1 and Contract 2) = P(Contract 1) * P(Contract 2|Contract 1) = 0.4 * 0.3 = 0.12

b) Calculate the probability of getting either contract:

The probability of getting either contract is given by P(Contract 1 or Contract 2) = P(Contract 1) + P(Contract 2) - P(Contract 1 and Contract 2) = 0.4 + 0.5 - 0.12 = 0.78

c) Calculate the probability of not getting either contract:

The probability of not getting either contract is given by P(Neither Contract) = 1 - P(Contract 1 or Contract 2) = 1 - 0.78 = 0.22.

So, there is a 22% chance that the construction firm will not get either contract.

Step-by-step explanation:

One thing that was not an impact of the Crusades was B. End of the Roman Empire.

The Crusades were a series of religious wars fought between Christians and Muslims in the 11th, 12th, and 13th centuries. The main objective of the Crusades was to recapture the Holy Land, which was considered the birthplace of Christianity, from Muslim rule.

The Crusades had a significant impact on the medieval world, but the end of the Roman Empire was not one of them. The Roman Empire ended several centuries before the start of the Crusades in the 11th century.

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By the equation formed by the relation to build 5 feet tall tower, Erica will need 20 bricks.

An equation is a mathematical statement consisting of two expressions joined by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation gives the value of the variable x as x = 7. 

According to the information given in the question:

1 brick = 1/4 Feet

Which means, 4 bricks = 1 feet

As Erica wants to make 5 feet tall tower,

5 feet tower = 5 x 4

                     = 20 bricks

Hence, Erica will need 20 bricks to build 5 feet tower.

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Answer: 0.32 or 32%

Step-by-step explanation: 8/25

Answer:

The difference in height is 8cm

Step-by-step explanation:

Volume of a cylinder=hπr²

When the bottle is full 5652:

5652=hπr²

5652=h*3.14*7.5²

5652=h*176.625

5652/176.625=h

Height=32cm

When the bottle is full by 4239:

4239=hπr²

4239=h*3.14*7.5²

4239=h*176.625

4239/176.625=h

Height=24cm

Difference in height:

32-24=8

The difference in height is 8cm

The distance of the point P to the plane is 42/√629 units. The solution has been obtained by using vectors.

What are vectors?

An item with both magnitude and direction is said to contain a vector. An object's motion from one point to another is described by a vector.

We are given three points Q, R and S. So, we will find equation of the plane defined by the three points.

Vector RQ = < 5, 1, -4 >  and RS = < 7, 6, -7>  and their cross product

RQ x RS = < 5, 1, -4 > x < 7, 6, -7> = < 17 , 7, 23>  = n  

This is a vector normal to the plane.

So, the equation of the plane is 17x + 4y + 18z = 139

The distance is calculated using

⇒d = (|A·Mx + B·My + C·Mz + D| )/(√A² + B² + C²)

⇒d = (|-17·3 + (-4)·1 + (-18)·7 + 139|)/((-17)² + (-4)² + (-18)²)

⇒d = 42/√629

Hence, the distance is 42/√629 units.

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The volume of the solid is -5.54 cubic units.

The region is bounded by the parabola x = 1 + (y-2)^2 and the line x = 2. To use the method of cylindrical shells, we imagine rotating this region around the x-axis, which gives us a solid shape.

The shell has thickness Δx and height y, and is located at a distance x from the y-axis. To find the volume of the solid, we'll add up the volumes of all the cylindrical shells.

The volume of a cylindrical shell is given by the formula V = 2πrhΔx, where r is the radius of the shell and h is its height. In this case, the radius of the shell is x - 2 (the distance from the y-axis to the edge of the region), and the height is y. So we have:

V = 2π(x - 2)yΔx

To find the total volume of the solid, we integrate this expression over the range of x values that corresponds to the region we're interested in. The region is bounded by x = 1 + (y-2)^2 and x = 2, so we integrate with respect to x from x = 1 + (y-2)^2 to x = 2:

V = ∫[1+(y-2)²]^2 2π(x - 2)y dx

To evaluate this integral, we can use the substitution u = y - 2, which gives us:

V = ∫1^0 2π(u^2 + 3) (1 + u)^2 du

This integral can be evaluated using the power rule and the substitution v = 1 + u:

V = 2π/5 [(1 + u)^5 - (1 + u)^3] from 1 to 0

V = 2π/5 [1 - 32/5]

V = 2π/5 ( -22/5)

V = - 8.8π/5

So the volume of the solid is approximately -5.54 cubic units. Note that the negative sign means that the solid is oriented in the opposite direction from what we might expect - in other words, it has a hole in it.

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The equation of the line that contains diagonal AH is  y = -4/7 x + 51/14.

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Given;

The endpoints of the diagonal MT are M(0,-1) and T(4,6).

Now, The point that it passes through in this case is the midpoint of the diagonal MT. Using the midpoint formula you get

( (0+4)/2 , (-1+6)/2 ) = (2,2.5).

The slope of MT is (6--1)/(4-0) = 7/4.

We need this because the other diagonal must be perpendicular, which means that the slopes must be negative reciprocals. So the negative reciprocal of 7/4 is -4/7.

Now that we have the slope and the point, we can just use y=mx+b. We have an x and y value as well as the m....so we can substitute them in and calculate b.

2.5 = -4/7 (2) + b

5/2 = -8/7 + b

5/2 + 8/7 = b

35/14 + 16/14 = b

51/14 = b

Therefore, in the rhombus diagonal line has the equation will be y = -4/7 x + 51/14

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The equation of line is y = -4x + 3 , where the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -4x + 3   be equation (1)

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = -4

And , the y intercept is 3

The equation of line is plotted on the graph

Hence , the equation of line is y = -4x + 3

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The complete question is :

Which of the following graphs matches the equation y=-4x+3?

On a coordinate plane, a line goes through (0, 3)

On a coordinate plane, a line goes through (-2, 5) and (0, -3).

On a coordinate plane, a line goes through (0, 3) and (3, -1).

Answer:

51°

Step-by-step explanation:

180°-129°=51°

I hope it helps you

Answer: the correct choice is b

Step-by-step explanation:

The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5

The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.

To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:

10, 13, 13, 14, 15, 15, 16, 17, 18

The low is the smallest value in the dataset, which is 10.

To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:

Q₁ = (13 + 13) / 2 = 13

The median is the middle value in the dataset, which is 15.

To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:

Q3 = (16 + 17) / 2 = 16.5

The high is the largest value in the dataset, which is 18.

Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:

IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5

Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The identity to be used here is [ (a - b)² = a² - 2ab + b² ]

First, try to get the given expression in form of terms on the RHS of the above identity

[tex]\qquad \sf  \dashrightarrow \: 4y {}^{2} - 6yz + 9 {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2 {}^{2})( {y}^{2}) - 2(3)(y)(z) + (3 {}^{2} ) {z}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (3z) {}^{2} [/tex]

[ it's in form of a² - ab + b² now, add and deduct ab here ]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - (2y)(3z) + (9z) {}^{2} - (2y)(3z) + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y) {}^{2} - 2(2y)(3z) + (3z) {}^{2} + (2y)(3z)[/tex]

[ Apply the identity ]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + (2y)(3z)[/tex]

[tex]\qquad \sf  \dashrightarrow \: (2y - 3z) {}^{2} + 6yz[/tex]

[ That's probably the answer, it can't be simplified more ]

To factorize the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex], we can use the quadratic formula.

We have the quadratic expression [tex]\sf\:ax^2 + bx + c \\[/tex], where $$\sf\:a = 4$$, $$\sf\:b = -6y $$, and $$\sf\:c = 9z^2 $$.

The quadratic formula states that for any quadratic equation of the form [tex]\sf\:ax^2 + bx + c = 0 \\[/tex], the solutions for $$\sf\:x $$ can be found using the formula:

[tex]\sf\:x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Applying this formula to our quadratic expression, we get:

[tex]\begin{align}\sf\:x &= \frac{-(-6y) \pm \sqrt{(-6y)^2 - 4(4)(9z^2)}}{2(4)} \\ &= \frac{6y \pm \sqrt{36y^2 - 144z^2}}{8} \\ &= \frac{6y \pm \sqrt{36(y^2 - 4z^2)}}{8} \\ &= \frac{6y \pm 6\sqrt{y^2 - 4z^2}}{8} \\ &= \frac{3}{4}y \pm \frac{3}{4}\sqrt{y^2 - 4z^2}\end{align} \\[/tex]

Thus, the factored form of the expression [tex]\sf\:4y^2 - 6yz + 9z^2 \\[/tex] is [tex]\sf\:(\frac{3}{4}y + \frac{3}{4}\sqrt{y^2 - 4z^2})(\frac{3}{4}y - \frac{3}{4}\sqrt{y^2 - 4z^2}) \\[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

✨[tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]