Charlotte and Pablo are each making purple paint by mixing blue
paint and red paint. Charlotte uses 1 cup of red paint for every
2 cups of blue paint. Pablo uses 2 cups of red paint for every
3 cups of blue paint. Whose paint is a bluer shade of purple?

The value of V = 2π/3. To find the volume of the solid, we need to use the method of cylindrical shells.

First, we need to solve for the x and y intercepts of the curve. Setting x = 0 gives y = 0, and setting y = 0 gives x = ±1. So the curve intersects the x-axis at (-1, 0) and (1, 0).

Next, we need to find the height of each cylindrical shell. The height is given by the difference between the y-values of the curve and the line x = 1. Solving for y in 2xy = 1 + x^2, we get y = (1 + x^2)/(2x). So the height of the cylindrical shell at x is given by (1 + x^2)/(2x).

Finally, we need to find the radius of each cylindrical shell. The radius is simply x.

So the volume of the solid is given by the integral from x = 0 to x = 1 of 2πx(1 + x^2)/(2x) dx. Simplifying and integrating, we get V = 2π/3.

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Complete Question:

Find the volume of the solid formed by revolving the region bounded by the curve 2x y = the line 1 + x2 y = 0, and the line x = 1 about the y-axis. V=?

Answer:

Step-by-step explanation:

[tex]\tt 12x=2y+7 \\ y=6-2[/tex]

Substitute y = 6x-2

[tex]\tt 12x=2\left(6x-2\right)+7[/tex]

[tex]\tt 12x=12x+3[/tex]

Cancel 12x from both sides:-

[tex]\tt {0=3}[/tex]

Since the sides are not equal, there's no solution.

___________________

Hope this helps!

The midpoint of a line segment is the point located halfway between two endpoints.

Therefore, if the points and have the coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of the midpoint, , are defined as:

[tex]M = (x1 + x2)/2, (y1 + y2)/2[/tex].

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the coordinates of the two points, we can calculate the slope of the line using the formula:

[tex]m = (y2 - y1)/(x2 - x1).[/tex]

Using the values of x1, y1, x2, and y2, we can calculate the slope of the line. We can then use the coordinates of and to calculate the y-intercept of the line, b.

Once we have determined the slope and y-intercept of the line, we can substitute these values into the equation of a line, y = mx + b, to determine the equation of the line.

The length of the line is equal to the distance between the two points and, for two points with coordinates (x1, y1) and (x2, y2), we can use the distance formula to calculate the length:

[tex]L = √((x2 - x1)^2 + (y2 - y1)^2)[/tex].

Substituting the values of x1, y1, x2, and y2 into this equation will give us the length of the line, which is equal to .

Therefore, the equation of the line and the length of the line are and , respectively.

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The measure of the angles are

1. 14°

2. 141°

3. 39°

4. 39°

The 4-letter code is DCAA

From the question, we ae to determine the measure of the angles and then the 4-letter code

From the diagram,

m ∠B + m ∠C = 180° (Sum of angles on a straight line)

Then,

1.

9x + 15° + 3x - 3° = 180°

12x + 12° = 180°

12x = 180° - 12°

12x = 168°

x = 168°/12

x = 14°

Thus, D

2.

m ∠B = 9x + 15°

m ∠B = 9(14) + 15°

m ∠B = 126° + 15°

m ∠B = 141°

Thus, C

3.

m ∠C = 180° - m ∠B

m ∠C = 180° - 141°

m ∠C = 39°

Thus, A

4.

m ∠A = m ∠C (Vertically opposite angle)

m ∠A = 39°

Thus, A

Hence, the code is DCAA

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Answer: A

Step-by-step explanation:

Option B. 2 K is the correct graph (check the attached image) of parent function after transformation.

In mathematics, a transformation is a function that, typically with some geometrical foundation, maps a set X to itself, i. e. f: X → X. Vector space linear transformations are one example.

A point, line, or geometric figure can be changed in four different ways that are all collectively referred to as transformations. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's final shape and location.

A graph can be altered in three basic ways: by shifting, or compressing, and by flipping. According to the definition of transformation, we can rotate around any point, reflect our image over any line, and translate any vector. These are rigid transformations in which the image is consistent with its pre-image.

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The polynomial in standard form is:

F(x) = 2x³ - x² + 5x - 3

Option B is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The standard form of a polynomial is ax³ + bx² + cx + d.

A.

F(x) = -3 - x² + 2x³ + 5x

This is not in standard form.

B.

F(x) = 2x³ - x² + 5x - 3

This is in standard form.

C.

F(x) = -3 + 5x - x² + 2x³

This is not in standard form.

D.

F(x) = 5x + 2x³ - x² - 3

This is not in standard form.

Thus,

F(x) = 2x³ - x² + 5x - 3 is in the standard form.

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Answer: a) The set W contains the zero vector, since (0,0,0) = (3s,-2s,s) for s = 0.

The set W is closed under addition and scalar multiplication:

If (3s1, -2s1, s1) and (3s2, -2s2, s2) are in W, then their sum, (3(s1 + s2), -2(s1 + s2), (s1 + s2)), is also in W.

If (3s, -2s, s) is in W and c is any scalar, then (3cs, -2cs, cs) is also in W.

The set W has a basis of {(3, -2, 1)}. To see this, we can write any vector in W as a scalar multiple of (3, -2, 1). For example, (3s, -2s, s) = s(3, -2, 1). The dimension of the set W is 1.

b) The set W contains the zero vector, since (t-2,0,6-3t) = (t-2,0,6-3t) for t = 2.

The set W is closed under addition and scalar multiplication:

If (t1 - 2, 0, 6 - 3t1) and (t2 - 2, 0, 6 - 3t2) are in W, then their sum, ((t1 + t2) - 2, 0, 6 - 3(t1 + t2)), is also in W.

If (t - 2, 0, 6 - 3t) is in W and c is any scalar, then (ct - 2c, 0, 6c - 3ct) is also in W.

The set W has a basis of {(1, 0, -3)}. To see this, we can write any vector in W as a scalar multiple of (1, 0, -3). For example, (t - 2, 0, 6 - 3t) = t(1, 0, -3) - 2(1, 0, -3). The dimension of the set W is 1.

c) The set H contains the zero vector, since (2b, a, 3b) = (0,0,0) for b = 0 and a = 0.

The set H is closed under addition and scalar multiplication:

If (2b1, a1, 3b1) and (2b2, a2, 3b2) are in H, then their sum, (2(b1 + b2), a1 + a2, 3(b1 + b2)), is also in H.

If (2b, a, 3b) is in H and c is any scalar, then (2cb, ca, 3cb) is also in H.

The set H has a basis of {(2,1,3)}. To see this, we can write any vector in H as a scalar multiple of (2,1,3). For example, (2b, a, 3b) = b(2,1,3) + a(0,1,0). The dimension of the set H is 2.

d) The set H contains the zero vector, since (−b + 2c, b, 4c) = (0,0,0) for b = 2c.

Step-by-step explanation:

The change in the position of the minute hand should be matched with the angle made by the change as follows;

The minute hand moves from 2 to 9 = 7π/6 radians

The minute hand moves from 5 to 10 = 5π/6 radians.

The minute hand moves from 3 to 7 = 2π/3 radians.

The minute hand moves from 4 to 6 = π/3 radians.

The minute hand moves from 1 to 4 = π/2 radians.

In Mathematics, a rotation can be defined as a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Generally speaking, the angle between numbers that represents the hands on an analog clock is equal to π/6 radians.

When the minute hand moves from 2 to 9, we have:

Difference = 9 - 2 = 7

Angle = 7 × π/6 = 7π/6 radians.

When the minute hand moves from 5 to 10, we have:

Difference = 10 - 5 = 5

Angle = 5 × π/6 = 7π/6 radians.

When the minute hand moves from 3 to 7, we have:

Difference = 7 - 3 = 4

Angle = 4 × π/6 = 4π/6 = 2π/3 radians.

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Answer:

y = -1/4x + 2

Step-by-step explanation:

First you have to pick 2 points on the line, then you find the slope of the line from those 2 points. The slope formula is m = (y2-y1) / (x2-x1), and filling the variables in with the points (0,2) and (4,1) gives you m = (1-2) / (4-0), which gives you m = -1/4.

Once you have found the slope, you look for the y-intercept which is the point where the x-value is 0, and that is 2 in this graph.

You can then put this information into slope-intercept form, y= mx + b. m represents the slope and b represents the y-intercept. The answer is y = -1/4x + 2

The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is 1/800x2−80x.

(a) The proportion of resistors with resistances less than 90 Ω is given by the integral of the probability density function f(x) from 80 to 90, which is 0.125.

(b) The mean resistance is given by the following formula:

Mean Resistance = [tex]∫x·f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the mean resistance to be 85 Ω.

(c) The standard deviation of the resistances is given by the following formula:

Standard Deviation = [tex]√∫(x−Mean Resistance)2·f(x)dx[/tex]

Substituting the given equation for f(x) and the mean resistance into this formula and integrating, we get the standard deviation of the resistances to be 8.66 Ω.

(d) The cumulative distribution function of the resistances is given by the following formula:

[tex]CDF(x) = ∫f(x)dx[/tex]

Substituting the given equation for f(x) into this formula and integrating, we get the cumulative distribution function to be [tex]1/800x2−80x[/tex] (where x is the resistance).

The proportion of resistors with resistances less than 90 Ω is 0.125, the mean resistance is 85 Ω, the standard deviation of the resistances is 8.66 Ω, and the cumulative distribution function of the resistances is [tex]1/800x2−80x[/tex].

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The part overlapped is showing the acute scalene triangles.

An acute scalene triangle can be defined as a triangle whose angles are less than 90 degrees and all three sides and angles are different in measurement.

Given that, in a graphic organizer, the left circle represents scalene triangles. The right circle represents acute triangles.

Here, we are asked to find that which figure belongs in the part of the organizer where the circles overlap,

In graphic organizers, the overlapped portion shows the common part between other portions.

Therefore, the common in both the triangles will be an acute scalene triangle,

Hence, the part overlapped is showing the acute scalene triangles.

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The required scale factor used to dilate Figure A to make Figure B is 5/4.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges.

The ratio of the volumes of two similar pyramids is equal to the cube of the ratio of their corresponding side lengths. Therefore, the scale factor used to dilate Figure A to make Figure B is equal to the cube root of the ratio of their volumes:

scale factor = cube root of (volume of Figure B / volume of Figure A)

scale factor = cube root of (375 / 192)

scale factor = cube root of (125 / 64)

scale factor = 5/4

Therefore, the scale factor used to dilate Figure A to make Figure B is 5/4.

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The equation of line k is y = x + 1.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1 = 1

At data point (-4, -3), a linear equation of this line can be calculated in point-slope form as follows:

y - (-3) = 1(x - (-4))

y + 3 = x + 4

y = x + 1

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Answer:

congruent

Step-by-step explanation:

The opposite sides of a parallelogram are congruent.

We can also determine this from the markings in the diagram.

Profitability ratios is a type of financial ratio shows the combined effects of liquidity, asset management and debt management of a business. So the statement is true.

Financial ratios are calculations used to assess various data to evaluate the company's performance. It is calculated using quantitative data from financial statements. There are mainly four financial ratios

So the statement given is true.

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The value of a + b + c is 42.

Let's set the arrival time of one of the mathematicians, let's say the first mathematician, to be t minutes after 9 a.m.

The likelihood that a second mathematician will show up while the first one is in the cafeteria is [tex]$ \frac{m}{60}[/tex], since the second mathematician has a [tex]\frac{m}{60} $-hour[/tex] window to arrive while the first is there.

⇒The probability that they arrive during some overlapping time is then [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right)$[/tex]. This probability must be equal to 0.4.

⇒So we have the equation [tex]$2\left(\frac{m}{60}\right)\left(1 - \frac{m}{60}\right) = 0.4$[/tex].

⇒Solving for m yields [tex]$m = 24 - 4\sqrt{14}[/tex].

Therefore, the a + b + c = 24 + 4 + 14 =42.

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(a) P = [tex](56035e^(0.3283t)) / (560 + 35(e^(0.3283t)-1))[/tex] (b) 345 panthers (c) 1.59 years (d) dP/dt = kP(1 - P/560), P(5) ≈ 373 panthers (e) 1.59 years.

(a) The logistic equation that models the population of panthers in the preserve is:

P = [tex](560P0e^{(kt)}) / (560 + P0(e^{(kt)-1}))[/tex]

where P0 is the initial population (35), k is the growth rate constant, and t is the time in years.

To solve for k, we can use the fact that after 2 years the population is 200:

200 =[tex](56035e^(2k)) / (560 + 35(e^{(2k)-1}))[/tex]

Solving for k, we get:

k = 0.3283 (rounded to 4 decimal places)

Therefore, the logistic equation is:

P = (56035e^(0.3283t)) / (560 + 35(e^(0.3283t)-1))

(b) To find the population after 5 years, we substitute t=5 into the logistic equation:

P = (56035e^(0.32835)) / (560 + 35(e^(0.32835)-1))

P ≈ 345 panthers (rounded to the nearest whole number)

(c) To find when the population reaches 280, we can solve the logistic equation for t when P=280:

280 = [tex](56035e^{(0.3283t)}) / (560 + 35(e^{(0.3283t)-1}))[/tex]

Solving for t, we get:

t ≈ 1.59 years (rounded to 2 decimal places)

(d) The logistic differential equation that models the growth rate of the panther population is:

dP/dt = kP(1 - P/560)

Using Euler's method with a step size of h=1, we get:

P(5) ≈ P(4) + hdP/dt(4)

P(4) = 345 (from part b)

dP/dt(4) = k345*(1 - 345/560) = 27.522

P(5) ≈ 345 + 27.522 = 373 panthers (rounded to the nearest whole number)

(e) The panther population is growing most rapidly when the growth rate is at its maximum, which occurs at half the carrying capacity (P=280). We can find the time by taking the derivative of the logistic equation and setting it equal to zero:

dP/dt = kP(1 - P/560)

0 = k280(1 - 280/560)

0.5 = 1 - 280/560

280 = 560/2

So, the panther population is growing most rapidly when P=280, which occurs at half the carrying capacity. Therefore, the time when the population is growing most rapidly is at t=1.59 years (from part c).

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Getting the correct answer in an online school environment can be achieved through a few methods:

Read the course materials carefully: Make sure you understand the material being covered before attempting to answer questions.

Participate in online discussions: If you have questions, participate in online discussions with your classmates or instructors. This can help you better understand the material and get clarification on any points you are unsure about.

Utilize online resources: Many online schools provide access to online resources such as videos, tutorials, and practice quizzes. These can help you reinforce your understanding of the material and prepare for exams.

Ask for help: If you are still having trouble finding the correct answer, don't be afraid to reach out to your instructor or classmates for help.

Use additional study materials: Consider using outside study materials such as textbooks, study guides, and online resources to help you better understand the material.

Remember, the key to success in online school is to stay organized, be proactive, and actively engage with the course materials and your classmates. Good luck!

Getting every answer in an online school course depends on several factors, including the format of the course, the resources available, and the instructor's teaching style. Here are some tips that may help:

Utilize course resources: Most online courses provide students with a variety of resources such as textbooks, lectures, discussion forums, and quizzes. Utilize these resources to gain a deeper understanding of the material.

Participate in discussions: Participating in online discussions can be an excellent way to get answers to questions you have about the course material. You can also collaborate with other students to gain a better understanding of the course content.

Ask the instructor: If you're still unsure about a particular topic, don't be afraid to reach out to your instructor for clarification. You can send an email, participate in virtual office hours, or use a discussion forum to ask questions.

Research outside sources: You can also conduct research outside of the course to supplement your understanding of the material. Search for reputable sources, such as academic journals, to gain a better understanding of the course content.

Form a study group: If you're taking the course with other students, consider forming a study group. Studying with others can be an effective way to get answers to questions you have and to collaborate on course assignments.

Remember, the key to getting every answer in an online course is to be an active and engaged learner. Utilize all the resources available to you and don't be afraid to ask for help when needed.

Answer: 3 < c < 13   (choice C or third answer choice)

======================================================

Explanation:

Consider a triangle with sides: a,b,c

Furthermore, we'll have a = 5 and b = 8 as the two known sides.

Due to a modification of the Triangle Inequality Theorem, the third side will have the condition that:

b-a < c < b+a

where b ≥ a must be the case.

----------

Let's plug in those a & b values to determine the range for c.

b-a < c < b+a

8-5 < c < 8+5

3 < c < 13

This points us to Choice C as the final answer.

Answer: 9.43398113206

Step-by-step explanation:

A^2 + B^2 = C^2

5^2 + 8^2 = √89

= 9.43398113206

The value of parameter under  null hypothesis which is not plausible , will not be contained in a 95% confidence interval when (a) p value is less than or equal to 0.05  .

The "P Value" is  the probability of observing a test statistic as extreme or more extreme than the one computed from the sample data, assuming the null hypothesis is true.

When the p value is less than equal to 0.05 , it indicates that the observed test statistic is statistically significant at the 5% level of significance, means that the null hypothesis will be rejected.

Therefore , the parameter value that is assumed under the null hypothesis is not plausible and is not likely to be in a 95% confidence interval.

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The given question is incomplete , the complete question is

When conducting a two-sided test of significance, the value of the parameter under the null hypothesis is not plausible and will not be contained in a 95% confidence interval when  

(a) The p-value is less than or equal to 0.05

(b) The p-value is greater than 0.05.

(c) There is no relationship between the p-value and the confidence interval.

The surface area Sam needs to paint on the cylinder is  πx² + 2πxy i.e. B.

What exactly is a cylinder?

In geometry, a cylinder is one of the fundamental 3d forms with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

Because the cylinder is a three-dimensional form, it has two primary properties: surface area and volume. The cylinder's total surface area (TSA) is equal to the sum of its curved surface area and the area of its two circular bases.

The volume of a three-dimensional cylinder is the space it occupies (V).

TSA=2πr²+2πrh, where r is the radius and h is the height.

Now,

Given that the radius of the roof is x feet and the silo is y feet high

Area of roof=πx² and

curved surface area=2πxy

then the surface area Sam needs to paint=πx²+2πxy

Hence,

        The surface area Sam needs to paint on the cylinder is

πx² + 2πxy.

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The percentage of students with more than 1 brother or sister is 41%.

To find the percentage, first complete the table:

118 - 62 = 56 female students with 1 brother and sister.
8 + 14 = 22 7th years with 3 brothers and sisters.
118 + x + 22 + 6 = 200, x = 200 - 146, x = 54 7th years with 2 brothers and sisters.
54 - 24 = 30 male students with 2 brothers and sisters.
62 + 30 + 8 + y = 104, y = 104 - 100, y = 4 male students with 4 brothers and sisters.
6 - 4 = 2 female students with 4 brothers and sisters.
56 + 24 + 14 + 2 = 96 total female students of 7th year.

The percentage of students with more than i brother and sister is:

54 + 22 + 6 = 82 students or 200 - 118 = 82 students.

% = 82 / 200 x 100 = 41%.

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Answer:

28/35 and 25/35

Step-by-step explanation:

To find the equivalent fraction of 4/5 and 5/7 with a common denominator, we can find the least common multiple (LCM) of the two denominators. The LCM of 5 and 7 is 35. So, to get the equivalent fractions with a common denominator of 35, we can multiply both the numerator and denominator of each fraction by the same number so that the denominators become 35:

4/5 becomes 4 x 7/5 x 7 = 28/35

5/7 becomes 5 x 5/7 x 5 = 25/35

So, the equivalent fractions of 4/5 and 5/7 with a common denominator of 35 are 28/35 and 25/35, respectively.

The  cosine of angle R is 3/5 and tangent of angle R is 4/3.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given right triangle is RTS.

We have to find the cosine of angle R

We know that cos theta = Adjacent side/hypotenuse.

CosR=6/10

=3/5

Now let us find tangent of angle R

Tan theta = opposite side/adjacent side

=8/6

=4/3

Hence, the  cosine of angle R is 3/5 and tangent of angle R is 4/3.

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Answer:

B.10

Step-by-step explanation:

√2.√10.√5

√2.10.5

√100

√2².5²

2.5

10

The correct way to start finding g(h(x)) is to replace the output of h(x) in

the variables of g(x).

When the output of one function is given to the input of another function they are called composite functions.

In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, g(x) = x² - 8 and h(x) = - 6x + 1,

Now, g(h(x)) is the output of h(x) is the input of g(h(x)).

Therefore, g(h(x)) is g(- 6x + 1) = (- 6x + 1)² - 8.

g(h(x)) = - (6x - 1)² - 8.

g(h(x)) = - (36x² - 12x + 1) - 8.

g(h(x)) = - 36x² + 12x - 1 - 8.

g(h(x)) = - 36x² + 12x - 9.

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Answer:

Step-by-step explanation:

To find the product of the factors 3.78 and 9.2, we simply multiply them together:

3.78 × 9.2 = 34.776

Therefore, the product of the factors 3.78 and 9.2 is 34.776.

Exact:  1436.75504cm3

About: 1436.8cm3

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