If z=xey,x=u2+v2,y=u2−v2, find ∂z∂u and ∂z∂v. The variables are restricted to domains on which the functions are defined. ∂z∂u= ∂z∂v=

Step-by-step explanation:

Refer to pics...............

The number of ways the class can choose the representatives is 17160.

The correct option is D.

This problem involves selecting a group of four people from a group of thirteen.

There are 13 choices for the first position, 12 choices for the second position, 11 choices for the third position, and 10 choices for the fourth position.

Therefore, the number of ways the class can choose the representatives is:

13 x 12 x 11 x 10 = 17,160

So, the answer is D.

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Answer:

D

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer: m = 2, (0, –2)  

Step-by-step explanation:

c

False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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The factored form of the given equation as calculated from the data is found to be as 3x( x -2 )  , and on further solving we get the roots of the equation to be as x- 0 and 2.

The expression given is 3x²- 6x, in order to get it's factored form we will factorize this expression ,

Let ,  3x²- 6x =0

therefore,

3x( x -2 ) = 0

which means,

3x = 0 and x - 2 = 0

hence ,

x = 0 and x = 2.

A statement that supports the equality of two expressions and is equated using the equals sign "=" is called as an equation.

For instance,  3x²- 6x = 13 , here  3x²- 6x and 13 are expressions which are separated by the "=" is the sign that connects these two expressions.

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Answer:1/12 or 8.3

Step-by-step explanation:

Given :-

A line having a slope of 3/2 passes through (2,-1) .

To Find :-

The equation of the line .

Answer :-

According to the question ,

m = 3/2

Point = (2,-1)

We know Point slope form of the line as ,

y - y¡ = m ( x - x ¡ )

Substitute ,

y - (-1) = 3/2 ( x - 2 )

y + 1 = 3/2x - 3/2*2

y +1 = 3/2x - 3

2( y +1) = 3/2x *2 - 3*2

2y + 2 = 3x - 6

3x -2y -8 = 0

Answer:

  -6

Step-by-step explanation:

You want to know where the line y=6 intersects the graph of h(x) shown as a series of line segments.

The attached graph shows the value of h(x) is 6 for x=-2 (known) and x=-6.

The other input value is -6.

My reactions to this:

???

My notes to you:

This is confusing... (At least for me it is...)

Answer:

X= 6.6

Length of de = 16.2

Step-by-step explanation:

Answer:

A) 9.1%

B) 7.4%

Step-by-step explanation:

Part A

Because you are replacing each marble before selecting the next, the probability of choosing one red marble remains the same, so choosing 3 red marbles with replacement would mean the probability gets multiplied by itself 3 times:

\(\displaystyle P(\text{Red+Replace})=\biggr(\frac{9}{20}\biggr)^3=\frac{9}{20}*\frac{9}{20}*\frac{9}{20}=\frac{729}{8000}\approx9.1\%\)

Part B

\(\displaystyle P(\text{Red+No Replace})=\frac{C(9,3)C(4,0)C(7,0)}{C(20,3)}=\frac{\frac{9!}{3!(9-3)!}}{\frac{20!}{3!(20-3)!}}=\frac{\frac{9*8*7}{3*2*1}}{\frac{20*19*18}{3*2*1}}=\frac{9*8*7}{20*19*18}=\frac{7}{95}\approx7.4\%\)This can also be calculated with \(\frac{P(9,3)}{P(20,3)}\) because the order does matter in which you pick the 3 red marbles with no replacement.

Answer:

9.1%

7.4%

Step-by-step explanation:

Answer:

The missing sides are 13 (small) and 2424 (big)

Step-by-step explanation:

The bigger triangle is bigger by 2 so multiply or divide the sides you do know by 2 to find the missing sides.

BC=12

ED= 12*2= 24

FD= 26

AC= 26/2= 13

Answer:

To find the surface area of the surface S, we need to find the area of the curved surface of the cylinder and the area of the plane surface.

First, let's find the equation of the cylinder. We can see that the sides of the cylinder are given by the equations y = 4x^2 and y = 8 - 4x^2. These are equations of parabolas with vertex at the origin and axis along the y-axis. The cylinder is formed by sweeping the region between the two parabolas along the y-axis. We can write the equation of the cylinder in terms of x and y as:

4x^2 ≤ y ≤ 8 - 4x^2

Next, let's find the intersection of the cylinder with the plane. We can substitute 3x + 4y + 12z = 7 into the equation of the cylinder:

4x^2 ≤ y ≤ 8 - 4x^2

3x + 4y + 12z = 7

Solving for z, we get:

z = (7 - 3x - 4y) / 12

Substituting this into the equation of the cylinder, we get:

4x^2 ≤ y ≤ 8 - 4x^2

z = (7 - 3x - 4y) / 12

This gives us the equation of the surface S.

To find the surface area of S, we need to integrate the square root of the sum of the squares of the partial derivatives of z with respect to x and y over the region of S. This is given by the surface area integral:

∫∫S √(1 + (dz/dx)^2 + (dz/dy)^2) dA

where dA is the area element of S.

We can simplify the integral by using the fact that dz/dx = -3/12 = -1/4 and dz/dy = -4/12 = -1/3:

∫∫S √(1 + (dz/dx)^2 + (dz/dy)^2) dA

= ∫∫S √(1 + 1/16 + 1/9) dA

= ∫∫S √(325/144) dA

= (5/12) ∫∫S dA

The integral ∫∫S dA is the area of the region enclosed by the cylinder and the plane. We can find this area by integrating over the projection of the region onto the xy-plane. The projection is the region between the parabolas y = 4x^2 and y = 8 - 4x^2. We can integrate this region using polar coordinates, with the limits for r from 0 to (2/y)^(1/2) and the limits for θ from 0 to π:

∫∫S dA = ∫₀^π ∫₀^(2/y)^(1/2) r dr dθ

= π ∫₀^∞ (2/y)^(1/2) r dr

= π (2/y)^(1/2) ∫₀^∞ r dr

= π (2/y)^(1/2) (1/2) [r^2]₀^∞

= π (2/y)

Substituting this into the surface area integral, we get:

Surface area of S = (5/12) ∫∫S dA = (5/12) π (2/y) = (5/6) π (3x + 4y -

Step-by-step explanation:

Answer:

cfc

Step-by-step explanation:

cfc

Answer:

3

Step-by-step explanation:

you suck

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

Maximum value is y=24 when x=20

Step-by-step explanation:

The maximum value of the downward parabola is its vertex. Since the vertex is (20,24) then the maximum value is y=24 when x=20

Answer:

4      HAH AHQ HQH!!!

Step-by-step explanation:

1 1 1 1

Answer:

4

Step-by-step explanation:

2+2 is 4

Answer:

3 cm

Step-by-step explanation:

The formula for the volume of a pyramid is :

Given

Solving

If a number is multiplied by 8 instead of 5, the product increases by 39

to find: the number

Let the number be x

Product of number is and 8 = 8x

Product of number is and 5 = 5x

A number is multiplied by 8 instead of 5, the product increases by 39

so,     8x-5x=39

         3x=39

          x=13

so,

Hence the number is 13

Multiplication is an arithmetic operation, where we find the product of two or more than two numbers.

The Number System contain any of the numerous sets of symbols and the rules for using them to denote numbers, which are used to state how many objects are there in a given set.

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Answer:

The answer is B. 60°

Step-by-step explanation:

The Unit Circle.

A =  sin^-1 ( \(\frac{\sqrt{3} }{2}\)) = 60°

Given a table of polygons

For the first row,

Given that the 1 exterior angle of the polygon is given, to find the number of sides, n, the formula is

The number of sides, n, of the polygon is three, thus it is a triangle.

A regular triangle has

For the second row

Given that sum of the interior angles of the polygon is 720°, to find the number of sides of the polygon,

Using the formula to find the sum of the interior angles of a polygon which is

Since the number of sides is 6, thus, it is a hexagon.

For a regular hexagon, is tas

The table is shown below

Using Naïve Bayes multinomial with alpha=1, we classify the given messages based on their content. Message 4, "Tokyo Japan Chinese," is classified as spam.

To classify the messages using Naïve Bayes multinomial, we consider the content of the messages and their corresponding classifications. We calculate the probabilities of each message belonging to the "Normal" or "Spam" classes.

3 messages are classified as "Normal."

1 message is classified as "Spam."

We calculate the probabilities as follows:

P(Class = Normal) = 3/4 = 0.75

P(Class = Spam) = 1/4 = 0.25

Next, we analyze the occurrence of words in each class:

For the "Normal" class:

The word "Chinese" appears 5 times.

The word "Beijing" appears 1 time.

The word "Shanghai" appears 1 time.

The word "Macao" appears 1 time.

For the "Spam" class:

The word "Tokyo" appears 1 time.

The word "Japan" appears 1 time.

The word "Chinese" appears 1 time.

Now, we calculate the probabilities of each word given the class using Laplace smoothing (alpha=1):

P(Chinese|Normal) = (5 + 1)/(5 + 4) = 6/9

P(Beijing|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Shanghai|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Macao|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Tokyo|Spam) = (1 + 1)/(3 + 4) = 2/7

P(Japan|Spam) = (1 + 1)/(3 + 4) = 2/7

P(Chinese|Spam) = (1 + 1)/(3 + 4) = 2/7

To classify Message 4, "Tokyo Japan Chinese," we compute the probabilities for each class:

P(Normal|Message 4) = P(Chinese|Normal) * P(Tokyo|Normal) * P(Japan|Normal) * P(Class = Normal)

≈ (6/9) * (0/9) * (0/9) * 0.75

= 0

P(Spam|Message 4) = P(Chinese|Spam) * P(Tokyo|Spam) * P(Japan|Spam) * P(Class = Spam)

≈ (2/7) * (2/7) * (2/7) * 0.25

≈ 0.017

Since P(Spam|Message 4) > P(Normal|Message 4), we classify Message 4 as spam.

In summary, using Naïve Bayes multinomial with alpha=1, we classify Message 4, "Tokyo Japan Chinese," as spam based on its content.

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Using Naïve Bayes multinomial with alpha=1, we classify the given messages based on their content. Message 4, "Tokyo Japan Chinese," is classified as spam.

To classify the messages using Naïve Bayes multinomial, we consider the content of the messages and their corresponding classifications. We calculate the probabilities of each message belonging to the "Normal" or "Spam" classes.

3 messages are classified as "Normal."

1 message is classified as "Spam."

We calculate the probabilities as follows:

P(Class = Normal) = 3/4 = 0.75

P(Class = Spam) = 1/4 = 0.25

Next, we analyze the occurrence of words in each class:

For the "Normal" class:

The word "Chinese" appears 5 times.

The word "Beijing" appears 1 time.

The word "Shanghai" appears 1 time.

The word "Macao" appears 1 time.

For the "Spam" class:

The word "Tokyo" appears 1 time.

The word "Japan" appears 1 time.

The word "Chinese" appears 1 time.

Now, we calculate the probabilities of each word given the class using Laplace smoothing (alpha=1):

P(Chinese|Normal) = (5 + 1)/(5 + 4) = 6/9

P(Beijing|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Shanghai|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Macao|Normal) = (1 + 1)/(5 + 4) = 2/9

P(Tokyo|Spam) = (1 + 1)/(3 + 4) = 2/7

P(Japan|Spam) = (1 + 1)/(3 + 4) = 2/7

P(Chinese|Spam) = (1 + 1)/(3 + 4) = 2/7

To classify Message 4, "Tokyo Japan Chinese," we compute the probabilities for each class:

P(Normal|Message 4) = P(Chinese|Normal) * P(Tokyo|Normal) * P(Japan|Normal) * P(Class = Normal)

≈ (6/9) * (0/9) * (0/9) * 0.75

= 0

P(Spam|Message 4) = P(Chinese|Spam) * P(Tokyo|Spam) * P(Japan|Spam) * P(Class = Spam)

≈ (2/7) * (2/7) * (2/7) * 0.25

≈ 0.017

Since P(Spam|Message 4) > P(Normal|Message 4), we classify Message 4 as spam.

In summary, using Naïve Bayes multinomial with alpha=1, we classify Message 4, "Tokyo Japan Chinese," as spam based on its content.

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The equation y = 3x +a / 2x - 5 can be expressed in terms of a and y as x = (a - 5y) / (2y-3)

Given equation y = 3x + a / 2x - 5

= y(2x - 5) = 3x + a

= 2xy - 5y = 3x + a

= 2xy - 3x = a - 5y

= x(2y-3) = a - 5y

Hence, x = (a - 5y) / (2y - 3)

First, we will move the denominator 2x-5 and multiply it by y giving us 2xy-5y. Next, we will move all the terms which contain only a and y to one side and the rest remaining to another side, giving us 2xy - 3x = a - 5y. Since we need to express the equation in terms of x we take it as common from left-hand side of the equation and the remaining part we move to the right-hand side as the denominator. Hence we get our equation in terms of a and y as x = (a - 5y) / (2y - 3).

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a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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The answer is 16.7 %.

The necessary calculation is below:

observations  Systolic(x)  Diastolic(y)  x^2      y^2

        1          120               79    14400 6241

         2          130               74    16900 5476

         3          157               75    24649 5625

         4          96               50     9216 2500

         5          156                89    24336 7921

         6         124               87    15376 7569

         7          116               59    13456 3481

         8          137               66    18769 4356

         9          124               71    15376 5041

        10          118               81     13924 6561

       sum         1278      731   166402 54771

For Systolic (x)

mean= sum(x)/10 = 1278/10 = 127.8

stdev= s =sqrt( (sum(x^2 - 10*127.8^2)/9) = sqrt ( (166402 - 10*127.8^2)/9) =18.48

So coefficient of variation ( systolic)  is = (stdev/mean )*100 = (18.48/127.8)*100 = 14.5 %

For Diastolic (x)

mean= sum(y)/10 = 731/10 = 73.1

stdev= s =sqrt( \((sum(x^2 - 10*73.1^2)/9) = sqrt ( (54771 - 10*73.1^2)/9)\)= 12.18

so coefficient of variation ( systolic)  is = (stdev/mean )*100 = (12.18/73.1)*100 = 16.7 %

Here, systolic is less varied than the diastolic.

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Answer:

D. g(-13) = 20

Step-by-step explanation:

Given information:

Option A, g(-4) = -11 cannot be true for g since the y-value of -11 is not in the given range.

Option B, g(7) = -1 cannot be true for g since the x-value of 7 is not in the given domain.

Option C, g(0) = 2 cannot be true for g since we have been given g(0) = -2.

Option D, g(-13) = 20 is true for g since the x-value of -13 is in the given domain, and the y-value of 20 is in the given range.

Answer:

640\(x^{6}\)

Step-by-step explanation:

(5x³)(4x) ³2

(4x) ³ is the same as

4³ * x³ = 64x³

--

(5x³)(64x³)2

5*64*2 = 640

x³ * x³ = \(x^{6}\)

640\(x^{6}\)