For each H and G given below, find all left cosets of H in G, then state the index (G : H]. (a) H = (4), G = C20 (b) H = (f), G = D4

The solutions to the given implicit function is

\(∂z/∂x = -2xz / (2x + x^2 - y*sin(yz))\)

and

\(∂z/∂y = (-y - z*sin(yz)) / (1 + z*sin(yz)^2)\)

To find ∂z/∂x and ∂z/∂y given that z is given implicitly as a function of x and y

use implicit differentiation for the equation

\(x^2z + y^2 + z^2 = cos(yz)\)

Take the partial derivative of both sides of the equation with respect to x

\(2xz + x^2(∂z/∂x) + 2z(∂z/∂x) \\ = -y*sin(yz)(∂z/∂x)\)

Simplifying, we get:

\((2x + x^2 - y*sin(yz))(∂z/∂x) \\ = -2xz\)

Divide both sides by 2x + x^2 - y*sin(yz), we get:

\(∂z/∂x = -2xz / (2x + x^2 - y*sin(yz))

\)

Take partial derivative of both sides of the equation with respect to y, we get:

2yz + 2z(∂z/∂y) = -z*sin(yz)(y + yz∂z/∂y) + 2y

Simplifying, we get:

\((2z - z*sin(yz)y - 2y)/(1 + z*sin(yz)^2)(∂z/∂y) \\ = -y - z*sin(yz)\)

Divide both sides by (2z - z*sin(yz)y - 2y)/(1 + z*sin(yz)^2),

\(∂z/∂y = (-y - z*sin(yz)) / (1 + z*sin(yz)^2)\)

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Given equation x²z+y²+z²=cos(yz) is given implicitly as a function of x and y.

Here, we have to find out the partial derivatives of z with respect to x and y.

So, we need to differentiate the given equation partially with respect to x and y.

To find ∂z/∂x,
Differentiating the given equation partially with respect to x, we get:

2xz+0+2zz' = -y zsin(yz)

Using the Chain Rule: z' = dz/dx and dz/dy

Similarly, to find ∂z/∂y, differentiate the given equation partially with respect to y, we get: 0+2y+2zz' = -zsin(yz) ⇒ 2y+2zz' = -zsin(yz)

Again, using the Chain Rule: z' = dz/dx and dz/dy

We can write the above equations as: z'(2xz+2zz') = -yzsin(yz)⇒ ∂z/∂x = -y sin(yz)/(2xz+2zz')

Also, z'(2y+2zz') = -zsin(yz)⇒ ∂z/∂y = [1-zcos(yz)]/(2y+2zz')

Thus, ∂z/∂x = -y sin(yz)/(2xz+2zz') and ∂z/∂y = [1-zcos(yz)]/(2y+2zz')

Hence, the answer is ∂z/∂x = -y sin(yz)/(2xz+2zz') and ∂z/∂y = [1-zcos(yz)]/(2y+2zz')

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Answer: $2.60

Step-by-step explanation:

raspberry pancake mix = 1.30/kg

bought = 2kg

2kg x $1.30/kg = $2.60

Answer: $2.60

Step-by-step explanation: 1.30 x 2 = 2.60

To determine whether the series ∑(n=1 to infinity) 7n/n is convergent or divergent, we can apply the ratio test. The ratio test helps us determine the convergence or divergence of a series by examining the limit of the ratio of consecutive terms.

In this case, let's calculate the ratio of consecutive terms using the formula for the ratio test:

lim(n→∞) |(7(n+1)/(n+1))/((7n/n)|

Simplifying the expression, we get:

lim(n→∞) |7(n+1)/n|

As n approaches infinity, the limit evaluates to:

lim(n→∞) |7(n+1)/n| = 7

Since the limit is a finite positive value (7), which is less than 1, the ratio test tells us that the series is convergent.

However, you mentioned identifying an (term) in the series, and it seems there may be an incomplete part of the question. Please provide additional information or clarification about identifying an term in the series so that I can provide a more specific answer.

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Answer:

Step-by-step explanation:

5/8 divided by 3/8 is the same as 5/8 x 8/3 = 40/24 = 1 2/3

Answer: 12/3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

12:1,2,3,4,6,12

18:1,2,3,6,9,18

32:1,2,4,8,16,32

h.c.f = 2

Answer:

The answer would be

y-2 greater than one

Step-by-step explanation:

y>1

y=2,3,4,5.....

y-2=0,1,2,3...

Answer: D \(10\sqrt{2}\)

Step-by-step explanation:

It says that the measure of angle B is 45 degrees. So if we were to put in 45 degrees  we could see that is is opposite AC and BC which we needs to find is the hypotenuse. So since we know the opposite of angle B  is 10 ft we can using that to find the length of BC.  Opposite hypotenuse is the sine function so we will use it to calculate the length of BC.

sin(45) = \(\frac{10}{BC}\)       multiply both sides by BC  

BC sin(45) = 10      divide both sides by sin(45)

BC = \(\frac{10}{sin(45)}\)

BC = \(10\sqrt{2}\)

Answer:

\(\huge\boxed{Option\ D : \ BC = 10\sqrt{2}\ ft }\)

Step-by-step explanation:

Since it's a right angled triangle, We'll use trigonometric rations.

Given that m∠B = 45°

So,

Sin B = opposite / hypotenuse

Where m∠B = 45°, opposite = 10 ft and hypotenuse = BC

Sin 45 = 10 / BC

\(\sf \frac{\sqrt{2} }{2} = \frac{10}{BC}\)

BC = 20 / √2

Multiplying and Dividing by √2

BC = 20√2 / √(2)²

BC = 20 √2 / 2

BC = 10√2 ft

To find the equation of the tangent plane to the given equation 2(x-2)^2 (y-1)^2 (z-3)^2=10, we need to find the gradient of the function and use the point-slope form of a plane.

First, we find the gradient of the function by taking the partial derivatives with respect to x, y, and z:

∂f/∂x = 4(x-2)(y-1)^2(z-3)^2

∂f/∂y = 4(x-2)^2(y-1)(z-3)^2

∂f/∂z = 4(x-2)^2(y-1)^2(z-3)

Next, we find the point on the surface where we want to find the tangent plane. For simplicity, let's choose the point (2,1,3), which is on the surface because 2(2-2)^2(1-1)^2(3-3)^2=0=10.

Now we plug in the point into the gradient to find the normal vector to the plane:

∂f/∂x(2,1,3) = 4(2-2)(1-1)^2(3-3)^2 = 0

∂f/∂y(2,1,3) = 4(2-2)^2(1-1)(3-3)^2 = 0

∂f/∂z(2,1,3) = 4(2-2)^2(1-1)^2(3-3) = 0

So the normal vector is <0,0,0>.

Finally, we use the point-slope form of a plane to find the equation of the tangent plane:

0(x-2) + 0(y-1) + 0(z-3) = 0

Simplifying, we get:

0 = 0

This means that the tangent plane is the entire xyz-space, since any point satisfies this equation.

Therefore, the equation of the tangent plane to the given equation at the point (2,1,3) is 0 = 0.

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Answer:

a) 30.24%

b) 15.12%

c) 0.09%

Step-by-step explanation:

a) 5 digit zip code with no repeated digits

Firstly, there are 10 digits. After each digit in the zip code, one is used up.

The total number of zip codes possible is 10^5, or 100,000

The number of zip codes with no repeated digits can be found with:

(10-0)*(10-1)*(10-2)*(10-3)*(10-4)

which equals

10 * 9 * 8 * 7 * 6 = 30240

30240 divided by 100,000 is 0.3024

b) same process, but the numbers used are only 1-9.

(9-0)*(9-1)*(9-2)*(9-3)*(9-4) = 9 * 8 * 7 * 6 * 5 = 15120

15120 divided by 100,000 is 0.1512

c) back to using 1-10, but with a 1/10 chance for three digits

(10-0)*(10-1)*(1)*(1)*(1) = 8 * 9 = 90

90 divided by 100,000 is 0.0009

The probability of a 5-digit zipcode having no repeated digits is 0.3024, no 0's is 0.59049, and exactly two 1's and two 3's is 0.0012.

The probability of a 5-digit zipcode having no repeated digits, no 0's, and exactly two 1's and two 3's can be calculated using the formula for probability, which is P(event) = a number of favorable outcomes/number of possible outcomes.

(a) No repeated digits:

The number of favorable outcomes is 10*9*8*7*6 since there are 10 choices for the first digit, 9 for the second, 8 for the third, 7 for the fourth, and 6 for the fifth.

The number of possible outcomes is 10^5 since there are 10 choices for each of the 5 digits. Therefore, the probability is (10*9*8*7*6)/(10^5) = 0.3024.

(b) No 0's:

The number of favorable outcomes is 9*9*9*9*9 since there are 9 choices for each of the 5 digits (excluding 0).

The number of possible outcomes is 10^5 since there are 10 choices for each of the 5 digits. Therefore, the probability is (9^5)/(10^5) = 0.59049.

(c) Exactly two 1's and two 3's:

The number of favorable outcomes is 5*4*3*2*1 since there are 5 choices for the first 1, 4 for the second 1, 3 for the first 3, 2 for the second 3, and 1 for the remaining digit.

The number of possible outcomes is 10^5 since there are 10 choices for each of the 5 digits. Therefore, the probability is (5*4*3*2*1)/(10^5) = 0.0012.

Therefore, the probability is 0.0012.

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Answer:

Step-by-step explanation:

Sale price of the coat:

Total of three items:

Add tax to get the total:

Answer:

7s

Step-by-step explanation:

17s-10=3(2s+1)

17s-10 = 7s

2s+1=3s

7s+3s=10

10-3=7s

The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.

The burning of fossil fuels is not an example of a human activity that directly threatens the biodiversity of species. While burning fossil fuels can contribute to climate change, which can have indirect impacts on biodiversity, such as changing habitats or altering migration patterns, it is not a direct threat to individual species or their populations.

On the other hand, the picking of flowers, overexploitation of resources, introduction of invasive species, and destruction of habitats are all examples of human activities that directly threaten the biodiversity of species. For example, overexploitation of resources such as fishing can lead to the depletion of fish populations, while the introduction of invasive species can outcompete and displace native species. The destruction of habitats, such as deforestation, can also have a direct impact on the populations of species that rely on those habitats for survival.

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These values are based on the t-distribution table and represent critical values for the given probabilities and degrees of freedom.

To answer this question, we need to use a t-table. The values we are looking for are the t-values associated with specific probabilities and degrees of freedom.

(a) t0.10, 10 = 1.372 (from the t-table, using 10 degrees of freedom and the probability of 0.10)

(b) t0.05, 10 = 1.812 (from the t-table, using 10 degrees of freedom and the probability of 0.05)

(c) t0.05, 21 = 1.721 (from the t-table, using 21 degrees of freedom and the probability of 0.05)

(d) t0.05, 60 = 1.671 (from the t-table, using 60 degrees of freedom and the probability of 0.05)

(e) t0.005, 60 = 2.660 (from the t-table, using 60 degrees of freedom and the probability of 0.005)

Note that we round all answers to three decimal places, as specified in the question. The values we have found are the t-values for the specified probabilities and degrees of freedom. These values can be used in calculations involving t-distributions.

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Answer:is 230

Step-by-step explanation:

230 i hoped i helped

Answer:

D 80

Step-by-step explanation:

step by step

350 +(-350)=0 + 5h = 750 + (-350) =400

5h/5 =400/5=80

h=80

Answer:

B. 4.09 cm²

Step-by-step explanation:

Let point O be the center of the circle.

As the center of the circle is the midpoint of the diameter, place point O midway between P and R.

Therefore, line segments OP and OQ are the radii of the circle.

As the radius (r) of a circle is half its diameter, r = OP = OQ = 5 cm.

As OP = OQ, triangle POQ is an isosceles triangle, where its apex angle is the central angle θ.

To calculate the shaded area, we need to subtract the area of the isosceles triangle POQ from the area of the sector of the circle POQ.

To do this, we first need to find the measure of angle θ by using the chord length formula:

\(\boxed{\begin{minipage}{5.8 cm}\underline{Chord length formula}\\\\Chord length $=2r\sin\left(\dfrac{\theta}{2}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the central angle.\\\end{minipage}}\)

Given the radius is 5 cm and the chord length PQ is 6 cm.

\(\begin{aligned}\textsf{Chord length}&=2r\sin\left(\dfrac{\theta}{2}\right)\\\\\implies 6&=2(5)\sin \left(\dfrac{\theta}{2}\right)\\\\6&=10\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{3}{5}&=\sin \left(\dfrac{\theta}{2}\right)\\\\\dfrac{\theta}{2}&=\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=2\sin^{-1} \left(\dfrac{3}{5}\right)\\\\\theta&=73.73979529...^{\circ}\end{aligned}\)

Therefore, the measure of angle θ is 73.73979529...°.

Next, we need to find the area of the sector POQ.

To do this, use the formula for the area of a sector.

\(\boxed{\begin{minipage}{6.4 cm}\underline{Area of a sector}\\\\$A=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Substitute θ = 73.73979529...° and r = 5 into the formula:

\(\begin{aligned}\textsf{Area of section $POQ$}&=\left(\dfrac{73.73979529...^{\circ}}{360^{\circ}}\right) \pi (5)^2\\\\&=0.20483... \cdot 25\pi\\\\&=16.0875277...\; \sf cm^2\end{aligned}\)

Therefore, the area of sector POQ is 16.0875277... cm².

Now we need to find the area of the isosceles triangle POQ.

To do this, we can use the area of an isosceles triangle formula.

\(\boxed{\begin{minipage}{6.7 cm}\underline{Area of an isosceles triangle}\\\\$A=\dfrac{1}{2}b\sqrt{a^2-\dfrac{b^2}{4}}$\\\\where:\\ \phantom{ww}$\bullet$ $a$ is the leg (congruent sides). \\ \phantom{ww}$\bullet$ $b$ is the base (side opposite the apex).\\\end{minipage}}\)

The base of triangle POQ is the chord, so b = 6 cm.

The legs are the radii of the circle, so a = 5 cm.

Substitute these values into the formula:

\(\begin{aligned}\textsf{Area of $\triangle POQ$}&=\dfrac{1}{2}(6)\sqrt{5^2-\dfrac{6^2}{4}}\\\\ &=3\sqrt{25-9}\\\\&=3\sqrt{16}\\\\&=3\cdot 4\\\\&=12\; \sf cm^2\end{aligned}\)

So the area of the isosceles triangle POQ is 12 cm².

Finally, to calculate the shaded area, subtract the area of the isosceles triangle from the area of the sector:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Area of sector $POQ$}-\textsf{Area of $\triangle POQ$}\\\\&=16.0875277...-12\\\\&=4.0875277...\\\\&=4.09\; \sf cm^2\end{aligned}\)

Therefore, the area of the shaded region is 4.09 cm².

Answer:

Jeff Bezos, is Amazon's founder, who's one of the richest people in the world.

The federal government won't require everyone to get vaccinated.

The federal government also won't required everyone in america to carry a passport.

New York recently because the first state to have a cov id passport.

Florida banned the co vid passport.

Restraunt owners think its against peoples rights to have a co vid passport, so they won't need them there!

Theatres are requiring a passport for the vaccine, due to wanting to fill the audience.

Heinz makes more ketchup than anyone

12 billions ketchup packets will be made this year from h einz, which is enough to reach the moon and back.

astronauts had a lot of ketchup in space

1 hundred and forty miles per hour is reached on the fasted roller coaster according to genius world records.

Step-by-step explanation:

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(1/2)²-6(2-2/3)

(1/2)²-6(2-2/3)

LCM=6

1/2²-6(2/1-2/3)

12-4

______

6

1/2²-6(8/6)

1-(48/36)

1-(4/3)

= -4/3

\(g(a+h)=a^{2} + h^{2}+2ah+2\)

The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer:

11

Step-by-step explanation

We first let the side of the square be defined as x.

Therefore, we have ax/2 = 4, and bx/2= 3. Where a and b are the legs of the triangles with areas 4 and 3 respectively.

For the Triangle with area 6, we then have ((x-a)(x-b))/2 = 6. Expanding gives us x^2-bx-ax+ab=12. Using the equation above and plugging in values where bx = 6, ax=8, a = 8/x, and b = 6/x. We get

x^2-6-8+48/x^2 = 12.

Simplified gives us,

x^4-26x^2+48.

Factored gives us,

((x^2-2)(x^2-24).

Since the area cannot be any negative values and bigger than 6 (since there is already a triangle with area 6), we then have x^2 = 24.

Therefore a of unshaded region = 24-6-4-3= 11

The area of a shape is the amount of space it occupies.

The area of the unshaded triangle is: \(\mathbf{x^2 - 13}\)

The area of three triangles are:

\(\mathbf{A_1 = 3}\)

\(\mathbf{A_2 = 4}\)

\(\mathbf{A_3 = 6}\)

Assume the side length of the square is x.

So, the area of the square is:

\(\mathbf{Area = x \times x}\)

\(\mathbf{Area = x^2}\)

The area of the unshaded triangle (A) is the sum of the areas of the three triangles, subtracted from the area of the square

So, we have:

\(\mathbf{A = Area - (A_1 + A_2 + A_3)}\)

Substitute known values

\(\mathbf{A = x^2 - (3+4+6)}\)

\(\mathbf{A = x^2 - 13}\)

Hence, the area of the unshaded triangle is: \(\mathbf{x^2 - 13}\)

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The solution to the system (a) is "NO solution"

From the question, we have the following parameters that can be used in our computation:

4m-3n=27

8m-6n=16

Multiply (1) by 2

So, we have

8m-6n=54

8m-6n=16

Subtract the equations

So, we have the following representation

0 = 38

The above equation is false

Hence, the system has no solution

The second system of equation has missing details

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The constant of proportionality for x gallons water and y miles is k = 25

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality.

Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.

A proportionate connection is simple to represent as a straight line on a coordinate plane. It is a straight line because it is directly proportional; the slope serves as the constant of proportionality.

The proportionate change along the x and y axes never varies, hence the slope or increase is constant.

According to the question,

x(gallons)     y(miles)

 1                       25

 2                      50

 3                      75

 4                      100

As we know, If y is proportional to x

=> y ∝ x

=> y = kx , where k is constant of proportionality

Using the table,

when x = 1 => y = 25

=> 25 = k(1)

=> k = 25

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Answer:

1. 130

2. 0=120

Step-by-step explanation:

1. 7*10+9*7-3

pemdas

70+63-3

130

2. kind of hard to explain but this is what i got

(1+9) + (1+4)*2 = 140

pemdas

10+5*2=140

10+10= 140

20=140

you could subtract at this point...?

140-20=120

0=120

not much context but this is what i got

The total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds i.e., it takes the elevator 135 seconds to complete the entire trip.

The remote control car travels forward for 4 seconds at a speed of 2.0 m/s, then stops for 3 seconds, and finally travels backward for 3 seconds at a speed of 1.5 m/s.

The elevator travels from the lobby to the 36th floor in 45 seconds, stops for 15 seconds, descends to the 28th floor, stops for 15 seconds again, and returns to the lobby.

The total time taken by the elevator to complete this trip is calculated by adding up the times for each segment.

For the remote control car, it travels forward at 2.0 m/s for 4 seconds, covering a distance of 2.0 m/s * 4 s = 8 meters.

It then stops for 3 seconds, and finally travels backward at 1.5 m/s for 3 seconds, covering a distance of 1.5 m/s * 3 s = 4.5 meters.

Therefore, the total distance covered by the car is 8 m + 4.5 m = 12.5 meters.

For the elevator, it takes 45 seconds to go from the lobby to the 36th floor, and it stops for 15 seconds to let people off.

Similarly, it takes 15 seconds to go from the 36th floor to the 28th floor, and another 15 seconds to let people off.

Finally, it takes 45 seconds to return from the 28th floor to the lobby.

Therefore, the total time taken by the elevator for the entire trip is 45 s + 15 s + 15 s + 15 s + 45 s = 135 seconds.

In conclusion, it takes the elevator 135 seconds to complete the entire trip, including stops at different floors, based on the given information.

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Answer: I believe it is A.