GivenG​=(G;∗)is group andH​≤G​and given setN(H)N(H)={g∈G∣gHg−1=H}Prove thatH​◃G​↔N(H)=G

Answer: x = 47.2°

Step-by-step explanation:

     We can use a trigonometry function to solve this question since it's a right triangle.

     Equation:

tanx = [tex]\frac{27}{25}[/tex]

     The tangent inverse of both sides of the equation:

[tex]\displaystyle tan^{-1} (\text{tan}x)=(\frac{27}{25} )tan^{-1}[/tex]

x = 47.2°

The coordinates of point L are (s/2, s√3/2). If we know the value of s, we can determine the specific coordinates of point L.

To determine the coordinates of point L in an equilateral triangle with vertices J and K, we first need to know the location of J and K.

Since the triangle is equilateral, the distance from J to K is the same as the distance from J to L or from K to L. Let's assume that the side length of the equilateral triangle is s. Then, the distance from J to K is also s. We can assume that J is located at the origin (0,0), and K is located at (s,0).

To find the coordinates of point L, we can use some trigonometry. Let's draw a line from point K to point L, and let the angle between this line and the x-axis be θ. Since the triangle is equilateral, this angle is 60 degrees.

The x-coordinate of point L is then given by s cos θ. Since cos 60 = 1/2, the x-coordinate of point L is s/2.

The y-coordinate of point L is given by s sin θ. Since sin 60 = √3/2, the y-coordinate of point L is s√3/2.

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Answer:

(a) Since Zul's password consists of 4 digits and the first three digits are 970, there is only one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/10.

(b) If there are three 1s in the password, there is only one possible arrangement for the other digit. There are four places where the other digit can be placed, so there are four possible passwords. Thus, the probability to unlock the screen in one attempt is 4/10^4, which simplifies to 1/2500.

(c) If the last two digits are 00, there is only one possible arrangement for the first two digits. There are ten possible digits for the third digit and one possible digit for the fourth digit. Thus, the probability to unlock the screen in one attempt is 1/(101010*1), which simplifies to 1/1000.

Using synthetic division, h(2) = -9.

To find h(2) using synthetic division, we will divide the polynomial h(z) by (z-2). The steps are as follows:

1. Write the coefficients of the polynomial in a row: 2 -10 20 -25 3
2. Write the value of z we are dividing by in the upper left corner: 2 | 2 -10 20 -25 3
3. Bring down the first coefficient: 2 | 2 -10 20 -25 3
      -------------------
          2
4. Multiply the first coefficient by the value of z and write the result below the second coefficient: 2 | 2 -10 20 -25 3
      -------------------
          2   4
5. Add the second coefficient and the result from step 4: 2 | 2 -10 20 -25 3
      -------------------
          2  -6
6. Repeat steps 4 and 5 for the remaining coefficients: 2 | 2 -10 20 -25 3
      -------------------
          2  -6  8  -6
7. The last number in the bottom row is the remainder: 2 | 2 -10 20 -25 3
      -------------------
          2  -6  8  -6  -9
8. The value of h(2) is the remainder, so h(2) = -9.

Therefore, the answer is h(2) = -9.

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Answer:

Area of a triangle =L*W

A= 45*15

A=270cm²

The equation that describes the plant's height is y = 3 + 0.5x .

The equation that describes the plant's height is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.

The general form of a linear equation is:

y = mx + c

Where:

m = slope

c = intercept

Plant's height = starting height + (rate of growth x number of weeks)

y = 3 + (0.5 x x)

y = 3 + 0.5x

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Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37

A = P(1 + r/n)^nt

Where

P = $1500

r = 3.7% = 0.037

n = monthly = 12

t = 10 years

So,

A = P(1 + r/n)^nt

A = 1,500.00(1 + 0.037/12)^(12×10)

A = 1,500.00(1 + 0.0030833333333333)¹²⁰

A = $2,170.37

Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.

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The key shows that 1|1 represents the score 11.

The stem-and-leaf plot that depicts the data set accurately is as follows:

Season Points for the 2021 Riverside Red Dragon Football

0 | 0 3

1 | 0 1 7 7 7 7 7

2 | 0 0 2 4 8 8

3 | 1 3

Key: 1|1 = 11

The stems represent the tens digit and the leaves represent the ones digit in this stem-and-leaf plot, which accurately depicts the frequency of each score in the data set. For instance, the stem 2 and the leaves 0 and 0 indicate the two instances of the score 20, which appears twice. The score 11 is represented by the key as 1|1.

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Answer:

C is the answer

Answer: 210 ( it hope this is a best answer)

Step-by-step explanation:

2 hours and 20 minutes is 2 and a third hours. Multiply 90 by 2 and a third.

90 × 2.333

209.999

If you round to the nearest kilometer, the answer is 210 km

The slope of a line perpendicular to given line is 4.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The given equation of a line is x+4y=4.

Here, 4y=4-x

y=1-x/4

So, slope m is -1/4

The slope of a line perpendicular to given line is m1=-1/m2

Slope of perpendicular to line is -1/(-1/4)

= 4

Therefore, the slope of a line perpendicular to given line is 4.

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The slope of parallel line is,

m = - 1/4

And, Slope of perpendicular line are,

m = 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ x + 4y = 4

Now, We can write as;

⇒ x + 4y = 4

⇒ 4y = - x + 4

⇒ y = - 1/4x + 4

Hence, The slope of the line is,

⇒ y = - 1/4x + 4

⇒ dy/dx = - 1/4

⇒ m = - 1/4

Now, We know that;

The slope of parallel line are equal.

Hence, The slope of parallel line is,

m = - 1/4

And, Product of Slopes of perpendicular lines are - 1.

Hence, Slope of perpendicular line are,

m = - 1/ (- 1/4)

m = 4

Thus, The slope of parallel line is,

m = - 1/4

And, Slope of perpendicular line are,

m = 4

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angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

To answer this question, we need to use a protractor, a straightedge, and the given graph to estimate the height of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90°. The arc on the graph represents a portion of the blade tip's path. Assume the blade rotates counterclockwise and the blade is at an angle of 0° when the blade tip is directly to the right of the top of the vertical shaft. This position has been labeled as 0° on the graph.

Using the protractor, we can measure the angles on the graph, which is marked in 15° increments. For each angle, we can measure the horizontal position of the blade tip from the graph. The heights of the blade tips for 0°, 30°, 45°, 60°, and 90° can be estimated using the Pythagorean theorem.

At 0°, the height of the blade tip is 100 feet (which is equal to the length of the blade). At 30°, the height of the blade tip is 86.6 feet. At 45°, the height of the blade tip is 71.4 feet. At 60°, the height of the blade tip is 50 feet. At 90°, the height of the blade tip is 0 feet.

Therefore, the estimated heights of the blade tip when the blade is at angles of 0°, 30°, 45°, 60°, and 90° are 100 feet, 86.6 feet, 71.4 feet, 50 feet, and 0 feet, respectively.

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Answer: practice 2.  8 inches   practice 3. 220[tex]ft^2[/tex]  

practice 4. 78° , 78° , 102° , 102 ° Practice 5. 12.5

Step-by-step explanation:

(2,1) is a solution to the system of equations 8x+7y=11 and x+y=3.

Two or more expressions with an Equal sign is called as Equation.

To check if (2,1) is a solution to the system of equations:

8x + 7y = 11

x + y = 3

We substitute x = 2 and y = 1 into both equations:

For the first equation: 8(2) + 7(1) = 16 + 7 = 23

For the second equation: 2 + 1 = 3

Hence, we can see that both equations are true when x = 2 and y = 1.

Therefore, (2,1) is a solution to the system of equations.

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There will be 40 cans that contain between 11.95 and 11.98 ounces of drink.

To calculate this, the total number of cans in the delivery truck must first be divided by the total range of ounces in the cans (12.00-11.95 = 0.05). 1500/0.05 = 30000.

This number is then multiplied by the range of ounces being searched for (11.98-11.95 = 0.03). 30000*0.03 = 900.

Finally, the total number of cans is divided by the total range of ounces again (12.00-11.95 = 0.05). 900/0.05 = 40 cans.

Therefore, 40 cans contain between 11.95 and 11.98 ounces of drink.

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If p-hat is equal to 0.65, then the complement (q-hat) is equal to 0.35.

We must deduct p-hat from 1 to obtain the complement q-hat when p-hat is known. The complement is the probability that the event won't occur, which is the same as the likelihood of every other scenario that isn't the one we're interested in.

Take p-hat out of 1 to get:

q-hat = 1 - p-hat

The value of p-hat is 0.65, therefore replace it as follows:

q-hat = 1 - 0.65

Condense the phrase:

q-hat = 0.35

As a result, the complement q-hat is 0.35 if the p-hat is 0.65.

It's critical to keep in mind that the probabilities p-hat and q-hat are complimentary and always sum up to 1. The equation q-hat = 1 - p-hat can be used to quickly compute the other if the first is known.

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We have the following response after answering the given question: To interest the nearest penny, the balance in the account after 12 years is thus $17,821.76.

To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to calculate interest is with this approach. The most popular method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a friend and agrees to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The yearly percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.

Continuously compounded interest is calculated as follows:

[tex]V = Pe^(rt) (rt)[/tex]

where: V = the investment's final value

P is the original investment's principle.

r equals the yearly interest rate (as a decimal)

t is the duration of the investment, in years.

P = $8290, r = 0.06 (6% as a decimal), and t = 12 years in this example.

So, [tex]V = 8290e^(0.06*12) = $17,821.76[/tex]

To the nearest penny, the balance in the account after 12 years is thus $17,821.76.

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The total surface area of the two hemispherical domes is 6.16m^2

To find the TSA (total surface area) of two hemispherical domes, we need to first find the surface area of one hemispherical dome, and then multiply it by 2.

The surface area of one hemispherical dome can be found using the formula:

SA = 2πr^2

where r is the radius of the base of the hemisphere.

Given that the base radius of each hemisphere is 0.7m, the total diameter of each hemisphere is 1.4m (since the diameter is twice the radius), and therefore the radius is 0.7m.

So the surface area of one hemisphere is:

SA = 2π(0.7m)^2

= 3.08m^2

Therefore, the TSA of two hemispherical domes is:

TSA = 2 × SA

= 2 × 3.08m^2

= 6.16m^2

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We can expect 2 black horses out of a sample of 15 horses from the stable.

To determine how likely something is gonna occur, use probability. The event is typically stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty.

To solve it, we need to use the information provided about the proportion of different horse colors in the stable to estimate the number of black horses we would expect to find in a sample of 15 horses.

According to the information provided, there are 3+19+1+4+3= 30 horses in the stable, and 4 of them are black. Therefore, the proportion of black horses in the stable is:

4/30 = 0.1333...

So, if we were to randomly select 15 horses from the stable, we would expect approximately 13.33% of them to be black. To find the expected number of black horses in a sample of 15 horses, we can multiply the proportion by the sample size:

0.1333... x 15 = 1.999...

Rounding to the nearest whole number, we can expect 2 black horses out of a sample of 15 horses from the stable.

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a) The sales 2 months after the end of the campaign will be $29,600. b)  it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.

The sales 2 months after the end of the campaign can be found by plugging x = 2 into the equation:
S = 80,000e-0.5x
S = 80,000e-0.5*2
S = 80,000e-1
S = 80,000 * 0.37
S = 29,600

Therefore, the sales 2 months after the end of the campaign will be $29,600.

We can solve this by setting the equation equal to 1000 and solving for x:
1000 = 80,000e-0.5x
1000/80,000 = e-0.5x
0.0125 = e-0.5x
ln(0.0125) = ln(e-0.5x)
-4.81 = -0.5x
x = 9.62

Therefore, it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.

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The height of the plane is modeled by the linear equation:

height = 3000ft - 2000ft*t

If the rate at which the plane descends is constant, then the height is modeled by a linear equation.

We can write:

height = initial height - rate*time

We know that the initial height is 3000ft, and that the plane descends at ar ate of 2,000ft per minute, then we can write the linear equation:

height = 3000ft - 2000ft*t

Where t is the time in minutes.

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Complete question:

"an airplane 3,000 ft above the ground begin descending at a rate of 2,000 ft per minute​, which will be the height of the plane after t minutes?"

Answer:

5x4

Step-by-step explanation:

The dimensions of the rectangle are 20x16

The reducing factor is 0.25.

Multiple 20 * 0.25= 5

Multiple 16 * 0.25= 4

Therefore the new dimensions are 5x4.

The solution set in interval notation, 19(7 − x) ≥ 88 − 14x, is (-∞, 9]

To solve the inequality 19(7 - x) ≥ 88 - 14x, we will first distribute the 19 on the left side of the inequality and then combine like terms to isolate the variable x.

19(7 - x) ≥ 88 - 14x
133 - 19x ≥ 88 - 14x
-5x ≥ -45
x ≤ 9

Now, we can write the solution set in interval notation. Interval notation uses brackets or parentheses to indicate the endpoints of an interval. Brackets indicate that the endpoint is included in the interval, while parentheses indicate that the endpoint is not included.

Since x is less than or equal to 9, the solution set in interval notation is (-∞, 9]. This means that any value of x less than or equal to 9 will satisfy the inequality.

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The correct answer is for the equation is C, "minimizes the sum of the squared distances from the actual y-value to the predicted y-value," as explained below.

The least-squares regression line is a line that best fits the given data by minimizing the sum of the squared distances between the predicted y-value (ŷ) and the actual y-value (y) for each data point. In other words, the line is chosen so that the sum of the squares of the vertical distances between the data points and the line is as small as possible.

In this case, the equation provided represents the least-squares regression line for the given data, which suggests that for every unit increase in x, y increases by 0.5 units.

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The value of m and n is 5√2 and 5 respectively.

The hypotenuse side of a right-angled triangle's square is equal to the sum of the squares of its other two sides, according to Pythagoras' Theorem.

A right-angled triangle.

A 45° angle is found in a triangle.

The triangle is therefore a right-angled isosceles triangle.

Hence, n = 5.

To find m:

Apply Pythagoras' theorem,

m = √{n² + 5²}

m = √(25 + 25)

m = √50

m = 5√2

Therefore, m = 5√2.

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The following function can be used to find b:

b= 7d

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

7 boxes per day

=> For d days , the number  boxes will be 7d

total number of boxes

b= 7d

when b=  3,500 ,

3500= 7d

=> d= 3500/7 = 500 days

The following function can be used to find b:

b= 7d

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The vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

If k is a real number, then the vectors (1,k), (k,3k+18) are linearly independent precisely when k≠a,b, where a=-18 and b=1/3. This is because for the vectors to be linearly independent, the equation c1(1,k) + c2(k,3k+18) = (0,0) should only have the trivial solution of c1 = c2 = 0. If k = a or k = b, then there will be nontrivial solutions for c1 and c2, making the vectors linearly dependent.

To find the values of a and b, we can set the equations for the x and y components equal to 0 and solve for k:

c1 + c2k = 0

c1k + c2(3k+18) = 0

From the first equation, we can solve for c1 in terms of c2 and k:

c1 = -c2k

Substituting this into the second equation:

-c2k^2 + c2(3k+18) = 0

c2(-k^2 + 3k + 18) = 0

Since c2 cannot be 0, we can divide both sides by c2 and solve the quadratic equation for k:

-k^2 + 3k + 18 = 0

(k-1/3)(k+18) = 0

So k = 1/3 or k = -18. Therefore, the vectors are linearly independent precisely when k≠a,b, where a=-18 and b=1/3.

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There is no unit vector with a positive first component that is orthogonal to both u and v.

The unit vector we are looking for is (1/√14, √13/14, √15/14, -√12/14). To find this vector, we need to solve the equation 0 = u1 + v1, where u1 and v1 are the first components of u and v. From the given vectors, u1 = 1 and v1 = 6. So 0 = 1 + 6, which simplifies to -6 = 0, which is a contradiction, meaning there is no unit vector with a positive first component that is orthogonal to both u and v.

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The height of the kite from the ground is 620.5 feet.

The angle of elevation from your hand to a kite is 65∘ and the distance from your hand to the kite is 287 feet.

Therefore, the height of the kite when your hand is 5 feet from the ground can be found as follows:

The situation forms a right angle triangle. Therefore, the height of the kite can be found using Pythagoras's theorem.

Hence,

tan 65 = opposite / adjacent

tan 65 = h / 287

cross multiply

h = 287 × tan 65

h = 615.473486186

Therefore,

height of the kite = 615.473486186 + 5

height of the kite = 620.5 feet

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The volume of the oblique cone is  5887.5 ft³.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

We know, The volume of an oblique cone is, (1/3)×B×h.

Where h = height and B = area of the base.

Here the area of the base is, π(15)² = 706.5 ft², and the height is 25 feet.

Therefore, The volume is,

= (1/3)×706.5×25.

= 5887.5 ft³

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