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a.) The standard deviation is(round to two decimal places)
b.) The variance is(round to one decimal place)

c.) The range is

Hence, the arrangements to the quadratic equation  (3x-1)(x-2) = 5x + 2 are x = and x = 4.

To unravel the quadratic equation  (3x-1)(x-2) = 5x + 2, let's to begin with grow the cleared out side of the equation:

(3x - 1)(x - 2) = 5x + 2

Growing the condition:

3x^2 - 6x - x + 2 = 5x + 2

Streamlining the condition:

3x^2 - 7x + 2 = 5x + 2

Another, let's move all terms to one side of the condition:

3x^2 - 7x - 5x + 2 - 2 =

Combining like terms:

3x^2 - 12x =

Presently, we have a quadratic condition in standard shape: ax^2 + bx + c = 0, where a = 3, b = -12, and c = 0.

To fathom the quadratic equation, able to calculate out the common calculate of x:

x(3x - 12) =

From this equation, we are able see that the esteem of x can be or unravel for 3x - 12 = 0:

3x - 12 =

Including 12 to both sides:

3x = 12

Isolating both sides by 3:

x = 4

Hence, the arrangements to the condition (3x-1)(x-2) = 5x + 2 are x = and x = 4.

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The value of "c" such that the random variable cY has an x² distribution is 4.

To find the value of "c" such that the random variable cY has a chi-squared (x²) distribution, we need to consider the properties of the chi-squared distribution and the given expression for Y.

The chi-squared distribution with "k" degrees of freedom is obtained by summing the squares of "k" independent standard normal random variables. Each standard normal variable contributes one degree of freedom to the chi-squared distribution.

In the given expression for Y, we have two squared terms: (X₁ + X₃ + X₅ + X₇)² and (X₂ + X₁ + X₆ + X₈)². To obtain an x² distribution, we need to rewrite the expression in terms of squared standard normal random variables.

To achieve this, we can divide each squared term by its corresponding degrees of freedom and take the square root:

Y = (X₁ + X₃ + X₅ + X₇)² + (X₂ + X₁ + X₆ + X₈)²

= (1/4)(X₁ + X₃ + X₅ + X₇)² + (1/4)(X₂ + X₁ + X₆ + X₈)²

Now, we can rewrite Y as:

Y = (1/4)χ²₁ + (1/4)χ²₁

Here, χ²₁ and χ²₂ represent chi-squared random variables with 1 degree of freedom each.

To obtain an x² distribution, we need to make the coefficients of the chi-squared random variables equal to their degrees of freedom. In this case, we want the coefficient to be 1.

So, setting the coefficient of χ²₁ to 1, we get:

(1/4) = 1/c

Solving for "c", we find:

c = 4

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Answer:

c) 54 feet

Step-by-step explanation:

Let the  side of the square be x

perimeter = 4x

⇒ 36 = 4x

⇒ x = 36/4 = 9 feet

Each side is 9 feet

When we join the two squares, it becomes a rectangle with

b = 9

l = 9 + 9 = 18

The perimeter of a rectangle is 2(l + b)

perimeter = 2(18 + 9)

= 2(27)

= 54 feet

Answer:

Option (c) 54 feet

Step-by-step explanation:

Perimeter of one square is 36 feet.

Side of square = 36 / 4 = 9 feet

When combined together one side of each square merged.

So, the perimeter of rectangular shape will be;

(9+9+9) + (9+9+9)

27 + 27

54 feet.

The future value of the loan, or the total amount due at the end of 6 months, is $9,450.

We can use the following formula to calculate the future value of a loan:

[tex]A = P + P * r * t[/tex]

Given: $9,000 principal (P).

10% interest rate (r) = 0.10

6 months is the time period (t).

When we enter these values into the formula, we get:

A=9,000+9,000*0.10*6/12

First, compute the interest portion:

Interest is calculated as = 9,000*0.10*6/12=450

We may now calculate the future value:

A=9,000+450=9,450

As a result, the loan's future value, or the total amount payable in 6 months, is $9,450.

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The total surface area of the pyramid is option c [tex]72 cm^2[/tex].

The total surface area of a pyramid is given by the formula;S= ½Pl + BWhere B is the area of the base and P is the perimeter of the base.

To find the perimeter, add the length of all the sides of the base. Here, the base of the pyramid is a square with sides measuring 6 cm each.Therefore, its perimeter = 6 + 6 + 6 + 6 = 24 cm.

Now, to find the total surface area, we need to find the area of all four triangular faces. To find the area of one of the triangular faces, we can use the formula:

A = 1/2bhWhere b is the base of the triangle and h is the height.

To find the height, we can use the Pythagorean theorem:

[tex]h = \sqrt(6^2 - 3^2) = \sqrt(27) = 3 \sqrt(3)[/tex]

Therefore, the area of one of the triangular faces is:

A = 1/2bh = [tex]1/2(6)(3\sqrt(3)) = 9\sqrt(3)[/tex]

We have four triangular faces, so the total area of the triangular faces is:

[tex]4(9\sqrt(3)) = 36\sqrt(3)[/tex]

Finally, we can find the total surface area by adding the area of the base and the area of the triangular faces:

S = ½Pl + B = [tex]1/2(24)(3\sqrt(3)) + 6^2 = 36\sqrt(3) + 36 = 36(\sqrt(3) + 1).[/tex]

Therefore, the total surface area of the pyramid is 36(sqrt(3) + 1) cm², which is approximately 72 cm². Hence, the correct option is C. [tex]72 cm^2[/tex].

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Hello!

[tex]x^2 - 3x + \dfrac{9}{4} = 0\\\\4x^2 - 12x + 9 = 0\\\\\\x = \dfrac{-b\±\sqrt{b^2 - 4ac} }{2a} \\\\\\x = \dfrac{-(-12)\±\sqrt{(-12)^2 - 4 \times 4 \times 9} }{2 \times 4} \\\\\\\\boxed{x = \dfrac{3}{2} }[/tex]

The resulting equation after multiplying the first equation by 2 and subtracting the second equation is:

-5y = -375

1. Given equations:

  - x + 3y = 350    (Equation 1)

  - 2x + 4y = 625   (Equation 2)

2. Multiply Equation 1 by 2:

  - 2(x + 3y) = 2(350)

  - 2x + 6y = 700    (Equation 3)

3. Subtract Equation 2 from Equation 3:

  - (2x + 6y) - (2x + 4y) = 700 - 625

  - 2x - 2x + 6y - 4y = 75

  - 2y = 75

4. Simplify Equation 4:

  -2y = 75

5. To isolate the variable y, divide both sides of Equation 5 by -2:

  y = 75 / -2

  y = -37.5

6. Therefore, the resulting equation is:

  -5y = -375

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The initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex] and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.

To calculate the initial stress in the tie bar, we can use the formula:

Stress = Load/Area

The area of the tie bar can be calculated using the formula for the area of a circle:

Area = π * [tex](diameter/2)^2[/tex]

Plugging in the values, we get:

Area = π * [tex]10 mm^{2}[/tex] = π *[tex](5 mm)^2[/tex] = 78.54 [tex]mm^2[/tex]

Converting the area to square meters, we have:

Area = 78.54 [tex]mm^2[/tex]* (1 m^2 / 1,000,000 [tex]mm^2[/tex]) = 7.854 × 1[tex]0^-5 m^2[/tex]

Now we can calculate the initial stress:

Initial Stress = 100 kN / 7.854 ×[tex]10^-5 m^2[/tex] = 1.273 × [tex]10^9 N/m^2[/tex]To calculate the resultant stress when the temperature rises to 50°C, we need to consider the thermal expansion of the tie bar. The change in length can be calculated using the formula:

ΔL = α * L0 * ΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature.

The induced force in the bar can be calculated using the formula:

Induced Force = Initial Stress * Area + E * α * ΔT * Area

Plugging in the values, we get:

Induced Force = (1.273 × 10^9 N[tex]m^2[/tex] * 7.854 × [tex]10^-5 m^2[/tex]) + (200 × [tex]10^9[/tex] N/[tex]m^2[/tex] * 14 × [tex]10^-6[/tex] /K * (50 - 15) K * 7.854 × [tex]10^-5 m^2[/tex])

Simplifying the equation, we find:

Induced Force = 100.03 kN

Therefore, the initial stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], the resultant stress is 1.273 × [tex]10^9[/tex] N/[tex]m^2[/tex], and the induced force in the bar when the temperature reaches 50°C is 100.03 kN.

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The probable question may be:

A rigidly held tie bar in a heating chamber has a diameter of 10 mm and is tensioned to a load of 100 kN at a temperature of 15°C. What is the initial stress, the resultant stress and what will be the induced force in the bar when the temperature in the chamber has risen to 50°C? E= 200 GN/ m2 and the coefficient of linear expansion of the material for tie bar = 14 × 10−6 /K.

The z - score z = (x - μ)/σ equals z = (p' - p)/[√(pq/n)]

The z-score is the statical value used to determine probability in a normal distribution

Given the z-score z = (x - μ)/σ where

We need to show that

z = (p' - p)/√(pq/n)

We proceed as follows

Now, the z-score

z = (x - μ)/σ

Substituting in the values of μ and σ into the equation, we have that

So, z = (x - μ)/σ

z = (x - np)/[√(npq)]

Now, dividing both the numerator and denominator by n, we have that

z = (x - np)/[√(npq)]

z = (x - np) ÷ n/[√(npq)] ÷ n

z = (x/n - np/n)/[√(npq)/n]

z = (x/n - p)/[√(npq/n²)]

z = (x/n - p)/[√(pq/n)]

Now p' = x/n

So, z = (x/n - p)/[√(pq/n)]

z = (p' - p)/[√(pq/n)]

So, the z - score is z = (p' - p)/[√(pq/n)]

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Answer:

Sure. First, we need to find the inverse function of f(x). We can do this by using the following steps:

1. Let y = f(x).

2. Solve the equation y = 4x3 + 6x - 10 for x.

3. Replace x with y in the resulting equation.

This gives us the following inverse function:

```

f^-1(y) = (-1 + sqrt(1 + 12y)) / 2

```

Now, we need to find f^-1′ (0). This is the derivative of the inverse function evaluated at y = 0. We can find this derivative using the following steps:

1. Use the chain rule to differentiate f^-1(y).

2. Evaluate the resulting expression at y = 0.

This gives us the following:

```

f^-1′ (0) = (3 * (1 + 12 * 0) ^ (-2/3)) / 2 = 1.5

```

Therefore, f^-1′ (0) = 1.5.

Step-by-step explanation:

The row operation on the matrix [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex] is [tex]\left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as

1/2R₁

This means that we divide the entries on the first row by 2

Using the above as a guide, we have the following:

[tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

Hence, the row operation on the matrix is [tex]\left[\begin{array}{ccc|c}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right] = \left[\begin{array}{ccc|c}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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Answer:10cm 5cm 7 Jim's lunch box is in the shape of a half cylinder on a rectangular box. To the nearest whole unit, what is a The total volume it contains? b The total area of the sheet metal in 10 in needed to manufacture it? This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts

Step-by-step explanation:

Answer:

Step-by-step explanation:Angle EDH=Angle FDH, so A must be correct.

Also, we don't have more information to prove B, C, D is right

Answer:

A.

Step-by-step explanation:

An angle bisector is a line, ray, or segment that divides an angle into two equal parts. It divides the angle into two congruent or equal angles. The angle bisector originates from the vertex of the angle and extends towards the interior of the angle. It essentially cuts the angle into two smaller angles of equal measure.

Answer:

(x + 13)(x - 7) = 69

x² + 6x - 91 = 69

x² + 6x - 160 = 0

(x + 16)(x - 10) = 0

x = 10, so the area of the original square is 100 m².

The sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.

To add the given time durations, we start by adding the seconds:

12 sec + 25 sec = 37 sec.

Since 60 seconds make a minute, we carry over any excess seconds to the minutes place, which gives us a total of 37 seconds. Moving on to the minutes, we add 30 min + 16 min = 46 min.

Again, we carry over any excess minutes to the hours place, resulting in a total of 46 minutes.

Finally, we add the hours: 5 hr + 2 hr = 7 hr.

Thus, the sum of the two time durations is 7 hours, 46 minutes, and 37 seconds.

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Given the following diagram: We need to find the coordinates of triangle ABC, translate the triangle (-2, 5) and draw the new image on the grid above, and determine the amount each coordinate will move on the x-axis and y-axis during translation.

1. Coordinates of triangle ABC:A = (2, 6)B = (5, 8)C = (6, 3)2. Translation of triangle (-2, 5)The translation of a triangle can be done by adding or subtracting a constant value from the x-coordinates and y-coordinates of each vertex of the original triangle.

For example, if we want to translate a triangle by 3 units to the right and 2 units up, we would add 3 to the x-coordinates and add 2 to the y-coordinates of each vertex of the original triangle. Using this method, we can translate the triangle (-2, 5) as follows:

New coordinates of A = (2 + (-2), 6 + 5) = (0, 11)New coordinates of B = (5 + (-2), 8 + 5) = (3, 13)New coordinates of C = (6 + (-2), 3 + 5) = (4, 8)3. New image of triangle (-2, 5)The new image of the triangle (-2, 5) is shown in the following diagram:4. Amount each coordinate moves on x-axis During translation, each coordinate moves 2 units to the right (from -2 to 0).5. Amount each coordinate moves on y-axis During translation, each coordinate moves 6 units up (from 5 to 11).

Therefore, the coordinates of the translated triangle image are (0, 11), (3, 13), and (4, 8).

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Answer:

[tex]y = |x - 2| + 3[/tex]

The correct answer is C.

Answer:

x = 4

Step-by-step explanation:

By property, if two tangents are drawn from an external point , then they are equal

⇒ 2x + 3 = 11

⇒ 2x = 11 - 3

⇒ 2x = 8

⇒ x = 8/2

⇒ x = 4

Answer:

x = 4

Step-by-step explanation:

To find the value of x, we can use the Two-Tangent Theorem.

The Two-Tangent Theorem states that if two tangent segments are drawn to a circle from the same external point, the lengths of the two tangent segments are equal.

Therefore:

[tex]\begin{aligned}AD &= AB\\\\2x+3&=11\\\\2x+3-3&=11-3\\\\2x&=8\\\\\dfrac{2x}{2}&=\dfrac{8}{2}\\\\x&=4\end{aligned}[/tex]

Therefore, the value of x is 4.

The function f(x) and the inverse function h(x) for which the function f(x) is defined by the values (0,3), (1,1), (2,-1) are f(x) = 3 -2x and h(x) = [tex]\frac{3 - x}{2}[/tex]

A function is a rule which takes each member x of a set and assigns, or maps it to the same value y known at its image.x → Function → yA letter such as f, g or h is often used to stand for a function.

The Function which squares a number and adds on a 3, can be written as f(x) = x2+ 5.

Let the linear function be f(x) = mx + cwhen x = 0, f(x) = 33 = m(0) + cTherefore, c = 3

when x = 1, f(x) = 11 = m(1) + c but c = 31 = m + 3

Therefore m = 1 - 3, which is -2

The linear equation f(x) = 3 - 2x

To solve for inverse function h(x)let y = 3 - 2xmaking x the subject of the equation2x = 3 - yx =[tex]\frac{3 - y}{2}[/tex]replacing x with h(x) and y with x, we haveh(x) = [tex]\frac{3 - x}{2}[/tex]

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Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

[tex]\log 3+ 9\log x +4 \log y[/tex]

Step-by-step explanation:

Given logarithmic expression:

[tex]\log 3x^9y^4[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log 3+\log x^9 +\log y^4[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\log 3+ 9\log x +4 \log y[/tex]

The surface area of a cylinder is 284m² and it's volume is 366.9m³

To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:

From the given question, the data are;

a. The surface area of the cylinder is;

SA = 2π(4)² + 2π(4)(7.3)

SA = 283.999≈284m²

b. The volume of the cylinder is

v = πr²h

v = π(4)²(7.3)

v = 366.9m³

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[tex] \sf \hookrightarrow \: {8}^{2} + {b}^{2} = {17}^{2} [/tex]

[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 17 \times 17[/tex]

[tex] \sf \hookrightarrow \: 8 \times 8 + {b}^{2} = 289[/tex]

[tex] \sf \hookrightarrow \: 64 + {b}^{2} = 289[/tex]

[tex] \sf \hookrightarrow \: {b}^{2} = 289 - 64[/tex]

[tex] \sf \hookrightarrow \: {b}^{2} = 225[/tex]

[tex] \sf \hookrightarrow \: b = \sqrt{225} [/tex]

[tex] \sf \hookrightarrow \: b = \sqrt{15 \times 15} [/tex]

[tex] \sf \hookrightarrow \: b = 15[/tex]

The length of the unknown side x using the concept of similar triangles is: x = 4

Similar triangles are referred to as triangles that have the same shape but different sizes. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, their corresponding angles are the same and their corresponding side proportions are the same.

Now, we are told that triangle PQR is similar to Triangle STU and as such their corresponding sides are similar and therefore to find the missing side x, we have:

12/x = 15/5

x = (12 * 5)/15

x = 60/15

x = 4

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The expression for m<3 is 349° - 7x.

To find the measure of angle 3 (m<3), we need to apply the angle sum property, which states that the sum of the angles around a point is 360 degrees.

In the given figure, angles 1, 2, 3, and 4 form a complete revolution around the point. Therefore, we can write:

m<1 + m<2 + m<3 + m<4 = 360°

Substituting the given angle measures, we have:

(x + 6)° + (2x + 9)° + m<3 + (4x - 4)° = 360°

Combining like terms:

7x + 11 + m<3 = 360°

To isolate m<3, we subtract 7x + 11 from both sides:

m<3 = 360° - (7x + 11)

m<3 = 360° - 7x - 11

m<3 = 349° - 7x

Therefore, the expression for m<3 is 349° - 7x.

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Answer:

A) No solutions

Step-by-step explanation:

First of all, we know that option B will always be incorrect. You cannot have two solutions. To illustrate this, try drawing two lines. You will find that they will either intersect once (one solution), or they will not intersect, (no solutions, parallel lines), or they are the same line and thus they will always intersect (infinitely many solutions).

With that in mind, let's solve the equation.

4x-4-5x=7-x+5

First, combine all like terms.

-x-4=12-x

Now add 4 to both sides to leave x by itself.

-x=16-x

This statement cannot be true. Therefore, this equation has no solutions (parallel lines. One line starts from 0, or the origin. That line is -x. The other line starts from 16. That line is -x+16.)

Hope this helps!

Answer:

?

Step-by-step explanation:

?

Answer/Step-by-step explanation:

C., the first proof we would be given if a little box is shown, which indicates a 90 degree angle at the place where to lines touch  in a T kind of manor. So C is the answer.

Answer:

[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4

Step-by-step explanation:

(8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex]) - (4 + [tex]x^{3}[/tex] + 6x)

= 8x + 2[tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4 - [tex]x^{3}[/tex] - 6x

= 2x + [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] - 4

= [tex]x^{3}[/tex] - 4[tex]x^{2}[/tex] + 2x - 4

The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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