Find the geometric mean of the two lo and 90

The total area of the rectangle and the two right-angled triangles is 50 square units.

What is meant by area?

Area refers to the measurement of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units, such as square meters or square feet.

What is meant by a rectangle?

A rectangle is a four-sided polygon with two pairs of parallel sides and four right angles. The opposite sides of a rectangle are equal in length, and the area can be calculated as length x width.

According to the given information

Area of rectangle = h * x

Area of one right-angled triangle = (1/2) * h * y

Total area of two right-angled triangles = 2 * (1/2) * h * y = h * y

Adding the area of the rectangle and the area of the triangles, we get the total area:

Total area = Area of rectangle + Total area of two right-angled triangles

Substituting the given values, we get:

Total area = (5 * 4) + (5 * 6)

Total area = 20 + 30

Total area = 50 square units

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Applying the inscribed angle theorem, the value of x is calculated as: 47 degrees.

If an inscribed angle intercepts an arc in a circle, according to the inscribed angle theorem, we have:

measure of inscribed angle = 1/2(measure of intercepted arc) or 1/2(measure of central angle)

x is an inscribed angle, while 94 degrees is a central angle. Therefore, we have:

x = 1/2(94)

x = 47 degrees.

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Answer: (a) Let the circle roll along the x-axis with the center at the origin. Then, the parametric equations of the cycloid are given by:

x = t - sin(t)

y = 1 - cos(t)

where t is the angle in radians that the circle has rotated from its initial position.

(b) The arclength of one period of the cycloid is given by the integral:

L = ∫(0,2π) √[dx/dt]^2 + [dy/dt]^2 dt

Substituting the parametric equations from part (a), we get:

dx/dt = 1 - cos(t)

dy/dt = sin(t)

Therefore,

[dx/dt]^2 + [dy/dt]^2 = 2 - 2cos(t)

Substituting back into the arclength integral, we get:

L = ∫(0,2π) √(2 - 2cos(t)) dt

This integral can be evaluated using the half-angle formula:

cos(t) = 1 - 2sin^2(t/2)

Substituting this into the integral and simplifying, we get:

L = 8∫(0,π/2) √(sin^3(t/2)) dt

This integral can be evaluated using a substitution u = cos(t/2), du = -sin(t/2)dt:

L = 16∫(0,1) √[(1-u^2)^3] du

This integral can be further simplified by making the substitution u = sin(θ):

L = 16∫(0,π/2) cos^4(θ) dθ

This integral can be evaluated using integration by parts and trigonometric identities. After some algebraic manipulations, we get:

L = 8π

Step-by-step explanation:

The retailer would pay $1,339.20 for 30 dozen work gloves.

One dozen is equal to 12, so 30 dozen would be equal to 360 gloves.

The wholesaler's list price for one dozen gloves is $62.

The discount given by the wholesaler is 28%

The retailer pays 100% - 28% = 72% of the list price.

The price the retailer pays for one dozen gloves is:

$62 x 0.72 = $44.64

Therefore, the price the retailer pays for 30 dozen gloves is:

$44.64 x 30 = $1,339.20

So the retailer would pay $1,339.20 for 30 dozen work gloves.

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Answer:

Example of the distributive property: a(b + c) = ab + ac

Question #1:

a) 6(3a + 2) = 18a + 12

b) 2(7 - 5y) = 14 - 10y

c) 3(r + 1/3) = 3r + 1

d) 8(2m - 3/8) = 16m - 3

e) 5(x/5 + 4) = x + 20

Question #2:  

a) 3y + 1/4 = 4

4 (3y + 1/4) = 4 (4)

12y + 1 = 16

b) x/6 + 7 = 10

6 (x/6 + 7) = 6 (10)

x + 42 = 60

c) 11/3 - 4c/3 = 2

3 (11/3 - 4c/3) = (3) 2

11 - 4c = 6

d) 2n - 1 = 1/2

2 (2n - 1) = 2 (1/2)

4n - 2 = 1

e) r/2 + 8 = 1/2

2 (r/2 + 8) = 2(1/2)

r + 16 = 1

Hope this helped!

The area of the parallelogram is 30 square inch.

A parallelogram is simply a quadrilateral with two pairs of parallel sides.

The area of parallelogram is expressed as:

A = base × height

From the diagram:

Plug the given values into the above equation and solve for area.

Area = base × height

Area = 10 in × 3 in

Area = 30 in²

Therefore, the area is 30 in².

Option D) 30 in² is the correct answer.

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The domain and the range of the function are given as follows:

The values of x of the function are from an open circle at x = -6 to a closed circle at x = 1, hence the domain is given as follows:

(-6, 1].

The minimum value of the function is y = -2, while the maximum value is an open circle at y = 4, hence the range of the function is given as follows:

[-2, 4).

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The correct answer is,

Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''

We have to given that;

Debt is usually expected in any of the following cases EXCEPT ....

Now, We know that;

it's important to note that there may be individual situations where debt is expected when buying a car.

Hence, The correct answer is,

Debt is usually expected in any of the following cases EXCEPT ''purchase of car.''

Thus, Option C is true.

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The inequality to represent the possible number of hours Kat can afford to book the DJ is 80x + 225 ≤ 970 and one possible length Kat can afford to book the DJ is 9 hours.

(a) Let x be the number of hours that Kat can book the DJ. Then, the total cost of the DJ is 80x, and the total cost of the party is 80x + 225.

Since Kat has $410 saved and will earn another $560, the total amount she can spend on the party is $410 + $560 = $970.

Therefore, we can write the following inequality to represent the possible number of hours Kat can afford to book the DJ:

80x + 225 ≤ 970

b) To solve for x, we can start by subtracting 225 from both sides of the inequality:

80x ≤ 745

Then, we can divide both sides by 80:

x ≤ 9.3125

Since Kat can only book the DJ in whole hours, the largest integer less than or equal to 9.3125 is 9. Therefore, one possible length Kat can afford to book the DJ is 9 hours.

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Answer:

CT is the perpendicular bisector of AB

Step-by-step explanation:

calculate the segments using x = 2

AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7

BT = x + 5 = 2 + 5 = 7

thus AT = BT

CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5

DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9

thus CT ≠ DT

∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°

Thus CT is the perpendicular bisector of AB

The value of x is given as follows:

x = 12.25

Similar triangles are triangles that share these two features listed as follows:

The proportional relationship for the side lengths in this problem is given as follows:

x/7 = 3.5/2

Applying cross multiplication, the value of x is obtained as follows:

2x = 7 x 3.5

x = 7 x 3.5/2

x = 12.25.

The triangle is given by the image presented at the end of the answer.

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Given statement "If we project the area of a hip roof onto a horizontal plane, it will appear as two triangles and two trapezoids"

Given statement is True.
Because, A hip roof has four sloping sides that meet at the top ridge, forming a pyramid-like shape. When projected onto a horizontal plane, the following shapes will appear:

Two triangles:

These are formed by the two ends of the roof, where the sloping sides meet the ridge.
Two trapezoids:

These are formed by the two sides of the roof, where the eave edges meet the ridge.
So, when projecting the area of a hip roof onto a horizontal plane, it will indeed appear as two triangles and two trapezoids.

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The series can be represented in summation notation as follows: ∑(n = 7 to 207) (4n - 1)

In this notation, the Greek letter sigma (∑) represents the summation symbol, and n represents the index of summation. The series starts from n = 7 and goes up to n = 207, with each term being (4n - 1). The notation "n = 7 to 207" indicates the range of values that n takes on in the summation. The expression (4n - 1) represents the general term in the series, which changes as n varies from 7 to 207.

Summation notation, denoted by the Greek letter sigma (∑), is a shorthand way to represent the sum of a sequence of numbers. In this case, the series you provided is:

7 + 11 + 15 + … + 203 + 207

The general term of the series, which changes as "n" varies, is (4n - 1). This means that for each value of "n", we substitute it into the expression (4n - 1) to get the corresponding term in the series. For example, when "n" is 7, the corresponding term is (4 * 7 - 1) = 27. When "n" is 11, the corresponding term is (4 * 11 - 1) = 43, and so on, up to "n" = 207.

The summation notation "∑(n = 7 to 207) (4n - 1)" represents the sum of all the terms in the series, where "n" takes on values from 7 to 207, and the term for each "n" is (4n - 1). This notation allows us to compactly represent the entire series in a concise mathematical form.

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Answer:

s=3

Step-by-step explanation:

Equation: s=(50-44)/2

First, do the operation(s) in parenthesis:

s=(50-44)/2

s=(6)/2

Next, do the division, since it's the last operation:

s=6/2

s=3

So, your answer is s=3

Answer:

100

Step-by-step explanation:

2 x [(7)^2+1]

2x(49+1)

2x(50)

100

By simplifying the given square root , we get Simplified Root : 6 xz • [tex]\sqrt{(2xz) }[/tex]

Factor 72 into its prime factors

          72 = 23 • 32

To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.

Factors which will be extracted are :

          36 = 22 • 32

Factors which will remain inside the root are :

          2 = 2

To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :

          6 = 2 • 3

At the end of this step the partly simplified square root looks like this:

        6 • [tex]\sqrt{ (2x3z3) }[/tex]

Simplify the Variable part of the square root

Rules for simplifing variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

   [tex]\sqrt{(x8)}[/tex]=x4

 [tex]\sqrt{ (x^6)}[/tex]=x-3

   (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

   [tex]\sqrt{ (x5)}[/tex]=x2•[tex]\sqrt{x}[/tex]

  [tex]\sqrt{ (x^7)}[/tex]=x-3•[tex]\sqrt{x}[/tex]

Applying these rules to our case we find out that

[tex]\sqrt{ (x3z3)}[/tex] = xz • [tex]\sqrt{(xz) }[/tex]

Combine both simplifications

      [tex]\sqrt{ (72x3z3)}[/tex] = 6 xz •[tex]\sqrt{(2xz) }[/tex]

Simplified Root :

6 xz • [tex]\sqrt{(2xz) }[/tex]

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Using trigonometric functions, we can find the value of w to be = 9.688cm.

The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, which return a range of numbers as their output. The angle, expressed in degrees or radians, is the domain of the trigonometric function of f(x) = sin, also referred to as the "trig function," and its range is [-1, 1]. In terms of their domain and scope, the other functions are comparable. Algebra, geometry, and calculus all make extensive use of trigonometric functions.

Here in the question,

We have a right-angled triangle.

Basse of the triangle = 8√3cm.

It's an isosceles triangle.

So, cos45° = w/8√3

⇒ 0.70 = w/8√3

Cross multiplying:

⇒ w = 0.70 × 8√3

⇒ w = 9.688 cm.

Therefore, the measure of the length of the side w = 9.688cm.

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1. The radius (r) of the space swept is 1.5 m; 2. The angle measure is 75°.

3. The formula to use is Area = ∅/360 * πr²; 4. Area of the space is approximately 1.47 m².

The formula to use to find the area of a sector is given as:

Area = ∅/360 * πr², where:

r is the radius; and ∅ is the angle measure.

From the image given, we will solve the problem as follows:

1. The radius (r) = 1.5 m

2. The angle measure (∅) = 75°

3. The formula is:

Area = ∅/360 * πr²

4. Plug in the values:

Area = 75/360 * π * 1.5²

Area ≈ 1.47 m²

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According to the concept of inequality, the maximum value of A is obtained when a = 2 and c = 28.

Let's assume that each minute of advertising attracts 40,000 viewers and each minute of comedy attracts 45,000 viewers. Therefore, the total audience (in thousands) that can be reached is given by:

A = 40a + 45c

Firstly, we know that the total time allotted for advertising and comedy cannot exceed 30 minutes. Therefore, we can rewrite the inequality as:

a + c ≤ 30

Solving for c, we get:

c ≤ 30 - a

Now, we can substitute this expression for c in the equation for A:

A = 40a + 45c

A = 40a + 45(30 - a)

A = 1350 - 5a

To maximize A, we need to find the value of a that will result in the maximum value of A. Taking the derivative of A with respect to a and setting it equal to zero, we get:

dA/da = -5 = 0

a = 0

This does not make sense, as a cannot be zero. Therefore, we need to check the endpoints of the interval [2,4] to see if they give a maximum value for A.

When a = 2, we get:

A = 40(2) + 45c

A = 80 + 45c

Substituting c = 30 - a, we get:

A = 80 + 45(30 - 2)

A = 80 + 1350

A = 1430

When a = 4, we get:

A = 40(4) + 45c

A = 160 + 45c

Substituting c = 30 - a, we get:

A = 160 + 45(30 - 4)

A = 160 + 1215

A = 1375

This means that the producer should allocate 2 minutes for advertising and 28 minutes for the comedy program in order to maximize the number of viewers.

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a) The conjugate of the denominator is given as follows: 2 - 14i.

b) The division has the result given as follows: 0.375 - 1.15i.

A complex number is a number that is composed by a real part and an imaginary part, as follows:

z = a + bi.

In which:

The division for this problem is given as follows:

(16 - 3i)/(2 + 14i).

For the conjugate of the denominator, we keep the real part, changing the sign of the imaginary part, hence it is given as follows:

2 - 14i.

Hence we can solve the division multiplying by the conjugate, considering that i² = -1, as follows:

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (32 - 224i - 6i + 42)/(4 + 196)

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = (74 - 230i)/200

(16 - 3i)/(2 + 14i) x (2 - 14i)/(2 - 14i) = 0.375 - 1.15i.

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Answer:

12

Step-by-step explanation:

4 x 4= 16 so 4 x 3=12 and 3/4 = 4 x 3

We can use a normal probability model to represent the distribution of sample means when the sample size is large enough to ensure that sample means will be normally distributed, option (C) is correct.

The central limit theorem (CLT) states that when sample sizes are sufficiently large (typically, n > 30), the distribution of sample means will be approximately normal, regardless of the distribution of the variable in the population.

This is because as the probability of sample size increases, the sample mean becomes a more reliable estimate of the population mean, and the variability in the sample means decreases. This results in a distribution that is bell-shaped and symmetric, similar to a normal distribution, option (C) is correct.

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– The question is inappropriate, The correct question is:

We can use a normal probability model to represent the distribution of sample means for which of the following reasons? check all that apply.

A) the sample is randomly selected

B) the distribution of the variable in the population is normally distributed

C) the sample size is large enough to ensure that sample means will be normally distributed flag –

Answer:

$2,611.9.

Step-by-step explanation:

To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.

Using the formula:

z = (x - μ) / σ

where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.

For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.

Looking up 0.02 in the z-table gives a z-score of approximately -2.05.

So we have:

-2.05 = (x - 3403) / 398

Solving for x, we get:

x = -2.05 * 398 + 3403 = $2,611.9

Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.

The femur length for someone with a height of 187 cm is; 55 cm

The formula for the equation of a line formed by 2 coordinates is;

(y2 - y1)/(x2 - x1) = (y - y1)/(x - x1)

Using the coordinates (30, 127) and (35, 139), we have;

(139 - 127)/(35 - 30) = (y - 127)/(x - 30)

12/5 = (y - 127)/(x - 30)

12(x - 30) = 5(y - 127)

12x - 360 = 5y - 635

5y = 12x + 275

Thus, when the height is y = 187 cm, we have;

5(187) = 12x + 275

935 = 12x + 275

12x = 935 - 275

12x = 660

x = 660/12

x = 55 cm

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a.

the value of s that yields the coordinate (2, 0) is 2.

b.

the value of s that yields the coordinate (9, 1) is estimated 9.055.

we  use the distance formula between the origin and point P on the path:

d(P) = √ (x^2 + y^2) = s

For the coordinate (2, 0), we have x = 2 and y = 0. So, we can plug these values into the distance formula and solve for s:

d(P) = √(x^2 + y^2)

= √t(2^2 + 0^2) = 2

For the coordinate (9, 1), we have x = 9 and y = 1. So, we can plug these values into the distance formula and solve for s:

d(P) = √t(x^2 + y^2)

= √t(9^2 + 1^2)

= √(82)

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We have (0, 1) and (3, 5) as two points on the line y = 4/3x + 1.

The equation y = 4/3x + 1 represents a line in slope-intercept form, where the coefficient of x (4/3) represents the slope of the line and the constant term (1) represents the y-intercept.

To select two points on the line, we can choose any values for x and use the equation to find the corresponding values of y.

For example, let's choose x = 0:

y = 4/3x + 1

y = 4/3(0) + 1

y = 1

So one point on the line is (0, 1).

Now let's choose x = 3:

y = 4/3x + 1

y = 4/3(3) + 1

y = 5

So another point on the line is (3, 5).

Since both equations hold true, we can conclude that (0, 1) and (3, 5) are two points on the line y = 4/3x + 1.

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the values of $a$ and $b$,is So, $b - a = 6$.using the smallest and largest integers within this interval. Since "integer" refers to whole numbers (both positive and negative), we can identify $a$ and $b$

let's first solve the given inequality $x^2 - 15 < 2x$. We can rewrite this inequality by moving all terms to one side:

$x^2 - 2x - 15 < 0$

Now, we want to factor the quadratic:

$(x - 5)(x + 3) < 0$

From this factored form, we can see that the quadratic changes sign at x = -3 and x = 5. This means the inequality holds between these values:

-3 < x < 5

Now, we want to find the smallest and largest integers within this interval. Since "integer" refers to whole numbers (both positive and negative), we can identify $a$ and $b$ as follows:

$a = -2$ (the smallest integer greater than -3)
$b = 4$ (the largest integer less than 5)

Finally, we need to find the difference $b - a$:

$b - a = 4 - (-2) = 4 + 2 = 6$

So, $b - a = 6$.

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Hence, the rectangular prism has a surface area of 272 square centimetres.

For instance, by multiplying the length and breadth of a rectangle, the area of the shape can be determined. Pi (roughly 3.14), multiplied by the square root of the radius, can be used to get a circle's area. Calculating the size of numerous forms and figures, including triangles, circles, squares, and polygons, involves the usage of area, a key topic in geometry. The size of a piece of land, a building's floor area, or the surface of such an object are just a few examples of the many real-world uses for it.

given

We must add up the areas of all six faces of a rectangular prism in order to determine its surface area.

In this instance, the dimensions are as follows: width (w), length (l), and height (h), all in centimetres.

You can compute the surface area (A) as follows:

A = lw + lh + lw

Inputting the values provided yields:

A is equal to 2 (4 x 4 cm) + 2 (4 x 15 cm) + 2. (4 cm x 15 cm)

[tex]A=32 cm^2 + 120 cm^2 + 120 cm^2[/tex]

A = 272 cm²

Hence, the rectangular prism has a surface area of 272 square centimetres.

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From the given dimensions, area of the figure is approximately equal to 75.8 cm².

A regular polygon is a closed shape with straight sides and equal-length edges, as well as equal angles between those sides. Examples of regular polygons include equilateral triangles, squares, and hexagons. The number of sides a regular polygon has is referred to as its order, while the measure of each interior angle of a regular polygon can be calculated using the formula (n-2) x 180/n, where n represents the number of sides.

From the image we can see that, ABHI is a square with sides 6 cm, BCDGH is a regular pentagon with sides 6 cm (BH = AI = 6 cm) and DEFG is a rectangle with length 11 cm and breadth 6 cm ( DG = AI = 6 cm).

To find the area of the figure we have to find the area of each shape and add it together.

Area of square = side × side = 6 × 6 = 36 cm²

Area of regular pentagon = [tex]\frac{1}{4} \sqrt{5(5+25)a^{2} }[/tex]

= [tex]\frac{1}{4} \sqrt{5(5+25)6^{2} }[/tex]

= [tex]\frac{1}{4} \sqrt{25 + 10*1.41*36}[/tex]

= [tex]\frac{1}{4} \sqrt{532.6 }[/tex]

≈ 5.77 cm²

Area of rectangle = 2(l + b) = 2(11 + 6) = 34 cm²

Therefore area of the figure = 36 cm² + 5.77 cm² + 34 cm² ≈ 75.8 cm².

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