what is the surface area of the polyhendron?here is a net made of right triangle all measurements are given in centimeters

Answer: 0.04 inches²

Step-by-step explanation:A of Triangle = 1/2*B*H where B is base and H is height. Find the area of the bigger triangle and then subtract the area of the smaller triangle

1/2*(0.4)*(0.3) = 0.06

1/2*(0.4)*(0.1) = 0.02

0.06 - 0.02 = 0.04

The Cartesian coordinates of the point (r, θ, z) = (1, 11π/6, -1) can be expressed as (x, y, z) = (0.5√3, -0.5, -1).

To convert the point from cylindrical coordinates (r, θ, z) to Cartesian coordinates (x, y, z), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

z = z

In this case, r = 1, θ = 11π/6, and z = -1.

Using the formula for x:

x = 1 * cos(11π/6) = 1 * (cos(π) * cos(π/6) - sin(π) * sin(π/6))

= 1 * (1 * √3/2 - 0 * 1/2)

= √3/2

Using the formula for y:

y = 1 * sin(11π/6) = 1 * (sin(π) * cos(π/6) + cos(π) * sin(π/6))

= 1 * (0 * √3/2 + 1 * 1/2)

= 1/2

And z remains -1.

Therefore, the Cartesian coordinates of the point (r, θ, z) = (1, 11π/6, -1) are (x, y, z) = (√3/2, 1/2, -1).

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Answer:

Step-by-step explanation:

\(\left[\begin{array}{ccc}1&-5\\0&4\end{array}\right]\) \(2R{1}\)+\(R{2}\)→\(R_{1}\)\(\left[\begin{array}{ccc}2&-6\\0&4\end{array}\right]\) the 2x2 Square Matrix

First we have to multiply the \(R{1\\}\) with 2  which we get [2(1)  and 2(-5)] which results in [2 and -10 ] in Row1 and after add Row2 with the result we got in Row1 after multiplying with 2 then we get [2+0 =2 and -10+4= -6].

Now add the elements of Row1\(R{1}\) to Row1\(R{1}\) and now perform the entire operation

\(\left[\begin{array}{ccc}2(1)+0&2(-5)+4\\0&4\\\end{array}\right]\)

after solving the above matrix we get

\(\left[\begin{array}{ccc}2&-6\\0&4\end{array}\right]\)

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Answer:

15%

Step-by-step explanation:

Answer:

184 cm^2

Step-by-step explanation:

To find the surface area, find the area of each of the faces and add them up.

Let's start with the base/bottom.

The dimensions are 6 and 10, and it is a rectangle.

Area = 6 x 10 = 60 cm^2

Next, lets do the slanted sides.

The dimensions are 10 and 5, and they are both rectangles.

Area = 10 x 5 = 50 cm^2

Since there are 2 of the slanted sides, multiply 50 by 2.

50 x 2 = 100 cm^2

Then, do the triangles.

The dimensions are 6 (base) and 4 (height)

Area = 6 x 4 / 2

Area = 24 / 2

Since there are 2 triangles, we do not need to divide by 2. We will need to multiply by 2 afterwards, so there's no point in dividing by 2.

24 cm^2

Finally, add up all the areas.

60 + 100 + 24 = 184 cm^2

Heh, funny, there's no answer choice for that... maybe ask your teacher?

The value of r. in the scenario is 3%

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

Principal = $50

Rate = r

Time = 4 years

Total amount = $56

The formula for simple interest is:

I =A - P = Prt

substitute the known values in the above equation, so, we have the following representation

56 - 50 = 50 * r * 4

So, we have

200 * r = 6

Dividing both sides by 200, we get:

r = 0.03 = 3%

Hence, Ferdinand's annual interest rate is 3%.

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Step-by-step explanation:

2-5(68-60)=2-5×8=2-40=38

Different logs measure different physical properties of the formation that are related to porosity, and the relationship between the log measurement and porosity can be expressed through equations.

The different logs used to obtain porosity and their principles of measurement, quantities measured, and relation to porosity.
There are three main types of logs used to obtain porosity: neutron logs, density logs, and sonic logs.
Neutron logs: These logs measure the hydrogen content in a formation, which is directly related to porosity. The tool emits neutrons that interact with hydrogen atoms, and the resulting gamma rays are measured. The count rate decreases with increasing porosity. The neutron log can be expressed as:
Porosity = (neutron log reading - matrix reading) / (fluid reading - matrix reading)
Density logs: Density logs measure the bulk density of a formation, which can be related to porosity. The tool emits gamma rays that interact with the formation, and the scattered gamma rays are measured. The bulk density decreases with increasing porosity. The density log can be expressed as:
Porosity = (matrix density - bulk density) / (matrix density - fluid density)
Sonic logs: Sonic logs measure the travel time of sound waves through a formation, which can be related to porosity. The tool sends an acoustic wave and measures the time it takes to travel a specific distance. The travel time increases with increasing porosity. The sonic log can be expressed using Wyllie's time-average equation:
Porosity = (sonic log reading - matrix reading) / (fluid reading - matrix reading)
In summary, neutron logs measure hydrogen content, density logs measure bulk density, and sonic logs measure travel time of sound waves. These measurements can be used to calculate porosity using the respective equations provided.

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Answer:

2=x

Step-by-step explanation:

tell me if im wronng

Answer:

x=2

Step-by-step explanation:

3x-(9)=-3

    +9    +9

3x=6

/3  /3

x=2

Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

Answer:

a) Parabola opens up

b) 6

c) -3/2 and -2

Step-by-step explanation:

a) The general form of a parabolic graph is;

y = ax^2 + bx + c

if a is positive, it faces up, if negative, it opens down

Since a = 2 here, it is positive and thus the parabola faces or opens up

b) The y-intercept is simply the c term

the value here is 6

The y intercept is obtained when the x value is zero

So by simply setting the x value to zero, we can easily get the y value since x is zero at that point

c) The x-intercepts refer to the roots of the equation

By solving the quadratic equation i.e substituting 0 for y, we can get the two x values as follows;

2x^2 + 7x + 6 = 0

2x^2 + 4x + 3x + 6 = 0

2x(x + 2) + 3(x + 2) = 0

(2x + 3)(x + 2) = 0

2x + 3 = 0 or x + 2 = 0

2x = -3 or x = -2

x = -3/2 or x = -2

One meter is equal to 100 centimeters.

Now, we need to know 3.06 meters in centimeters:

Use the rule of three to find this value

1meter-------------------- 100cm

3.06------------------------- x cm

Where x is = (3.06*100)/1

Then x=306

The ceiling is 306 centimeters tall.

Answer:

Step-by-step explanation:

Sparkling grape juice is made with 1.5 quarts sparkling water and 0.75 quarts grape juice. When these two get mixed we get 2.25 quarts sparkling grape juice

So for 2.25 quarts sparkling grape juice we require 1.5 quarts sparkling water

⇒ For 100 quarts sparkling grape juice we require  * 100 quarts of sparkling water

⇒ Sparkling water required for 100 quarts of sparking grape juice = 66.67 quarts

The exact value of sin(π/6) is 1/2.

To find the exact value of sin(π/6), we can use the unit circle or the trigonometric identity for the sine function. In the unit circle, π/6 corresponds to an angle of 30 degrees, which lies in the first quadrant.

At this angle, the y-coordinate of the corresponding point on the unit circle is 1/2. Since sin(θ) represents the ratio of the opposite side to the hypotenuse in a right triangle, for an angle of 30 degrees, sin(π/6) is equal to 1/2.

Alternatively, we can use the trigonometric identity sin(θ) = cos(π/2 - θ). Applying this identity, we have sin(π/6) = cos(π/2 - π/6) = cos(π/3). Now, π/3 corresponds to an angle of 60 degrees, which lies in the first quadrant.

At this angle, the x-coordinate of the corresponding point on the unit circle is 1/2. Therefore, cos(π/3) = 1/2. Substituting this value back into sin(π/6) = cos(π/3), we get sin(π/6) = 1/2.

In both approaches, we find that the exact value of sin(π/6) is 1/2, indicating that the sine function of π/6 radians is equal to 1/2.

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Answer: 2100 square feet

Step-by-step explanation: 60 x 35=2100

Answer:

2100 ft squared!

Step-by-step explanation:

The formula to find the area of a rectangle is L * W = A

Where A is the total area, and L and W are the dimensions.

Since we know what the dimensions of the rectangles are, we can replace L and W to find out the area. This will look like this: 60 * 35 = A

Now we just have to multiply 60 and 35 to find A. This will simplify to 2100, which means the total are of the rectangle, or in this case, the soccer field, is 2100 ft squared!

Answer:

86 adults and 270 children

Step-by-step explanation:

Let x = # of adult tickets;

then the number of children tickets is (356-x).

Write the total money equation (revenue equation)

   \(1.75*(356-x) + 2.25x = 666\)  dollars.

From the equation

  \(x = \frac{666-1.75*356}{2.25-1.75} = 86\)

ANSWER.  86 adults and 356-86 = 270 children.

CHECK.

\(86*2.25 + 270*1.75 = 666\)  dollars.   ! Correct !

In a circle with a diameter of 30 cm and a chord of length 15 cm, the length of the minor arc associated with the chord is 15 * pi cm or approximately 47.12 cm.

To find the length of the minor arc associated with this chord, we need to consider the central angle subtended by the arc. The central angle is an angle whose vertex is the center of the circle, and its arms pass through the endpoints of the arc.

To find the central angle, we can use the fact that the chord divides the circle into two equal halves. This means that the central angle subtended by the minor arc is twice the angle formed by connecting the center of the circle, one endpoint of the chord, and the other endpoint of the chord.

Using the Pythagorean theorem, we can find the length of the other side of the triangle, which represents the distance from the center of the circle to the midpoint of the chord. Let's call this length 'r'. We have:

r² + 15² = 15²

r² + 225 = 225

r² = 225 - 225

r² = 0

From this, we can see that the other side of the triangle has a length of 0. This means that the midpoint of the chord coincides with the center of the circle. Therefore, the central angle subtended by the minor arc is 180 degrees (or π radians), which is the maximum possible angle for a chord.

Since the central angle is 180 degrees, the minor arc associated with the chord is half the circumference of the circle. The circumference of a circle is given by the formula 2 * π * r, where 'r' is the radius.

In our case, the radius is half the diameter, which is 15 cm. Therefore, the circumference of the circle is 2 * π * 15 = 30 * π cm.

The length of the minor arc associated with the chord is half the circumference, so it is (30 * π) / 2 = 15 * π cm.

Therefore, the length of the minor arc of the chord is 15 * π cm, or approximately 47.12 cm (rounded to two decimal places).

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Complete Question:

In a circle of diameter 30cm, the length of a chord is 15cm. Find the length of the minor arc of the chord.

The mean for the discrete probability distribution is 3.73

Generally, To calculate the mean of a discrete probability distribution, you can use the formula:

Mean = ∑x * P(x)

Using this formula, the mean of the given distribution is:

Mean = (2 * 0.2) + (6 * 0.3) + (10 * 0.3) + (14 * 0.2) = 4

To calculate the standard deviation of a discrete probability distribution, you can use the formula:

Standard Deviation = √∑(x - mean)^2 * P(x)

Using this formula and the mean that we calculated above, the standard deviation of the given distribution is:

Standard Deviation = √( (2 - 4)^2 * 0.2 + (6 - 4)^2 * 0.3 + (10 - 4)^2 * 0.3 + (14 - 4)^2 * 0.2 )

= √( (-2)^2 * 0.2 + (2)^2 * 0.3 + (6)^2 * 0.3 + (10)^2 * 0.2 )

= √( 4 * 0.2 + 4 * 0.3 + 36 * 0.3 + 100 * 0.2 )

= √( 0.8 + 1.2 + 10.8 + 20 ) = √( 13.8 )

= approximately 3.73

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Answer:

1. 9 cm

2. 50%

3. Assuming the photo is a rectangle, the answer would be 90 degrees on every angle (in a dilation, angle measurements are congruent).

Step-by-step explanation:

1. The long side is clearly the 6 cm side. multiply it by 1.5x (150%) and you get 9.

2. 2 is 50% of 4 and 3 is 50% of 6.

3. Assuming the photo is a rectangle, the answer would be 90 degrees on every angle (in a dilation, angle measurements are congruent).

Answer:

56,000

Step-by-step explanation:

Answer:

56000

Step-by-step explanation:

6,2 is closest to 6

To determine Justin's error, let's examine the expression 12.5 * 3.8 x, where x is 7.9 * 12.5 * 3.8 * (7.9 * 16.3) * (7.9 * 128.77).

The expression can be simplified by applying the correct order of operations, which is typically represented by the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division from left to right, Addition, and Subtraction from left to right).

Looking at the expression, we can identify that the multiplication operation is present in two places: 12.5 * 3.8 and 7.9 * 12.5 * 3.8.

To evaluate the expression correctly, we need to perform the multiplication operations first. This means that Justin's error lies in not multiplying 12.5 and 7.9 first.

Therefore, the correct evaluation would be:

12.5 * 7.9 * 3.8 * (7.9 * 16.3) * (7.9 * 128.77)

By multiplying 12.5 and 7.9 first, we would obtain a different result than what Justin likely calculated.

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The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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If area of "square-field" is 40000 ft square, and Mr. Blackburn is putting a fence diagonally in field, then the length of fence be is 282.84 ft.

The area of the square-field is = 40000 ft²,

We equate this with area formula,

We get,

⇒ (side)² = 40000,

⇒ side = 200,

substituting the side-length as 200 ft, in the diagonal formula,

we get,

⇒ Length of diagonal of field is = (side)√2,

⇒ Length of diagonal of field is = (200)√2,

⇒ Length of diagonal of field is ≈ 282.84 ft.

Therefore, the length of the fence of the field is 282.84 ft.

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Answer:

6 is the greater one ................

Answer:

>

Step-by-step explanation:

l-8l > l6l

l8l > l6l. l l turns # inside into a positive number

Let:

x = Speed of the jet

y = Speed of jetstream

so:

and

Solve the system using elimination method:

Replace x into (1)

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph

The solutions to the equation 4x² + 4x = 3 are x = 1/2 and x = -3/2.

The given equation is 4x² + 4x = 3.

we can rearrange it into a quadratic equation and then solve for x.

Rewrite the equation in the form ax² + bx + c = 0

4x² + 4x - 3 = 0

Solve the quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 4, b = 4, and c = -3.

x = (-4 ± √(4² - 4 × 4 × -3)) / (2 ×4)

x = (-4 ± √(16 + 48)) / 8

x = (-4 ± √64) / 8

x = (-4 ± 8) / 8

x₁ = (-4 + 8) / 8 = 4 / 8

=1/2

x₂ = (-4 - 8) / 8

= -12 / 8

= -3/2

Therefore, the solutions to the equation 4x² + 4x = 3 are x = 1/2 and x = -3/2.

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Answer:

2nd and 5th answer options

Step-by-step explanation:

Multiply the vertices of polygon ABCD by One-half.

Reflect the intermediate image.

The measured angle ABD=24° and ABC=71°

The figure in the question is either a triangle or a quadrilateral, but this has not been stated. It is possible to solve this regardless of shape. The accompanying graphic shows the two potential shapes and angles.

Now, based on the information provided, we may deduce that line BD divides angle ABC into two parts: Angle ABC is equal to angle ABD plus angle DBC.

Additionally, we know that angle DBC is 47 degrees and angle ABC is 1 degree less than 3 times angle ABD.

Angle ABC Equals 3x-1 if angle ABD is x.

Angle ABC also equals Angle ABD plus Angle DBC.

Changing the values in the equations above 3x-1 = x+47 ⇒ 2x = 48⇒ x = 24

Angle ABD thus equals 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree

∴∠ABD=24° and ∠ABC=71°

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