Justify Step 4 of this Proof

a) Surface area of this cuboid = 214 cm²

b) Surface area of the tower   = 474 cm²

Dimensions of cuboid :

  Length (l) = 6 cm

  Width (w) = 7 cm

 Height (h) = 5 cm

The Surface Area of Cuboid (SA) = 2(lw + lh + hw)

                                            SA = 2(6×7 + 6×5 + 5×7)

                                                         = 2(42 + 30 + 35)

                                                         = 2×107

       The Surface Area of Cuboid  = 214 cm²

Dimensions of tower :

Length (l) = 6 cm

  Width (w) = 7 cm

 Height (h) = 15 cm

The Surface Area of Tower = 2(lw + lh + hw)

                                               = 2(6×7 + 6×15 + 15×7)

                                               = 2(42 + 90 + 105)

                                               = 2 × 237

The Surface Area of Tower = 474 cm²

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It was discovered that the pressure in atmospheres (atm), when applied to a balloon, was inversely related to the height in meters, squared root. The pressure was 1.44 atm when the balloon was 25 meters height in the air. What was the pressure like at a 9-meter height?

The pressure is 2.4 atm when the height is 9m.

Inversely proportion means when one variable is directly proportional to the reciprocal of the other, there is an inverse fluctuation between the two variables. In other words, the two variables' product has a fixed value. Therefore, as one variable rises, the other falls.

Here, We take pressure of atmosphere as P and the height of the balloon as H.

Given that, The pressure of atmosphere was inversely proportional to the square root of the height.

We write this as [tex]P[/tex]∝[tex]\frac{1}{\sqrt{H} }[/tex].

Taking constant of the proportionality as k.

[tex]P[/tex]=[tex]\frac{k}{\sqrt{H} }[/tex].

We have, The pressure was 1.44 atm when the balloon was 25 meters height in the air.

P=1.44 and H=25

[tex]1.44=\frac{k}{\sqrt{25} }[/tex].

[tex]1.44=\frac{k}{5}[/tex]

[tex]k=5\times1.44[/tex]

[tex]k=7.2[/tex]

Now [tex]P=\frac{7.2}{H}[/tex]

We have to find If H is 9m then what is P?

[tex]P=\frac{7.2}{\sqrt{9} }[/tex]

[tex]P=\frac{7.2}{3}[/tex]

[tex]P=2.4\\[/tex]

Therefore, The pressure is 2.4 atm when the height is 9m.

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5 IS THE DERIVATIVE OF k(x)= 5x at x=10

The rate at which a function alters in relation to a variable is known as a derivative in mathematics. Problems involving calculus and differential equations need the use of derivatives.

f(x)=5x

∴f'(10)=f(10+h)−f(10)h

=5(10+h)−5(10)

= h→0/h

=[tex]\lim_{h\to 0}[/tex]5h/h

=[tex]\lim_{h\to 0}[/tex]5

=5.

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Answer:

b = ± 5

Step-by-step explanation:

8b² = 200 ( divide both sides by 8 )

b² = 25 ( take square root of both sides )

b = ± [tex]\sqrt{25}[/tex] = ± 5

b = - 5 , x = 5

Answer: 115+85+60+x=360

x=100 degrees

Step-by-step explanation:

115+85+60+x=360==> 115, 85, 60, and x are all 4 angles in the quadrilateral

200+60+x=360

260+x=360

260-260+x=360-260

x=360-260

x=100 degrees

Among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.

Given three options as under:

1)  {(1,4), (2,5), (3,6), (4,7)}

2)  {(1,4), (2,4), (3,5), (6,10)}

3) {(-3,9), (-2,4), (0,0), (1,1), (-3,8)}

We are required to choose the relation which represents a function.

Function is basically from a set X to a set Y assigns to each element of X exactly one element of Y.

Among the given options the relation which is a function is

{(1,4),(2,5), (3,6), (4,7)} because the other options have two values for one value of x or one value is giving two values of y which is opposite to the characteristics of a relation to be a function.

Hence among the given relations {(1,4),(2,5), (3,6), (4,7)} represents a function.

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Answer:

Mean:39

Mode:37

Median:37

Range:82-19=63

x(2x+5) = 3 and 2x²+5x = 3 are equivalent algebraic expression.

Equivalent expressions are those expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). They are same but looks different.

Given that, x(2x+5) = 3 and 2x²+5x = 3 and we have to conclude how both expressions are related to each other.

Let's procced to solve this.

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

2x²+5x = 3 ...............(2)

Now, solving equation (1), we get

x(2x+5) = 3 ⇒2x²+5x = 3, which is equation (2)

So, when we solve equation (1), we get equation (2) and vice-versa.

Hence, x(2x+5) = 3 and 2x²+5x = 3 are equivalent algebraic expression.

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Answer:

write all the prime number between 7 and 15

Check the picture below.

Answer:

24.5 = 3.50 * 7

Step-by-step explanation:

I used multiplication.

Answer:

y=x+b

3.50=7x

Step-by-step explanation:

7 is how many apples sally bought

it is $3.50 for 7 apple so $3.50 is y

7 times the price for one apple is $3.50

which also means each apple is $0.50

Answer:

m = [tex]\frac{7}{4}[/tex]

Step-by-step explanation:

We are given the points (2, -3), and (6,4), and we want to find the slope through these 2 points.

The formula for the slope (m) is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

Even though we have 2 points (as stated in given), let's label their values to help avoid any confusion and mistakes.

[tex]x_1=2\\y_1=-3\\x_2=6\\y_2=4[/tex]

We can substitute the values of [tex]x_1, y_1, x_2,[/tex] and [tex]y_2[/tex] into the formula to find the slope. Remember that the formula has subtraction.

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{4--3}{6-2}[/tex]

Simplify.

m = [tex]\frac{4+3}{6-2}[/tex]

Add/subtract.

m = [tex]\frac{7}{4}[/tex]

The slope of the line is [tex]\frac{7}{4}[/tex].

Topic: slope

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Answer: A

Step-by-step explanation:

Angles on a straight line must add up to 180 so angle BCA is 180-132=48

Because the triangle BAC is an isosoles angle BCA and ABC must be the same so 48

We can now use the angle on a straight line rule to figure out angle DBA 180-48=132

We know that triangle DBA is an isosoles trianlge so and x and DAB must be the same and both be x, and we know that angles in a triangle add up to 180 so the equation can be written as:

180=2x+132

48=2x

x=24

Possibly measurement error are recording error, differences in environmental conditions at the time of measurement.

Given in a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, 22, 26, 27, and 31.

An error in measurement is the difference between a taken measurement and the known actual value (the accepted true measurement) of what is being measured.

Here experiment was conducted to study the time taken for light to travel from one place to another place.

From the given problem obtained 66 observations are obtained.

Since the experiment conducted in different times, the density of the material changes with temperature/environmental conditions which may result the difference in measurement.

So possibly measurement error, recording error, differences in environmental conditions at the time of measurement, etc.

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So possibly measurement error, recording error, differences in environmental conditions at the time of measurement

Given In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were 31, 23, 32, 36, 22, 26, 27, and 31.

Here experiment was conducted to study the time taken for light to travel from one place to another place.

From the given problem obtained 66 observations are obtained.

Since the experiment conducted in different times, the density of the material changes with temperature/environmental conditions which may result the difference in measurement.

So possibly measurement error, recording error, differences in environmental conditions at the time of measurement, etc.

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21124

Answer:

B

Step-by-step explanation:

Unknown or unidentified numbers are denoted in mathematical equations by lowercase, italicized letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.

Denumerable sets include the set Z. Denumerability is the property that even if a set may include an endless number of members, any element in the set may be represented by a list that implies its identity.

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Answer:

x = 2

y = 5

Step-by-step explanation:

-x - 3y = -17

2x - 6y = -26

--------------------

(-x - 3y = -17) × 2

-2x - 6y = -34

-------------------------

-2x - 6y = -34

2x - 6y = -26

-------------------------

       -12y = -60

       ÷-12      ÷-12

-------------------------------

               y = 5

-x - 3y = -17

-x - 3(5) = -17

-x - 15 = -17

    +15 + 15

--------------------

-x = -2

÷-1  ÷-1

-----------

x = 2

I hope this helps!

The equation used is 50 = (2w + 5) × w which can be used to find its width, w.

According to the question we are Given,

Length of rectangle = 5 inches more than its width

Area of rectangle = 50sq. inches

Let width of rectangle = w

So, According to the question,

length = 2w + 5

Area of rectangle = Length × Breadth

50 = (2w + 5) × w

So, our required equation is 50 = (2w + 5) × w

The quantity of space occupied by a flat surface with a specific form is referred to as the area. It is calculated as a "number of" square units (square centimeters, square inches, square feet, etc.) The quantity of unit squares that may fit within a rectangle called its area. The flat surfaces of laptop monitors, blackboards, painting canvases, etc. are a few instances of rectangular forms.

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Answer: t = 1.33333

Step-by-step explanation:

Answer: division property of inequality

Step-by-step explanation:

you would devide 3 by 4 which is 0.75 then add you varible. Thats 0.75t  that means that 0.75t  is less than 4

So Cyclist marked at O position is slowest.

Interpreting graphs involves understanding what the shape of a curve represents in real life situations. We should also understand what slope means and how to interpret what a high or low slope value represents. An understanding of plotting points is also important.

We have been given an image in terms of graph that is attached

We all know that velocity is the directional speed of a object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time and it can be written as Velocity = [tex]\frac{S}{T}[/tex]

So position at N: V= [tex]\frac{100}{4}[/tex]= 25km/h

So position at M: [tex]V= \frac{80}{5}[/tex] = 16Km/h

So position at O: x[tex]V= \frac{80}{5}[/tex] = 12Km/h    

So as we all know 12<16<25

So O cyclist is slowest one with 12Km/h speed

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To meet her goal of riding a total of 28.8 miles, Keilantra needs to ride an average of 6.2 miles.

Here we know that Keilantra wants to rude her bicycle for a total of 28.8 miles.

We know that she has already ridden 4 miles, so the distance left to meet her goal is:

D = 28.8mi - 4mi = 24.8mi

Now we know that she wants to meet her goal in 4 days, so the average that she needs to ride in each of these 4 days is given by the quotient:

24.8mi/4 = 6.2 mi

To meet her goal, Keilantra needs to ride an average of 6.2 miles.

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The solutions to the given absolute value equations are given as follows:

A. t = -1, t = 1.4.

B.

The graph of item A is given at the end of the answer.

The absolute function is defined by:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

For item a, we have that two possibilites, as follows:

The graph is given at the end of the answer(correct solutions dashed in blue).

For item b, following the same procedure, the solutions are:

The graph is also given at the end of the answer, with the -1 marked in blue. (you have to remove the marking from 1).

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Answer:

The scale factor is 3.

Step-by-step explanation:

9÷3=6÷2

3=3

this makes the scale factor be 3.

Power is the result of multiplying same number for n number of times.  The value of the given expression when simplified is equal to 75.

Power is the result of multiplying same number for n number of times. Power is typically expressed by a base number and an exponent. The base number indicates the number being multiplied. The exponent, which is a little number printed above and to the right of the base number, indicates the number of times the base number is multiplied.

The given expression can be simplified as shown below.

(5⁴ × 3³) / (5² × 3²)

= (625 × 27) / (25 × 9)

= 16,875 / 225

= 75

Hence, the value of the given expression when simplified is equal to 75.

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Answer:

8/3

Step-by-step explanation:

Divide 8/3

Answer:

Option D: 8/3

Step-by-step explanation:

(2 x 3 + 2)/3 = 2 2/3

(6 + 2)/3 = 2 2/3

8/3 = 2 2/3

NUSS is a device for propagating multigroup nuclear information covariances in pointwise ace-formatted nuclear information the use of stochastic sampling method.

Stochastic sampling (SS) method for quantifying nuclear facts uncertainties is finished with the resource of the use of the use of perturbed nuclear facts in recurring neutronics calculations and identifying the variance of output parameters due to the input nuclear facts uncertainties. In this work, an SS-based absolutely device, called NUSS is carried out which perturbs pointwise ACE-formatted nuclear facts the use of multigroup nuclear facts covariance. The use of pointwise ACE-formatted nuclear facts in NUSS can accommodate flexible multigroup covariance structures and allows for nuclear facts uncertainty propagation through the continuous/pointwise-energy delivery code MCNPX. Next, Light Water Reactor (LWR) pin mobileular models from the OECD/NEA UAM Phase-1 benchmark were analyzed. Results of pass section and uncertainties in interest of numerous nuclear facts covariance libraries are presented.

Therefore, NUSS is a device for propagating multigroup nuclear information covariances in pointwise ace-formatted nuclear information the use of stochastic sampling method.

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Answer: L

Step-by-step explanation: