There are 20 points on a line, each spaced two inches apart. How far, in inches, is it from the first point to the last one?

Step-by-step explanation:

Volume of the cube = Side

Since,

All the sides of the cube are equal

Then if the length of a side of the cube is

increased

So, the side of the cube becomes

Side of the cube = 2 × Side

Assume

Side of the cube be ‘s’

Side of the cube = 2s

Now,

Volume of the cube = 2s × 2s × 2s

Volume of the cube = (2s)

Volume of the cube = 8s

To find how many times the volume of the cube is

increased

Answer:

25

Step-by-step explanation:

⟨A = 7•x + 40° and ⟨B = 3•x + 112°

From a possible diagram of the question, ⟨A = ⟨B, which gives;

Given;

⟨A = 7•x + 40°

⟨B = 3•x + 112°

In the diagram from a similar question posted online, we have;

Corresponding angles formed by parallel lines having a common transversal are congruent, therefore;

Which gives;

7•x + 40° = 3•x + 112°

7•x - 3•x = 112° - 40° = 72°

7•x - 3•x = 4•x = 72°

x = 72° ÷ 4 = 18°

Therefore;

Which gives;

⟨A = 7•x + 40°

⟨A = 7 × 18 + 40° = 166°

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Answer:d

Step-by-step explanation:

khan

The equation for the plane through the points p(0, 1, 1), q(1, 0, 1) and r(1, 1, 0) is x + y + z = 2

Given,

Three points :- p(0, 1, 1), q(1, 0, 1), r(1, 1, 0)

We can take this as ([tex](x_{1} ,y _{1}, z_{1} ), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] respectively.

Thus,

The equation for the plane through the points

Here,

The formula of equation of the plane passing through three non collinear points

[tex]x-x_{1} y-y_{1} z-z_{1} \\x_{2} -x_{1} y_{2} -y_{1} z_{2} -z_{1} = 0\\x_{3} -x_{2} y_{3} -y_{2} z_{3} -z_{2}[/tex]

by substituting the values in the formula of equation of the plane

x-0  y-1  z-1

1-0  0-1  1-1    = 0

1-0  1-1  0-1

x  y  z

1  -1  0   =  0

1  0  -1

x(1) - (y-1)(-1) - (z-1)(-1) = 0

x + y - 1 + z - 1 = 0

x + y + z + 2 = 0

x + y + z = 2

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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The equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

For given question,

We have been given three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0)

We need to find an equation for the plane through the given three points.

We know that the equation of the plane through the points [tex](x_1,y_1,z_1),(x_2,y_2,z_2),(x_3,y_3,z_3)[/tex] is,

[tex]\begin{vmatrix}x-x_1 & y-y_1 & z-z_1\\x_2-x_1 & y_2-y_1 & z_2-z_1\\x_3-x_1 & y_3-y_1 & z_3-z_1\end{vmatrix}=0[/tex]

Assume that for given points,

[tex](x_1,y_1,z_1)=(0, 1, 1)\\\\(x_1,y_1,z_1)=(1, 0, 1)\\\\(x_1,y_1,z_1)=(1, 1, 0)[/tex]

So, the equation of the plane passing though given points would be,

[tex]\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1-0 & 0-1 & 1-1\\1-0 & 1-1 & 0-1\end{vmatrix}=0\\\\\\\Rightarrow \begin{vmatrix}x-0 & y-1 & z-1\\1 & -1 & 0\\1 & 0 & -1\end{vmatrix}=0\\\\\\\Rightarrow x(1-0)-(y-1)(-1-0)+(z-1)(1-0)=0\\\\\Rightarrow x+y-1+z-1=0\\\\\Rightarrow x+y+z=2[/tex]

Therefore, the equation of the plane through the three points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2

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The probability is 1/3.

Probability is sincerely how likely something is to show up. whenever we're unsure about the final results of an event, we will communicate about the probabilities of positive consequences—how probably they're. The evaluation of events governed by way of possibility is called information.

Probability is the branch of mathematics concerning numerical descriptions of ways likely an occasion is to arise, or how in all likelihood it's far that a proposition is actual. The opportunity of an event is more than a few among 0 and 1, wherein, kind of talking, zero suggests impossibility of the occasion and 1 shows the truth.

Chance = the wide variety of approaches to achieving achievement. the whole range of viable consequences. as an example, the opportunity of flipping a coin and its being heads are ½ because there may be 1 manner of getting a head and the overall wide variety of feasible results is two (a head or tail). We write P(heads) = ½.

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Canceling units is also called unit analysis.

This is also called dimensional analysis.

What is a unit of analysis in statistics?

For example -

1 ft = 12 in

3 ft =  [tex]3 ft * \frac{12 in }{1 ft}[/tex]

3 ft = ( 3 * 12 )  in ⇒ 36 in

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The surface area of the cylinder is 18.84 square feet

The given parameters are

Height, h = 2 ft

Diameter, d = 2 ft

The radius (r) is half of the diameter (d)

This is calculated as:

Radius = Diameter/2

So, we have:

r = d/2

Substitute 2 for d

r = 2/2

Evaluate the quotient i.e. divide 2 by 1

r = 1

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2

Evaluate the exponents

A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2

Evaluate the products

A = 6.28 + 12.56

Evaluate the sum

A = 18.84

Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet

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Expand the binomials.

[tex](x+y)^2 - (x-y)^2 = (x^2 + 2xy + y^2) - (x^2 - 2xy + y^2) = 4xy[/tex]

Now let [tex]x=1[/tex] and [tex]y=\sin(A)[/tex].

If [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.

Given that [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because [tex]MU_{x}/P_{x}[/tex]<[tex]MU_{y} /P_{y}[/tex]

So to equalise the ratio we need to reduce [tex]MU_{y} /P_{y}[/tex]. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if [tex]MU_{x}/P_{x}[/tex]=30 and [tex]MU_{y} /P_{y}[/tex]=40 then the consumer should buy the commodity y to maximise utility.

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The probability of winning exactly 21 times is:-0.32

Given,

The probability of winning on an arcade game, p = 0.659

Number of times you play arcade game, n = 30

By assuming this as a normal distribution, we get

Mean=μ=30×0.659 =19.77

Standard deviation, σ = [tex]\sqrt{np(1-p)}[/tex]

= [tex]\sqrt{30(0.659)(1-0.659)}[/tex]

≈ 2.60

Let X be a binomial variable

Then, the z score for x = 21 will be:

z = (x - μ) / σ = [tex]\frac{21-19.77}{2.60}[/tex]

≈ 0.47

Now, the probability of winning exactly 21 times

P (x ≥ z) = P (21 ≥ 0.47) = 0.32

Hence the probability of winning exactly 21 times is 0.32

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Using proportions, it is found that Jada drinks more water than Elena, as her proportion is 3/2 of Elena's proportion.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Jada drank 3/4 the amount x that Elena drank, hence:

J = 3x/4.

Lin drank twice as much water as Jada, hence her proportion relative to Elena is given by:

L = 2J = 2 x 3x/4  = 6x/4 = 1.5x.

1.5x = 50% more than Elena.

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The Total surface area of the square pyramid = 115.2 in.²

The Volume of the square pyramid = 1,024 in.³.

The total surface are of a square pyramid is given as: TSA = SA = 1/2(P × l), where:

P = perimeter of the square base

l = slant height of the pyramid

The volume of a square pyramid = 1/3(a³ × h), where:

a = edge of the square base

h = height of the pyramid

Find the Total surface area of the Pyramid:

P = 4(a) = 4(8) = 32 in.

l = 7.2 in.

Total surface area of the square pyramid = 1/2(32 × 7.2)

Total surface area of the square pyramid = 115.2 in.²

Volume of the square pyramid:

a = 8 in.

h = 6 in.

Volume of the square pyramid = 1/3(8³ × 6)

Volume of the square pyramid = 1,024 in.³

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[tex]CD=14.37cm.[/tex]

Find CD:

Let,

[tex]r_{1}[/tex] be a radius of Circle A

[tex]r_{2}[/tex] be a radius of Circle B

Given:

[tex]r=4cm.[/tex]

Circumference: [tex]2\pi r[/tex]

[tex]2\pi r_{1} =20[/tex]

[tex]r_{1} =\frac{10}{\pi }[/tex]

[tex]CD=D_{1} +D_{2}[/tex]

[tex]=2r_{1} +2rx_{2}[/tex]

[tex]=2*(\frac{10}{\pi } )+2*4[/tex]

[tex]CD=14.37cm.[/tex]

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Answer:

(0, -5)

Step-by-step explanation:

The two different lines have point (0, -5) in common, so the solution is (0, -5).

The computation shows that the number of people expected to get infected is 5.

It should be noted that the chance of chance of getting a viral infection is 0.0005. out of 10,000 people.

Therefore, the number of people expected to get infected will be:

= 0.0005 × 10000

= 5

The number of people expected to get infected is 5.

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Answer:

(x + 6, y + 1)

Step-by-step explanation:

Just look at 1 point of ABCD. For example, look at point D.

Point D must become point F.

When you reflect ABCD over the x-axis, point D will end up at (-1, -2).

Now it has to be translated to (5, -1).

For x to go from -1 to 5, you need to add 6.

For y to go from -2 to -1, you need to add 1.

Answer: (x + 6, y + 1)

Answer:

a) 20

Step-by-step explanation:

when we have an exponent of an exponent, we simply multiply them for the overall exponent.

so, we actually have

a^((1/4)×12) × b^((1/3)×12) = a³b⁴ = 5000

let's find the prime factors of 5000 :

5000 ÷ 2 = 2500

2500 ÷ 2 = 1250

1250 ÷ 2 = 625

625 ÷ 3 no

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

so,

5000 = 2³ × 5⁴

so, a = 2, b = 5

a²b = 2²×5 = 4×5 = 20

A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.

In this context, we can logically deduce that the geometric shape which best models the object (cell phone tower) shown in the image attached above is a square pyramid.

Mathematically, the surface area of a square pyramid is given by this formula:

A = a² + 2a√(a²/4 + h²)

Where:

Given the following parameters:

Edge of the base = 50 feet.

Height = 200 feet.

Substituting the given parameters into the formula, we have;

A = 50² + 2(50)√(50²/4 + 200²)

A = 2,500 + 100√(2500/4 + 40,000)

A = 2,500 + 100√(625 + 40,000)

A = 2,500 + 100√(40,625)

A = 2,500 + 100(201.56)

A = 2,500 + 20,156

A = 22,656 ≈ 22,500 ft².

In conclusion, the best geometric shape for the model is a square pyramid and the approximate surface area is equal to 22,500 square feet.

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Answer:The best shape for the model is a square pyramid.

The approximate surface area is 22,500 square feet.

Step-by-step explanation: edmentum/plato answers

Answer:

f(x) = 5x - 5

Step-by-step explanation:

f(x) = 5x - 5 is a linear equation as it has no power.

During the Civil War, the North's heavy industrialization provided an advantage.

According to the information:

The distinct economic division between the northern and southern economies played a key role in the Union's Civil War victory. First, the vast capitalist industry was expanding, with a significant concentration of salaried labor, in full force, and on the verge of the Second Industrial Revolution (to which the development of new military technologies, such as battleships and the mass production of weapons, helped to the war. These northern bourgeois sectors were represented by the liberal nationalist new Republican Party, which worked to enact protectionist laws.

On the other hand, the south remained rooted in an economic structure that was adverse to the growth of capitalism (mechanization and hiring of workers were cheaper than the maintenance of slaves). To protect slavery would be the Democratic Party. This party, which had spearheaded the nation's significant southern expansion (pro-Mexican territorial annexation movement), now served as a proxy for the region's elites, who essentially favored the growth of the slave trade and unrestricted trade in manufactured products and raw resources.

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I understand that the question you are looking for is:

A resource comparison of the Union and Confederacy during the Civil War. The title is Comparing Resources. The data are as follows. For each category, the Union percentage is listed first, the Confederate percentage, second. Horses, 72, 28, Food Crops, 72, 28, Cotton, 1, 99, Prewar Exports, 30, 70, Soldiers, 67, 33, Firearm Production, 97, 3, Railroad Tracks, 71, 29, Factories, 86, 14, Bank Deposits, 81, 19, Total Population, 71, 29. Public domain Use the graph and your knowledge of U.S. history to answer the question. Which of these explains the differences in Union vs. Confederate firearm production during the Civil War? The North had a highly skilled labor force to make them. The North's heavy industrialization provided an advantage. The South had fewer men who were trained as metalworkers. The South's means of production were destroyed by General William Tecumseh Sherman.

Answer:

a) -6/2

b) -9/2

Step-by-step explanation:

a) rearrange by making y the subject as y = mx+c

y = -6/2x-9/2

the gradient = -6/2

b) c is the y-intercept as it touch the y-axis, therefore -9/2 is where the line crosses the y-axis

Answer:

Step-by-step explanation:

Remember the midpoint formula:

[tex](\frac{x2+x1}{2},\frac{y2+y1}{2} )\\[/tex]

Substitute in your values

 [tex](\frac{7.6+21.8}{2},\frac{1.7+9.3}{2} )\\[/tex]

Solve

[tex](\frac{29.4}{2},\frac{11}{2} )\\(14.7,5.5)\\[/tex]

Answer: (14.7,5.5)

Step-by-step explanation: I got it right on the test...

Answer:

1 boy to 15 girls.

Step-by-step explanation:

Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!

The ratio of boys to all children in the group is 1:16.

Given that in a group there are 2 boys and 30 girls.

We need to find the ratio of boys to all children.

To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.

Then, we can express the number of boys as a fraction of the total number of children.

Number of boys = 2

Number of girls = 30

Total number of children = Number of boys + Number of girls

Total number of children = 2 + 30 = 32

Now, we can express the number of boys as a fraction of the total number of children:

Ratio of boys to all children = Number of boys / Total number of children

Ratio of boys to all children = 2 / 32

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Ratio of boys to all children = 1 / 16

So, the ratio of boys to all children in the group is 1:16.

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The estimated standard error for the sample mean difference is  2.5 .

According to the question

A repeated-measures study comparing two treatments

n = 4

MD(mean difference) = 2

SS (sum of square) = 75

Now,

error for the sample  

Formula for standard error

[tex]S^{2} = \frac{SS}{n-1}[/tex]

by substituting the value

[tex]S^{2} = \frac{75}{4-1}[/tex]

[tex]S^{2} = \frac{75}{3}[/tex]

S² = 25

S = 5 (s is never negative)

Standard error of the estimate for the sample mean difference

As

The standard error of the estimate is the estimation of the accuracy of any predictions.

The formula for standard error of the mean difference

standard error of the mean difference  =[tex]\frac{standard\\\ error}{\sqrt{n} }[/tex]  

standard error of the mean difference = [tex]\frac{5}{\sqrt{4} }[/tex]  

standard error of the mean difference = 2.5

Hence, the estimated standard error for the sample mean difference is  2.5 .

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Answer:

Step-by-step explanation:

elastic, inelastic, inelastic

Answer: elastic, inelastic, inelastic

Step-by-step explanation:

Answer:

x=14

Step-by-step explanation:

4(x-7)= 14(2)

4x - 28 = 28

4x = 56

x = 14

By using algebra properties and trigonometric formulas we find that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equivalent to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex].

In this question we have trigonometric expression whose equivalence to another expression has to be proved by using algebra properties and trigonometric formulas, including the fundamental trigonometric formula, that is, cos² x + sin² x = 1. Now we present in detail all steps to prove the equivalence:

[tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex]       Given.

[tex]\frac{1 + \sin x - 1 + \sin x}{1 - \sin^{2}x}[/tex]      Subtraction between fractions with different denominator / (- 1) · a = - a.

[tex]\frac{2\cdot \sin x}{\cos^{2}x}[/tex]      Definitions of addition and subtraction / Fundamental trigonometric formula (cos² x + sin² x = 1)

[tex]\frac{2\cdot \tan x}{\cos x}[/tex]      Definition of tangent / Result

By using algebra properties and trigonometric formulas we conclude that the trigonometric expression [tex]\frac{1}{1 - \sin x} - \frac{1}{1 + \sin x}[/tex] is equal to the trigonometric expression [tex]\frac{2\cdot \tan x}{\cos x}[/tex]. Hence, the former expression is equivalent to the latter one.

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A major advantage of a direct implementation is that people whose roles span modules do not have to switch back and forth between old and new modules.

With this technique, the machine is implemented and tested to make certain it plays well. Then the antique machine is removed and the brand new one is put in its area without any overlap or restricted rollout.

There are three predominant methods used: phased implementation, direct changeover, and parallel going for walks. Phased implementation: A staged technique whereby one part of the overall system that desires change is changed.

Structures implementation is the process of defining how the data device needs to be built (i.e., physical machine design), ensuring that the records gadget is operational and used, and ensuring that the information device meets greatly preferred i.e. nice warranty.

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Answer:

a) Class A has the larger interquartile range.

b) Class A has the highest test score.

c) Class B has higher median test score.

d) Class B has smaller range of test score.

Step-by-step explanation:

a) Inter quartile range (IQR) =  upper quartile - lower quartile

  Class A:  IQR = 79 - 65 = 14

  Class B: IQR = 77 - 70 = 7

Class A has larger interquartile range.

b)  Class A has the highest test score.

c) Median of class A = 70

 Median of class B   = 74

Class B has higher median test score.

d) Range is the difference between the highest and lowest score.

Range = highest score - lowest score

 Range of Class A = 85 - 62 = 23

 Range of class B  =  79 - 68 = 11

Class B has smaller range of test score.