Identify a sequence of transformations that maps triangle ABC onto triangle A”B”C” in the image below

The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

Some points about standard deviation using Empirical Formula:

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The sample space for x, where x is the number of shots the basketball player makes out of 5 free throws, is,{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}There are 32 possible outcomes in the sample space.

The sample space for x is the set of all possible outcomes of the experiment of shooting 5 free throws. Since each shot can either be made or missed, there are 2 possible outcomes for each shot. Therefore, there are 2^5 = 32 possible outcomes for the experiment.

To enumerate the sample space, we can use the notation S for made shots and F for missed shots. Then, each outcome of the experiment can be represented by a string of 5 letters, where each letter represents the outcome of a single shot.

Using this notation, the sample space for x is:

{SSSSS, FSSSS, SFSSS, SSFSS, SSSF S, SSSSF, FSSF S, FSFSS, FSSSF, SFFSS, SFSSF, SSFFS, FSSFS, FSFSS, FFSSS, SFFSF, SFSSF, SSFSF, FSSSF, FSFSS, SFSFS, FSSFS, FSSSF, SFFFS, SSFFS, FFSFS, FFSFF, FSFFS, SFSFF, SFSSS}

Note that there are 6 outcomes where the player makes 0 shots, 5 outcomes where the player makes 1 shot, 10 outcomes where the player makes 2 shots, 10 outcomes where the player makes 3 shots, 5 outcomes where the player makes 4 shots, and 1 outcome where the player makes all 5 shots.

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Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

• [tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

(1)

[tex]\sqrt{108}[/tex]

= [tex]\sqrt{36(3)}[/tex]

= [tex]\sqrt{36}[/tex] × [tex]\sqrt{3}[/tex]

= 6[tex]\sqrt{3}[/tex]

(2)

[tex]\sqrt{14}[/tex] × [tex]\sqrt{35}[/tex]

= [tex]\sqrt{14(35)}[/tex]

= [tex]\sqrt{490}[/tex]

= [tex]\sqrt{49(10)}[/tex]

= [tex]\sqrt{49}[/tex] × [tex]\sqrt{10}[/tex]

= 7[tex]\sqrt{10}[/tex]

(3)

[tex]\sqrt{\frac{28}{64} }[/tex]

= [tex]\frac{28}{\sqrt{64} }[/tex]

= [tex]\frac{\sqrt{28} }{8}[/tex]

= [tex]\frac{\sqrt{4(7)} }{8}[/tex]

= [tex]\frac{\sqrt{4}(\sqrt{7}) }{8}[/tex]

= [tex]\frac{2\sqrt{7} }{8}[/tex]

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

The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

What is probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

Based on the experiment described, a two-sample z-test for the difference in proportions was conducted to determine if there is a significant difference between the proportion of rats that succeeded in the maze after being given substance m and the proportion of rats in the control group that succeeded in the maze.

This suggests that the difference in proportions between the two groups is statistically significant at the 0.05 level of significance (since the p-value is less than 0.05).

In other words, the results of the experiment suggest that substance m may be effective in helping to restore memory, as a greater proportion of rats in the substance m group succeeded in the maze compared to the control group. However, it's important to note that further experiments and analyses would be necessary to confirm these findings and determine the extent of the effect of substance m on memory restoration.

Therefore, The z-value obtained from the test was 2.25, and the p-value was less than 0.02.

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Answer:20

Step-by-step explanation:2 times with 10 hours becase per hour the temperature 2 degree celsius

We are proving that two triangles are congruent by an ASA (angle-side-angle).

In the process of proof we already have two congruent angle pairs and the missing bit is the included side.

In order to complete the proof we need to show that AE and CF are congruent segments.

We can show this as:

     Statement              Reason                                                                

Answer:

18√8 = 3√2 * 3√2

Step-by-step explanation:

I factored the square root of 8 into the square root of 2 times the square root of 2, because I believe that the square root of 8 was supposed to be factored based upon the hint provided.

This resulted in the expression 3√2 * 3√2, which is equivalent to 3*3*sqrt(2) * sqrt(2).

The coordinates of point B are (1,2).

How to find Reflection of a point?

When a point is reflected across the X-axis, the x-coordinates remain the same. But the Y-coordinates are transformed into their opposite signs. Therefore, the reflection of the point (x, y) across X-axis is (x, -y).

The reflected point will be equidistant from the point over which it is reflected as the original point and in the same line as the original point and the reflected point.

Find the difference between the x and y values of the given points and add that value (distance) to the reflection point.

x-values: 4-3 = 1   y-values: 0-(-2) = 2

Add to reflection point  x: 4-3 = 1     y: 0 -(-2)= 2

Hence, The coordinates of point B are (1,2).

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The slope of the line on the given graph in the image below is: 2.

To find the slope of the line in a graph, use any two points on the line and plug in the coordinates of the two points in the slope formula which is given as:

Slope (m) = change in y / change in x = rise/run = y2 - y1 / x2 - x1

Picking two points on the line, (0, 1) and (1, 3):

Slope (m) = change in y / change in x = (3 - 1) / (1 - 0)

Slope (m) = 2/1

m = 2

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The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = [tex](1 - lm z)^{-1}[/tex] as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + [tex]2^{1/z}[/tex] as z approaches infinity does not exist. This is because as z approaches infinity, the term  [tex]2^{1/z}[/tex] approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of [tex]2^{1/z}[/tex] approaches 1, but if we approach infinity along the imaginary axis, the limit of [tex]2^{1/z}[/tex] approaches infinity. Therefore, the limit of f(z) does not exist.

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Answer:

Step-by-step explanation:

A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:

For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).

For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)

B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:

(1/2x,1/2y) = (1/22, 1/20) = (1,0)

Therefore, the point (2,0) will go to the ordered pair (1,0).

C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.

As a result, option B is the equation that finds the equation of the line: y/x = 2/3.

An equation is a mathematical statement that indicates that two expressions are equal. It is a statement of equality that contains one or more variables, which are usually represented by letters. An equation consists of two sides separated by an equal sign (=). The left-hand side (LHS) and the right-hand side (RHS) of the equation may contain different expressions, which may include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

To find the equation of the line that passes through the points (0,0) and (6,4), we can use the slope-intercept form of the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope of a line is given by the rise over run, or the change in y divided by the change in x, between any two points on the line.

We can use the coordinates (0,0) and (6,4) to find the slope of the line:

slope = (change in y) / (change in x)

= (4 - 0) / (6 - 0)

= 4/6

= 2/3

Therefore, the slope of the line is 2/3.

To find the equation of the line, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where (x1, y1) is any point on the line. We can use the point (0,0), so the equation becomes:

y - 0 = (2/3)(x - 0)

Simplifying, we get:

y = (2/3)x

Therefore, the expression that finds the equation of the line is option B: y/x = 2/3.

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The shareholder's equity if $450 was put on credit is $175. Option D

The purchase of equipment for $625 represents a decrease in the company's shareholder equity, since assets have increased while the equity has not changed.

If $450 was put on credit, this means that the company has only paid $625 - $450 = $175 towards the equipment.

The shareholder's equity is reduced by this amount, so the new shareholder's equity is:

Shareholder's equity = Initial equity - Decrease in equity

Shareholder's equity = 0 - $175

Shareholder's equity = -$175

Since the shareholder's equity is negative, it means that the company owes more than it owns. Therefore, the answer $175.

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80 cubic inches is the volume of the given prism'

The given figure is made of triangular prisms. The formula for calculating the volume of rectangular prism is expressed as:

Volume = length * width * height

The given composite figure is made of 2 prisms. The volume is calculated as:

V = (5*1*6) + (2*5*5)

V = 30. + 50

V = 80 cubic inches

Hence the required volume of the figure is 80 cubic inches

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Answer:

Step-by-step explanation:

We can represent the 5 consecutive odd integers as:

1. x

2. x + 2

3. x + 4

4. x + 6

5. x + 8

"...the sum of the first three integers", then, is

x + (x + 2) + (x + 4)

That is "the sum of the last two plus 7", which is

(x + 6) + (x + 8) + 7.

The connecting word "is" means there is an equals sign right there. Therefore,

x + (x + 2) + (x + 4) = (x + 6) + (x + 8) + 7 which simplifies down to

3x + 6 = 2x + 21 after we combine like terms.

x = 15. That means the first integer is 15, the next one is 17, the third one is 19, the fourth one is 21, and the fifth one is 23.

Rounding this to the nearest foot, we get that the length of the guy wire is approximately 19 feet.

Units of length may have historically been determined by the lengths of human body parts, the distance traversed in a specified number of paces, the distance between well-known sites or locations on Earth, or randomly by the length of a well-known object.

The Pythagorean theorem can be used to resolve this issue. The guy wire is the hypotenuse of a right triangle made up of the guy wire, the pole, and the ground. The formula is as follows:

Guy wire length = stake to pole length + pole length to tower length

By entering the specified values, we obtain:

Guy wire length two equals two plus nineteen, or 365.

Guy wire length = 365 + 19.10 + guy wire length

If we round this number to the next foot, the guy wire's length is roughly 19 feet.

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Answer:

12 feet

Step-by-step explanation:

Let x be the length of the shorter part of the pipe.

According to the problem, the longer part is three times as long as the shorter part. Therefore, the length of the longer part is 3x.

We also know that the sum of the lengths of the two parts is equal to the original length of the pipe, which is 16 feet.

So we can write an equation:

x + 3x = 16

Simplifying this equation, we get:

4x = 16

Dividing both sides by 4, we get:

x = 4

So the length of the shorter part is 4 feet, and the length of the longer part is 3 times as long, or 3 × 4 = 12 feet.

what u need help with

5 - 1/4 in simplest form is 19/4.

The phrase "expressing a number, fraction, or statement in its simplest form" has a mathematical meaning. This signifies that further simplification or reduction of the result would cause a change in the result's value.

By dividing the numerator and denominator by their 4 greatest common factors, for instance, the fraction 4/8 can be made simpler. In its simplest form, this gives us 1/2. A different number, such as 0.5, which is not in its simplest form, results from additional simplification.

To simplify 5 - 1/4, we need to find a common denominator and combine the terms. The common denominator is 4, so we can write:

5 - 1/4 = 20/4 - 1/4

= (20 - 1)/4

= 19/4

Therefore, 5 - 1/4 in simplest form is 19/4.

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Answer:

if Hassan got 48/50 and scored an overall 5.7/6.0, and Emily got 32/40, her overall score would be approximately 5.6/6.0 (rounded to one decimal place).

Step-by-step explanation:

If Hassan got 48/50 and scored an overall 5.7/6.0, what would Emily's overall score be is she got 32/40?​

To determine Emily's overall score, we can use a proportion:

Hassan's score / Hassan's total = Emily's score / Emily's total

Substituting the given values, we get:

48/50 = 32/Emily's total

To solve for Emily's total, we can cross-multiply:

48/50 * Emily's total = 32

Simplifying the left-hand side, we get:

0.96 * Emily's total = 32

Dividing both sides by 0.96, we get:

Emily's total = 33.33 (rounded to two decimal places)

Now, we can use another proportion to find Emily's overall score:

Emily's score / Emily's total = 5.7/6.0

Substituting the value of Emily's total that we just found, we get:

Emily's score / 33.33 = 5.7/6.0

Solving for Emily's score, we get:

Emily's score = 31.4 (rounded to one decimal place)

Therefore, if Hassan got 48/50 and scored an overall 5.7/6.0, and Emily got 32/40, her overall score would be approximately 5.6/6.0 (rounded to one decimal place).

The numbers in the set can be compared by placing them in the number line, arranging the numbers from least to greatest as follows;

[tex]|-2\frac{1}{2} |[/tex], [tex]-\frac{1}{2}[/tex], [tex]1\frac{1}{2}[/tex], [tex]|\frac{1}{2} |[/tex] |-2|, [tex]-2\frac{1}{2}[/tex]

A number line is a series of numbers placed on the a line at regular intervals that can be used to express mathematical operations.

The elements in the set includes;

|-2 1/2|, -1/2, 1 1/2, |1/2|, |-2|, -2 1/2

The numbers within the absolute sign have a positive result, therefore;

|-2 1/2| = 2 1/2

|-2| = 2

The numbers in the set can be arranged in the order from least to the greatest as follows;

The above ordered numbers indicates that the specified numbers arranged in order from least to the greatest are;

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The baseball team won 87.5% of their games in that month.

In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.

The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.

Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.

Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance

To find the percentage of games won, we need to divide the number of games won by the total number of games played and multiply by 100%:

percentage of games won = (number of games won / total games played) x 100%

total games played = number of games won + number of games lost = 21 + 3 = 24

percentage of games won = (21 / 24) x 100%

percentage of games won = 87.5%

Therefore, the baseball team won 87.5% of their games in that month.

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Therefore , the solution of the given problem of percentage comes out to be  the original price of the hammer is $23, and the customer saved $5.75 with the discount code.

In mathematics, a percentage is any value that can be represented as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." Nonetheless, it is typically denoted by the "%" symbol. The proportional amount is flat and lacks any dimensions. As percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage. .

Here,

Let x be the original price of the hammer.

With the 25% discount, the customer pays 75% of the original price:

0.75x

And since there is free shipping, the customer pays only the price of the hammer:

0.75x = 17.25

Solving for x, we have:

x = 17.25 / 0.75 = 23

Therefore, the original price of the hammer is $23, and the customer saved $5.75 with the discount code.

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so the whole rectangle has an area of 22x18, now there's a tiny triangle on the corner, that we can say it has a base of 22 - 19 = 3, and a height of 18 - 14 = 4, so let's get both areas and subtract that of the triangle's from the rectangle's.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ rectangle }{(22)(18)}~~ - ~~\stackrel{ triangle }{\cfrac{1}{2}(\underset{b}{3})(\underset{h}{4})}}\implies 396-6\implies \text{\LARGE 390}~m^2[/tex]

The solution is, The volume is 1,260 in³ & The surface area is 864 in^2.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

First, let's find the volume

Volume = length × width × height

30 × 6 × 7 = 1260

The volume is 1,260 in³

Surface Area:

Small squares: 84

(7 × 6) · 2

Smaller rectangles: 360

(30 × 6) · 2

Bigger rectangles: 420

(30 × 7) · 2

Now, let's add all

84 + 360 + 420 = 864

The surface area is 864 in^2.

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The solution to the inequality  is [-∝, -6]

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

2/3x + 9 ≤ -2/3x + 1

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

Evaluate the like terms

4/3x ≤ -8

Cross multiply

4x ≤ -24

Divide by 4

x ≤ -6

As an interval notation, we have

[-∝, -6]

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The most appropriate inference procedure for the researchers to use is this:

The best inference to use for the scenario described in the text is a matched pair t-interval for a mean difference. This form of testing is used in order to determine the differences between variables that occur within a specific subject.

So, in this instance, we are measuring the timed differences between the mice and associating this with their learned behavior. The matched pairs t-interval will help the researcher to accurately identify any changes with respect to time.

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The solution of the equation is to the nearest ten-thousandth is x = 2.7712.

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459. Typically, the natural logarithm of x is expressed as ln x, loge x, or, if the base e is implicit, just log x.

The given equation is [tex]3^{x-1} = 7[/tex].

Take natural log on both sides of the equation:

[tex]\ln (3^{x-1} )=\ln( 7)[/tex]

(x - 1) ln(3) = ln(7)

x - 1 = ln(7) / ln(3)

x = 1 +  ln(7) / ln(3)

x = 2.7712

Hence, the solution of the equation is to the nearest ten-thousandth is x = 2.7712.

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(a) The vertex of ∠1 is B.

(b) The sides of ∠ABC are BA and BC.

(c) Two other names for ∠2 are ∠CBD and  ∠DBC

In geometry, the vertex of an angle is the common endpoint of the two rays that form the angle. The rays that form the angle are called the sides of the angle.

In the figure, the point B is the vertex of the angle ∠ABC (angle ∠ABC is equal to ∠1). The sides of the angle are BA and BC.

Thus, the vertex of ∠1 is B.

The sides of ∠ABC are BA and BC.

Two other names for ∠2 are ∠CBD and  ∠DBC

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Answer:

[tex]z = -2.1875[/tex]

Step-by-step explanation:

The z score is given by the formula
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

where

[tex]z =[/tex] standard score

[tex]x[/tex] = data point = 45 for this problem
[tex]\mu[/tex] = mean = 52 for this problem
[tex]\sigma =[/tex] standard deviation = 3.2 for this problem

Therefore
[tex]z = \dfrac{45 - 52}{3.2} = -2.1875[/tex]