A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)

Answer:

C. A clothing store claims that 45% of its customers prefer skinny jeans over regular jeans. They concluded this from a survey which asked 120 randomly selected teenage customers which style they prefer.

E. A report by a company that manufactures hair brushes says 56% of people who buy their brushes own only one hair brush. The conclusion comes from a survey of 500 males who bought the company's brush.

Step-by-step explanation:

These two are the biased reports because they don't include the full population.

C is biased because it only includes teens, not people of any other age.

E is biased because it only included males, not females.

A isn't biased because it includes the stated population, high school students in the city.

B isn't biased because the sample was of 50 random customers, which is the general population.

D isn't biased as it included all data from the website.

Hope this helps!

The solution is,:

1) A clothing store claims that 45% of its customers prefer skinny jeans over regular jeans. They concluded this from a survey which asked 120 randomly selected teenage customers which style they prefer.

3) A report by a company that manufactures hair brushes says 56% of people who buy their brushes own only one hair brush. The conclusion comes from a survey of 500 males who bought the company's brush.

A portion of population taken and analyzed to predict information about population is called sample of that population.

Ex: When someone surveys a group, then he/she surveys a portion and not whole population in general.

Those numbers who summarize information about sample are called statistic.

(Statistic is different than statistics)

The  numbers which summarize information about the sample are called statistic.

The scenarios in which the statistics are misleading;

1) A clothing store claims that 45% of its customers prefer skinny jeans over regular jeans. They concluded this from a survey which asked 120 randomly selected teenage customers which style they prefer.

3) A report by a company that manufactures hair brushes says 56% of people who buy their brushes own only one hair brush. The conclusion comes from a survey of 500 males who bought the company's brush.

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The distance at which the height of the pumpkins are the same.

What is Distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Reason:

Both equations' graphs would be at an intersection, which would indicate that their x and y coordinates are identical. The same y coordinate would indicate being at the same height at that precise distance since y refers to the pumpkin's height.

The distance at which pumpkins are the same height.

For Full question refer the statement below:

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent? the height at which the pumpkins reach their greatest horizontal distance from the launch site the horizontal distance of the pumpkins from the launch site when they reach the ground the starting height of the pumpkins when they are at the launch site the horizontal distance of the pumpkins from the launch site when their heights are the same

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Answer:

Area of the shape is 244.98cm² is B

Step-by-step explanation:

Area of shape=Area of semi circle+Area of trapezoid

A=1/2 πr² + 1/2(a+b)h

A=1/2×3.142×7² + 1/2(14+18)10.5

A=1/2×3.142×49 + 1/2×32×10.5

A=76.98+168

A=76.98+168

A=244.98cm²

Answer:

The answer would be approximately 53.976

Step-by-step explanation:

Answer:

53.976

Step-by-step explanation:

I hope this helps!

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)  

=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)  

From the above calculations given fractions are 31/36 and 32/36

Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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The slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line passes through points (8, 7) and (4, 5). The slope of the line will be calculated as,

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( 5 - 7 ) / ( 4 - 8 )

Slope = -2 / -4

Slope = 1 / 2

Calculate the y-intercept,

y = mx + c

5 = 1 / 2 x 4 + c

c = 5 - 2 = 3

The equation is written as,

y = mx + c

y = 1/2x + 3

Therefore, the slope of the line is 1 / 2. The equation of the line is y = 1/ 2 x + 3.

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The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.

In this problem we find a polar equation, that is, f(r, θ) = C, whose Cartesian form must be found by using the following substitutions:

x² + y² = r²                 (1)

x = r · cos θ               (2)

y = r · sin θ                (3)

Then, the Cartesian form of r² = 5 is:

x² + r² = 5

The polar equation represents a circle centered at the origin and with a radius of √5.

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The Cartesian equation of the polar equation r² = 5 represents a circle centered at the origin and with radius √5.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points.

Given that r²=5

we find a polar equation,

x²+y²=r²

whose Cartesian form is found by substituting

x=rcosθ

y=rsinθ

as r²=5 then r=√5

So x²+y²=5.

This is equation of circle in polar form.

Hence it represents a circle with a radius of √5.

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Answer:

no one and i am doing time pass and

6 130 will be a right answer

whe it is rong i am sorry

Answer:

6 teachers, and 130 student's

Step-by-step explanation:

With constant of proportionality=2, the direct proportion equation for the given information is m = 2n.

What is a constant of proportionality?

A constant of proportionality is a value that relates two variables that are directly proportional to each other. In a direct proportion, if one variable (say, x) increases by a certain factor, then the other variable (say, y) also increases by the same factor. The constant of proportionality is the ratio of the two variables.

For example, if y varies directly with x, we can write:

y = kx

where k is the constant of proportionality.

Now,

If m varies directly as n, then we can write:

m = k * n

where k is a constant of proportionality. To find the value of k, we can use the given information that m = 14 when n = 7:

14 = k * 7

Solving for k:

k = 14/7

k = 2

Substituting this value of k in the direct proportion equation:

m = 2n

Therefore,

                the direct proportion equation for the given information is m = 2n.

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Answer:

The 1st word problem.

Step-by-step explanation:

In the second word problem, the beginning elevation is -60 meters. The ending elevation is a forest with an elevation of 60 meters.

The question asks how much higher the elevation where Hayley goes camping than the elevation of desert shores.

Hayley's elevation=60 meters

Desert Shore's elevation = -60 meters.

60-(-60) = 60+60 = 120

The first word problem asks for the elevation where Hayley is going camping.

Hayley's elevation is Deserts shore's elevation + 60.

DSE= -60

-60+60=0

The first answer is correct.

we have the points

(7,2) and (7,4)

Note that the x-coordinate of both points is the same

that means

we have a vertical line

so

The slope is undefined

The other two points could be

(7,6) (7,7)

any point with the x-coordinate equal to 7

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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Answer:

-7/12

Step-by-step explanation:

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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This is not a literal equation but you can divide 3.14 divide by 5

Step-by-step explanation:

Ken will receive a total dividend payment of $75 for that quarter.

We have to given that,

Ken owns 500 shares of LaceNBrace, which makes hockey equipment.

And, He receives a notice stating the company will be paying $0.15 dividend per share.

Now, For the total dividend payment Ken receives for that quarter, we can multiply the dividend per share by the total number of shares he owns:

= $0.15 per share x 500 shares

= $75

Therefore, Ken will receive a total dividend payment of $75 for that quarter.

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The standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

In order to use the formula sigma x = sigma/ to calculate the standard deviation of the sampling distribution of the sample mean, all three conditions must be met. The first condition is that n must be greater than or equal to 30. This is because the larger the sample size, the more likely it is that the population's distribution is approximately normal. The second condition is that the population's distribution is approximately normal. This is because the Central Limit Theorem states that when the sample size is large enough (usually n ≥ 30) the sample means will have an approximately normal distribution. The third condition is that the sample size is less than 10% of the population size. This is because samples that are too large can lead to sample means that are not representative of the population.

To calculate the standard deviation of the sampling distribution of the sample mean, we can use the following formula:

σx = σ/√n

Where σ is the population standard deviation, and n is the sample size. For example, if the population standard deviation is 5, and the sample size is 30, then the standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

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Answer:

y = - 1/5x - 6

Step-by-step explanation:

Slope: -1/5

y-intercept: -6

The medians are about the same.

Option C is the correct answer.

The median, in statistical terms, refers to the value in the center of a dataset that has been sorted either in ascending or descending order, and it is a commonly used measure of central tendency. This contrasts with the mean, which calculates the total value of all figures, then divides by the number of figures.

We have,

Movie theater 1.

From the box plot given,

The median is 995.

Movie theater 2.

From the box plot given,

The median is 995.

Thus,

The median in both the box plot is the same.

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Enseñanza Básica is the term used to describe the first level of education in the Chilean education system, which includes the first to eighth grades. A teacher of Enseñanza Básica asked his students to choose three-digit mixed numbers that can be formed.

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The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

The three digits different from {1, 2, 3, 4, 5} can be chosen from {0, 6, 7, 8, 9}.

The greatest mixed number is formed by placing the largest digit as the whole number and the remaining two digits as the fraction in descending order, i.e., 9 87/100 or 9.87.

The smallest mixed number is formed by placing the smallest non-zero digit as the whole number and the remaining two digits as the fraction in ascending order, i.e., 6 07/90 or 6.0789.

The difference between the greatest and the least mixed numbers is 9.87 - 6.0789 ≈ 3.7911.

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The Question in English

A Basic Education teacher tells his students to choose three digits

different from the set {1, 2, 3, 4, 5} and form mixed numbers by placing the digits

in the locker It also reminds them that the fractional part has to be

less than 1, for example

2

3

5

. What is the difference between the greatest and the least of the

mixed numbers that can be formed?

Answer: the first one .5 second 5 third 8.5

Step-by-step explanation:

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:6.24

Step-by-step explanation:

\(\text{Given that,}\\\\(x_1,y_1) = (-1,-8)~~ \text{and}~~\text{Slope,}~ m = \dfrac 12\\\\\text{Point - slope form:}\\\\y-y_1 = m(x-x_1)\\\\\implies y-(-8) = \dfrac 12[x-(-1)]\\\\\implies y+8 = \dfrac 12 (x+1)\)

Applying the two-tangent theorem, the length of AN is: 21 units.

The two-tangent theorem is a geometric theorem that states that if two tangents are drawn to a circle from a point outside the circle, then the lengths of the tangent segments are equal. This theorem is often used in geometry to find the length of tangent segments and to prove the existence of tangents to circles.

More formally, the two-tangent theorem states that if P is a point outside a circle with center O, and if PA and PB are tangents to the circle from point P, then PA = PB. In other words, the lengths of the two tangent segments are equal.

From the image above, AM and AN are two tangents from the same circle. Also, AN is also tangent with 29 - 2y.

This implies that the three tangents are congruent. Therefore:

6y - 3 = 29 - 2y

6y + 2y = 29 + 3

8y = 32

y = 32/8

y = 4

AN = 6y - 3

Plug in the value of y

AN = 6(4) - 3

AN = 21 units.

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Answer:

so 1/4 of a circle is 90 degrees 1/4 is equal to 90 over 360 C it's 90 parts of 360. so here we go with this one. this angle is 20 degrees remember that's 90 alright the square one and this little part would be 20 degrees each angle appears wider as the Rays get longer.

Step-by-step explanation:

Let me know if this help's you lol :)

18 miles/s x 60 s/min = 1080 miles/min

6 min x 1080 miles/min = 6480 miles

Answer:

The number of miles that the earth travels in 2 minutes is 2,160 miles.

Step-by-step explanation:

So 18 miles in per minute is

=18 x  60

= 1,080 miles per minute

Now there are 2 minutesSo, the total miles should be

=1,080 x 2

= 2,160 miles

Therefore we can conclude that the number of miles that the earth travels in 2 minutes is 2,160 miles.