The coordinates of triangle ABC are (1,4), (4, 1) and (1,1). Find the new points of A'B'C' with a dilation centered at the origin and a scale factor of 2.
A' (___)
B' (___)
C' (___)
Draw the image on the Coordinate plane.

Answer: I believe 20.

Take one pair of lines. They will intersect at a point (no lines parallel). The other four lines will intersect at different points (no more than two lines through one point) giving four triangles. There are 6C2 = 15 different pairs of lines so 15*4 = 60 triangles. However, each triangle will come from three different points so we need 60/3 = 20 distinct triangles.

EDIT: Now that I’m more awake, it occurs to me there is a much easier answer. Since no two lines are parallel and no three lines are coincident, every combination of three lines must form a triangle. There are 6C3 = 20 triangles.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

combinations

C(n,r)= n! / (r! * (n−r)!)

n = 6 : total number of lines

r = 3 : because its 3 lines to make a triangle

6 lines

6C3 = 20 triangles

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The statement regarding the correlation coefficient (r) that is true is b) "the correlation coefficient describes the direction of the association between two variables."

The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 1 implies a strong positive correlation between the variables, meaning that as one variable increases, the other variable also tends to increase.

A correlation coefficient of -1 implies a strong negative correlation between the variables, meaning that as one variable increases, the other variable tends to decrease. A correlation coefficient of 0 implies no correlation between the variables. The sign of the correlation coefficient (positive or negative) indicates the direction of the association between the variables, while the magnitude of the coefficient (closer to 1 or -1) indicates the strength of the association.

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The number of ways in a class of size 60 where no two students will have the same birth date is 365 x 364 x 363 x 362 x ........... x 306.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of students = 60

We will assume 365 days in a year.

Now,

The first student will have 365 possible days for his birthday.

The second student will have 364 possible days for his birthday.

In this way,

The last student will have (365 - 59) possible days for his birthday.

Now,

The number of possible ways for 60 students.

= 365 x 364 x 363 x 362 x ........... x 306

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The Answer Is 1,837 cm

Answer: The mean is less than the median IQ

Step-by-step explanation:

When a distribution is skewed left (there is an obvious tail going in the left direction, which is true in this case), then the mean is drawn down because it is not resistant to any outliers, or unusual data points.

The median, however, is resistant to outliers and will not move as much.

Therefore, the mean will be less than the median.

The relationship between the mean and median of a data set is determined by whether the data is symmetrically distributed, positively skewed, or negatively skewed. However, without a visual representation or specific values, we cannot definitively compare the mean and median of the IQ scores.

In order to determine the relationship between the mean and the median of a data set, we need to know the nature of its distribution. If the data is symmetrically distributed, the mean and the median will be equal. If the data is positively skewed (has a long right tail), the mean will be larger than the median. If the data is negatively skewed (has a long left tail), the mean will be less than the median.

However, in the absence of the actual histogram in your question, the correct answer would be 'It cannot be determined because we cannot tell the exact values of the IQ scores in the sample.' This is because without a visual representation or specific values, we cannot determine the distribution's skewness, and by extension, cannot compare the mean and median.

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The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.

Every point in a circle is equally distance from the center. Similar to a sphere, every point on a sphere is equally distance from the center.

Two equal chords on a circle indicate that they are equally spaced from the circle's center.

The incenter of a triangle is the point that is equally far from each of its sides. A median is a line segment that has one of its endpoints in the vertex of a triangle and the other endpoint in the midpoint of the side opposite the vertex. The three medians of a triangle meet in the centroid.

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By using the property of combination, it can be calculated that -

This is a problem of combination.

There are 15 ways to choose the students who will go to the meeting

What is combination?

Combination is the process of selection some objects from a group of items where the order of the selection do not matter

This is a problem of combination

Number of seniors = 6

Number of students will go to the all district meeting = 2

Number of ways to choose the students who will go to the meeting =

                                                                                                       [tex]{6 \choose 2}[/tex]

                                                                                                = [tex]\frac{6!}{(6 - 2)! \times 2!}[/tex]

                                                                                                = 15

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Horizontal asymptotes is a horizontal line and its equation is y=k

vertical asymptotes is a vertical line and its eqaution is x=k

In these given lines we can find horizontal and vertical asymptotes.

To find the horizontal asymptotes ,we compare the degree of the numerator with the degree of denomenator.

f(x)=ax^n/bx^m

if degree of numerator is greater than degree of denominator then does not exist horizontal asymptotes.

To find  the vertical asymptotes , we use

f(x)= p(x)/q(x)

To set the denominator q(x) to zero ,and solve the value for x.

where p(x) and q(X) are polynomial functions and q(x) [tex]\neq[/tex] 0

vertical asymptotes is x=k where k represents real zero of q(x).

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Answer:0.5x - y -7.5 = 0

Step-by-step explanation:

For the given observation 5,6,7,8,9,11 the Median is 7.5

The median is one of the metrics of central tendency. The middle value in a group of numbers is known as the median. It divides a given data sample into the higher half and the lower half. At least half of the observations fall below the median and at least half of the observations fall above the median.

If a data collection contains an even number of observations, the median can be determined as follows:

Sort the information either by ascending or by descending.

Identify the (n/2)nd and [(n/2) + 1] th observations if there are an even number of observations (let's say n).

The median of the provided data is equal to the average of the top two observations (as determined in step 2).

Here n = 6, So [6/2 + (6/2)+1}/2

=>  Median = 7.5.

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According to question,

Given data,

We know that;

Zero product property,

ab =0

either a or b or both must be zero.

(x-5) (x+7) = 0

Where a=(x-5)

b= (x+7)

then,

x-5=0(both side equation adding +5)

 +5=+5

So,

x = 5

therefore,

x+7=0(both side equation substrate -7)

 -7=-7

So,

x=7

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The equation to form 5 with 4 2s is 2 + 2+ (2/2).

Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.

The formation of 5 with 4 2s is -

= 2 + 2+ (2/2)

= 2 + 2 + 1

= 5

Thus, the expression to form 5 with 4 2s is 2 + 2+ (2/2).

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Answer:

x is 5 cm

Step-by-step explanation:

x is half of the diagonal and we can see that the diagonal is 10 cm

and half of 10 is

The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

What is Standard Deviation?

It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.

The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.

The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.

To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.

Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.

So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

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Answer:

Slope

Angle (degrees) Gradient Grade (%)

Therefore, the correct answer is 5.24

[tex]y=2[/tex] ± [tex]\sqrt{28+4x}[/tex] is the equation that equals 2(x - 2)2 = 8(7 + y).

Addition and subtraction, multiplication, and division are examples of inverse operations, which are pairs of mathematical operations where one operation reverses the effects of the other. In most cases, a number's inverse refers to its reciprocal, or x - 1 = 1 / x. When a number is combined with its reciprocal, or inverse, the result is 1, or 1.

Considering the equation:

[tex]2(x-2)^2=8(7+y)[/tex]

Change the x and y variables.

[tex]2(y-2)^2=8(7+x)[/tex]

In terms of x, solve for y.

We have two sides, therefore divide them by two.

[tex](y-2)^2=4(7+x)[/tex]

Using the distribution property, [tex]a.(b+c)=a.b+a.c[/tex]

[tex](y-2)^2=28+4x[/tex]

Square-rooting both sides yields:

[tex]y-2=[/tex]±[tex]\sqrt{28+4x}[/tex]

our two sides plus two;

[tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex]

As a result, equation [tex]y=2[/tex]±[tex]\sqrt{28+4x}[/tex] is the opposite of [tex]2(x-2)^2=8(7+y)[/tex]

The complete question is:-

Which equation is the inverse of 2(x – 2)2 = 8(7 + y)?

Options:

–2(x – 2)^2 = –8(7 + y)

y= 1/4 x^2 -x -6

y= -2 +/- sqrt of 28+4x

y= 2 +/- sqrt of 28+4x

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Answer:

The tree is 10.77 meters tall.

Step-by-step explanation:

The given diagram is an example of similar triangles. Look at the image I attached to my response to see this problem in terms of triangles.

The triangle that is formed by Alyssa and her shadow and the triangle that is formed by the tree and its shadow is an example of similar triangles because they both share an internal angle.

As per the similar triangles theorem, the ratios of the corresponding sides of both sides are proportional.

Thus, we have to make a proportion of the corresponding sides of both triangles to solve for the height of the tree. Let x = the height of the tree.

Proportion: [tex]\frac{BE}{BC} = \frac{DE}{AC}\\[/tex]

BE = 4.25 meters

BC = 27.75 meters

DE = 1.65 meters

AC = x meters

[tex]\frac{4.25}{27.75} = \frac{1.65}{x}[/tex]

Now, cross multiply to solve for x.

[tex]4.25x = 1.65(27.75)\\4.25x = 45.7875\\x = 10.77[/tex]

∴ The tree is 10.77 meters tall!

The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

We have to given that;

Alyssa is 1.65 meters tall. At 11 a.m., she measures the length of a tree's shadow to be 27.75 meters. She stands 23.5 meters away from the tree.

Now, we can make a proportion of the corresponding sides of both triangles to solve for the height of the tree.

And,  Let us assume that,

x = the height of the tree

Hence, We get;

⇒ (27.75 - 23.5) / 27.75 = 1.65 / x

Solve for x;

⇒ 4.25 / 27.75 = 1.65 / x

Cross multiply we get;

⇒ 4.25x = 1.65 x 27.75

⇒ 4.25x = 45.78

⇒ x = 10.77 meters

Thus, The height of the tree to the nearest hundredth of a meter is,

⇒ 10.77 meters

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Answer:

$218.5

Step-by-step explanation:

its $218.5 because 250 - 56.50 = 193.5 and 193.5 + 25.00 + 218.5

The number of two-points and three points shot The Cruisers scored are 24 and 19 points respectively.

The Cruisers scored a total of 105 points in a basketball game. They also had a total of 43 baskets, of which some were two-point shots and some of were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

x = number of two-points

y = number of three-points

So;

x + y = 43 -------1

Also;

2x + 3y = 105 -----2

Multiplying equation(1) by 2

2x + 2y = 86

2x + 3y = 105

Subtract equation(i) from equation(ii)

y = 19

To find x:

x = 43 - 19

x = 24

Therefore,

number of two-points = 24

number of three-points = 19

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The denominator of a fraction represents the number of equal parts in a whole, while the numerator represents the number of parts considered.

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Answer:

increase 10.5 percent

Step-by-step explanation:

..

Therefore , the 2 year old children can able to count to 1 to 100 counting by making them learn.

The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number,

variable then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."

Here,

Every child is different in how they grow and learn, yet many

Children as young as two years old may count past ten and learn their numbers from 1 to 100.

They could be ready to try numbering in fives or using other skip counting strategies (5, 10, 15, 20, and so on).

As soon as you can, begin teaching your child how to recognise

numbers.

As a result, by making the toddlers study, two-year-olds can count to one hundred.

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Answer:

0

Step-by-step explanation:

Rise over run.

Difference between y is 0.

Difference between x is 5.

0/5 = 0.

Answer:

m = 0

Step-by-step explanation:

Slope is rise/run or (y2 - y1) / (x2 - x1)

We see the y stay the same, and the x decrease by 5, so the slope is

m = 0/5

Answer:

Step-by-step explanation:

Your question asks what is  -[tex]3^{2}[/tex] / 2    but,  since it's on the Unit circle, I know you meant   - [tex]\sqrt{3}[/tex] /2    Also, it's one of those known angles on the unit circle.

note that the angles can all be put in the form of  [tex]\sqrt{x}[/tex] / 2 , where x = 0,1,2,3,4 ,  for the five special points on the unit circle.  

as the attached pic shows,   Cos(t) for the given point would be 180-150°= 30 and sin(t) would be 90 - 30 = 60 °

it's not easy to understand how I got those angles,  just ask if you don't get it.  :)

We can find out the missing values of the sides of a triangle by using trigonometry functions like sin, cos, and tan.

If one angle and perpendicular are given then the other side means hypotenuse can be found out by sin function.

Sin Ф = perpendicular/hypotenuse

If one angle and hypotenuse are given then the other side means base can be found out by the Cos function.

CosФ = base/ hypotenuse

If one angle and base are given then the other side means perpendicular can be found out by the tan function.

Tan Ф= perpendicular/ base

Therefore the missing sides can be found by trigonometric function while one angle is given.

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The property that represents the commutative law of sets is given as follows:

d. (A ∪ B) ∪ C = A ∪ (B ∪ C)

The cumulative law of sets states that the order in which the union operation is made does not change the resulting set of these multiple union operations.

The symbol that represents the union operation is given as follows:

∪.

Hence statement d is the correct statement of the commutative law of sets, as:

For both cases, the resulting set is the same.

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Answer: You are correct, because negative number don't have real square roots

Step-by-step explanation:

Using the geometry of the right angle triangle. Since, The narrower hallway is 6ft. The answer is 6ft.

A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.

A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

Larger hallway= 9 ft

narrower hallway=6 ft

Since, After turning in the corner, The pole should be carried through the 6ft wide hall. The maximum length of the pole is 6ft.

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According to good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats.

It might be challenging to calculate or estimate the precise amount of paint that you will need when painting your home.

Every paint has a spread rate that controls how many square feet may be covered each gallon. A good rule of thumb is 250 to 400 square feet per gallon for each coat, and 170 to 200 square feet per gallon for two coats. Choosing the proper quantity of paint for steel is a tough matter because high-quality paint is expensive and you don't want to overbuy. To avoid overbuying paint, we advise simply purchasing 80% of the projected amount at first and the remaining 20% after you are nearly completed.

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The required solution would be h = 3Vr²/3.14 for h, where V is the volume of a cone.

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

The volume of the cone (V ) = 1/3πhr²

We have been given that the volume of a cone is (1/3)3.14r²h

We have to determine the solution for h

As per the given question, we have

⇒ V = (1/3)3.14r²h

Multiply by 3 into the above equation,

⇒ 3V = 3.14r²h

Divided by 3.14 into both sides

⇒ 3V/3.14 = r²h

⇒ h = 3Vr²/3.14

Therefore, the required solution would be h = 3Vr²/3.14.

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