Write this ratio as a fraction in simplest form without any units.

There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

Division is breaking a number up into an equal number of parts.

Given that, Willy Wonka makes a 13-metre chocolate and the chocolate bar is then cut into 4/11 of a metre.

Number of bars made = 13/4/11 = 35.75 ≈ 35

Hence, There will be 35 chocolate bar cut out from the 13-meter chocolate bar.

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Applying the exterior angles and triangle sum theorems, the statements that are true are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

All three interior angles of a triangle is equal to a sum of 180 degrees, based on the triangle sum theorem, while the exterior angle theorem states that the exterior angle of a triangle is equal to the two remote interior angles of the triangle.

Given the image showing the triangles and its exterior angles, the following can be deduced:

m∠2 + m∠3 + m∠5 = 180° [based on the triangle sum theorem]

m∠2 + m∠3 = m∠6 [based on the exterior angles theorem]

m∠5 + m∠6 = 180° [based on the triangle sum theorem]

Therefore, the true statements are:

C. m∠5 + m∠6 = 180°

D. ∠2 + m∠3 = m∠6

E. m∠2 + m∠3 + m∠5 = 180°

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By using the law of exponents, it has been proved that

[tex]a^{-n} = \frac{1}{a^n}[/tex]

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),

a is the base and m is the index.

The laws of exponents are

[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]

We know this law

[tex]a^p \times a^q = a^{p + q}[/tex]

Putting  p = n and q = -n

[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]

So,

[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

Absolute value is always non-negative.

B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)

1000 + 25 + 200 = 1225

Answer: 12 inches

Step-by-step explanation:

Answer: 15 cm

Step-by-step explanation:

There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume

The volume of cube is calculated by using a × a × a = a³ where "a" is the edge.

The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches

The volume of the smallest cube = 3.375inches³

The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches

The volume of the largest cube = 421.875inches³

Thus, the number of the smallest cubes it would take to fill the largest cube is derived by

421.875inches³/3.375inches³ = 125.

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The length of the line segment will be 4 units. Then the correct option is A.

The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,

D² = (2 - 2)² + (2 + 2)²

Simplify the equation, then we have

D² = (2 - 2)² + (2 + 2)²

D² = (4)²

D = 4 units

The length of the line segment will be 4 units. Then the correct option is A.

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The missing diagram is attached below.

The sale price is $13.5 and discount is $1.5.

A price that is lower than the usual price.

Given that, a store sells a shirt at $15, and there is a discount of 10%.

Price reduced after discount = 10% of 15 = $1.5

Selling price = 15 - 1.5 = $13.5

Hence, The sale price is $13.5 and discount is $1.5.

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Answer:

3

Step-by-step explanation:

Hope this helps..

Answer:

B) x + 1

Step-by-step explanation:

Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.

Eg: 5 , 6 , 7 ,.....

6 = 5 + 1

7 = 6 + 1

So, if first number is x, then the next number will be x + 1

From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|

What is graph of a function?

The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.

Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.

Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|

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1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches  form a right triangle.

What is Right traingle?

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.

When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),

assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;

The Pythagoras Theorem is:

[tex]a^2+b^2=c^2[/tex]

Making substitutions and applying the math results in:

[tex]15^2 + 36^2= 39^2[/tex]

225 + 1296 = 1521

1521 = 1521

Therefore, it is a right traingle.

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The difference between 2 parts of congruency is as follows.

What is congruent?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’

Main Body:

ASA vs AAS:

            ASA stands for “Angle, Side, Angle”,

            AAS means “Angle, Angle, Side”

ASA  ===

two triangles are congruent if they need associate equal aspect contained between corresponding equal angles. If the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the enclosed aspect of 1 triangle are congruent, severally, to the 2 angles and therefore the enclosed aspect of the second triangles, then it satisfies the condition that the triangles are congruent.

AAS===

two angles and an opposite facet. AAS is one amongst the 5 ways that to see if 2 triangles are congruent. It states that if the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the facet opposite to at least one of them in one triangle are congruent to the corresponding angles and therefore the non-included facet of the second triangle, then the triangles are congruent.

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First, 108/9=12

This means that are 12 groups of people.

If there are 8 students in each group, 12 x 8 = 96.

96 should be your answer.

Answer:

Step-by-step explanation:

1) 4 1/4 + 5 1/2

= 9 3/4

2) 10 4/5 - 6 1/5

= 4 3/5

3) 3 1/4 - 1 3/4

= 1 1/2

4) 3 2/5 + 7 7/10

= 11 1/10

5 ) 10 3/13 + 2 10/13

= 13

Answer:

1

Step-by-step explanation:

Its for sure 1

The exponential decay formula can take one of three forms:

f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]

Where,

a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality

What is Exponential Decay ?

Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.

The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:

f (x) = abx

f (x) = a (1 – r)x

P = P0 e-k t

Where,

a (or) P0 = Initial amount

b = decay factor

e = Euler’s constant

r = Rate of decay (for exponential decay)

k = constant of proportionality

x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).

In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as

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Answer: 96

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Isosceles triangle problem can be solved by given steps

what is isosceles triangle ?

An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.

explanation:

In isosceles triangle

1. Two sides of the triangle are congruent

2. The angle opposite those sides are congruent

x + 72 +72 = 180

             x  = 180 -144

             x = 36

Hence the isosceles triangle problem can be solved by above steps and explanation

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The value of the solution is 6.6%

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation might be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!

According to the above question :-

= (3 × 4)C3 × (52 — 3 × 4)C(5 — 3) / 52C5

= 12C3 × 40C2 / 52C5

= 12! × 40! × 47! × 5! / (52! × 9! × 3! × 38! × 2!)

= 12!/9! × 40!/38! × 47!/52! × 5!/(3!2!)

= ((10 × 11 × 12) × (39 × 40) / (48 × 49 × 50 × 51 × 52)) × (5 × 4 / 2)

= 10 × (1 × 11 × 1 × 3 × 40) / (4 × 49 × 5 × 51 × 4)

= (10 × 40 / (4 × 5 × 4)) × (11 × 1 / (49 × 17))

= 5 × 11 / (49 × 17)

= 55 / (17 × (50 — 1))

= 55 / (850 — 17)

= 55 / 833

≈ 6.6%

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The range and the domain of the function f(x) =  1 - x^2 is less than or equal to 1 and all values of x are a real number (R).

Domain: x ∈ R

Range: f ( x ) ≤ 1, ∈ R

f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).

x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.

Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.

So, the range of f(x)≤ 1, and the domain is all real values ( R ).

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The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

we know that

The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.

therefore

Is the point of concurrency of the angle bisectors of the triangle

Part 2)

we know that

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side

therefore

Is a segment drawn  from a vertex to the midpoint of the opposite side

Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle

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A. Congruence means the same.

B. Angle addition postulate states that two angles side by side sum the measure of the two angles.

C. Linear pair theorem states that linear pair angles add up to 180 degrees.

D. Vertical angles theorem states that vertical angles are congruent.

Congruence in angles simply means the same or equals to.  Two angles are congruent when they are the same.

The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.

The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.

The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value

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The rate of change in the given interval would be 1.25 ft/s.

What is the rate of change?

The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.

By observation, we can take the points from the graph in between the given interval.

The points would be (3, 2.5) and (5, 4)

Then the rate of change = y2 - y1/ x2 - x1

                                         = 4 - 2.5/5 - 3

                                         = 2.5/2

                                         = 1.25 ft/s.

Hence, the rate of change in the given interval would be 1.25 ft/s.

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The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.

Two triangles are congruent if and only if they have the same three sides and angles.

SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.

ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.

AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.

HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.

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Y = 1x – 2 is the equation for linear regression.

A linear regression line is represented by the equation Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of a line, b, is equal to the intercept of that line, which is the value of y when x = 0.

Based on the value of another variable, linear regression analysis can be used to predict the value of a variable. You want to be able to predict the dependent variable. You create a forecast about the value of the other variable using the independent variable.

A positive linear relationship exists if the slope of the line is positive, meaning that when one rises, the other rises as well.

Y = -2 -1 x

Y= -2 -1x

Y = 1x - 2

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The concurrency point for medians of a triangle is known as centroid.

A median is a line drawn from one of the vertices of a triangle that bisects the side opposite to the vertex. Since there are 3 vertices in a triangle, there are also 3 medians in a triangle. A median divides the triangle into 2 equal halves.

The 3 medians of a triangle intersect at a point inside the triangle. This point is known as the centroid of the triangle. It is the center point of a triangle and divides the medians in the ratio of 2 : 1.

Thus, the name of concurrency for medians of a triangle is centroid.

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The lowest form of 6/42 is 1/7 and,

the lowest form of 14/28 is 1/2.

What is the lowest form of fraction?

When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form. This is also known as its Lowest form.

In fraction 6/42, both denominator and numerator have common factor as 6, So we divide the denominator and numerator by 6.

Hence, we get 1/7.

Similarly, In fraction 14/28, both denominator and numerator have common factor as 14, So we divide the denominator and numerator by 14.

Hence, we get 1/2.

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