Please help ASAP!! and show step by step pls worth 35 points! and brainliest :)


After talking back to Grandma Sinko, Grandson Rinko is tasked with organizing Grandma Sinko's huge collection of silverware. He begins by sorting the forks. If he puts them in groups of 4, there are three forks left over. If he puts them in groups of 6, there are still three forks left over. If he puts them in groups of 12, how many forks will be left over?

We have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

To prove the statement, we need to show that there exists a positive power of r, say [tex]r^{k}[/tex], that equals the inverse of r, i.e.,  [tex]r^{k}[/tex], = [tex]r^{-1}[/tex].

Suppose all the powers of r are distinct, i.e.,  [tex]r^{n}[/tex]≠ [tex]r^{m}[/tex] for all n ≠ m in Z. Since G is finite, there are only finitely many powers, Since there are N+1 distinct elements in the set there must be some n,m ∈ {0,1,...,N} such that n < m and [tex]r^{n}[/tex] =  [tex]r^{m}[/tex]

Without loss of generality, assume n < m. Then we have:

[tex]r^{n}[/tex] =  [tex]r^{m}[/tex]

[tex]r^{m-n}[/tex]= 1

Let k = m - n > 0. Then we have:

[tex]r^{k}[/tex] = [tex]r^{m-n}[/tex]= 1

[tex]r^{-1}[/tex]= [tex]r^{(k-1)}[/tex]

Thus,  [tex]r^{k}[/tex] =  [tex]r^{(k-1)}[/tex], which is the desired result.

Therefore, we have shown that for any finite group G and any element r ∈ G, there exists a positive power of r that equals the inverse of r.

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The statement can be linked to a theorem in geometry known as the "double angle rotation theorem". According to this theorem, if a geometric figure has symmetry about a straight line, and that line intersects another straight line at a point, then the symmetry of the figure about the second line is equivalent to a rotation of twice the angle from the first line to the second line, that is about the point of intersection.

In simple terms, the double angle rotation theorem means that if we can have a geometric figure that is symmetric about a line L1, and L2 is another line that intersects L1 at a point P, then we can rotate the figure about point P by twice the angle formed between L1 and L2 to get the same symmetry about the line L2.

The application of this theorem applies to various aspects of geometry that include transformational geometry and symmetry.

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Plotting the equation shows that the graph crosses the

The value of h is 8

To find the value of y when x is 3, we need to substitute 3 for x in the given equation -x^2 - x + 20:

y = -x^2 - x + 20 (substitute x = 3)

y = -(3)^2 - 3 + 20

y = -9 - 3 + 20

y = 8

Therefore, when x is 3, y is 8.

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The terrarium has 594 cm³ volume of dirt.

What is volume?

Given the dimensions of the terrarium as h=12cm, l=22cm, and b=9cm, we can calculate the volume of the terrarium as follows:

Volume of terrarium = length x width x height

= 22 cm x 9 cm x 12 cm

= 2,376 cm³

Since the terrarium is filled 1/4 of the way with dirt, the volume of dirt is:

Volume of dirt = (1/4) x Volume of terrarium

= (1/4) x 2,376 cubic cm

= 594  cm³

Therefore, the terrarium has 594 cubic centimeters of dirt.

what is terrarium?

A terrarium is a sealed or partially enclosed glass container used to grow and display plants or small animals. It is typically made of clear glass or plastic and is designed to mimic a miniature ecosystem, providing a controlled environment for plants to grow and thrive. Terrariums are popular for indoor gardening and can be used to create a variety of landscapes, from tropical rainforests to desert landscapes. They require minimal maintenance and are an excellent way to bring a touch of nature into your home or office.

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Complete question is: A terrarium is filled 1/4 of the way with dirt. the  terrarium have 594 cubic centimeters of dirt.

Elaine needs tο buy 350 inches οf fabric fοr her windοws.

A fractiοn represents a part οf a number οr any number οf equal parts. There is a fractiοn, cοntaining numeratοr(upper value) and denοminatοr(lοwer value).

If each windοw is 35 inches wide, then the tοtal width οf fabric Elaine needs is:

Tοtal width = 4 windοws x 35 inches per windοw

Tοtal width = 140 inches

Fabric = 2 1/2 x Tοtal width

Tο simplify this, we can first cοnvert the mixed number tο an imprοper fractiοn: 2 1/2 = 5/2

Then, we can multiply this fractiοn by the tοtal width:

Fabric = 5/2 x Tοtal width

Substituting the value οf Tοtal width, we get:

Fabric = 5/2 x 140 inches

Fabric = 350 inches

Therefοre, Elaine needs tο buy 350 inches οf fabric fοr her windοws.

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Answer:

It will take them 9756 minutes

Step-by-step explanation:

10 students take 813

How do you get from 10 to 120?

times 10 by 12

Now times 813 by 12

9756

The fraction for 6 and 10 is 6/10, which can be simplified to 3/5 by dividing both the numerator and denominator by their greatest common factor, which in this case is 2.

So 6/10 is equivalent to 3/5.

Answer:After layla adds a tip, the price of the item is $16.20. The percent of the tip is 10 %

Step-by-step explanation:

What is a tip?

A tip is a gift or a sum of money placed or given for a service performed or anticipated, by extension, a form of gratuity. Even if the service is poor, it's recommended you leave at least 10 percent.

How to calculate a tip?

There are four ways of calculating a tip:

Method 1: Move over the decimal in the bill total and then double that number.

Method 2: Multiply the tax of the bill by two.

Method 3: Double the pretax bill and then move the decimal over one space.

Method 4: Determine 10% of the bill and add half

a. The function that models the fox population t years after 2000 is:

[tex]p(t) = 12500 * e^{(0.05t)[/tex]

b. The estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).

Amοng the crucial kinds are: When there is a mapping fοr a range fοr each dοmain between twο sets, this is knοwn as an injective functiοn οr οne tο οne functiοn. When mοre than οne element is transferred frοm dοmain tο range, the functiοn is said tο be surjective οr tο be an οntο functiοn

(a) Since the fox population has a continuous growth rate of 5% per year, the population can be modeled using the exponential growth formula:

[tex]p(t) = p(0) * e^{(rt)[/tex]

where p(0) is the initial population, r is the continuous growth rate (expressed as a decimal), t is the time elapsed in years, and e is the mathematical constant e ≈ 2.71828.

Using the given information, we have:

p(0) = 12500 (the population in the year 2000)

r = 0.05 (the continuous growth rate)

Therefore, the function that models the fox population t years after 2000 is:

[tex]p(t) = 12500 * e^{(0.05t)[/tex]

(b) To estimate the fox population in the year 2008, we need to find the value of p(8) using the function from part (a):

[tex]p(8) = 12500 * e^{(0.05*8)} = 19121[/tex]

Therefore, the estimated fox population in the year 2008 is 19121 (rounded to the nearest integer).

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By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction is 8/21 .

To express a portion of a whole or the division of a quantity, use a fraction. It consists of a horizontal or slant line separating the two integers that make up the numerator and denominator. The total quantity of components in the whole is represented by the denominator, while the numerator is the number of equal parts that are being taken into account. As an illustration, the numerator and denominator of the fraction 3/4 are 3 and 4, respectively. Parts of a set, chunks of a pie, and ratios between quantities can all be represented using fractions. Using particular guidelines and algorithms, they can be multiplied, divided, added, or subtracted. To make calculations and comparisons simpler, fractions can be changed to decimals or percentages.

given

We combine the numerators and denominators together to multiply two fractions. So:

(4/9) x (6/7) = (4 x 6) / (9 x 7) = 24/63

By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction can be made simpler:

24/63 = (3 x 8) / (3 x 21) = 8/21

Because of this, 4/9 x 6/7 Equals 8/21.

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The linear equation that represents the cost of visiting the gym x times is: y = 2x + 25

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

The cost of joining a gym includes an initial fee of $25 and then $2 per visit. Let y be the total cost of visiting the gym x times.

To find the equation that represents this relationship, we need to determine the slope and the y-intercept.

The slope represents the rate of change of the cost with respect to the number of visits, which is the cost per visit. Since the cost per visit is $2, the slope is 2.

The y-intercept represents the initial cost of joining the gym, which is $25.

Therefore, the linear equation that represents the cost of visiting the gym x times is: y = 2x + 25

In this equation, x represents the number of visits to the gym, and y represents the total cost of those visits.

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The area of the regular polygon and rounded  to the nearest hundredth is 200 sq. units.

How to find the area of any polygon?

Area of Regular Polygon Formula = [tex]\frac{l^2n}{4tan\left(\frac{180}{n}\right)}[/tex] Square units

Length of side of the regular polygon is 5.2 and have n= 9 sides

Let's say, Area is A for the polygon,

[tex]A = \frac{(5.2)^2 \times 9}{4 tan\left(\frac{180}{9}\right)}\\\\A= 167.16\ sq.\ units\\A= 200\ sq.\ units\ (round-off\ to\ nearest\ hundred)[/tex]

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area is approximately 158.72 square centimeters

To find the area of a regular octagon with a given side length and apothem, we can use the formula:

Area = (1/2) × Perimeter × Apothem

where Perimeter is the total length of all the sides of the octagon.

We are given that the side length of the octagon is 5.2 cm and the apothem is 7.6 cm.

To find the perimeter of the octagon, we can use the fact that the octagon is a regular polygon and has eight equal sides. Thus:

Perimeter = 8 × side length = 8 × 5.2 cm = 41.6 cm

Now we can substitute the values we have into the formula to get:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 41.6 cm × 7.6 cm

Area = 158.72 cm²

Therefore, the area of the regular octagon with a side length of 5.2 cm and an apothem of 7.6 cm is approximately 158.72 square centimeters.

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Answer: What is minor arc and major arc?

Image result for 1. Name a minor arc. 2. Name a major arc. 3. Name a point of tangency. 4. Name a radius.

Every pair of endpoints defines two arcs. An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.

Step-by-step explanation:

Answer:

D) 105

Step-by-step explanation:

All 4 side shape's interior angle add up to 360

360 - 45 = 315

315 / 3 = 105

If 88% of the stamps were foreign, then the remaining 12% must be domestic stamps.

To find out how many domestic stamps Blake collected, we can start by calculating what 12% of 275 is:

12% of 275 = 0.12 x 275 = 33

The remaining stamps are foreign stamps.

Therefore, Blake collected 33 domestic stamps.

The square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).

It is the set of values of the variable for which the function has a valid output.

To find the domain and range of the function f(x) = [tex]sqrt(x^2 - 49)[/tex], we need to consider the possible values of x that make the function well-defined and the corresponding values of f(x) that the function can take.

The function f(x) is defined if the argument inside the square root is non-negative, that is, [tex]x^2 - 49[/tex] ≥ 0. This inequality can be solved as:

(x - 7)(x + 7) ≥ 0

The solution to this inequality is x ≤ -7 or x ≥ 7, so the domain of the function is D: (-∞, -7] ∪ [7, ∞).

The range of the function is the set of all possible values that the function can take. Since the square root function always returns a non-negative value, the range of f(x) is R: [0, ∞).

Therefore, the correct answer is (B) D: (-∞, -7] ∪ [7, ∞), R: [0, ∞).

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Answer:

Step-by-step explanation:

To simplify 5(y+2) +5(y-1), we distribute the 5 to each term inside the parentheses, and then combine like terms as follows:

5(y+2) +5(y-1)

= 5y + 10 + 5y - 5 // Distribute the 5

= 10y + 5 // Combine like terms

Therefore, 5(y+2) +5(y-1) simplifies to 10y + 5.

Answer:65

Step-by-step explanation:

Answer:

You can start by changing 12 3/4 into a decimal, which would be 12.75.

The formula for perimeter of a rectangle is (l + w) x 2, so you could write it like this:

(12.75 + 6.4) x 2

Then solve the question in the parenthesis...

19.15 x 2 = 38.30

Now, the question says to write the perimeter into simplest fraction form.

38.30 = 38 3/10.

So, there you have it!

38 3/10 meters

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The length of OI is 6.5 units. The solution has been obtained by using the Pythagoras theorem.

What is Pythagoras theorem?

Pythagoras' Theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given a circle with two tangents drawn from a external point and the radius perpendicular to the tangent measures 3.9 units.

We know that the tangents when drawn from a external point are equal in length.

So,

IK = IJ = 5.2 units

Now, in triangle OJI, using the Pythagoras theorem, we get

⇒ [tex]OI^{2}[/tex] = [tex]OJ^{2}[/tex] + [tex]IJ^{2}[/tex]

⇒ [tex]OI^{2}[/tex] = [tex]3.9^{2}[/tex] + [tex]5.2^{2}[/tex]

⇒ [tex]OI^{2}[/tex] = 15.21 + 27.04

⇒ [tex]OI^{2}[/tex] = 42.25

⇒ OI = 6.5 units

Hence, the length of OI is 6.5 units.

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The required solution of the given inequality is {m | 6 ≤ m < 9}.

In mathematics, inequality is a statement of an order relationship between two numbers or algebraic expressions that is greater than, greater than or equal to, less than, or less than or equal to.

According to question:

We can solve the inequality as follows:

3 + m ≥ 9 or 1 + 2m < 19

Subtracting 3 from both sides of the first inequality, we get:

m ≥ 6

Subtracting 1 from both sides of the second inequality and then dividing by 2, we get:

m < 9

Putting these two inequalities together, we get:

6 ≤ m < 9

This is the solution in interval notation. To write it in set-builder notation, we can use the following notation:

{m | 6 ≤ m < 9}

This means the set of all values of m such that m is greater than or equal to 6, and less than 9.

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Based on the given information, the measure of angle Y is 30 degrees.

A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.

There are several types of transformations, including:

Rotation: A transformation that rotates a figure around a fixed point, called the center of rotation, by a certain angle.

Reflection: A transformation that produces a mirror image of a figure across a line, called the line of reflection.

To start, let's first find the vertices of triangle XYZ after the given transformations:

Rotation of 90 degrees counterclockwise about the origin:

The rotation of point (x, y) by 90 degrees counterclockwise about the origin gives us the point (-y, x). So we can apply this transformation to each vertex of triangle ABC to get the vertices of triangle XYZ after rotation:

A = (cos(45), sin(45)) = (√2/2, √2/2) → A' = (-√2/2, √2/2)

B = (cos(55), sin(55)) → B' = (-sin(55), cos(55))

C = (cos(80), sin(80)) → C' = (-sin(80), cos(80))

Reflection across the line y=x:

To reflect a point (x, y) across the line y=x, we simply swap the x and y coordinates to get (y, x). So we can apply this transformation to each vertex of triangle XYZ to get the final vertices:

A'' = (√2/2, -√2/2)

B'' = (cos(55), -sin(55))

C'' = (cos(80), -sin(80))

Now we can use the law of cosines to find the measure of angle Y:

cos(Y) = [B''C''² + A''C''² - A''B''²] / [2 * B''C'' * A''C'']

= [cos(55)² + cos(80)² - (√2/2)²] / [2 * cos(55) * cos(80)]

≈ 0.866

So we have cos(Y) = 0.866, which means Y ≈ 30 degrees. Therefore, the measure of angle Y is approximately 30 degrees.

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Answer:

32°

Step-by-step explanation:

2x + 1 + x - 7 = 90

3x + 1 - 7 = 90

3x - 6 = 90

3x = 96

x = 32

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Answer:

Step-by-step explanation:

Value of x:-

[tex]\mathrm{(2x+1)+(x-7)=90^o}[/tex]

[tex]\mathrm{2x+1+x-7=90}[/tex]

[tex]\mathrm{(2x+x)+(1-7)=90}[/tex]

** [tex]\mathrm{2x+x=\bf 3x}[/tex]

** [tex]\mathrm{1-7=\bf -6}[/tex]

[tex]\mathrm{3x-6=90}[/tex]

[tex]\mathrm{3x-6+6=90+6}[/tex]

[tex]\mathrm{3x=96}[/tex]

[tex]\mathrm{\cfrac{3x}{3}=\cfrac{96}{3}}[/tex]

[tex]\mathrm{x=32}[/tex]

Therefore, the value of x is 32°.

____________________

Hope this helps!

This test is left-tailed and the test statistic is -1.53

Since the alternative hypothesis is that less than 10% of treated subjects experienced headaches, and this is a lower bound, the test is left-tailed.

To find the test statistic, we first need to calculate the expected number of subjects who would experience headaches if the null hypothesis were true (i.e., if the true proportion were 10%). This is found by multiplying the total number of treated subjects by the hypothesized proportion:

Expected number of subjects with headaches = 0.10 * 288 = 28.8

We then use the formula for the z-score of a sample proportion:

z = (p - P) / √(P(1 - P) / n)

where p is the sample proportion (21/288), P is the hypothesized proportion (0.10), and n is the sample size (288).

Plugging in the values, we get:

z = (0.073 - 0.10) / √(0.10 * 0.90 / 288) = -1.53

Therefore, the test statistic is z = -1.53.

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Answer:

(a) 7

(b) 7

(c) 27

The property of addition used in all three equations is the associative property, which allows us to regroup the numbers being added without changing their sum.

The measurement of angle EFG is 42.

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.

A straightforward illustration of a sector with a center angle of 180o is a protractor. The angle created by a circle's arc at its center is another way to describe the term "central angle."

We have a circle with center H and the central angle is 84 degrees

The central angle of the circle is double of circumference angle.

Then the measurement of angle EFG is 42.

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It be concluded that figure A and figure C are showing similar triangle but they are not congruent.

If two triangles are similar then they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are said to be similar figures.

Similarity of two triangles mean when two triangles satisfy the AAA property that is when three angles of one triangle is equivalent to angles with another triangle.

Here for the figure A and C they satisfy the AAA property.

Hence it be concluded that figure A and figure C are showing similar triangle but they are not congruent. The triangles have same shape but not in same size.

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