Hexagonal chess is played on a regular hexagonal board comprised of 92 small hexagons in three colors. The chess pieces are arranged so that a player can move any piece at the start of a game.

a. What is the sum of the measures of the interior angles of the chess board?

Answer: 21

the hcf of 315 and 42 is 21.

Answer:

HCF of 315 and 42:

Your answer is 21 !

The rectangle with an area of 24cm^2 and a perimeter of 20 cm can have dimensions of either 4cm x 6cm or 6cm x 4cm.

To find the dimensions of the rectangle, we first set up two equations based on the given information:

A = L x W and P = 2L + 2W.

We substitute the values of the area and perimeter and simplify the equations to get

L x W = 24cm^2 and L + W = 10cm.

We then use the second equation to solve for L in terms of W and substitute the expression for L into the first equation.

This leads to a quadratic equation, which we solve to get the possible values of W.

We then use the expression for L to find the corresponding values of L for each value of W.

Thus, we find that the rectangle can have dimensions of either 4cm x 6cm or 6cm x 4cm.

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The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

Given that

In a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal. Calculate a 90% confidence interval for the percentage of all U.S. adults who support the proposal based on the results of this poll (at the time of the poll). Complete the table below after that. Carry your calculations to a minimum of three decimal places.

We have to find the lower limit of 90%.

We know that

In a poll of 200 randomly selected U.S. Among adults, 104 expressed support for the novel idea.

p-hat = 104/200 = 0.52

ME = z×√[pq/n] = 2.5758×√[0.52*0.48/200] = 0.091

Now, the lower limit of the 90% confidence interval well be

p-hat-ME = 0.52-0.091 = 0.429

Therefore, The lower limit of the 90% confidence interval is 0.429 when in a survey of 200 randomly chosen American adults, 104 responded in favor of the proposed proposal.

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The table of values that represents exponential decay is (c)

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

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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Answer:

\(\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}\)

\(36 - 5x = 7x + 48 \\ 36 - 48 = 7x + 5x \\ - 12 = 12x \\ \frac{ - 12}{12} = x \\ 1 = x\)

✏ The value of x is 1.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

\( \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}\)

Answer:

153.45

Step-by-step explanation:

15.5 x 9.9 = 153.45

just move the protractor to the diagram/line and measure the angle from the side of the lil curved line :)

The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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Answer:

286

Step-by-step explanation:

Given that:

For every 13 people who prefer football ; 7 prefer basket ball

At an event;

Number who prefer basketball = 154

Number who prefer football :

[(Total who prefer basketball) ÷ 7] * 13

(154 / 7) * 13

= 22 * 13

= 286

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

A. 10/11

Step-by-step explanation:

(I just know) Have a Beautiful day.

Answer:the answer is A

To get the answer, just divide the answers to see if you will get a number closer to one

Step-by-step explanation:

Answer:

The answer is already in the correct formation, there is nothing to change.

Answer:

 the person above is right.

A perpendicular bisector is a line segment or a ray or a line that intersects a given line segment at a 90-degree, and also it passes through the midpoint of the line segment

At its midway, a segment bisector crosses another segment. A Perpendicular Bisector is a segment, ray, line, or plane that is perpendicular to another segment at its halfway.

A perpendicular bisector is a line that precisely splits a given line segment into two halves, generating a 90-degree angle at the junction point. A perpendicular bisector is a line segment that crosses through the midway. It can be built with a ruler and a compass.

When two lines cross at 90 degrees or at right angles, they are said to be perpendicular to each other. A bisector, on the other hand, is a line that divides a line into two equal halves.

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The solution to the given system of equations is (x, y, z) = (2, 2, 0).

To solve the system of equations, we can use the method of elimination or substitution. Here, we'll use the method of elimination:

Multiply the second equation by 2 and the third equation by -1 to eliminate the x variable:

2(x - y + 3z) = 2(4)

-> 2x - 2y + 6z = 8 (equation 2)

-(x + 3y + 2z) = -1

-> -x - 3y - 2z = -8 (equation 3)

Add equation 1, equation 2, and equation 3 together:

(x + 2y + z) + (2x - 2y + 6z) + (-x - 3y - 2z) = 8 + 8 - 8

2x + 3z = 8

Rearrange equation 1 to express x in terms of y and z:

x = 8 - 2y - z

Substitute the value of x in equation 2 with the expression found in step 3:

2(8 - 2y - z) + 3z = 8

16 - 4y - 2z + 3z = 8

16 - 4y + z = 8

Rearrange equation 4 to express z in terms of y:

z = 8 - 16 + 4y

z = 4y - 8

Substitute the value of z in equation 3 with the expression found in step 5:

-x - 3y - 2(4y - 8) = -8

-x - 3y - 8y + 16 = -8

-x - 11y = -24

Rearrange equation 6 to express x in terms of y:

x = 24 - 11y

Substitute the expressions found in step 3 and step 5 into equation 1:

24 - 11y + 2y + 4y - 8 = 8

18 - 5y = 8

-5y = 8 - 18

-5y = -10

y = 2

Substitute the value of y in equation 7:

x = 24 - 11(2)

x = 24 - 22

x = 2

Substitute the value of y in equation 5:

z = 4(2) - 8

z = 8 - 8

z = 0

After solving the system of equations, we find that the solution is (x, y, z) = (2, 2, 0).

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The number of board games Ryan has at t = 3 years can be determined by calculating the net change in his collection over that time period.

In the given scenario, Ryan buys board games at a rate of B(t) = t per year, and donates them at a rate of D(t) = 3t per year. To find the net change in his collection, we need to subtract the rate of donation from the rate of acquisition.

At t = 3 years, the rate at which Ryan buys board games is B(3) = 3 games per year, and the rate at which he donates board games is D(3) = 3(3) = 9 games per year. Therefore, the net change in his collection is 3 - 9 = -6 games per year.

Since the net change is negative, it means that Ryan is losing board games from his collection at a faster rate than he is acquiring them. Starting with 80 board games at t = 0 years, after 3 years, he would have 80 - 6(3) = 80 - 18 = 62 board games.

Therefore, to the nearest board game, Ryan would have approximately 62 board games at t = 3 years. Hence, the answer is not listed among the options given.

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Answer:

y=2x+17 is the answer Hope that helps

Step-by-step explanation:

Answer:

a=12

Step-by-step explanation:

Let (a) be the undefined variable

from the sentence you get the equation

(8+a)/4 = 1+a/3

times both sides by 4

8+a=4+4a/3

times by 3

24+3a=12+4a

12=a

\( \implies12\)

\(\therefore\) The number is 12.

Transformations that may have been used to construct A'B'C include a 90° upward rotation and a 3 unit up and 3 unit right shift.

Transformation in mathematics refers to the process of changing the position, size, or shape of a geometric object. The following are the most common types of transformations: Translation: It involves moving an object from one location to another without changing its size or orientation. Reflection: It involves flipping an object over a line of reflection, so that the object and its image are mirror images of each other. Rotation: It involves rotating an object around a fixed point, called the center of rotation. Dilation: It involves changing the size of an object, either making it larger or smaller, while preserving the shape of the object. Shear: It involves skewing an object in a given direction, causing its shape to be distorted. Similarity Transformation: It is a combination of transformations that preserve the shape of an object, but changes its size and orientation.

Here,

Triangle A’B’C’ is the image of triangle ABC. Transformations could have been used to create A’B’C,

Rotation of 90° upwards.

Shift of 3 units up and 3 units to the right.

Transformations could have been used to create A’B’C is Rotation of 90° upwards and Shift of 3 units up and 3 units to the right.

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Answer:

very hard

this is a really hard problem but ignore the graph and pay attention to the numbers

Step-by-step explanation:

The probability of being dealt a jack, given that you were dealt a card above a 9 (counting aces high), depends on the number of cards above a 9 in the deck.

The explanation below will consider a standard deck of 52 cards.

In a standard deck of 52 cards, there are 4 jacks. Given that you were dealt a card above a 9, there are 12 cards (10, J, Q, K, and A) that satisfy this condition. Among these 12 cards, there is 1 jack.

Therefore, the probability of being dealt a jack, given that you were dealt a card above a 9, can be calculated as the number of favorable outcomes (1 jack) divided by the number of possible outcomes (12 cards above a 9).

Hence, the probability is 1/12, which can also be expressed as approximately 0.083 or 8.33%. This means that there is an approximately 8.33% chance of being dealt a jack when you are already dealt a card above a 9 in a standard deck of 52 cards.

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In order to find the fraction of the pie Ralph eat after dinner, you take into account that after dinner He ate 1/3 of the pie he leaft before dinner.

You can write that the pie before dinner is variable x, then, before dinner Ralph ate 1/2 of such a pie, that is, Ralph ate 1/2x, hence, He leaft x - 1/2x=1/2x before dinner.

He ate 1/3 of the Pie he leaft before dinner, that is He ate 1/3(1/2x) = 1/6x

Hence, Ralph ate 1/6 of the pie after dinner.

Step-by-step explanation:

what is the question. what am I to do with those random numbers without a question, I'm just writing all this because they said at least 20 characters so don't get offended but pls give a detailed question

Answer:

The easiest way to solve this is

A(-2,0), B(-2, -2), C(x, y), D(2, 2)

Connect adjacent points:

Point C will be (2, 4) in this case

A(-1,-3), B(x,y), C(1, 2), D(-1, -2)

Connect adjacent points:

Point B will be (1, 1) in this case

Answer:

√3

Step-by-step explanation:

Spanish

Racionalización de denominadores 3 / v3 tres sobre raíz cuadrada de 3

da

Usando el método de índices

3 / √3 = 3¹ / 3¹ / ²

= 3¹ / 3⁰.⁵

= 3¹⁻¹ / ²

= 3 ¹ / ²

= √3

Esto también se puede resolver multiplicando tanto el numerador como el denominador por √3

3 / √3 * √3 / √3

= 3√3 / √3 * 3

= 3√3 / √9

= 3√3 / 3

Los tres se cancelan y nos queda √3

English

Rationalization of denominators 3 /v3 three over square root of 3

gives

Using the method of indices

3 / √3 = 3¹/ 3¹/²

= 3¹/ 3⁰.⁵

= 3¹⁻¹/²

=3 ¹/²

=√3

This can also be solved multiplying both the numerator and the denominator by √3

3 / √3 * √3/√3

= 3√3/ √3*3

= 3√3/ √9

= 3√3/ 3

The three are cancelled and we are left with √3

Answer:

\(\frac{y^2}{4x^5}\)

Step-by-step explanation:

Used Exponents Properties :

\(\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}\)

==========================

\(\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}\)

To arrive at school on time with 40 minutes available, you would need to maintain an average speed of 22.5 miles per hour.

To calculate the average speed needed to arrive at school on time, we need to determine the distance traveled and the time available.

Given that you live 15 miles from school and have 40 minutes until school starts, we can convert the time to hours by dividing by 60:

40 minutes = 40/60 = 2/3 hours

Now, we can use the formula speed = distance/time to find the required average speed:

Average speed = 15 miles / (2/3 hours)

= 15 miles * (3/2) hours

= 22.5 miles per hour

It's important to note that this calculation assumes a constant speed and doesn't account for factors such as traffic or stops along the way. Adjustments may be necessary to ensure a timely arrival based on real-world conditions.

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The average of the middle two figures, which are 18 and 19, is the median of the lower half. Q1 = (18+19)/2, which equals 18.5. The average of the middle two values—32 and 32—represents the median of the upper half. Q3 = (32+32)/2 = 32 as a result.

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.

First, we calculate the median for the lower and higher halves of the data. The values up to the median are found in the lower half and are as follows:

9, 12, 18, 18, 19, 20, 26, 28

The upper half consists of the values from the median onwards, which are:

29, 31, 31, 32, 32, 34, 35, 37

The median of the lower half is the average of the middle two values, which are 18 and 19. Therefore,

Q1 = (18+19)/2

= 18.5.

The median of the upper half is the average of the middle two values, which are 32 and 32. Therefore,

Q3 = (32+32)/2

= 32.

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Answer:

x=27

Step-by-step explanation:

To evaluate the expression: \([(3^{-5})(3^4)]^3\)

Step 1:  Innermost group, apply the product of powers (\(a^x \times a^y =a^{x+y}\)

Therefore:

\((3^{-5})(3^4)=3^{-5+4}=3^{-1}\)

We then have:

\(=[3^{-1}]^3\)

Step 2: Apply the power of a power

\([3^{-1}]^3=3^{-1 \times 3} =3 ^{-3}\)

Step 3: Apply the negative exponent

\(3 ^{-3} =\dfrac{1}{3^3}\)

Step 4: Simplify

\(\dfrac{1}{3^3}=\dfrac{1}{27}\)

Therefore, the value of x in the simplified expression is 27.

Answer:

27

Step-by-step explanation:

:)

Answer:

G(x) = 2x - 3 has a linear inverse which is a function.

k(x) = -9x2 has a square root inverse that is a function on only the interval x < 0.

Step-by-step explanation:

The inverse of a function is a reflection across the y=x line. This results in switching the values of the input and output or (x,y) points to become (y,x). This can be done algebraically in an equation as well. Begin by switching the x and y in the equation then solve for y.

x = 2y - 3 -------> y = x/2 + 3/2 is linear and a function.

-9y2 = x --------> y = √(-x/9)  is a square root that is a function on only the interval x < 0.

Absolute value does not have an inverse function.

x = -20 is a vertical line which is not a function.

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