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Concave hexagon with two pairs of congruent sides is:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

A hexagon is a six-sided polygon. A concave hexagon is a hexagon with at least one interior angle greater than 180 degrees.

We can start with a regular hexagon, which has six congruent sides and six interior angles of 120 degrees each.

We can then extend two opposite sides of the regular hexagon outwards to create two pairs of congruent sides. The extended sides should not be parallel to each other, but rather at an angle, so that the resulting hexagon is concave.

Here is an example of a concave hexagon with two pairs of congruent sides:

   /\

   /  \

  /    \

 /      \

/        \

/_____\

\        /

\      /

 \    /

  \  /

   \/

In this hexagon, sides AB and CD are congruent, and sides EF and GH are also congruent. However, the angles at vertices A and H are greater than 180 degrees, making this a concave hexagon.

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Answer:

Recall that the equation we created was:

y = 2x + 10

where y represents the number of leaves and x represents the number of weeks since spring has started.

To find the expected average number of leaves on a tree 8 weeks after spring has started, we need to evaluate the equation for x = 8:

y = 2(8) + 10

y = 16 + 10

y = 26

Therefore, the expected average number of leaves on a tree 8 weeks after spring has started is 26.

In the above case, the  law of joint proportionality is the one I am going to use to write the equation that stands for the above  situation:

V = k x h  x g²

Note that from the equation written:

V =  the volume of wood produced by the tree

h  = the height of the tree

g =  the circumference of the tree

k = a constant of proportionality.

For one to know the  value of k, we have to make use the data given in the problem.

Since h = 40 m

g = 1.5 m

V = 288 m³

Hence the volume of wood produced is:

288 = k   x  40 x (1.5)²

Simplifying this equation, we have:

288 = k    x  90

When we Divide both sides by 90, we have :

k = 3.2

So one can say  the equation that stands the situation is:

V = 3.2 x   h x  g²

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Answer:

y=41/3 and x = -14

Step-by-step explanation:

system of the linear equation :

-3y-4x=15       eq[i]

9y+7x=25      eq[ii]

multiplying eq[i] by -7 and eq[ii] by 4,we get

21y+28x= -105    eq[iii]

36y+28x= 100     eq[iv]

subtracting eq[iii] from eq[iv],we get

15y=205

y=205/15=41/3

and x= -14

The difference between the volumes of the solids is given as follows:

A. 72π.

The volume of a sphere of radius r is given by the equation presented as follows:

V = 4πr³/3.

The radius is of 6 inches, hence the volume is given as follows:

V = 4π x 6³/3

V = 288π cubic inches.

The volume of a cylinder of radius r and height h is given by the equation presented as follows:

V = πr²h.

Both the radius and the height are of 6 inches, hence the volume is given as follows:

V = π x 6³

V = 216π cubic inches.

Then the difference of the volumes is given as follows:

π(288 - 216) = 72π.

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Answer:

Step-by-step explanation:

To find the mean, we need to calculate the sum of all the values and divide by the number of data values. Using the stem and leaf plot and the key, we can determine the following data values:

12, 15, 17, 22, 25, 26, 28, 32, 33, 34, 36, 37, 39, 42, 44, 45, 46, 47, 48, 49, 52, 53, 55, 57, 57, 59, 62, 65, 68, 72, 73, 75, 75, 77, 79, 82, 85, 88, 92, 95

There are 37 data values in total. To find the sum of the data, we can add up all the individual values:

12 + 15 + 17 + 22 + 25 + 26 + 28 + 32 + 33 + 34 + 36 + 37 + 39 + 42 + 44 + 45 + 46 + 47 + 48 + 49 + 52 + 53 + 55 + 57 + 57 + 59 + 62 + 65 + 68 + 72 + 73 + 75 + 75 + 77 + 79 + 82 + 85 + 88 + 92 + 95 = 2098

So the sum of the data is 2098. To find the mean, we divide the sum by the number of data values:

MEAN = sum of data / number of data values

MEAN = 2098 / 37

MEAN = 56.7568

Rounded to the nearest hundredth, the mean of the data is 56.76. Therefore, the answer is closest to option A) 57.

Answer:

GCF, Greatest Common Factor

Step-by-step explanation:

Hope this helped

On solving the query we can say that In conclusion, while option D does not meet the condition, alternatives A, B, and C are equivalent to equations that represent y as a function of x.

Mathematics is concerned with numbers and their variations, equations and related structures, shapes and their places, and possible placements for them. The relationship between a collection of inputs, each of which has an associated output, is referred to as a "function". An relationship between inputs and outputs, where each input yields a single, distinct output, is called a function. Each function has a domain and a codomain, often known as a scope. The letter f is frequently used to represent functions (x). X is the input. The four main types of functions that are offered are on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

Let's investigate each choice:

A: 3x - 4y = -2

We must put y on one side of the equation in order to describe y as a function of x. We may do this by dividing by -4 after removing 3x from both sides:

-4y = -3x - 2 y = (3/4)x + 1/2

C: x² - 3y = 0

We must isolate y in order to express y as a function of x. This may be done by dividing by -3 after removing x2 from both sides of the equation: y = (1/3)x2.

The condition is met by option C since this equation expresses y as a function of x.

In conclusion, while option D does not meet the condition, alternatives A, B, and C are equivalent to equations that represent y as a function of x.

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The equations that are equivalent to an equation that expresses y as a function of x are A, B, and C.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

The equation that expresses y as a function of x is y = f(x). To be equivalent to this equation, an equation must also express y as a function of x. Let's examine each equation:

A: 3x-4y=-2 can be rewritten as y = (3/4)x + 1/2, which expresses y as a function of x. Therefore, A is equivalent to an equation that expresses y as a function of x.

B: x-y⁴=0 can be rewritten as y = ±√x, which expresses y as a function of x. Therefore, B is equivalent to an equation that expresses y as a function of x.

C: x²-3y=0 can be rewritten as y = (1/3)x², which expresses y as a function of x. Therefore, C is equivalent to an equation that expresses y as a function of x.

D: lxl + lyl = 2 does not express y as a function of x because for every x value, there are two possible y values that satisfy the equation. Therefore, D is not equivalent to an equation that expresses y as a function of x.

Therefore, the equations that are equivalent to an equation that expresses y as a function of x are A, B, and C.

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The statement which is true include the following: B. The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.

In Mathematics and Geometry, a polynomial graph simply refers to a type of graph that touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Generally speaking, the zero of a polynomial function simply refers to a point where it crosses or cuts the x-axis of a graph.

By critically observing the graph of the polynomial function shown in the image attached below, we can logically deduce that the y-coordinates of the solutions to the system of equations and the zeros of the equation are not equal;

3x³ + x = 2x + 1

P(x) = 3x³ + x - 2x - 1

3x³ + x - 2x - 1 = 0

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Erik plans to run approximately 8.63 miles this week.

To find out how many miles Erik plans to run this week, we need to multiply the distance he ran last week (3 miles) by 2 7/8, which is the factor by which he plans to increase his distance. To do this, we first need to convert the mixed number 2 7/8 into an improper fraction:

2 7/8 = (2 x 8 + 7) / 8 = 23/8

Now we can multiply:

3 miles x 23/8 = (3 x 23) / 8 = 69/8 miles

This means that Erik plans to run 69/8 miles, or 8 5/8 miles, this week. This is a mixed number, which means that Erik plans to run 8 whole miles and 5/8 of a mile.

Alternatively, we can express 69/8 as a decimal by dividing the numerator (69) by the denominator (8):

69/8 ≈ 8.63

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Answer:

67 miles per hour

Step-by-step explanation:

We can set up a proportion to find how many miles per hour this person travels:

268/4

=67

So, the rate is 67 miles per hour.

Hope this helps :)

— driving 268 miles in 4 hours is a total rate of 67 miles per hour

why???

268/4 = 67

The value of x is 12

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar, the corresponding angles of the triangles must be equal.

Also the ratio of the corresponding sides of the similar triangles are equal.

Therefore ;

x/4 = 36/x

x² = 36×4

x² = 144

x = √144

x = 12

therefore the value of x using similar triangles is 12.

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The metric prefixes for [tex]10^1^2, 10^9, 10^6[/tex] and [tex]10^3[/tex] are tera (T), giga (G), mega (M), and kilo (k) respectively. The metric prefix for 2.1 is deca (da). The negative metric prefixes for [tex]10^1^2, 10^9, 10^6[/tex], and [tex]10^3[/tex] are pico (p), nano (n), micro (μ), and milli (m) respectively. The negative metric prefix for 2.1 is deci (d). So the symbols for these are: T (tera), G (giga), M (mega), k (kilo), da (deca), p (pico), n (nano), μ (micro), m (milli), d (deci)

1. [tex]10^1^2[/tex]: The metric prefix for [tex]10^1^2[/tex] is tera, and its symbol is T.
2. [tex]10^9[/tex]: The metric prefix for [tex]10^9[/tex] is giga, and its symbol is G.
3.[tex]10^6[/tex]: The metric prefix for [tex]10^6[/tex] is mega, and its symbol is M.
4. [tex]10^3[/tex]: The metric prefix for [tex]10^3[/tex] is kilo, and its symbol is k.
5. 2: There is no specific metric prefix for 2.
6. 1: There is no specific metric prefix for 1.

Now for the negative powers of these numbers:

1. [tex]10^-^1^2[/tex]: The metric prefix for[tex]10^-^1^2[/tex] is pico, and its symbol is p.
2. [tex]10^-^9[/tex]: The metric prefix for [tex]10^-^9[/tex] is nano, and its symbol is n.
3. [tex]10^-^6[/tex]: The metric prefix for[tex]10^-^6[/tex] is micro, and its symbol is µ.
4. [tex]10^-^3[/tex]: The metric prefix for[tex]10^-^3[/tex] is milli, and its symbol is m.

Please note that there are no metric prefixes for the negative powers of 2 and 1.

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The probability of selecting two different counters that are of two different colors is 0.193

In the given question, we have a total of 20 counters, 8 are yellow and 12 are green.

The probability of choosing a 2 different colors will be;

P = 7/20 * 11/20

P = 77 / 400

P = 0.193

This is because the first probability of choosing a green is 11/20 and the second probability of choosing a yellow is 7/20. This is an example of probability without replacement

When we multiply both together to determine the probability of choosing different colors, we would have 0.193

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Answer: No profit

Step-by-step explanation: because break even point are when produce costs and selling costs are the same therefore no profit

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Using Chebyshev's theorem, we can conclude that at least 56% of the gym members' ages fall between 26 and 70.

Chebyshev's theorem states that for any given dataset, regardless of its distribution, at least 1 - 1/k² of the data will fall within k standard deviations from the mean.

We can use Chebyshev's theorem to determine the percentage of gym members aged between 26 and 70. We need to determine how many standard deviations away from the mean these ages are.

To do this, we calculate the z-scores for both ages using the formula z = [tex](x - μ) / σ[/tex], where x is the value (in this case, either 26 or 70), [tex]μ[/tex] is the mean (48), and σ is the standard deviation (10). For x = 26: z = (26 - 48) / 10 = -2.2 For x = 70: z = (70 - 48) / 10 = 2.2

Both ages are 2.2 standard deviations away from the mean. Using Chebyshev's theorem, we know that at least 1 - 1/2.2² = 56% of the gym members' ages fall within this range.This is a lower bound - the actual percentage of gym members aged between 26 and 70 could be higher than 56%, as the distribution of ages may not be perfectly symmetrical or may have outliers.

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A reason not to use a chi-square test of homogeneity to analyze a set of data is if the assumptions of the test are not met. These assumptions include:

1. The data must be categorical, meaning it consists of counts or frequencies in different categories.

2. The sample size must be large enough, with an expected frequency of at least 5 in each cell of the contingency table.

3. The observations must be independent, meaning each data point should not influence the others.

If any of these assumptions are not met, it may not be appropriate to use a chi-square test of homogeneity to analyze the data. Instead, you may need to consider alternative statistical methods that better suit your data and research question.

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The values of the missing sides are;

1. 6. 7 Option C

2. 6. 9. Option D

3. 7. 6 Option C

4.6.3 Option C

From the information given, we have that;

1. Using the sine identity;

sin 72 = x/7

cross multiply the values

x = 6. 66

2. Using the sine identity;

sin 60 = x/8

cross multiply the values

x = sin 60(8)

find the value

x = 6. 93

3. Using the cosine identity;

cos 23 = 7/x

cross multiply the values

x = 7/0. 9205

x = 7. 60

4. Using the cosine identity;

cos 25 = x/7

cross multiply the values

x = 6. 34

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Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

[tex]\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}[/tex]

So, the dressmaker has 360 in of ribbon.

Answer:

  (a)  4.2

Step-by-step explanation:

You want an estimate of √18 to one decimal place.

The squares on either side of 18 are 4² = 16 and 5² = 25. The value 18 is about (18 -16)/(25 -16) = 2/9 of the way between these numbers. So, an estimate of the square root is ...

  4 + 2/9 ≈ 4.2

__

Additional comment

A fast way to improve the estimate is to take the average of this value and the quotient of 18 and this value:

  (4.2 +18/4.2)/2 ≈ 4.2429

Compare this to the actual root of 4.2426.

Using that same method again gives a value that matches the root when rounded to 8 decimal places.

Answer:Mode = 33, Mean = 35.5

Step-by-step explanation:

The mode is whatever number appears the most.

To find the mode, first put the numbers in order from least to greatest.

29, 31, 33, 33, 37, 38, 40, 43

In this case, 33 appears the most, so the mode is 33.

The mean is the average of all of the numbers.

Firstly, add up all of the numbers:

29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284

Now that you have all of them added up, divide the final sum by the number of numbers you have in the list. In this case, you have 8 numbers.

284/8 = 35.5

Your mean is 35.5

The area of this figure based on the information will be 10mm²

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

From the information, the shape gas sides 5mm and 2mm. The area of this figure will be:

= Length × Width

= 5mm × 2mm

= 10mm²

In conclusion, the area of this figure based on the information will be 10mm²

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A shape gas sides 5mm and 2mm. What is the area of this figure 9mm 7mm 2mm 3mm 10mm

The size of the angle TAC is calculated to be equal to 70.52° to the nearest hundredth degree using trigonometric ratios of cosine and tangent.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right triangle ABM;

cos A = AM/AB {adjacent/hypotenuse}

cos 45° = AM/6

AM = 6 × cos 45 {cross multiplication}

AM = 6 × √2/2 {recall cos 45° = √2/2}

AM = 3√2

For the right triangle ATM;

tan A = TM/AM {opposite/adjacent}

tan A = 12/3√2

tan A = 2√2

A = tan⁻¹(2√2)

A = 70.5288

Therefore, the size of the angle TAC is calculated to be equal to 70.53° to the nearest hundredth degree using trigonometric ratios of cosine and tangent.

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The percent increase in temperature when an oven changes from 350 to 362 is approximately 3.4%.

To calculate the percent increase in temperature, we need to find the difference between the initial temperature and the final temperature, divide that difference by the initial temperature, and then multiply the result by 100 to convert it to a percentage.

The difference between the initial temperature of 350 and the final temperature of 362 is

362 - 350 = 12

To find the percent increase, we divide the difference by the initial temperature

12 / 350 = 0.0342857...

Multiplying by 100, we get

0.0342857... * 100 = 3.42857...

Rounding to the nearest tenth of a percent, we get

3.4%

Therefore, the percent increase in temperature is approximately 3.4%.

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Completely factored expressions are:

1. x² - 7x - 18 can be factored as:

(x - 9)(x + 2)

Expand the expression using FOIL:

(x - 9)(x + 2) = x² + 2x - 9x - 18 = x² - 7x - 18

2. p² - 5p - 14 can be factored as:

(p - 7)(p + 2)

Expand the expression using FOIL:

(p - 7)(p + 2) = p² + 2p - 7p - 14 = p² - 5p - 14

3. m² - 9m + 8 can be factored as:

(m - 1)(m - 8)

Expand the expression using FOIL:

(m - 1)(m - 8) = m² - 8m - m + 8 = m² - 9m + 8

Therefore, the completely factored expressions are:

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The probability of pulling two skittles of the same colour in a row is 4/13.

Finding the likelihood that the first skittle will be any colour and then the likelihood that the second skittle will be the same colour as the first will allow you to calculate the likelihood of pulling two Skittles of the same colour in a row.

There are a total of 27 Skittles in the bag because there are 9 of each colour there. As a result, there is a one-in-one chance that the first skittle will be of any hue.

There will be a total of 26 skittles left in the bag when the first skittle is pulled, along with 8 skittles of the same colour. The likelihood that the second skittle will be the same colour as the first is thus

Probability = 8/26 or 4/13.

By adding these probabilities, we obtain:

1 x 4/13 = 4/13

Therefore, the probability of pulling two Skittles of the same colour in a row is 4/13.

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