Find the apothem and the area

Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)

When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.

This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.

Mathematically, this can be represented by the formula

pi ≈ circumference / diameter

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An [tex]11[/tex]-vertex full graph has around [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph.

At one vertex, the Hamiltonian route begins, and at another, it finishes. Yet, when following a Hamiltonian route, every vertex is encountered. At the same vertex, the Hamiltonian circuit begins and terminates. For instance, if a Hamiltonian circuit's path began at vertex 1, the loop will also conclude at that vertex.

Single circuit is the sole trip a Hamiltonian circuit makes to each vertex. It must begin and terminate at same vertex since it is a circuit. A Hamiltonian route does not start and end in a single location, but it does visit each vertex just once with no repetitions.

We have to divide by [tex]2(n-2)[/tex]

[tex]11!/(2(11-2)!) = 11!/2,520[/tex] Hamiltonian circuits we get:

[tex]11!/2,520 = 19,958,931,200[/tex]

Therefore, there are approximately [tex]19,958,931,200[/tex] Hamiltonian circuits in a complete graph with [tex]11[/tex] vertices.

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The equation that represents the situation is (4 + x) / (10 + 25 + x) = 0.25

Let's start by finding the amount of medicine in the original mixture before adding any pure medicine.

The amount of medicine in the 10 grams of 15% solution is

0.15 × 10 = 1.5 grams

The amount of medicine in the 25 grams of 10% solution is

0.10 × 25 = 2.5 grams

So the total amount of medicine in the original mixture is,

1.5 + 2.5 = 4 grams

Now let x be the amount of pure medicine added.

The total amount of medicine in the final mixture is,

4 + x

The total amount of solution in the final mixture is,

10 + 25 + x

So the concentration of the final mixture is,

(4 + x) / (10 + 25 + x)

We know that this concentration is 25%, so we can write:

(4 + x) / (10 + 25 + x) = 0.25

This is the equation that represents the situation.

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The given question is incomplete, the complete question is:

A pharmacist mixes 10 grams of a 15% medicine solution with 25 grams of a 10% medicine solution. Suppose we know that after she adds the x grams of pure medicine the pharmacists mixture is 25% medicine solution. Write an equation that represents the situation

The probability of getting one marble of each color will be 0.044.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

In this question,

Total number of balls=4+5+6=15

probability of red ball= 4/15

probability of white ball = 5/14  (Since the number of balls are decreasing

probability of blue ball= 6/13

probability of getting one marble of each color= 4/15×5/14×6/13    

                                                                              = 0.044

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The perimeter of the smaller polygon is 20 yards.

Two polygons are similar.

The perimeter of the larger polygon is 120 yards and the ratio of the corresponding side lengths is 1/6.

Find the perimeter of the other polygon.

In similar polygons, the ratio of the corresponding side lengths is equal to the ratio of their perimeters.

Since the larger polygon has a perimeter of 120 yards and the ratio of the corresponding side lengths is 1/6,

the smaller polygon must have a perimeter that is 1/6 of the larger polygon's perimeter.

That is, Perimeter of smaller polygon =  [tex]\frac {1}{6}[/tex]

The perimeter of larger polygon= [tex]\frac{1}{6} \times120\][/tex]

Multiplying 1/6 by 120 yields

[tex]\frac{120}{6}[/tex] =20

So the perimeter of the smaller polygon is 20 yards.

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Answer: D

Step-by-step explanation:

Its the fairest way to pick a random person

The average number of items in all the gift bags is 7.4.

Average, also known as mean, is a numerical value that represents the central or typical value in a set of numbers. It is calculated by adding up all the numbers in a set and dividing the sum by the total number of values in the set. The average is a useful tool for summarizing a large amount of data into a single value that can be easily understood and compared to other values.

In the given question,

We can use the weighted average formula to find the average number of items in all the gift bags:

Average number of items = (proportion of green bags x average items in green bags) + (proportion of yellow bags x average items in yellow bags) + (proportion of blue bags x average items in blue bags)

Proportion of green bags = 50% = 0.5

Proportion of yellow bags = 20% = 0.2

Proportion of blue bags = 30% = 0.3

Average items in green bags = 8

Average items in yellow bags = 5

Average items in blue bags = 8

Substituting the values into the formula, we get:

Average number of items = (0.5 x 8) + (0.2 x 5) + (0.3 x 8)

Average number of items = 4 + 1 + 2.4

Average number of items = 7.4

Therefore, the average number of items in all the gift bags is 7.4

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Since there are students who play both sports, the events of playing basketball and playing soccer are not mutually exclusive.

A Venn diagram is a visual representation of sets or groups and their relationships to one another.

It consists of two or more circles or other shapes that overlap, with each shape representing a different set, and the overlap representing the elements that belong to both sets.

Looking at the diagram, we see that there is a region where the two circles overlap, which means there are elements (points) that are in both circles. Therefore, the events shown in the Venn diagram are not mutually exclusive.

In this particular case, the circles represent the events of students who play basketball and students who play soccer, respectively. The overlap represents students who play both basketball and soccer.

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The complete question is given below-

Answer:

  4/33

Step-by-step explanation:

You want to write 0.1212...(repeating) as a simplified fraction.

A repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.

Here, there are 2 repeating digits, so the basic fraction is ...

  12/99

This can be reduced by removing a factor of 3 from numerator and denominator:

  [tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]

__

Additional comment

Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.

  0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99

Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.

You can also approach this by writing the number as a continued fraction. The basic form is ...

  [tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]

where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.

A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.

Answer:

(3x - 10)(x - 5)

Step-by-step explanation:

That expression is equal to (3x^4 -73x^2 - 50). This factored expression can be written as (3x^2 -17x - 17) * (x+2.5) and can be factored using the FOIL method. (FOIL) - First, Outer, Inner, Last. This method ensures that you include all of the terms with the same variables. The FOIL method is very easy and helpful for factoring complex equations and is something that is good to be familiar with for future study if you are looking to delve deeper into math!

The expression (3x^4 - 73x^2 - 50) factored is an example of a quadratic equation and the expression can be factored into (3x - 10)(x - 5). I think this is a good exercise because it shows how quadratic equations can be factored and the process involved, so students can apply the principles learned to other situations and problems they may encounter later on. It's important to understand how to factor quadratics since they often show up in real-world situations such as physics or statistics, so it's a great thing to have these skills locked in.

Answer:

please give question properly

6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.

The given data is as follows:

Snowfall months and their fallen depth is:

November = 2

December = 8.4

January = 11.2

February = 7.9

First, we need to first find out the total snowfall for the five months of November, December, January, February, and March.

Total snowfall = 2 + 8.4 + 11.2 + 7.9 + March

The average snowfall =  7.28 iches.

7.28 inches/month x 5 months = 36.4 inches

2 + 8.4 + 11.2 + 7.9 + March  = 36.4

29.5 + March = 36.4

March =  36.4 - 29.5

March = 6.9 inches.

Therefore, we can conclude that more than 6.9 inches of snow would be necessary for march for Chicago to exceed its monthly average snowfall of 7.28 in. for these five months.

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The  probability that at least 3 customers out of the first 6 will buy bread is 88.3% that is option B.

The binomial distribution is the discrete probability distribution used in probability theory and statistics that only allows for Success or Failure as the potential outcomes of an experiment. For instance, if we flip a coin, there are only two conceivable results: heads or tails, and if we take a test, there are only two possible outcomes: pass or fail. A binomial probability distribution is another name for this distribution.

The formula used is :

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

65% of customers who come into this store buy bread, hence p = 0.65.

A sample of 6 customers is taken, hence n = 6.

The probability that at least 3 customers out of the first 6 will buy bread is given by:

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

In which

P(X=x) = [tex]C_n.x.p^x.(1-p)^n^-^x[/tex]

P(X = 3) = C₆,₃(0.65)³ x (0.35)³ = 0.2355

P(X = 4) = C₆,₄(0.65)⁴ x (0.35)² = 0.328

P(X = 5) = C₆,₅(0.65)⁵ x (0.35)¹ = 0.2437

P(X = 6) = C₆,₆(0.65)⁶ x (0.35)⁰ = 0.0754

Then,

P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6)

= 0.2355 + 0.328 + 0.2437 + 0.0754 = 0.8826

The probability that at least 3 customers out of the first 6 will buy bread is 0.8826 ≈ 88.3%.

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Complete  question;

A local bakery sells the freshest bread in town. In fact, 65% of customers who come into this store buy bread. What is the probability that at least 3 customers out of the first 6 will buy bread?

23.5%

88.3%

11.7%

76.5%

Answer: 20/3 mph or 6.667 mph.

Step-by-step explanation:

Since the athlete runs 1/3 of a mile per 1/20 of an hour, to find how much they run in an hour, you multiply both values by 20 to get: the athlete runs 20/3 miles per 20/20 of an hour, or 20/3 miles per hour.

Thus, 4.0 moles of NH3 would be produced when 6.0 moles of H2 react with sufficient N2.

Suppose 6.0 mol of H2 reacts with sufficient N2 to produce ammonia, NH3. We can determine the number of moles of NH3 produced using stoichiometry.The balanced chemical equation for the reaction is:[tex]3H2(g) + N2(g) → 2NH3(g)[/tex]

From the equation, we can see that 3 moles of H2 react with 1 mole of N2 to produce 2 moles of NH3.

Therefore, using the mole ratio from the balanced equation, we can calculate the number of moles of NH3 that would be produced when 6.0 mol of H2 reacts with [tex]N2:6.0 mol H2 × (2 mol NH3/3 mol H2) = 4.0 mol NH3[/tex]

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The expected number of shots required to make one free-throw is approximately 1.85.

To calculate the expected value of Y, denoted by E[Y], we need to consider the probability distribution of Y.

The probability distribution of Y is a geometric distribution, since we are counting the number of trials required until the first success (i.e., making a free-throw). The probability of success on each trial is p = 0.54, since you have a 54% chance of making each free-throw. The probability of failure (missing the free-throw) on each trial is q = 1 - p = 0.46.

The probability mass function (PMF) of a geometric distribution is given by:

P(Y = k) = q^(k-1) * p

where k is the number of trials required to achieve the first success.

In this case, we want to find the expected value of Y, which is defined as:

E[Y] = Σ(k=1 to ∞) k * P(Y = k)

We can simplify this expression using the PMF of the geometric distribution:

E[Y] = Σ(k=1 to ∞) k * q^(k-1) * p

This sum can be evaluated using the formula for the sum of an infinite geometric series:

E[Y] = 1/p

Substituting in the value of p = 0.54, we get:

E[Y] = 1/0.54 ≈ 1.85

This means that on average, you need to take about 2 shots to make one free-throw if you have a 54% free-throw shooting percentage.

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Complete question is:

If you are a 54 % free-throw shooter and the random variable y denotes the total number of shots in order to make one free-throw, then:

Calculate E[Y]

Answer:

Step-by-step explanation:

Answer: 4y - (2/3)x + 20

Step-by-step explanation:

Write out problem: 4(y+5) - (2/3)x

Expand: 4y + 20 - (2/3)x

Reorder: 4y - (2/3)x + 20

Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.

The total length of the poster board is 3 feet, which is equivalent to 3 x 12 = 36 inches.  

Each piece of poster board is 1/4 of a foot long, which is equivalent to 3 inches (since 1 foot is equal to 12 inches).

To find out how many banners can be made from the poster board, we need to divide the total length of the poster board by the length of each banner:

Number of banners = Total length of poster board / Length of each banner

Number of banners = 36 inches / 3 inches

Number of banners = 12 banners

Therefore, Mrs. McGee's class can make 12 banners from the 3-foot piece of poster board.

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Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.

Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.

Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.

This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.

To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.

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Sinusoidal functions can model natural phenomena and periodic patterns in data, aiding in better understanding and more accurate predictions, while also solving real-world problems.

The idea of a sinusoidal function can be used to model real-world phenomena or solve real-world problems. Many natural phenomena can be modeled using sinusoidal functions, including tides, sound waves, and electromagnetic waves.

In addition, sinusoidal functions can be used to model periodic patterns in data, such as seasonal trends or cyclical patterns in financial data. By using sinusoidal functions to model these phenomena, we can gain a better understanding of their behavior and make more accurate predictions about their future behavior.

Sinusoidal functions can also be used to solve real-world problems, such as calculating the amplitude, frequency, or period of a wave or predicting the behavior of a system that exhibits periodic patterns.


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Answer:

Step-by-step explanation:

You can read the answers right off the graph.

a)  When t=5: Find 5 on the x-axis (time (h)), go straight up vertically until you hit the line, then go straight to the left horizontally until you hit the y-axis (distance (km));  at that point d ≈ 14 km

b)  When d=20:  Find 20 on the y-axis (distance (km)), go straight to the right horizontally until you hit the line, then go straight down vertically until you hit the x-axis (time (h));  at that point t ≈ 7 hr

The expected profit of Ayo is  $ 79.95.

The probability of an event happening can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Here in this problem, we use probability to calculate the total profit. Calculate the probability of winning 150 people so that we can calculate the total winning amount of 150 persons.

Now calculate the total amount gained by Ayo by costing each turn. Now subtract both values and will get the expected profit.

Here we have

Ayo runs fairground games

In each turn, a player rolls a fair dice numbered from 1 - 6 and a spin numbered 1 - 5

Every player can win £ 8 or £ 3

In total there are 150 to play

Here probability of winning £ 8 i.e rolling 2 and rolling 5  

= [ 1/6 × 1/5 ] = 1/30  

Probability of winning £ 3 i.e getting at least one 3 in roll or spin

Here we have taken 3 cases that are getting 3 in a roll but not in spin, getting 3 in a spin but not in roll, and getting 3 in both roll spin

= [ 1/6 × 4/5 ] + [5/6 × 1/5 ] + [ 1/6 × 1/5 ]  

= 4/30 + 5/30 + 1/30 = 10/30 = 1/3

Hence, the expected amount in 1 a single game

= 8 × 1/30 + 3 1/3 = 8/30 + 1 = 0.267 + 1 = 1.267

There are 150 player  

Total amount won by 150 = 150 (1.267) = $ 190.05  

Here It cost a player 1.80 for every turn  

Ayo will get for 150 players = 1.80 × 150 = $ 270

If 150 players won $ 190.05,

then the profit won by Ayo = 270 - 190.05 = 79.95

Therefore,

The expected profit of Ayo is  $ 79.95.

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Answer:

About 92.1 °

Step-by-step explanation:

[tex]cos(U)=(58.8^{2} +38.4^{2} -71.4^{2} )/2(58.8)(38.4)\\[/tex]

[tex]cos(U)= (3457.44+1474.56-5097.96)/4515.84[/tex]

[tex]cos(U)= (-165.96)/4515.84[/tex]

[tex]cos(U)= -0.03675063775[/tex]

[tex]U= cos^{-1} (-0.03675)[/tex]

[tex]U=92.1[/tex]

Answer:

cosA=b^2+c^2-a^2/2xbxc

58.8^2+38.4^2-71.4^2/2x58.8x38.4=-461/12544

cos^-1 (because finding angle)

cos^1(-461/12544)=92.10613071

Answer:

Step-by-step explanation:

Your equation is 0.75L +  0.5L + x = 2L
x = Orange juice

0.75L + 0.5L = 1.25L
2L - 1.25L = 0.75L

[tex]\frac{0.75L}{2L}[/tex] is your fraction
[tex]\frac{75}{200}[/tex]  simplified is [tex]\frac{3}{8}[/tex]
I hope this helped,

The percent change in the price of the lawnmower over the 2 years is -8.1%.

To find the percent change in the price of the lawnmower over the 2 years, we can use the formula:

percent change = (new value - old value) / old value * 100%

Plugging in the values given in the problem, we get:

percent change = (329.99 - 358.99) / 358.99 * 100%

percent change = -8.1%

Therefore, the percent change in the price of the lawnmower over the 2 years is -8.1%. Note that the negative sign indicates a decrease in price.

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(a) The ratio of sin A as a fraction is 63/65, cos A is 16/65 and the tan of angle A is 63/16.

(b) The ratio of sin B as a fraction is 16/65, cos B is 63/65 and the tan of angle B is 16/63.

The missing parts of the right triangle is calculated using the trigonometry principle as shown below.

For angle A:

opposite side = 63

adjacent side = 16

hypothenuse side = 65

sin A = opp/hypo = 63 / 65

cos A = adj/hypo = 16 / 65

tan A = opp/adja = 63/16

For angle B:

opposite side = 16

adjacent side = 63

hypothenuse side = 65

sin B = opp/hypo = 16 / 65

cos B = adj/hypo = 63 / 65

tan A = opp/adja = 16/63

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Reason:

a+b = 15+24 = 39 is NOT larger than c = 39

Since a+b > c is false, a triangle is NOT possible.

The sum of any two sides must exceed the third side for a triangle to be possible. For more information, check out the triangle inequality theorem.

Answer:

C

Step-by-step explanation:

A (- 6, - 8 ) and C (9, - 8 )

since the y- coordinates of both points are equal, both - 8

then AC is a horizontal line

the distance AC can be calculated by calculating the absolute value of the x- coordinates, that is

AC = | 9 - (- 6) | = | 9 + 6 | = | 15 | = 15 units

or

AC = | - 6 - 9 | = | - 15 | = | 15 | = 15 units

given 1 unit = [tex]\frac{1}{2}[/tex] mile , then

AC = 15 units = 15 × [tex]\frac{1}{2}[/tex] = 7.5 miles

The box and whisker plot can be created by :

Minimum value - 6

Maximum Value - 15

Median - 10

Quartiles - Q1 - 7.5, Q2 - 10, Q3 - 13.5

To create a box and whisker plot for the given data set {6,7,7,8,9,10,10,10,10,13,13,14,14,15,15}, we need to first find the minimum value, maximum value, median, and quartiles.

Minimum value: 6

Maximum value: 15

Median: To find the median, we need to first arrange the data set in ascending order:

6,7,7,8,9,10,10,10,10,13,13,14,14,15,15

The median is the middle value in the data set, which is 10.

Quartiles: To find the quartiles, we need to divide the data set into four equal parts.

First quartile (Q1): The first quartile is the median of the lower half of the data set. In our case, the lower half of the data set is:

6,7,7,8,9,10

The median of this set is (7+8)/2 = 7.5.

Second quartile (Q2): The second quartile is the median of the entire data set, which we already found to be 10.

Third quartile (Q3): The third quartile is the median of the upper half of the data set. In our case, the upper half of the data set is:

10,10,10,10,13,13,14,14,15,15

The median of this set is (13+14)/2 = 13.5.

Now, we can use the above information to create the box and whisker plot.

The horizontal line inside the box represents the median (10). The bottom of the box represents the first quartile (7.5), and the top of the box represents the third quartile (13.5). The whiskers extend from the box to the minimum value (6) and maximum value (15).

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