there are 15 equations and 15 unknowns. what are those 15 equations and 15 unknowns. list them all. explain the purpose of each set of equations. explain how they are derived. g

The author's purpose in the text is to teach readers how to make animal silhouette art using simple supplies.

The text provides a clear set of instructions, starting with finding a picture of an animal, copying its outline onto cardboard, cutting out the silhouette, and then using strips of magazine paper to create a colorful design. The author gives specific details on how to cut the strips, glue them to the cardboard, and trim them to make a finished piece of art. The use of the second-person point of view, such as "you will create," suggests that the author intends for the reader to follow the instructions and make their own animal silhouette art. Overall, the text is informative and instructional, providing a step-by-step guide to creating art with readily available materials.

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The complete question is:

One great thing about making art is that you can use almost any supplies. In this project, you will create animal silhouettes from three simple supplies: old magazines, cardboard, and glue.

First, find a picture of an animal that you like. Copy its outline onto a piece of cardboard, and cut out the cardboard silhouette. Next, cut narrow strips from the magazines. The pages you choose will determine what colors the animal will be.

Now, glue the side of the strip by side onto the cardboard shape, with the ends extending beyond the cardboard's edges. Trim the strips carefully along the edges. Ta-da! Your colorful animal art piece is finished.

Which author's purpose is suggested by the text?

Answer: 16x+3x^3−8

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The value of angle CI is equal to 40 for the triangle.

What is geometry?

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that I is the incenter of the triangle AI = 3x+7, BI = 5x-11, and CI = 52-2x.

The value of BI will be calculated as,

AI = BI

3x + 7 = 5x - 11

2x = 18

x = 6

Now for the value of angle CI:

CI = 52 - 2x

CI = 52 - 2 x 6

CI = 52 - 12

CI = 40

Therefore, the value of angle CI is equal to 40 for the triangle.

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Bayes' theorem is a concept that is frequently used in data science, machine learning, and artificial intelligence. It is a probabilistic approach to solving problems by utilizing prior knowledge to make inferences about the future. In this article, we will explain how to write the posterior class probability using Bayes' theorem. In the posterior expression, there are four terms involved are Prior probability of the hypothesis, Prior probability of the evidence, Likelihood of the evidence given the hypothesis and Posterior probability of the hypothesis given the evidence


To get started, let's begin with the general expression of Bayes' theorem. According to Bayes' theorem, the posterior probability of a hypothesis H, given some evidence E, is proportional to the likelihood of the evidence E given the hypothesis H, multiplied by the prior probability of the hypothesis H, and then divided by the prior probability of the evidence E.

Bayes' Theorem

P(H | E) = P(E | H) * P(H) / P(E)

where,
P(H) = Prior probability of the hypothesis
P(E) = Prior probability of the evidence
P(E | H) = Likelihood of the evidence given the hypothesis
P(H | E) = Posterior probability of the hypothesis given the evidence

The posterior probability of the hypothesis is the probability of the hypothesis given some evidence. In the posterior expression, there are four terms involved:

1. Prior probability of the hypothesis: This is the probability of the hypothesis before taking into account the evidence.

2. Prior probability of the evidence: This is the probability of the evidence before considering any hypothesis.

3. Likelihood of the evidence given the hypothesis: This is the probability of the evidence given that the hypothesis is true.

4. Posterior probability of the hypothesis given the evidence: This is the probability of the hypothesis after considering the evidence.

In conclusion, Bayes' theorem is an effective technique for calculating posterior probabilities. The theorem expresses the probability of a hypothesis given some evidence in terms of the prior probability of the hypothesis, the prior probability of the evidence, and the likelihood of the evidence given the hypothesis. The posterior class probability can be calculated using Bayes' theorem, and the terms involved in the posterior expression are the prior probability of the hypothesis, prior probability of the evidence, likelihood of the evidence given the hypothesis, and the posterior probability of the hypothesis given the evidence.

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The length of dDC is 16 cm. We can use the similarity of triangles ACD and ABE to find the length of DC.

We know A,B and c lie on a straight line segment A , E and d lie on a straight line segment

Substituting the given values, we get:

Simplifying the equation, we get:

AD = 20

Now, we can use the similarity of triangles ACD and ABE again, to find the length of DC.

CD/BE = AD/AE

Substituting the values, we get:

CD/4 = 20/(20+5)

Simplifying the equation, we get:

CD = 16

Therefore, the length of dDC is 16 cm.

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Answer:$69.99

Step-by-step explanation:

If you start with $100 and spend 3.5% of it every day for 10 days, the amount of money you will have left at the end of the 10 days can be calculated as follows:

Day 1:

Starting with $100

Spending 3.5% of $100 = $3.50

Money left = $100 - $3.50 = $96.50

Day 2:

Starting with $96.50 (money left from Day 1)

Spending 3.5% of $96.50 = $3.38

Money left = $96.50 - $3.38 = $93.12

Day 3:

Starting with $93.12 (money left from Day 2)

Spending 3.5% of $93.12 = $3.26

Money left = $93.12 - $3.26 = $89.86

Continue this process for each of the 10 days, and you will have:

Day 4: $86.72

Day 5: $83.68

Day 6: $80.75

Day 7: $77.92

Day 8: $75.18

Day 9: $72.54

Day 10: $69.99

Therefore, after 10 days of spending 3.5% of $100 every day, you will have $69.99 left.

Answer:

Step-by-step explanation:

69.99

If a ball is drawn randomly from a jar that contains 8 red balls, 3 white balls, and 6 yellow balls, the probability of drawing a red ball from the jar is approximately 0.47 or 47%.

The probability of a red ball being drawn from the jar can be calculated as follows:

Total number of balls in the jar = 8 red + 3 white + 6 yellow = 17

Probability of drawing a red ball = (Number of red balls in the jar) / (Total number of balls in the jar) = 8/17 ≈ 0.47

This means that if we were to draw a ball from the jar randomly, there is a 47% chance that the ball we draw will be red.

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Complete question is:

A ball is drawn randomly from a jar that contains 8 red balls, 3 white balls, and 6 yellow balls. find the probability of the given event.

What is what is the probability of a Red ball being drawn?

The probability that the first three questions have the same answer choice is 1/4, since there are four answer choices and the instructor is randomly selecting the answers according to a discrete uniform distribution. This means that each answer choice has an equal probability of being chosen. Therefore, the probability of all three questions having the same answer is 1/4.

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The range of Axel's training zone, assuming a moderate exercise intensity, would be approximately 123 to 164 beats per minute (BPM).

To calculate this range, we use the Karvonen formula, which takes into account Axel's resting heart rate (RHR) and desired training intensity. Assuming a moderate-intensity workout, we can use a target heart rate range of 60% to 80% of his MHR.

Target Heart Rate = ((MHR - RHR) x %Intensity) + RHR

Assuming a resting heart rate of 65 BPM and moderate intensity of 60% to 80% of his MHR, Axel's target heart rate range would be approximately 123 to 164 BPM.

Therefore, the range of Axel's training zone would be approximately 123 to 164 BPM.

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The answer of the Question EJERCICIO DE ECUACIONES (A) x con 2 (B) x con 1 (C) x con 5 (D) x con 2 (E) x con 4

4 + 6x - 12 - 2x
= (6x - 2x) + (4 - 12)
= 4x - 8
Comprobación:
Reemplazamos x con 2:
4 + 6(2) - 12 - 2(2) = 8

B) 8x + x + x = 10
= 10x = 10
= x = 1
Comprobación:
Reemplazamos x con 1:
8(1) + 1 + 1 = 10

C) 2x - 16 - 4
= 2x - 20
Comprobación:
Reemplazamos x con 5:
2(5) - 16 - 4 = 6

D) 5x - 8 = 12 - 5x
= 10x = 20
= x = 2
Comprobación:
Reemplazamos x con 2:
5(2) - 8 = 12 - 5(2)

E) 12 + 4x + 8 = 36
= 4x = 16
= x = 4
Comprobación:
Reemplazamos x con 4:
12 + 4(4) + 8 = 36

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The approximate monthly percent decrease in value of the boat is 0.5%.

The given value of a boat is 21 200, and it loses 6% of its value every year. We are to find the approximate monthly percent decrease in value.

The given information is as follows: The value of a boat = $21,200The percentage decrease in value = 6%We are to find the approximate monthly percent decrease in value. Annual decrease in value of a boat is 6% of $21,200= $1,272Monthly decrease in value of a boat will be 1/12 of the annual decrease = $1,272/12≈ $106Thus, the approximate monthly percent decrease in value of the boat will be

[tex]$\frac{106}{21,200}*100\%=0.5\%$[/tex]

Therefore, the approximate monthly percent decrease in value of the boat is 0.5%.

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Your question is incomplete, but probably the complete question is :

The value of a boat is $21,200. It loses 6% of its value every year. Find the approximate monthly percent decrease in value. Round your answer to the nearest hundredth of a percent.

Real GDP increase in 2019 was $16 trillion, representing a 6.67% increase from 2012. The price level rose by 5% from 2012 to 2019, with a GDP price index of 105 in 2019.

To calculate the percentage increase in production from 2012 to 2019, we need to use the following formula:

Percentage increase in production = ((Real GDP in 2019 - Real GDP in 2012) / Real GDP in 2012) x 100

Substituting the given values, we get:

Percentage increase in production = ((16 trillion - 15 trillion) / 15 trillion) x 100

Percentage increase in production = (1 trillion / 15 trillion) x 100

Percentage increase in production = 6.67%

Therefore, there was a 6.67% increase in production from 2012 to 2019.

To calculate the percentage increase in price level from 2012 to 2019, we can use the following formula:

Percentage increase in price level = ((GDP price index in 2019 - GDP price index in 2012) / GDP price index in 2012) x 100

Substituting the given values, we get:

Percentage increase in price level = ((105 - 100) / 100) x 100

Percentage increase in price level = (5 / 100) x 100

Percentage increase in price level = 5%

Therefore, the price level rose by 5% from 2012 to 2019.

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Answer:

Let's assume that the subset contains as many numbers as possible. We start by including all the numbers from 1 to 100 that are not divisible by 5. These are the numbers 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99.

This gives us a subset of 81 numbers. However, we need to remove any numbers that are multiples of other numbers in the subset. For example, if we include the number 6, we must remove 12, 18, 24, etc. Similarly, if we include the number 9, we must remove 18, 27, 36, etc. We can see that the only numbers that have multiples in the subset are 2, 3, 7, 8, 13, 17, 18, 19, 27, 28, 37, 38, 39, 52, 53, 54, 57, 58, 59, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 89, 92, 93, 94, and 98.

Therefore, we need to remove these 34 numbers from the subset. This leaves us with a subset of 81 - 34 = 47 numbers.

However, we can still include the number 5, since it is not a multiple of any other number in the subset. This adds one more number to the subset, giving us a total of 48 numbers.

Therefore, the largest number of members that such a subset can have is 48, which corresponds to answer choice (e).

Answer:29160

Step-by-step explanation:

The scale factor between polygon D and polygon D' is 1.67.

Dilation is a transformation in mathematics that alters a geometric figure's size while preserving its form and proportions. Enlargement or scaling are other names for it. Dilation can be achieved by multiplying each point's coordinates in a figure by a fixed number known as the scale factor. A figure is expanded when the scale factor is more than 1, and it is shrunk when it is between 0 and 1. Calculating ratios of areas or volumes, describing the relationship between like figures, and modelling real-world situations are all examples of how dilation is utilised in many different branches of mathematics, including geometry, algebra, and calculus.

The scale factor is given as:

scale factor = dimension of D' / dimension of D

Substituting the values:

scale factor = (8 / 4.8) = 1.67

Hence, the scale factor between polygon D and polygon D' is 1.67.

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Answer:

A 1.6

Step-by-step explanation:

In linear equation, 0.75x + 2y ≤ 16 , 2x + 4y ≤  40 are the solution represent .

What is the most effective way to explain linear equations?

An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x). In this scenario, y is referred to as the dependent variable because it depends on the independent variable, x.

if the small pair is x, the large pair is y.

45 minutes = 0.75 hour

120 minutes = 2 hour

 so, 0.75x + 2y ≤ 16

   2x + 4y ≤  40

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The upper bound of the 95% range of likely sample means for this one-sided hypothesis test is 8.681531567778452.

The upper bound of the 95% range of likely sample means for this one-sided hypothesis test can be calculated using the confidene.norm function, which computes the normal-based confidence interval.

We can use the following syntax to calculate the upper bound of the 95% range;

upper_bound = stats.norm.ppf(0.95, loc=sample_mean, scale=sample_std_dev)

Where:

sample_mean = 7.3

sample_std_dev = 2.8

Thus, the upper bound of the 95% range can be calculated as follows:

upper_bound = stats.norm.ppf(0.95, loc=7.3, scale=2.8)

upper_bound = 8.681531567778452

Therefore, the upper bound of the 95% range of likely sample means for this one-sided hypothesis test is 8.681531567778452.

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It will take approximately 23.1 years for 60% population of the species to remain, assuming that the decrease rate remains constant over time.

We can utilize the exponential decay formula, which is given by, to respond to this question.

[tex]N(t) = N0 * e^(-rt) (-rt)[/tex]

N(t) is the population at time t, where N(t) is the population at time t, t is the time in years, and r is the yearly growth rate (or in this example, the annual drop rate).

Assuming that t is the number of years it will take for 60% of the species to survive, let's divide the drop rate by 100 to convert it from a percentage to a decimal. As a result, we have:

[tex]N(t) = 5000 * e^(-0.03t) \s0.6 * 5000 = 3000[/tex]

Given that N(t) is equal to 3000, we can solve for t by using the following method:

[tex]3000 = 5000 * e^(-0.03t) (-0.03t)\\t = ln(0.6) / -0.03 0.6 = e(-0.03t) ln(0.6) = -0.03t[/tex]

Calculating the answer, we obtain:

t = 23.1

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In linear pair,  Value of x is 133° .

What is linear pair  in math?

When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.

                                       A pair of neighboring angles created by the intersection of two lines is referred to as a linear pair. A linear pair is formed in the illustration by the numbers 1 and 2. The same goes for pairs 2 and 3, 3 and 4, and 1 and 4. In a linear pair, the two angles are always supplementary, which implies that their sum total is 180 degrees.

 47° + x° = 180°

        x° = 180° - 47°

           = 133°

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The write-off of the receivable from Madonna Inc. is a necessary adjustment to ensure the accuracy of Marin Co.'s financial statements. Without it, the company's accounts receivable would be overstated and their financial statements would not provide an accurate portrayal of the company's financial position.

At the end of 2024, Marin Co. had accounts receivable of $673,200 and an allowance for doubtful accounts of $24,010. On January 24th, 2025, it was determined that the company's receivable from Madonna Inc. was not collectible and management authorized a write-off of $4,147. This action reduces the accounts receivable balance by $4,147, and reduces the allowance for doubtful accounts by the same amount. The net effect on the balance sheet is a reduction of $4,147 in both accounts receivable and allowance for doubtful accounts.

The impact of the write-off on the company's financial statements is a decrease in net income for the period. This is because a write-off is recognized as an expense, which reduces the amount of net income reported in the period. The amount of the write-off is recorded as an expense on the income statement. In this case, the amount of the write-off is $4,147.

The journal entry to record the write-off would be: Accounts Receivable 4,147; Allowance for Doubtful Accounts 4,147. This entry reduces the accounts receivable and allowance for doubtful accounts by $4,147. The write-off of $4,147 is recorded as an expense on the income statement, and this reduces the net income reported for the period.

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Sam would have to sample at least 1068 students.

Sam, a statistician at Mathmagic Land University wants to construct a 95% confidence interval with no more than 3% margin of error for the proportion of students who own their own car.

Let us calculate the least number of students he would have to sample. What is the least number of students Sam would have to sample?

Given that the confidence interval is 95% with a margin of error no more than 3%.The margin of error formula is given by Margin of error = Z-value * Standard error.

We know that Z-value for a 95% confidence interval is 1.96. This corresponds to 0.03 of the confidence interval. Hence, we can calculate the standard error as follows:

Standard error = Margin of error / Z-value= 0.03 / 1.96 = 0.0153We know that the standard error formula is given byStandard error = √p(1-p)/n.

Here, we need to find the minimum sample size required to get the least number of students who own their own car, hence the proportion can be assumed to be 0.5 (which will be the maximum value of p).0.0153 = √(0.5 × (1-0.5) )/n

On simplification, we get, n = 1067.55. Hence, Sam would have to sample at least 1068 students to construct a 95% confidence interval with no more than 3% margin of error for the proportion of students who own their own car.

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Ultimately, teleportation and time travel would certainly have both positive and negative effects on the graph of the lives of Noah's descendants, presenting both new chances and difficulties.

A graph shows the relationship between variables or values by visualising data or information. It comprises of a coordinate system with an x-axis and y-axis, and data points or lines plotted on it. In a variety of disciplines, including mathematics, physics, economics, and social sciences, graphs are used to convey and interpret data. They can be employed to display patterns, trends, comparisons, and connections between different data points. Bar graphs, line graphs, scatter plots, pie charts, and histograms are examples of common graph types.

given

Having the capacity to teleport and go through time could potentially present new difficulties and complexities for writers.

Plotlines could get more complicated and sophisticated if characters travel between several eras or parallel realities.

Also, being able to travel across great distances quickly can make the globe seem smaller and less mysterious, which could make it more difficult to convey a sense of awe and discovery through storytelling.

Ultimately, teleportation and time travel would certainly have both positive and negative effects on the graph of the lives of Noah's descendants, presenting both new chances and difficulties.

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The simplification of the expression ( x^1/2)^1/6 × x^(1/3) is given by x to the 5 twelfth power.

Apply the rule of exponents representing raise a power to another power and product of the exponents with same base,

(a^m)^n= a^(mn)

( a^m ) × ( a^n ) = a^(m + n)

Here, x^(1/2) raised to the (1/6)th power.

Using the rule of exponents, we have,

x^((1/2) x (1/6))

Simplification of the product of the exponents, we get ,

= x^(1/12)

Now, multiply this by x^(1/3), so using the rule of product of exponents with same base we get,

x^(1/12) x x^(1/3)

Combining the like terms by adding the exponents, we have,

= x^((1/12) + (1/3))

Simplifying the sum of the exponents,

= x^(5/12)

Therefore, the simplification of the given expression is equal to  x to the 5 twelfth power.

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The above question is incomplete, the complete question is:

Simplify open parentheses x to the 1 half power close parentheses to the 1 sixth power. X to the 1 third power

x to the 1 fourth power

x to the 1 twelfth power

x to the 2 thirds power

x to the 5 twelfth power

The probability of being able to toast at least 7 pieces of bread before the toaster catches on fire and destroys itself is approximately 0.0128

We can approach this problem using the negative binomial distribution, which models the number of successful trials (toasting without the toaster catching on fire) before a specified number of failures (the toaster catching on fire and destroying itself) occur.

Let X be the number of successful toasting trials before the toaster catches on fire and destroys itself. We want to find P(X ≥ 7), the probability that at least 7 pieces of bread can be toasted before the toaster is destroyed.

The negative binomial distribution can be expressed as

P(X = k) = (k+r-1)C(r-1) × p^r × (1-p)^k

where r is the number of failures (the toaster catching on fire and destroying itself), p is the probability of success (toasting without the toaster catching on fire), and (k+r-1)C(r-1) is a combination factor that represents the number of ways to arrange k successes and r-1 failures in a sequence.

In this case, r = 1 (we want to know the probability of the first failure occurring after at least 7 successes), p = 0.75 (the probability of successfully toasting a piece of bread), and we want to find P(X ≥ 7).

P(X ≥ 7) = 1 - P(X < 7)

= 1 - Σ[k=0 to 6] (k+1) × p × (1-p)^k

≈ 0.0128

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The given question is incomplete, the complete question is:

I bought a cheap toaster. Every time I use it there is a chance that it will catch on fire with

probability p = 0.25, burn my toast, and destroy itself. But with probability (1 − p) it makes

perfect toast!

What is the probability I put at least 7 pieces of bread into my cheap toaster before it

destroys itself?

This is true because coordinates (0.8, 0.6) satisfy the equation x² + y² = 1.

The approximate angle measures needed to intersect at (0.8, 0.6) and each of these new points is 38.66 degrees.

Other points on the unit circle are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6).

The coordinates (0.8, 0.6) lie exactly on the unit circle because they satisfy the equation x² + y² = 1, which defines the unit circle. Plugging in x = 0.8 and y = 0.6 gives 0.8² + 0.6² = 1, which is true.

To find the angle measure needed to intersect at (0.8, 0.6) and each of the new points, we can use the inverse tangent function. If we let theta be the angle between the positive x-axis and the line connecting the origin and the point of intersection, then we can use the equation tan(theta) = y/x to find the angle. For example, to find the angle needed to intersect at (0.8, 0.6) and (1, 1), we have tan(theta) = 0.6/0.8, which simplifies to theta = arctan(0.6/0.8) ≈ 38.66 degrees.

The other points on the unit circle that also lie exactly at the intersection of two grid lines are (0.6, 0.8), (-0.8, 0.6), (-0.6, -0.8), and (0.8, -0.6). These points can be obtained by reflecting (0.8, 0.6) across the x-axis, y-axis, or both.

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P(strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1

The probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is the same and is equal to 50%. This is because there are an equal number of strawberry chews (10) and cherry chews (10) in the bag of candy. Therefore, the probability of her selecting one of either is 1/2 = 0.5 = 50%.
The word or phrase that describes the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".Explanation:The candy bag of Kadeesha contains 10 strawberry chews and 10 cherry chews. This means there are two flavors of candies in the bag. The probability that she picks a strawberry chew at random without looking will be 10/20, which can be simplified to 1/2. Similarly, the probability of picking a cherry chew at random without looking will be 10/20, which can also be simplified to 1/2. When considering either of the probabilities, it implies that the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is the sum of the probability of picking a strawberry chew and the probability of picking a cherry chew.i.e. P (strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1Therefore, the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is 1, which implies that it is a sure event. Hence, the word or phrase that describes the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".

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The area of trapezium CDEF is 30 cm².

The area of a trapezium is given by the formula:

Area = (1/2) x (sum of parallel sides) x (distance between the parallel sides)

where;

So the area of trapezium CDEF is calculated as;

A = ¹/₂ (CD + EF ) x CF

where;

DC= 9 - CB

CB  = 20 - (FA + CF + AB )

CB= 20 - ( 6 + 6 + 6 )

CB= 2

DC = 9 - 2 = 7 cm

A = ¹/₂ (7 + 3 ) x 6

A = 30 cm²

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The number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.

Step-by-step explanation:

The differential equation is missing in your question. However, I will give a general overview of how to solve a differential equation numerically using Euler's method and how to find an analytical solution.

Numerical Solution using Euler's Method:

Suppose we have a first-order differential equation of the form y' = f(x, y), where y' represents the derivative of y with respect to x. To solve this numerically using Euler's method, we need to start with an initial condition y(x0) = y0, and we want to find the value of y at some other point x1 = x0 + h.

The Euler's method involves approximating the derivative y' by the difference quotient (y1 - y0) / h, where y1 is the value of y at x1. Rearranging this equation, we get:

y1 = y0 + h * f(x0, y0)

Using this equation, we can iteratively compute the value of y at different points by using the previous value of y. For example, to find y2, we can use the equation:

y2 = y1 + h * f(x1, y1)

We continue this process until we reach the desired endpoint.

Analytical Solution:

An analytical solution to a differential equation is an explicit expression for y(x) that satisfies the differential equation for all values of x. To find an analytical solution, we may use techniques such as separation of variables, integrating factors, or other methods specific to the type of differential equation.

For example, if we have a differential equation of the form y' = k * y, where k is a constant, we can use separation of variables to obtain:

dy / y = k * dx

Integrating both sides, we get:

ln|y| = k * x + C

where C is an arbitrary constant of integration. Solving for y, we get:

y = Ce^(kx)

where C = ±e^C is a constant determined by the initial condition.

Comparison of Solutions:

Once we have the numerical and analytical solutions, we can compare them by plotting the graphs of y(x) for each method. If the numerical solution was computed with a small enough step size, it should converge to the analytical solution as the number of iterations increases. If there is a significant difference between the two solutions, we may need to investigate the numerical method used or check for errors in our analytical solution.

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Answer:2/3

Step-by-step explanation:

Answer:

To calculate the fraction by which the income from sales decreases in August, we first need to calculate the total income from sales in July and August.

Let's assume that the laptop was sold at a price of $P in July, and the number of laptops sold was N.

So, the total income from sales in July would be I1 = P*N.

In August, the price of the laptop was 113% of P, which means the new price was (113/100)*P = 1.13P. Also, the number of laptops sold in August was 5 more than in July, which means the number of laptops sold in August was N+5.

So, the total income from sales in August would be I2 = 1.13P*(N+5) = 1.13PN + 5.65P.

Now, to find the fraction by which the income from sales decreases in August, we need to calculate the ratio of the income in August to the income in July:

I2/I1 = (1.13PN + 5.65P)/(PN) = 1.13 + 5.65/P.

The fraction by which the income from sales decreases in August is the difference between 1 and this ratio:

1 - (1.13 + 5.65/P) = (P - 1.13P - 5.65)/P = (0.87P - 5.65)/P.

So, the income from sales decreases in August by a fraction of (0.87P - 5.65)/P.