Simplify (step by steps, thanks!)

Answer: here

Step-by-step explanation:

Math is used in various careers such as construction. You will need to know the dimensions to make sure whatever it is being constructed is stable.

Math can help you financially. It can help you budget and prevent you from going into debt.

Math can help you understand real world problems better even if you may not use everything that you learn.

Answer:

Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art. It gives us a way to understand patterns, to quantify relationships, and to predict the future. Math helps us understand the world — and we use the world to understand math. The world is interconnected. Everyday math shows these connections and possibilities.

Step-by-step explanation:

1.we use mathematics for our daily living

2.from day care of school we started our mathematics lesson

3.mathematics is the most important specially when your in business 1.our daily living needs  simple mathematics to calculate. example; I buy a goods amounted 100 pesos then I have 500 pesos in my pocket so i am sure   400 pesos is my change.

2.From the very beginning or the early stage of our education we have to     start learning mathematics so the as we grow older math is in our brain system.

3.In business we know that math is very important because we calculate the capital, expenses, equals the profit.

The equivalent expression of the fraction 1/{5(n+45)} as,

1/{5(n+45)} = 1/ (5n + 225)

Equivalent expression of 1/{5(n+45)} can be expressed as,

By applying distributive property of addition in the denominator of the given fraction 1/{5(n+45)} , we get

5(n + 45) = 5·n + 5·45

⇒ 5(n + 45) = 5n + 225

The numerator of fraction 1/{5(n+45)} can be written in equivalent expression as,

1 = 1·1 = 1

Thus, we can write the equivalent expression of the fraction 1/{5(n+45)} as,

1/{5(n+45)} = 1/ (5n + 225)

Equivalent expressions are defined as expressions which work in same way even though they look different from each other.

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The angular velocity of the circle is approximately 19 m/s.

In order to find the missing quantity, we can use the relationship between linear velocity and angular velocity in a circle. The linear velocity of a point on the edge of a circle is the product of the radius and the angular velocity. This can be expressed as:

v = r * w

where v is the linear velocity, r is the radius, and w is the angular velocity.

To find the value of w, we can rearrange this equation to solve for w:

w = v / r

Substituting the given values of v and r, we get:

w = 1235 m/min / 65 m

w = 19 m/s

It's important to note that units must be consistent when using formulas to solve problems. In this case, we converted the given linear velocity from m/min to m/s before plugging it into the formula. Also, we rounded the answer to the nearest tenth, as instructed, since the given values were rounded to the nearest unit.

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The variables and gives a measure of the strength of the linear relationship that is independent of the units in which the variables are measured.

The formula is the population correlation coefficient, denoted by the Greek letter rho (ρ).

The population correlation coefficient is a measure of the strength and direction of the linear relationship between two variables, denoted by X and Y. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship.

The formula for the population correlation coefficient is:

ρ = Cov(X,Y) / (σX * σY

where Cov(X,Y) is the covariance between X and Y, and σX and σY are the standard deviations of X and Y, respectively.

The numerator, Cov(X,Y), measures the degree to which X and Y vary together. It is positive when above-average values of X tend to be associated with above-average values of Y, and negative when above-average values of X tend to be associated with below-average values of Y.

The denominator, σX * σY, is a normalizing factor that puts the covariance on a standardized scale. It represents the spread of X and Y around their respective means.

By dividing the covariance by the product of the standard deviations, the population correlation coefficient removes the scale effects of the variables and gives a measure of the strength of the linear relationship that is independent of the units in which the variables are measured.

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The event that have a sample space of h and t would be Flipping a fair, two-sided coin. That is option A.

To calculate the possibility of selecting an outcome form an event the formula that should be used is given as follows;

Probability = possible outcome/sample space.

For a coin, the possible sample space = H and T when flipped only once.

Therefore, the event that have a sample space of h and t would be Flipping a fair, two-sided coin.

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25. The area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.

29. The area of the region that lies inside both curves is approximately 1.648 square units.

A 3D solid shape called a cylinder is formed by connecting two parallel and identical bases with a curving surface. The shape of the bases is similar to a disc, and the axis of the cylinder runs through the middle or connects the two circular bases.

25. To find the area of the region that lies inside the first curve and outside the second curve, we need to find the points where the two curves intersect, and then integrate the difference in the areas between the two curves from one intersection point to the other.

The two curves are given by:

r² = 8 cos θ   (first curve)

r = 2           (second curve)

To find the intersection points, we substitute r = 2 into the first equation and solve for θ:

2² = 8 cos θ

cos θ = 1/2

θ = ±π/3

So the two curves intersect at θ = π/3 and θ = -π/3. To find the area between the curves, we integrate the difference in the areas between the two curves from θ = -π/3 to θ = π/3:

A = ∫[-π/3,π/3] [(1/2)r² - 2²] dθ

Using the equation r² = 8 cos θ, we can simplify this to:

A = ∫[-π/3,π/3] [(1/2)(8 cos θ) - 4] dθ

A = ∫[-π/3,π/3] (4 cos θ - 4) dθ

A = 4 ∫[-π/3,π/3] (cos θ - 1) dθ

[tex]A = 4 [sin \theta - \theta]_{(-\pi/3)^{(\pi/3)[/tex]

A = 4 [sin(π/3) - π/3 - (sin(-π/3) + π/3)]

A = 4 [√3/2 - 2π/3]

Therefore, the area of the region that lies inside the first curve and outside the second curve is 4[√3/2 - 2π/3] square units.

29. To find the area of the region that lies inside both curves, we need to determine the points where the two curves intersect and then integrate the area enclosed between the curves over the appropriate range of polar angles.

The two curves are given by:

r = 3 cos(θ)  (first curve)

r = sin(θ)    (second curve)

To find the intersection points, we substitute r = 3 cos(θ) into the equation r = sin(θ) and solve for θ:

3 cos(θ) = sin(θ)

tan(θ) = 3

θ = tan⁻¹(3)

The intersection point lies on the first curve when θ = tan⁻¹(3), so we need to integrate the area enclosed between the curves from θ = 0 to θ = tan⁻¹(3).

The area enclosed between the curves at any angle θ is given by the difference in the areas of the circles with radii r = sin(θ) and r = 3 cos(θ). Thus, the area enclosed between the curves is:

A = ∫[0,tan⁻¹(3)] [(1/2)(3 cos(θ))² - (1/2)(sin(θ))²] dθ

Simplifying, we get:

A = ∫[0,tan⁻¹(3)] [9/2 cos²(θ) - 1/2 sin²(θ)] dθ

Using the identity cos(2θ) = cos²(θ) - sin²(θ), we can simplify this to:

A = ∫[0,tan⁻¹(3)] [(9/2)(cos²(θ) - (1/2)) + (1/2)cos²(2θ)] dθ

We can evaluate the first term of the integrand using the identity cos²(θ) = (1 + cos(2θ))/2, and the second term using the identity cos²(2θ) = (1 + cos(4θ))/2:

A = ∫[0,tan⁻¹(3)] [(9/4)(1 + cos(2θ)) - (1/4)(1 + cos(4θ))] dθ

Integrating each term separately, we get:

[tex]A = [(9/4)\theta + (9/8)sin(2\theta) - (1/16)sin(4\theta)]_{0^{(tan^-1(3))[/tex]

Simplifying and evaluating, we get:

A = (9/4)tan⁻¹(3) + (9/8)sin(2tan⁻¹(3)) - (1/16)sin(4tan⁻¹(3))

Using the identity sin(2tan⁻¹(3)) = 6/10 and simplifying, we get:

A = (9/4)tan⁻¹(3) + (27/40) - (3/40)tan⁻¹(3)

Therefore, the area of the region that lies inside both curves is approximately 1.648 square units.

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Answer:

the midpoint would be (-2,-2)

Step-by-step explanation:

To find the number of zeros at the end of 2022!, we need to count the number of factors of 10 in its prime factorization. Since 10 = 2 x 5, we need to find the number of pairs of 2's and 5's that multiply to make 10.

First, we can count the number of factors of 5 in 2022!. There are 404 multiples of 5, 80 multiples of 25, and 16 multiples of 125. Therefore, there are 404 + 80 + 16 = 500 factors of 5.

Next, we need to count the number of factors of 2 in 2022!. This is equivalent to counting the number of multiples of 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 that are less than or equal to 2022. We can simplify this by noticing that each power of 2 is a multiple of the previous power of 2. So we only need to count the multiples of 2, 4, and 8, and then multiply by the number of each power of 2 that divides into 2022.

There are 1011 multiples of 2, 505 multiples of 4, and 252 multiples of 8. The highest power of 2 that divides into 2022 is 2^1, so we only need to consider the factors of 2. Therefore, there are 1011 + 505 + 252 = 1768 factors of 2.

Since we need to find the number of pairs of 2's and 5's, the number of zeros at the end of 2022! is equal to the minimum of the number of factors of 2 and the number of factors of 5, which is 500. Therefore, there are 500 zeros at the end of 2022!.

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The probability, provided that the windshield is a rectangle with the dimensions 28 inches by 54 inches and his line of site through the windshield is a rectangle with the dimensions 30 inches by 24 inches is 0.476

Continuous Probability is used for this information. Probability = Area of line of sight / total area of windshield

Probability = (30*24)/(28*54)

Probability = 0.476

The probability will be 0.476.

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Number of ways to choose three of these people to stand up is,

⇒ 84

We have to given that;

Nine people sit in chairs in a room.

And, We have to choose three of these people to stand up.

Hence, Number of ways to choose three of these people to stand up is,

⇒ ⁹C₃

⇒ 9! / 3! (9 - 3)!

⇒ 9! / 3! 6!

⇒ 9×8×7 / 3×2

⇒ 84

Thus,  Number of ways to choose three of these people to stand up is,

⇒ 84

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Answer: 504

Step-by-step explanation: i took the quiz

Experiment: "Favorite Cake Flavor"

Hypothesis: Different people have different favorite cakes flavors.

Now, Data collection enables us to identify the cakes flavors both popular and unpopular amongst users.

Furthermore, data analysis based on factors such as age, gender, and location allows for determining if disparities exist between consumer flavor preferences.

The findings of this study would be beneficial to cakes manufacturers and retailers, as they could enhance comprehension of preferred buyer choices and eventuate their products accordingly.  

Conclusively, improved knowledge of preferred flavor profiles would facilitate refining marketing methodologies to attract a broader target audience.

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From the table shown below, there are 40% of the people from the survey that were teachers.

Through the use of given information, the numbers can be used to fill in the frequency table as follows:

Vote                YES for later start       Vote NO for later start       Total

Students                 30                                 15                                    45

Teachers                 20                                10                                    30

Total                         50                                25                                      75

b) To be able to know the percentage of people that were surveyed and who were teachers, we  have to divide the number of teachers by the total number of people that were said to have been surveyed:

Percentage of teachers

= 30 /75  x 100%

= 40%

Therefore, based on the above, 40% of the people were surveyed and they were teachers.

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The correct answer is option D, the two-tailed single-sample t-test.

To determine which test should be used in this scenario, we need to consider the following factors:

Type of data: The data collected from the CT scans are continuous data.

Sample size: The sample size is small (11 in total).

Relationship between samples: The data from Jimmy's hippocampus is independent from that of his family members.

Based on these factors, we can eliminate options C and B, which both involve dependent samples.

Next, we need to determine whether we are comparing Jimmy's hippocampus volume to a known value or to the average volume of his family members. If we were comparing Jimmy's hippocampus to a known value (e.g. the population average), we would use a one-sample t-test (option A). However, since we are comparing Jimmy's hippocampus volume to the average volume of his family members, we need to use a two-sample t-test.

Therefore, the correct answer is option D, the two-tailed single-sample t-test.

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We can conclude that the marketing manager's claim is true.

To determine whether the marketing manager's claim is true, we need to conduct a hypothesis test.

Let p be the proportion of all children aged 8-12 who have cell phones. The marketing manager claims that p > 0.5, while the national consumers group survey found that 39/54 or p' = 0.722 have cell phones.

The null hypothesis is that the true proportion of children with cell phones is less than or equal to 0.5:

H0: p ≤ 0.5

The alternative hypothesis is that the true proportion of children with cell phones is greater than 0.5:

Ha: p > 0.5

We will conduct a one-tailed hypothesis test with a level of significance of 0.05.

Under the null hypothesis, the sample proportion follows a binomial distribution with parameters n = 54 and p = 0.5. The standard error of the sample proportion is given by:

SE = √[p(1-p)/n] = √[0.5(1-0.5)/54] = 0.070

The test statistic is calculated as:

z = (p' - p) / SE = (0.722 - 0.5) / 0.070 = 3.14

The critical value for a one-tailed test with a level of significance of 0.05 is 1.645, using the standard normal distribution table.

Since the test statistic (z = 3.14) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than half of the children aged 8-12 have cell phones.

Therefore, we can conclude that the marketing manager's claim is supported by the data from the survey.

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At some point in our lives, we come across a moment that presents an opportunity to showcase our talents and abilities. This moment, often referred to as "our moment to shine," can be a turning point that propels us to greater heights of success and achievement. For me, such a moment came when I least expected it, and it changed the course of my life.

It was during my senior year of high school when I got the chance to compete in a regional public speaking competition. I had always been interested in public speaking and had participated in a few contests in the past, but this was different. This competition was going to be fierce, with participants from some of the most prestigious schools in the region. The pressure was high, and the stakes were even higher.

As the day of the competition approached, I found myself getting more and more nervous. I had prepared extensively, spending countless hours rehearsing my speech and polishing my delivery. But still, the thought of standing in front of a panel of judges and a large audience was daunting.

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The missing value is 14, and option d is correct.

Consider the data table:

x      y

1      6

2     10

3      __

Data represent a linear  function.

To find:

The missing value.

Solution:

Let the missing value be p.

Slope Formula:

m= y2-y1/x2-x1

Data represent a linear function. So, the slope always remains the same.

10-6/2-1 = p -10/3-2

4= p- 10

Adding 10 on both sides, we get

p = 14

Therefore, the missing value is 14, and option d is correct.

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Answer:

7/4, 9/4, 11/4, 13/4

Step-by-step explanation:

+ In an arithmetic sequence, to find the pattern you must subtract a term from the term after it to find the common difference.

3/4 subtracted from 5/4 is 2/4

1/4 subtracted from 3/4 is 2/4

+ So the common difference is 2/4 (Aka 1/2, but you want to keep the same denominator)

+ Therefore, between each new term, you add 2/4

1/4, 3/4, 5/4, 7/4, 9/4, 11/4, 13/4... and so on

To find the rate of change of the marginal cost with respect to the production level, we need to take the derivative of the total cost function, C(q), with respect to q.

C'(q) = 6 + 11

C'(q) = 17

This gives us the marginal cost (MC) function:

MC(q) = 17

Therefore, the rate of change of the marginal cost with respect to the production level is constant at 17 dollars per unit.

To find the rate of change of the marginal cost when q=4 units, we simply plug in q=4 into the MC function:

MC(4) = 17

So the answer is not listed among the choices provided. Therefore, the correct answer is not A, B, C, or D.

In summary, the rate of change of the marginal cost with respect to the production level is constant at 17 dollars per unit. When q=4 units, the marginal cost is also 17 dollars per unit.
To find the rate of change of the marginal cost with respect to the production level when q=4 units, given the total cost function C(q) = 6q^3 + 11q + 124, we need to follow these steps:

Step 1: Find the derivative of the total cost function with respect to q. This will give us the marginal cost function.
C'(q) = d(C(q))/dq = d(6q^3 + 11q + 124)/dq

Step 2: Calculate the derivative.
C'(q) = 18q^2 + 11

Step 3: Substitute q=4 into the marginal cost function to find the rate of change at this production level.
C'(4) = 18(4^2) + 11

Step 4: Evaluate the expression.
C'(4) = 18(16) + 11 = 288 + 11 = 299

The rate of change of the marginal cost with respect to the production level when q=4 units is 299 dollars per unit per unit (Option C).

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The double-entry principle in the balance of payments states that every transaction in the balance of payments is recorded as both a credit and a debit.

In the first transaction, the Saudi Arabian oil company's purchase of $1 million worth of U.S. government bonds from a U.S. bank will appear as a credit in the financial capital account and as a debit in the current account.

In the second transaction, Arielle's payment of $400 for her hotel stay in San Francisco using her French bank-issued debit card will appear as a credit in the current account and as a debit in the financial capital account.

In the third transaction, Frank's receipt of yen 500,000 in dividend payments on his shares in a Japanese company, which are deposited in his account in a Japanese bank, will appear as a credit in the financial capital account and as a debit in the current account.

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The number of liters it would take to cover 120 km is 8 liters.

Looking at the graph that shows the liters consumed per kilometer, or rather the number of kilometers per liter, we see that each liter enables to car to go for 15 km.

This means that if we should want to go 120 km, the number of liters needed would be:

= Distance to cover / Kilometers per liter

Distance to cover = 120 km

Kilometers per liter = 15 km

The liters needed are:

= 120 / 15

= 8 liters

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The graph is attached.

Given is a triangle ABC, we need to find its coordinates if it is reflected over y = -x,

The rule of reflection over y = -x is,

(x, y) = (-x, -y)

So,

A = (-5, -4)

B = (1, -4)

C = (-1, -5)

After reflection,

A' = (5, 4)

B' = (-1, 4)

C' = (1, 5)

Hence the points after reflection are A' = (5, 4), B' = (-1, 4) and C' = (1, 5)

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The total surface area of the square pyramid is 585 in²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

To get the surface area:

Area of base = 15 in * 15 in = 225 in²

Area of one triangle lateral face = (1/2) * 15 in * 12 in = 90 in²

Area of four triangle lateral face = 4 * 90 in² = 360 in²

Total surface area = 225 in² + 360 in² = 585 in²

The total surface area is 585 in²

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The amount of money left for gift c is 15 5/10 dollars

Timothy had 30 dollars to spend on three gifts

He spent 10 9/10 dollars on gift A

He spent 3 3/5 dollars on gift B

The amount spent on gift C can be calculated as follows

10 9/10 + 3 3/5

= 109/10 + 18/5

= 545 + 180/50

= 725/50

= 145/10

30 - 145/10

= 30/1 - 145/10

= 300-145/10

= 155/10

= 15 5/10

Hence the amount of Money left for gift C is 15 5/10 dollars

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1. Draw the Lewis structure of the species, including all valence electrons.
2. Use the electron pair repulsion theory (VSEPR theory) to determine the electron pair geometry.
3. Identify the molecular geometry based on the arrangement of atoms around the central atom and Label the bond angles between the atoms.

Here are the steps for determining the geometry of a covalently bonded species in the correct order:

1. Determine the central atom: Identify the central atom in the molecule or ion, which is usually the least electronegative element or the one with the highest bonding capacity.

2. Count the number of electron domains: Calculate the total number of electron domains surrounding the central atom. This includes both bonding and non-bonding electron pairs.

3. Identify the electron domain geometry: Based on the number of electron domains, identify the corresponding electron domain geometry using the VSEPR (Valence Shell Electron Pair Repulsion) theory.

4. Determine the molecular geometry: Considering the positions of the bonded atoms only (ignoring non-bonding electron pairs), identify the molecular geometry of the species.

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The random variable is discrete because it can only take on integer values.

You cannot have a fraction or decimal number of passengers in a vehicle. For example, a vehicle can have 1, 2, 3, or 4 passengers, but it cannot have 2.5 passengers. Discrete variables have a countable number of possible values and can be listed and counted. In contrast, continuous variables can take on any value within a range and are not limited to specific values. Examples of continuous variables include time, weight, and height.

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it is 95% confident that the true proportion of heads in a large number of tosses of this coin lies between 0.4969 and 0.5165.

a) The proportion of heads obtained in the experiment is

[tex]\frac{5067}{10000} = 0.5067[/tex]. The null hypothesis is that the coin is unbiased, which means the probability of getting a head is 0.5. The standard error (SE) of the proportion is given by

[tex]SE = \sqrt{\frac{p(1-p)}{n} } = \sqrt{\frac{(0.5)(0.5)}{10000} } = 0.005[/tex]

The test statistic is [tex]Z=\frac{(P-0.5)}{SE} = \frac{0.5067-0.5}{0.005} = 1.34[/tex]. The one-tailed p-value for this test is P(Z > 1.34) = P(Z < -1.34) = 0.0901 (assuming a significance level of 0.1). Since this p-value is greater than the significance level, we fail to reject the null hypothesis and conclude that the data do not provide evidence that the coin is biased.

b) The margin of error (m) for a 95% confidence interval is given by                                 m = 2SE = 0.01. The critical value for a 95% confidence interval is z= 1.96. Therefore, the 95% confidence interval for the true proportion of heads is given by P +/- mz' = 0.5067 +/- 0.01*1.96 = (0.4969, 0.5165).

In summary, we can say that based on the given information, the data do not provide evidence that the coin is biased and we are 95% confident that the true proportion of heads in a large number of tosses of this coin lies between 0.4969 and 0.5165.

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The particular solution of the differential equation is given by:

y/x = sqrt(0.7652), or y = x sqrt(0.7652), which is equivalent to option (c).

We can rewrite the given differential equation as:

xyy' = x^2 + y^2

Dividing both sides by y^2, we get:

x/y + y'/y = x/y * (x/y + 1/y')

Letting v = y/x, we have:

y' = v + xv'

Substituting this in the above equation, we get:

x/y + v + xv'/y = x/y * (x/y + 1/(v + xv'/y))

Simplifying this equation, we get:

v' = -(v/x) * [(1+v^2)^(1/2) - v]

This is a separable differential equation. We can separate the variables and integrate:

(1+v^2)^(-1/2) dv = -dx/x

Integrating both sides, we get:

ln|x| - ln|x0| = -arcsin(v)

where x0 is the initial value of x, which is given to be 1. Simplifying this equation, we get:

ln|x| = -arcsin(v) = -arcsin(y/x)

Taking exponentials of both sides, we get:

|x| = e^(-arcsin(y/x))

Squaring both sides, we get:

x^2 = e^(-2arcsin(y/x))

Simplifying this equation, we get:

y/x = sqrt((e^(2arcsin(y/x))-1)/(e^(2arcsin(y/x))+1))

Using the initial condition y = 1 when x = 1, we get:

y/x = sqrt((e^(2arcsin1)-1)/(e^(2arcsin1)+1)) = sqrt((e^(pi/2)-1)/(e^(pi/2)+1))

Simplifying this expression, we get:

y/x = sqrt((e^(pi/2)-1)/(e^(pi/2)+1)) = sqrt((2.71828^(pi/2)-1)/(2.71828^(pi/2)+1)) = sqrt(0.7652)

Therefore, the particular solution of the differential equation is given by:

y/x = sqrt(0.7652), or y = x sqrt(0.7652), which is equivalent to option (c).

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Answer:
The correct is 60%

Step-by-step explanation:

The total number of marbles in the bag is:

2 + 4 + 10 + 9 = 25

The probability of selecting a yellow marble from the bag is:

P(yellow) = 10/25 = 2/5

Therefore, the probability of not selecting a yellow marble (i.e., selecting a red, green, or purple marble) is:

P(not yellow) = 1 - P(yellow) = 1 - 2/5 = 3/5 = 60%

Therefore, the answer is 60%.