Assuming that a soap bubble is a perfect sphere, what is the diameter of a bubble containing 1,000 cm3 of air?

The equation of the tangent plane to the surface z = ln(x - y) at the point (3, 2, 0) is x - y - z + 1 = 0.

To find the tangent plane to the surface z = ln(x - y) at the point (3, 2, 0), we can use the following steps

Find the partial derivatives of the surface with respect to x and y:

∂z/∂x = 1/(x - y)

∂z/∂y = -1/(x - y)

Evaluate these partial derivatives at the point (3, 2):

∂z/∂x (3, 2) = 1/(3 - 2) = 1

∂z/∂y (3, 2) = -1/(3 - 2) = -1

Use these values to find the equation of the tangent plane at the point (3, 2, 0):

z - f(3,2) = ∂z/∂x (3,2) (x - 3) + ∂z/∂y (3,2) (y - 2)

where f(x,y) = ln(x - y)

Plugging in the values we get:

z - 0 = 1(x - 3) - 1(y - 2)

Simplifying the equation, we get:

x - y - z + 1 = 0

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The student that correctly completed the task of Mr Brown is the student that gave the option as follows : Four boxes of tissue cost $10

Rate of change refers to the ratio which shows how a certain item changes over the another item.

In the question, Mr brown requested for a rate of change that is equal to 2.5. Zane gave an option that suits this by showing the example as explained mathematically

If Four boxes of tissue cost $10 then 1 will cost

4 boxes = $10

1 box = ?

cross multiply gives

? * 4 = 10 * 1

dividing through by 4 gives

? = 10 / 4

? = 2.5

Hence the rate at which the price of the boxes change is 2.5

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The rate representation when Mr.brown asked his students to create a representation is Marco - y = 2.5x.

Which of the students correctly completed the task?

Given that: Four boxes of tissue cost $10. The rate is the price of one tissue. To get the rate, we need to divide the cost by the number of tissue:

rate = 10 / 4 = 2.5

Let y and x represent the cost and number of tissue respectively. Since the rate is 2.5, that means x number of tissue will cost 2.5x.

Therefore, we can represent the cost as y = 2.5x. So the student Marco- y = 2.5x completed the task correctly.

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The cluster sample represents the the characteristic of group of same types objects.

What is the cluster sampling?

A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.

A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.

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The crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

Specific gravity at 60 °F: 0.88

API° at 60 °F: 28

Watson characterization factor: 1.014

Refractive index: 1.44

Surface tension: 20 dyne/cm

Paraffinic, naphthenic, or aromatic: Paraffinic

Specific gravity at 60 °F the specific gravity of a liquid is its density relative to the density of water. The specific gravity of crude oil is typically between 0.8 and 1.0. A specific gravity of 0.88 means that the crude oil is 88% as dense as water.

API° at 60 °F: The API°, or American Petroleum Institute gravity, is a measure of the lightness or darkness of crude oil. A higher API° indicates a lighter crude oil. A crude oil with an API° of 28 is considered to be a medium-heavy crude oil.

Watson characterization factor the Watson characterization factor is a measure of the aromaticity of crude oil. A higher Watson characterization factor indicates a more aromatic crude oil. A crude oil with a Watson characterization factor of 1.014 is considered to be a paraffinic crude oil.

Refractive index the refractive index of a liquid is a measure of how much light is bent when it passes through the liquid. The refractive index of crude oil is typically between 1.4 and 1.5. A refractive index of 1.44 indicates that the crude oil is slightly more refractive than water.

Surface tension the surface tension of a liquid is a measure of the force that acts at the surface of the liquid, tending to minimize the surface area. The surface tension of crude oil is typically between 20 and 30 dyne/cm. A surface tension of 20 dyne/cm indicates that the crude oil has a relatively high surface tension.

Based on the estimated values, the crude oil is likely to be paraffinic. Paraffinic crude oils are characterized by having a high API°, low Watson characterization factor, and low refractive index. They also tend to have a high surface tension.

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The total amount of money the server would have saved after 5 weeks is  $455.

The first step is to determine the total amount of money saved for the first four weeks.

Total amount of money saved in the first four weeks = 35% x (200 x 4) = $280

Amount saved on the 5th week = 7/8 x $200 = $175

Total savings = $175 + $280 = $455

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Answer:

5

This is essentially the third identical question that you posted with the same

type of solution ... if you look at the previous question you asked and the explanation.. you will see that the red line crosses a corner of a box at (4,20)

4 cups =  20 pralines thus the number you are looking for is 20/4 = 5

Step-by-step explanation:

lets try this "story" to explain...

assume that you can walk 3 miles in 1 hour

this means that at 0 hr you go 0 miles , 1 hr you go 3 miles etc

0,0

1,3

2,6

3,9

etc.

if you graph that you will have the red line in you graph, and the x values would be 0,1,2,3 with the y values being 0,3,6,9....

if you DIVIDE any of those points

3/1 ,6/2, 9,3 the result is always a "3" that is the speed that you are walking at

it is a CONSTANT (in this problem) ... note: if the speed is NOT constant then this basically becomes a calculus problem, ant an algebra one.

Answer:

A

Step-by-step explanation:

if 10x2=20 then to get the height of the pole you would do 8 x 2 and 8 x 2=20

a. Predictor (x): odometer readings. Response (y): price.

b. Predictor (x): household size. Response (y): monthly water bill.

c. Predictor (x): time spent in the gym. Response (y): weight.

a. In this case, we want to predict the price of a used car based on its odometer reading. The price is the response variable, and the odometer reading is the predictor variable. It is reasonable to assume that the more miles a car has on it, the lower its value will be, all else being equal.

b. In this case, we want to predict the monthly water bill based on household size. The monthly water bill is the response variable, and the household size is the predictor variable. It is reasonable to assume that the more people living in a household, the higher their monthly water bill will be, all else being equal.

c. In this case, we want to predict a client's weight based on the time they spend in the gym. Weight is the response variable, and time spent in the gym is the predictor variable. It is reasonable to assume that the more time a person spends in the gym, the more likely they are to lose weight or maintain a healthy weight, all else being equal.

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Answer:

She subtracted 7x instead of dividing it. Personally, i wouldn't have done that. I would subtract the 14 first, then divide.

Answer:

x:5⁰

y:52⁰

Step-by-step explanation:

triangle:180⁰

the triangleis isoceles triangle so y:52⁰

so B is 72⁰

(14x+6)⁰=(14(5)+6)⁰=72⁰

Answer:

Opposite interior angles of a rhombus are congruent (the same). All 4 of them equal up to 360

Answer:

15.24m

Step-by-step explanation:

1-foot=0,304m then 50-foot=0,304*50=15,2 m

Answer:

17/21

Step-by-step explanation:

The amount of people that ate eggs only are:

42* 1/7 = 6

The amount of people that ate both pancakes and eggs are:

42 * 2/3 = 28

That means 34 people ate pancakes only.

The fraction that represents this is 34/42 = 17/21

We can separate each differential equation as follows:

a. dy/dx = (x − y)/x is separable, linear in y, Bernoulli in x

c. (x + 1)dy/dx = −y + 20 is separable, linear in y

d. dy/dx = 1/(x(x − y2)) is separable, exact

e. dy/dx =(y² + y)/(x² + x) is separable, exact

f. dy/dx = 5y + y² is separable, Bernoulli in y

g. y dx = (y − xy²) dy is separable, exact

h. x dy/dx = \(ye^{xy}\) − x is linear in y

j.  2xyy' + y² = 2x² is linear, homogeneous

k. y dx + x dy = 0 is  linear, homogeneous

l. (x² + 2y/x) dx = (3 − ln x²) dy  is exact

n. (y/x²) dy/dx + \(e^{2x^3}\) + y² = 0 is separable, nonlinear

In differential equations, there are several types of equations that have different characteristics and require different methods to solve them.

These are equations that can be separated into two separate functions, one containing only the independent variable and the other containing only the dependent variable. They can then be integrated separately.

These are equations that can be written in the form M(x,y)dx + N(x,y)dy = 0, where M and N are functions of x and y, and have a solution that satisfies the condition d/dy(M) = d/dx(N).

These are equations that can be written in the form y' + p(x)y = q(x), where p and q are functions of x. They can be solved using integrating factor method.

These are equations that can be written in the form y' = f(y/x), and can be solved using substitution y = vx.

These are equations that can be written in the form y' + p(x)y = q(x)y^n, where n is a constant. They can be transformed into linear equations by using substitution z = y^(1-n).

Identifying the type of differential equation is important as it helps in choosing the appropriate method to solve it.

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Answer:

Slope is -4/5

Y-intercept is -2

Step-by-step explanation:

use equation y=mx+b

Answer:

Enlargement by ratio of 3, shift 2 units right, shift 4 units down

Step-by-step explanation:

There isn't really a way how to do this step by step, its just common sense

Feel free to ask my questions in the comments

Answer:

5.6ft squared

Step-by-step explanation:

4x7 = 28 divided by 5 which is 5.6

The total number of marbles present in the bag is 40.

Given the probability of finding a red marble in a bag containing red and blue marbles by randomly choosing is

                                                       \(P(r) =\)  \(\frac{5}{8}\)

Given the total number of red marbles are

                                                      \(N(r) = 25\)

Now the probability of selecting a specific color marble is given as

                                                        \(P = \frac{n}{N}\)

where, \(n\) = Number of a specific color marble

and      \(N\) = Total number of marbles

So from the given data for red marbles, we can get the total number of marbles(this is only possible as all red marbles are equally likely to be chosen)

                                                         \(\frac{5}{8} = \frac{25}{N}\)

Thus,                                            \(N = \frac{8}{5}*25 = 40\)

So we get the total number of marbles as 40.

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Given the value of aₙ=-1 and the value of a₁, we can list the first five terms of aₙ by using the relation: aₙ = a₁ + (n-1)dwhere a₁ = 92 and d = -7, therefore;a₅ = 92 + (5-1)(-7)= 92 - 28= 64a₄ = 92 + (4-1)(-7)= 92 - 21= 71a₃ = 92 + (3-1)(-7)= 92 - 14= 78a₂ = 92 + (2-1)(-7)= 92 - 7= 85a₁ = 92 + (1-1)(-7)= 92  Therefore, the first five terms of aₙ are {85, 78, 71, 64, -1}.

Then, we can use the formula aₙ = a₁ + (n-1)d to find the value of the n-th term. In this problem, we are given the value of aₙ=-1, but we need to find the value of a₁.To do that, we use the hint given in the problem: aₙ = a₁ + (n-1)dwhere aₙ = -1 and d = -7, therefore;

-1 = a₁ + (n-1)(-7)= a₁ - 7n + 7

Solving for a₁, we get:a₁ = 7n + 6Now, we have two pieces of information: a₁ = 7n+6 and aₙ = -1Using a₁ = 7n+6, we can list the first five terms of aₙ as follows:a₁ = 7(1) + 6 = 13a₂ = 7(2) + 6 = 20a₃ = 7(3) + 6 = 27a₄ = 7(4) + 6 = 34a₅ = 7(5) + 6 = 41However, these are not the correct values of the first five terms because we were not given the correct value of a₁.

We can use the formula aₙ = a₁ + (n-1)d again to find the correct value of a₁:aₙ = a₁ + (n-1)d-1 = a₁ + (n-1)(-7)a₁ = -1 + 7n - 7a₁ = 7n - 8

Now, we can use a₁ = 7n-8 and d = -7 to find the correct values of the first five terms of

aₙ:a₁ = 7(1) - 8 = -1a₂ = 7(2) - 8 - 1 = -8a₃ = 7(3) - 8 - 2(-7) = -1a₄ = 7(4) - 8 - 3(-7) = 6a₅ = 7(5) - 8 - 4(-7) = 13

Therefore, the first five terms of aₙ are { -1, -8, -1, 6, 13}.

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The probability that at least two students have the same birthday in a class of 35 is approximately 81.4%. This is due to the birthday paradox, which states that the probability of two or more people having the same birthday increases as the number of people in the group increases.

To calculate the probability that at least two students have the same birthday, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event of interest is that at least two students have the same birthday.

Let's assume that all birthdays are equally likely, and ignore leap years for simplicity. The probability that the first student has a unique birthday is 1. The probability that the second student has a unique birthday is (364/365), since there is one less possible birthday that would lead to a match. The probability that the third student has a unique birthday is (363/365), since there are now two fewer possible birthdays that would lead to a match, and so on.

Using this approach, the probability that all 35 students have unique birthdays is:

P(all unique birthdays) = 1 x (364/365) x (363/365) x ... x (332/365)

To find the probability that at least two students have the same birthday, we can use the complement rule:

P(at least two students have the same birthday) = 1 - P(all unique birthdays)

P(at least two students have the same birthday) = 1 - (1 x (364/365) x (363/365) x ... x (332/365))

Using a calculator, we can find that:

P(at least two students have the same birthday) ≈ 0.814

Therefore, the probability that at least two students have the same birthday in a class of 35 students is approximately 0.814, or 81.4%.

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The butterfly spread is constructed using the following three calls: - Buy 1 call with an exercise price of 120 at a price of $15.40.- Sell 2 calls with an exercise price of 125 at a price of $13.50 each.- Buy 1 call with an exercise price of 130 at a price of $11.35.


A butterfly spread involves buying one option with a lower exercise price, selling two options with a middle exercise price, and buying one option with a higher exercise price. In this case, we buy the call with an exercise price of 120, sell two calls with an exercise price of 125, and buy the call with an exercise price of 130.

To analyze the strategy, we need to consider the stock price at expiration. The breakeven stock prices are calculated by adding and subtracting the net debit or credit from the middle exercise price. In this case, the net debit is $1.60 ($15.40 – 2*$13.50 + $11.35), so the breakeven prices are $121.40 ($125 - $1.60) and $128.60 ($125 + $1.60).

The maximum profit of $1.60 occurs when the stock price is exactly at the middle exercise price of 125 at expiration. In this case, the two sold calls expire worthless, and the two bought calls have intrinsic value of $5 each. The minimum profit of -$1.40 occurs when the stock price is below $121.40 or above $128.60 at expiration. In this situation, all the options expire worthless, resulting in a loss of the net debit.

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Answer

5x-3

Step-by-step by explanation

3x-4+2x+1

3x+2x is 5x

-4+1 is -3

5x-3

Answer: $8.50

Step-by-step explanation:

The expected gain (loss) is a weighted average of the probability of the different gains (losses) and the gains or losses.

Expected gain or loss for stock JKL:

= (Probability of losing $25 * -25) + ( Probability of gaining $5 * 5) + ( Probability of gaining $45 * 45)

= (15% * -25) + (65% * 5) + (20% * 45)

= -3.75 + 3.25 + 9

= $8.50

Answer:8.50$

Step-by-step explanation:

The value of m∠GFE in the kite is determined as 74.5⁰.

The value of m∠GFE is determined by finding the value of x and corresponding value of angle GFD.

In a kite, the opposite angles are congruent, while the adjacent angles are supplementary.

12x - 16 = 74

12x = 90

x = 90/12

x = 7.5

The value of angle EFH = 3x - 1 = 3(7.5) - 1 = 21.5⁰

The value of angle GFD = angle GDF = x

2x + 74 = 180

2x  = 106

x = 106/2

x = 53⁰

m∠GFE  =  21.5⁰ + 53⁰ = 74.5⁰

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Answer:

11, 3, -1, -7

Step-by-step explanation:

y = -2x - 5

x = -7, -4, -2, 1

y = -2(-7) - 5

y = 14 - 5

y = 11

y = -2(-4) - 5

y = 8 - 5

y = 3

y = -2(-2) - 5

y = 4 - 5

y = -1

y = -2(1) - 5

y = -2 - 5

y = -7

Answer: It would be c x=12

Step-by-step explanation:

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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Answer:

64 m3

Step-by-step explanation:

Just need to divide it