please, explain the answer in details.
= = 1 1 if x² + 4y² = 4, then y" = 리 , c) - 4y3 c) d) a) 4y2 1 1 4y3 4y2

Answer:

Root( c square -9)

Step-by-step explanation:

The answer u have is the answer for a^2

Answer:

Root (c square -9)

Step-by-step explanation:

To find the distance between two parallel planes s1 : 2x − 3y z = 4 and   s2 : 4x − 6y 2z = 3, we can use the formula:

distance = |(d dot n)| / |n|

where d is a vector connecting any point on one plane to the other plane, n is the normal vector of the planes, and | | denotes the magnitude of a vector.

We can rewrite the equations of the planes as:

s1: 2x - 3y + 0z = 4

s2: 4x - 6y + 0z = 3

To find a vector connecting a point on s1 to s2, we can set one of the variables (say, z) to zero, and solve for the other variables:

2x - 3y = 4    (equation of s1 with z=0)

4x - 6y = 3    (equation of s2 with z=0)

We can solve for x and y by multiplying the equation of s1 by 2 and subtracting it from the equation of s2:

4x - 6y - (4x - 6y) = 3 - 8

0 = -5

This equation is inconsistent, which means that there is no point on s1 that lies on s2 with z=0.

Therefore, we can choose any point on one plane and use it to find a vector connecting the planes. For example, we can choose the point (0, 0, 4/3) on s1:

d = (0, 0, 4/3) - (0, 0, 0) = (0, 0, 4/3)

The normal vectors of the planes are the coefficients of x, y, and z in their equations, so we have:

n1 = (2, -3, 0)

n2 = (4, -6, 0)

The magnitude of the normal vectors is:

|n1| = sqrt(2^2 + (-3)^2 + 0^2) = sqrt(13)

|n2| = sqrt(4^2 + (-6)^2 + 0^2) = 2sqrt(13)

The dot product of d and n1 is:

d dot n1 = (0)(2) + (0)(-3) + (4/3)(0) = 0

Therefore, the distance between the planes is:

distance = |(d dot n2)| / |n2| = |(0)| / 2sqrt(13) = 0

So the distance between the planes s1 and s2 is 0. This means that the two planes are actually the same plane.

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Answer:

They are not proportional.

Step-by-step explanation:

The proportions of each survey differ in size.

                                    \(\frac{3}{5} \neq \frac{6}{11}\)

The first survey represents 60% and the second 54.5% (0.6 and 0.545 in decimal form). Therefore, they are not proportional.

Hope this helps.

Answer:

3 miles

Step-by-step explanation:

1/8*24=3

Answer:

Step-by-step explanation:

He ran 24 times around the track1

Circumfrence of track=1/8 Mile

Total distance he covered=1/8*24

Distance = 3 miles

Sin(300°) = -√3 / 2 .

The probability of selecting a green marble from the jar with 11 marbles, seven of which are red, and four of which are green, changes from 4/11 to 3/10 after your sister takes one red marble and still has it.

The probability of selecting a green marble from the jar with 11 marbles depends on the number of green marbles remaining in the jar after your sister takes one red marble. Initially, the probability of selecting a green marble would have been 4/11 since there are four green marbles out of a total of eleven marbles.

After your sister takes one red marble and still has it, there will be 10 marbles left in the jar, including three green marbles and seven red marbles. Therefore, the probability of selecting a green marble at random would be 3/10, or 0.3, which is less than the initial probability of 4/11.

It's important to note that the probability of selecting a green marble does not change based on the order of the selections. In other words, if you were to select a green marble first and then your sister selects a red marble, the probability of selecting another green marble would still be 3/10.

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Answer:

2,292/3 = x/12

Step-by-step explanation:

if you were to solve

2,292/3 finds you how many people per hour

and multiply that by 12 to find how many people for 12 hours.

Step-by-step explanation:

\(\frac{2292}{3} =\frac{x}{12}\)  

cross multiply divide.

x=9168

Answer:

\(x^2-4x+3\)

\(63\ \text{sq. units}\)

Step-by-step explanation:

l = Length = \(\dfrac{x^2-x-6}{x-5}\)

w = Width = \(\dfrac{x^2-6x+5}{x+2}\)

Area is given by

\(A=lw\\\Rightarrow A=\dfrac{x^2-x-6}{x-5}\times\dfrac{x^2-6x+5}{x+2}\\\Rightarrow A=\dfrac{x^2-3x+2x-6}{x-5}\times\dfrac{x^2-5x-1x+5}{x+2}\\\Rightarrow A=\dfrac{(x-3)(x+2)}{x-5}\times\dfrac{(x-5)(x-1)}{x+2}\\\Rightarrow A=(x-3)(x-1)\\\Rightarrow A=x^2-4x+3\)

Area of the room is \(x^2-4x+3\).

If \(x=10\)

Area of the room

\(A=x^2-4x+3=10^2-4\times 10+3\\\Rightarrow A=63\ \text{sq. units}\)

So, the amount of carpet needed would be \(63\ \text{sq. units}\).

Answer:

D

Step-by-step explanation:

The probability that an orange weighs more than 17 oz is 0.1587.

The probability that an orange weighs more than 17 oz is 0.1587. This value can be calculated using the Z-score formula, which is used to calculate the probability of an event occurring. The formula is as follows:

Z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, the Z-score is (17 - 14) / 2 or 1.5. We can find the probability using the Z-score table, which gives us 0.1587, the probability that an orange weighs more than 17 oz.

The Z-score formula is useful for determining the probability of an event occurring when the data follows a normal distribution. Knowing the mean and standard deviation, we can calculate the likelihood of a certain outcome occurring. In this case, the probability that an orange weighs more than 17 oz is 0.1587.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The system of equations is:

x^2 = y

x^2 + y^2 = 9

Substituting the first equation into the second, we get:

x^2 + (x^2)^2 = 9

x^4 + x^2 - 9 = 0

Using the quadratic formula, we can solve for x^2:

x^2 = (-1 ± sqrt(37))/2

Taking the positive root, we get:

x^2 = (-1 + sqrt(37))/2

Substituting this back into the first equation, we get:

y = (-1 + sqrt(37))/2

So the solution is the point (sqrt((-1 + sqrt(37))/2), (-1 + sqrt(37))/2)

Looking at the graphs, only graph (d) contains the point (sqrt((-1 + sqrt(37))/2), (-1 + sqrt(37))/2), so the answer is (d).

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QUESTION: Which graph shows the system (x^2 = y =2 x^2 + y^2 = 9

    |     /|

    |    / |

    |   /  |

    |  /   |

    | /    |

    |/     |

_____|______|______

    |

    |

    |

    |

    |

    |

To solve these probability questions, we can utilize the Poisson distribution, which is commonly used to model the number of events occurring in a fixed interval of time or space.

In this case, we assume the number of airplane crashes follows a Poisson distribution with an average of 2.2  per month.

(a) To find the probability of less than 5 accidents in the next month, we sum up the probabilities of having 0, 1, 2, 3, and 4 accidents using the Poisson distribution formula. The probability can be calculated as follows:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

(b) To calculate the probability of more than 2 accidents in the next 3 months, we need to find the complement of having 0, 1, or 2 accidents in the next 3 months. We can calculate the complement as follows:

P(X > 2 in 3 months) = 1 - [P(X = 0 in 3 months) + P(X = 1 in 3 months) + P(X = 2 in 3 months)]

(c) To determine the probability of exactly 6 accidents in the next 4 months, we use the Poisson distribution formula:

P(X = 6 in 4 months)

To calculate these probabilities, we need to use the Poisson distribution formula with the given average rate of 2.2 crashes per month.

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Answer:

d

Step-by-step explanation:hope this help

The mathematician who lent his name to a test often mentioned in NYT crossword puzzles is Emil Post.

Emil Post was an influential mathematician who lived from 1897 to 1954. He made significant contributions to the field of mathematical logic, particularly in the area of formal systems and decision problems. One of his notable contributions is the development of the Post's Correspondence Problem, also known as the Post's Test.

The Post's Test is a problem in theoretical computer science that involves finding a solution to a sequence matching problem. It deals with determining whether there is a sequence of strings that can be concatenated in different ways to form identical sequences. This problem has important implications in the study of formal languages and computational complexity.

Due to the relevance and popularity of the Post's Test in the field of mathematical logic and computer science, Emil Post's name became associated with this problem. As a result, his name often appears in crossword puzzles, including those featured in the New York Times (NYT) crossword, which often includes clues related to various fields of knowledge, including mathematics and science.

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Without more information, it is not possible to determine the name of the mathematician who lent his name to a test in the New York Times crossword.

The question is asking for the name of a mathematician who lent his name to a test in the New York Times crossword. Unfortunately, without any specific clues or context, it is difficult to determine which mathematician is being referred to. There have been several mathematicians who have had tests or concepts named after them, such as the Pythagorean theorem named after Pythagoras or the Fibonacci sequence named after Leonardo Fibonacci. However, without more information, it is not possible to provide a specific answer.

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Answer:

B

Step-by-step explanation:

Since sin is opposite over hypotenuse, the side opposite of angle T is RS and the hypotenuse is RT.

The answer is B, 1/9.

To determine the result of the integral ∫(1 to ∞) x^2/(x^3+2)^2 dx, we can use the comparison test for improper integrals:

First, observe that x^2/(x^3+2)^2 < x^2/x^6 = 1/x^4 for x > 1, since the denominator in the original integrand is larger than x^6.

Now, consider the integral of 1/x^4 from 1 to ∞:

∫(1 to ∞) 1/x^4 dx = [(-1/3)x^(-3)](1 to ∞) = (-1/3)(0 - 1/3) = 1/9

Since 0 < x^2/(x^3+2)^2 < 1/x^4 for x > 1 and the integral ∫(1 to ∞) 1/x^4 dx converges, the given integral ∫(1 to ∞) x^2/(x^3+2)^2 dx also converges by the comparison test.

Hence, the answer is B, 1/9.

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One pound is roughly equivalent to 0.45359237 kilogrammes (kg). As a result, 120 pounds equal 1200.45359237= 54.43104 kg.

A pound weighs less than a kilogramme. Because of something called conversion factors, I know that a pound is less than a kilogramme.

Simply put, a conversion factor is a number that can be multiplied or divided to convert one set of units to another. So, when we need to convert 120 pounds to kilogrammes, we use a conversion factor.
The lb to kg conversion factor is:
1 lb = 0.453592 kg
We can easily calculate the conversion of 120 lb to kg now that we know the conversion factor: multiply 0.453592 by the number of pounds we have, which is 120. 120 x 0.453592 = 54.43104 kg
As a result, the answer to the question is 54.43104 kg.

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One of the features of interactive model of communication is "Feedback where a recipient of communication such as a listener provides a response to a message, often to indicate understanding after a message has been received."

The Feedback is one of the key features that makes the Interactive Model of Communication different from the Linear Model  based on Shannon and Weaver's mathematical model .

The Feedback allow a reciprocal exchange of messages between the sender and receiver, making communication a dynamic and interactive process.

In the Interactive Model, the feedback enables the receiver to provide feedback to the sender, which allows clarification, confirmation, and correction of messages.

The given question is incomplete , the complete question is

One of the features of the interactive model of communication that is discussed by Turner and West which makes it different from the linear model that was based on Shannon and weaver's mathematical model of communication is ?

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\(\cfrac{1}{1+x^{a-b}}~~ + ~~\cfrac{1}{1+x^{b-a}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{1+x^{b-a}}\implies \cfrac{1}{1+x^{-(a-b)}} \implies \cfrac{1}{1+\frac{1}{x^{a-b}}}\implies \cfrac{1}{\frac{1+x^{a-b}}{x^{a-b}}}\implies \cfrac{x^{a-b}}{1+x^{a-b}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{1+x^{a-b}}~~ + ~~\cfrac{x^{a-b}}{1+x^{a-b}}\implies \cfrac{1+x^{a-b}}{1+x^{a-b}}\implies \text{\LARGE 1}\)

The parameters for HCP and FCC structures can be obtained as follows:

HCP structure: #atoms = 2N², coordination# = 12, c/a Ratio is the ratio of height to basal plane edge length, and atomic Packing factor (APF) is the volume of atoms divided by the total volume of the unit cell.

FCC structure: #atoms = 4, coordination# = 12, c/a Ratio = 1, and APF is the volume of atoms divided by the total volume of the unit cell.

The parameters for HCP (hexagonal close-packed) and FCC (face-centered cubic) structures can be determined as follows:

For HCP structure:

Number of atoms (#atoms): In the HCP structure, each unit cell contains two atoms. Hence, the number of atoms can be calculated using the formula #atoms = 2N², where N is the number of unit cells along the basal plane.

Coordination number: The coordination number for HCP is 12, as each atom is surrounded by 12 nearest neighbors.

Edge length c/a ratio: The c/a ratio represents the ratio of the height (c-axis length) to the basal plane edge length (a-axis length) of the HCP unit cell.

Atomic Packing Factor (APF): The APF is calculated by dividing the volume occupied by the atoms in the unit cell by the total volume of the unit cell.

For FCC structure:

Number of atoms (#atoms): The FCC unit cell contains four atoms.

Coordination number: The coordination number for FCC is 12, as each atom is surrounded by 12 nearest neighbors.

Edge length c/a ratio: In the FCC structure, the c/a ratio is equal to 1, as there is no distinction between the c-axis and a-axis lengths.

Atomic Packing Factor (APF): The APF is calculated by dividing the volume occupied by the atoms in the unit cell by the total volume of the unit cell.

Note: To convert between Angstroms and centimeters, 1 Angstrom is equal to 1 × 10^(-8) cm. And 1 picometer is equal to 1 cm / (10^10).

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Answer:

Domain= {XER}   Range= {YER}

Step-by-step explanation:

This is a line equation. Lines continue infinitely in both the horizontal direction and vertical direction, so that means that the domain and range are both a set of all real numbers.

4) The correct statement is B: LMN > QMP by SSS.  5) The correct statement is G: TRP > SRP by SSS.

Question 4

The correct answer is B: LMN > QMP by SSS.

In triangle LMN, all three sides are congruent, so it is an equilateral triangle. In triangle QMP, all three sides are also congruent, so it is also an equilateral triangle. Therefore, both triangles are congruent by SSS. This means that LMN and QMP have the same side lengths, and therefore LMN > QMP.

Question 5

The correct answer is G: TRP > SRP by SSS.

Since P is the midpoint of TS, then TP = SP. Also, TR = SR = 1.4 inches. This means that the two triangles TRP and SRP have all three sides congruent, so they are congruent by SSS. Therefore, TRP > SRP.

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the function f(x) that satisfies the given conditions is:

f(x) = x^2 + x^3 + 2x^4 + 7

We need to find a function f whose second derivative is given by 4 + 6x + 24x^2, and that satisfies f(0) = 3 and f(1) = 11.

Integrating the second derivative, we get:

f'(x) = ∫(4 + 6x + 24x^2)dx = 4x + 3x^2 + 8x^3 + C1

where C1 is an arbitrary constant of integration.

Using the initial condition f(0) = 3, we get:

f'(0) = C1 = 0

Substituting this back into the expression for f'(x), we get:

f'(x) = 4x + 3x^2 + 8x^3

Integrating f'(x), we get:

f(x) = ∫(4x + 3x^2 + 8x^3)dx = x^2 + x^3 + 2x^4 + C2

where C2 is an arbitrary constant of integration.

Using the second initial condition f(1) = 11, we get:

f(1) = 1 + 1 + 2 + C2 = 11

C2 = 7

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Triggering the secretion of vasopressin is not a mechanism by which angiotensin II elevates ECF volume.

Angiotensin II is a hormone that plays a crucial role in regulating blood pressure and fluid balance in the body. It is produced by the renin-angiotensin-aldosterone system (RAAS) in response to low blood pressure or decreased blood flow to the kidneys.

When released, angiotensin II acts on various targets to increase blood pressure and restore fluid balance. One of its effects is to stimulate the secretion of aldosterone from the adrenal glands, which promotes salt and water retention in the kidneys.

This, in turn, increases extracellular fluid (ECF) volume. Additionally, angiotensin II can also stimulate thirst, which encourages the intake of fluids, further increasing ECF volume. However, angiotensin II does not directly cause the release of vasopressin, which also promotes water retention.

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The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). In this case, Q1 is 9 and Q3 is 16, so the IQR is 7. The correct answer is Option C.

Interquartile range (IQR) is a measure of variability that is used in statistics and is calculated from a set of numerical data. It is the difference between the 75th and 25th percentile, and it provides an indication of how spread out the values in the data set are. The IQR is typically used to identify outliers in the data, as any values outside of the IQR are considered to be significantly different from the rest of the data. It is also used in box-and-whisker plots to show the spread of values in the data set.

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Answer:

7 fruit cups

Step-by-step explanation:

$3.75/3x + $1.50y = $15.50

So, if you have 4 protein bars, the equation would read:

1.25x + 1.5y = 15.5

1.25(4) + 1.5y = 15.5

5 + 1.5y = 15.5

1.5y = 10.5

y = 7