The Lake of Distress is contaminated with flesh-eating bacteria!! The lake started withonly 4 square feet infected, but as time has gone on, the bacteria are growing by a factorof 3 every hour. The relationship between the bacteria and time is...Linear0 Exponential

We will verify by substitution whether the given functions are solutions to their respective differential equations. The equations to be verified are:

y′ + 2xy^2 = 0  , x^2y′′ + xy′ − y = ln(x)

For the differential equation y′ + 2xy^2 = 0, we will substitute the given function y = f(x) into the equation and check if it satisfies the equation. Taking the derivative of y with respect to x, we have y′ = f'(x). Substituting these into the equation, we get f'(x) + 2xf(x)^2 = 0. If this equation holds true for all x in the domain, then the function y = f(x) is a solution to the differential equation.

For the differential equation x^2y′′ + xy′ − y = ln(x), we will substitute the given function y = f(x) into the equation and check if it satisfies the equation. Taking the first and second derivatives of y with respect to x, we have y′ = f'(x) and y′′ = f''(x). Substituting these into the equation, we get x^2f''(x) + xf'(x) - f(x) = ln(x). If this equation holds true for all x in the domain, then the function y = f(x) is a solution to the differential equation.

By substituting the given functions into their respective differential equations and verifying their validity, we can determine whether the functions satisfy the equations and hence confirm them as solutions.

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Answer:

1139621600

Step-by-step explanation:

The answer is 1139621600, because if it is in 2001. All you have to o is multiply by 4. I don't know if this is correct. If they gave you another year and another set of numbers I would be able to clarify it more. So...if this isn't correct. I'm so sorry.

If you think its incorrect please say so in comments below. Any questions? Say them below as well.

I hope this helped.

:)

Signed,

tyreefrankinjr

First replace x with -2 in the g(x) equation and solve:

G(x) = x + 4 = -2 + 4 = 2

Now replace x in the f(x) equation with the solution of g(x).

F(x) = 1-3(2) = 1-6 = -5

Fg(-2) = -5

We will prove two statements. First, every infinite decimal representing a rational number is recurring. Second, if a rational number is represented by a fraction in lowest terms as a/b, then the number of recurring digits in its decimal representation is less than b.

Statement 1: Every infinite decimal representing a rational number is recurring. Let's consider a rational number represented as a/b, where a and b are integers and b ≠ 0. The decimal representation of this rational number can be expressed as a quotient a/b in long division.

In long division, the remainder can have a maximum of b - 1 possible values because it ranges from 0 to b - 1. Since there are only b possible remainders, at least two remainders must be equal due to the pigeonhole principle. This means that at some point in the long division process, we encounter a repeated remainder. Once a repeated remainder is encountered, the long division process will continue in a repeating pattern. Therefore, the decimal representation becomes recurring, where the repeating pattern corresponds to the digits after the decimal point. Hence, every infinite decimal representing a rational number is recurring.

Statement 2: If a rational number is represented by a fraction in lowest terms as a/b, then the number of recurring digits in its decimal representation is less than b. Let's consider a rational number a/b in lowest terms, where a and b are integers and b ≠ 0. We know that the decimal representation of this rational number is recurring.

In the recurring part of the decimal representation, the repeating pattern can have a maximum length of b - 1. This is because if the repeating pattern has a length equal to or greater than b, we can simplify the fraction further, contradicting the assumption that it is in lowest terms. Therefore, the number of recurring digits in the decimal representation of a rational number a/b, in lowest terms, is less than b.

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The quadrants that satisfy the condition xy>0 are quadrant I and quadrant III.

The product of two numbers is positive if and only if both numbers have the same sign. In other words, if x and y are both positive or both negative, then xy will be positive.

Quadrant I and quadrant III are the only quadrants where both x and y are positive. Quadrant II and quadrant IV are the only quadrants where both x and y are negative.

Therefore, the only quadrants that satisfy the condition xy>0 are quadrant I and quadrant III.

Here is a table that shows the signs of x and y in each quadrant:

Quadrant | x | y | xy

------- | --- | --- | ---

I | + | + | +

II | + | - | -

III | - | - | +

IV | - | + | -

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The quadrants that satisfy the condition xy>0 are quadrant I and quadrant III.

The product of two numbers is positive if and only if both numbers have the same sign. In other words, if x and y are both positive or both negative, then xy will be positive.

Quadrant I and quadrant III are the only quadrants where both x and y are positive. Quadrant II and quadrant IV are the only quadrants where both x and y are negative.

Therefore, the only quadrants that satisfy the condition xy>0 are quadrant I and quadrant III.

Here is a table that shows the signs of x and y in each quadrant:

Quadrant | x | y | xy

------- | --- | --- | ---

I | + | + | +

II | + | - | -

III | - | - | +

IV | - | + | -

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Answer:

(8,0)

Step-by-step explanation

Yes, we can determine the percentage of people below 2 from the box plot. The answer is 0%

From the given data we can sketch out a box plot given as follows. Here since the left whisker ends at 2 and the right whisker ends at 43, there are no people less than 2 and no people more than 43.

5 and 15 are the 1st and the 3rd Quartile respectively.

Since the minimum value of this data is 2, there are no people who could be below 2. Therefore, the percentage of people below 2 is 0%

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Answer:

Their ages are 38,39 and 40.

Step by step explanation:

If they were all the same age, then their ages would be:

But, they are consecutive integers. So, you can make Elsa 40 and Edna 38.

Answer:

Do you have like an image or choices that we can go off of?

Answer:

I belive it is d and f

Step-by-step explanation:

I did a quiz similar to this a while back but if I am wrong please let me know! Have a great day!

2.

slope: rise(precipitation) / run (time)

In the real world, the slope means the relationship between time and precipitation.

3. AS the time increases, the precipitation increases. Is a linear function.

4. The y-intercept (0,y) means the amount of precipitation when no time passed since tracking.

Both y-intercepts have the same meaning.

We found a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = -10x + 3e^(-x) as y_p = -3/2 e^(-x).

To find a particular solution to the nonhomogeneous differential equation y'' + 4y' + 5y = -10x + 3e^(-x), we will use the method of undetermined coefficients.

Step 1: Homogeneous Solution

First, we need to find the solution to the corresponding homogeneous equation y'' + 4y' + 5y = 0. The characteristic equation is r^2 + 4r + 5 = 0, which has complex roots -2 + i and -2 - i. Therefore, the homogeneous solution is of the form y_h = e^(-2x)(c1cos(x) + c2sin(x)), where c1 and c2 are arbitrary constants.

Step 2: Particular Solution

We will look for a particular solution of the form y_p = ax + b + c e^(-x), where a, b, and c are constants to be determined.

Substituting y_p into the differential equation, we have:

y_p'' + 4y_p' + 5y_p = -10x + 3e^(-x)

Taking the derivatives and substituting back into the equation, we obtain:

(-c)e^(-x) + (-c)e^(-x) + 4(a - c)e^(-x) + 4a + 5(ax + b + c e^(-x)) = -10x + 3e^(-x)

Matching the coefficients of the terms on both sides, we get the following system of equations:

4a + 5b = 0 (for the x term)

4(a - c) = -10 (for the constant term)

-2c = 3 (for the e^(-x) term)

Solving this system of equations, we find a = 0, b = 0, and c = -3/2.

Therefore, a particular solution to the nonhomogeneous differential equation is y_p = -3/2 e^(-x).

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Variance and standard deviation are both measures of the dispersion or spread of a dataset, but they differ in terms of the unit of measurement.

Variance is the average of the squared differences between each data point and the mean of the dataset. It measures how far each data point is from the mean, squared, and then averages these squared differences. Variance is expressed in squared units, making it difficult to interpret in the original unit of measurement. For example, if we are measuring the heights of individuals in centimeters, the variance would be expressed in square centimeters.

Standard deviation, on the other hand, is the square root of the variance. It is a more commonly used measure because it is expressed in the same unit as the original data. Standard deviation represents the average distance of each data point from the mean. It provides a more intuitive understanding of the spread of the dataset. For example, if the standard deviation of a dataset of heights is 5 cm, it means that most heights in the dataset are within 5 cm of the mean height.

To illustrate the application of these measures, consider a dataset of test scores for two students: Student A and Student B.

If Student A has test scores of 80, 85, 90, and 95, and Student B has test scores of 70, 80, 90, and 100, we can calculate the variance and standard deviation for each student's scores.

The variance for Student A's scores might be 62.5, and the standard deviation would be approximately 7.91. For Student B, the variance might be 125 and the standard deviation would be approximately 11.18.

These measures help us understand how much the scores deviate from the mean, and how spread out the scores are within each dataset.

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Answer:

1:6

Step-by-step explanation:

you have one out of 6 chances to pick the yellow marble

Answer:

yellow is 1 out of 6

blue 1 of 5

Step-by-step explanation:

brainliest if u want

hope it helps

The function that describes the equation S = 10S = P x P - 2P + 2 is

\(f(P) = (P^2 - 2P + 2)/9.\)

The given equation S = 10S = P x P - 2P + 2 can be simplified by combining like terms and dividing both sides by 9:

\(9S = P^2 - 2P + 2\)

We can rearrange this equation to solve for S in terms of P:

\(f(P) = (P^2 - 2P + 2)/9\)

Therefore, the function that describes this equation is:

\(f(P) = (P^2 - 2P + 2)/9\)

This function takes an input value of P and outputs the corresponding value of S that satisfies the original equation. The domain of this function is all real numbers since any value of P can be plugged into the equation. However, the range of this function is limited to non-negative values, since S represents a sum of numbers and cannot be negative.

In summary, the function that describes the equation

S = 10S = P x P - 2P + 2 is

\(f(P) = (P^2 - 2P + 2)/9.\)

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Answer: y = -1/2x - 3

Step-by-step explanation:

When given triangles are given then the value of x and y is 5 and 14 respectively.

When BC is similar to EF.

19= 4x-1

19+1=4x

20=4x

x=5

When DE is similar to AB

y-6 =8

y=8+6

y=14

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.

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Answer:

\(D)\ -1,0\)

Step-by-step explanation:

Given

\(4x - 3y= -4\)

Required

Determine which of the options is on the line

The question requires options.

However, I'll answer using the following:

\(A) -3, 4\)

\(B) -4,3\)

\(C)\ 3, 4\)

\(D)\ -1,0\)

A point is always of the form (x,y).

So, we have to substitute values for x and y in the given equation

Considering option A:

\((x,y)= (-3,4)\)

Substitute \(-3\ for\ x\ and\ 4\ for\ y\) in \(4x - 3y= -4\)

\(4(-3) -3(4) = -4\)

\(-12 -12 = -4\)

\(-24 \neq -4\)

The above represents an inequality.

Hence, -3,4 does not lie on the equation

Considering option B:

\((x,y) = (-4,3)\)

Substitute \(-4\ for\ x\ and\ 3\ for\ y\) in \(4x - 3y= -4\)

\(4(-4) - 3(3) = -4\)

\(-16 - 9 = -4\)

\(-25 \neq -4\)

The above represents an inequality.

Hence, -4,3 does not lie on the equation

Considering option C:

\((x,y) = (3,4)\)

Substitute \(3\ for\ x\ and\ 4\ for\) y in \(4x - 3y= -4\)

\(4(3) - 3(4) = 4\)

\(12 - 12 = 4\)

\(0 \neq 4\)

The above represents an inequality.

Hence, 3,4 does not lie on the equation

Considering Option D:

\((x,y) = (-1,0)\)

Substitute \(-1\ for\ x\ and\ 0\ for\) y in \(4x - 3y= -4\)

\(4(-1) - 3(0) = -4\)

\(-4 - 0 = -4\)

\(-4 = -4\)

The above represents an equality.

So, -1,0 lies on the equation

Answer:

x = 3

Step-by-step explanation:

The angle measuring 5x and the angle measuring 165° are a linear pair, so they are supplementary. Their measures add to 180°.

5x + 165 = 180

5x = 15

x = 3

Answer:

5

7

..................

Answer:

y equals -2x -7

y equals 3/4 x plus 2 1/2

Answer: 3/5

Step-by-step explanation: I don't if its the right answer, because I'm not great at math

P(A) is the likelihood that a six-sided die will produce an even number when rolled (2, 4, or 6).

P(B) is the likelihood that a six-sided dice will land on four.

P(A) = 3/6 = 1/2

P(B) = 1/6

The probability of rolling an even number followed by a four, or P(C), equals P(A) * P(B) = 1/2*1/6 = 1/12 = 0.083 since events A and B are independent of one another.

With a six-sided die, there is a roughly 0.83*100 or 8.3% probability of rolling an even number (2, 4, or 6), followed by a four.

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Answer: B inches

Step-by-step explanation:

I took the quiz

Answer:

its B

Step-by-step explanation:

simply saying its circular measure

Answer:

VAT = 96 RS

SP with VAT = 896 RS

Step-by-step explanation:

To find the VAT (value added tax) amount we need to calculate 12% of 800 as follows:

12/100 × 800 = 96 RS

To find the SP (Selling price) includinf VAT we need to add 800 to 96 equals 896 RS.

Answer:

3

Step-by-step explanation:

Answer:

85.2459016%

Step-by-step explanation:

Answer:

85.245901639344%

Step-by-step explanation:

Answer:

192.5 kg

Step-by-step explanation:

220-12.5%=220*(100-12.5)/100=220*0.875= 192.5 kg

The median score of the sample size is actually 75, as it is the middle value of the sorted scores.

The median is a measure of central tendency, which gives us a better understanding of the data by telling us the middle value of a set of numbers. To calculate the median of a random sample of students, the scores must first be sorted in ascending order: 0, 50, 50, 70, 70, 80, 90, 90, 90, 100. Then, the middle value can be found. In this case, the middle value is the fifth out of the ten scores, which is 80. Therefore, the median score is 80. However, this statement is incorrect because the median is actually 75. This is because the fifth and sixth scores (80 and 90) are both middle values, and when there are two middle values, the median is found by taking the mean of the two numbers (80 + 90 = 170; 170 ÷ 2 = 85). Therefore, the median of this random sample size of students is 75.

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Answer:

Step-by-step explanation:

8x^2 - 8x + 2

2(4x^2 - 4x + 1)

2(2x - 1)(2x - 1) or 2(2x - 1)^2

answer is C

The complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

Factorization is a process consists of writing a number or another mathematical object as a product of several factors solving it into other factors.

We have,

\(8x^2 - 8x + 2\)

Using the mid term splitting method;

\(=8x^2-4x-4x+2\)

\(=4x(2x-1)-2(2x-1)\)

\(=(4x-2)(2x-1)\)

\(=2(2x-1)(2x-1)\)

\(=2(2x-1)^2\)

So, the factorization of the given expression is given in option \((c)\)  i.e.   \(2(2x-1)^2\) .

Hence, we can say that the complete factorization of \(8x^2 - 8x + 2\) will be  \(2(2x-1)^2\) .

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