A veterinarian surveys households in her area to find out how many pets they own. She estimates that households have 1.8 pets on average, with a margin of error of ±0.4 pets. There are 1,200 households in her area.

The general solution of the given differential equation is y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2) and the largest interval is (-infinity, -2) U (-1, infinity).

The general solution of the mentioned differential equation will be calculated as follows -

Firstly rewriting the differential equation in standard form:

(x+1) dy/dx + (x+2)y = 2x[tex] {e}^{(xy)} [/tex]

Calculating the integrating factor to make the LHS as a total derivative:

As known, formula for integrating factor is:

mu = [tex] {e}^{(integral of (x+2)/(x+1) dx)} [/tex]

= [tex] {e}^{(ln(x+1) + ln(x+2))} [/tex]

= (x+1)(x+2)

Now multiplying both sides of the equation by the integrating factor:

(x+1)(x+2) × (x+1) dy/dx + (x+1)(x+2) × (x+2)y = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

LHS will be a total derivative. Rearrange the equation for the same -

d/dx((x+1)(x+2)y) = 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2)

Integrating both sides of the equation:

(x+1)(x+2)y = integral of 2x[tex] {e}^{(xy)} [/tex] × (x+1)(x+2) dx

= 2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C

Now find the equation for y:

y = (2x[tex] {e}^{(xy)} [/tex] × (x+1) + [tex] {2x}^{ {2e}^{(xy)} } [/tex] + C) / (x+1)(x+2)

Equation for y is the general solution of the differential equation where constant C is the arbitrary constant of integration.

The general solution is not defined at the position x=-1 and x=-2. Hence, the largest interval over which the general solution is defined is (-infinity, -2) U (-1, infinity).

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2,092.1 is the population of the town after 5 years, and P(t)=2500*(1-0.035)^t is the exponential function.

In mathematics, exponential decay defines the process of diminishing an amount by a consistent percentage rate over a period of time.

It can be stated by the formula y=a(1-b)x wherein y is the total form and is the initial money, b is the decay factor, and x is the quantity of time that has passed.

So, we got:

r = 3.5%/100% = 0.035

We have our exponential function:

P(t) = 2500*(1 - 0.035)^t

The number after 5 years is provided by substituting t = 5, we will get:

P(5) =  2500*(1 - 0.035)^5 = 2,092.1

Therefore, 2,092.1 is the population of the town after 5 years, and P(t) = 2500*(1 - 0.035)^t is the exponential function.

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Correct question:
The population of the town is 2500 and is decreasing at a rate of 3.5% per year. Write an exponential decay function to find the population of the town after 5 years

Answer: 14%

The percentage is positive because the actual cost is a result of the estimated cost increased by 14%

Step-by-step explanation:

Formula

Subtract the actual value from the estimated value

850-730=120

Divide the results from step 1 by the real value

120/850= 0.14117647058*100

Multiply the results by 100 to find the total percentage

0.14117647058*100=14.1176

Round

14%

Answer:

D both are decreasing

Step-by-step explanation:

In both, as x is increasing, y is decreasing.

Average speed of Usain Bolt is 10.41 m/s.

The distance travelled by an object in relation to the amount of time it takes to travel that distance can be used to define speed. In plainer terms, it is a gauge of how quickly an object moves.

Average speed = (Total distance travelled)/(Total time required)

SI unit of speed is m/s.

Distance Travelled by Usain Bolt = 100m

Time required to travel this distance =  [tex]9\frac{3}{5}[/tex] = 48 ⁄ (5 sec)

Average speed = (Total distance travelled)/ (Total time required)

Average speed = 100/ (48/5)

                          = 500/48

                          = 10.41 m/s

Therefore, average speed of Usain Bolt is 10.41 m/s.

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The function f(x) = −16x² + 48x + 64 represents the height of an object above the ground in feet, x seconds after being launched.

To find f(-1), we plug -1 into the function:

f(-1) = −16(-1)² + 48(-1) + 64

= 16 - 48 + 64

= 32

This means that 1 second after the object was launched, it was 32 feet above the ground.

To find f(0.5), we plug 0.5 into the function:

f(0.5) = −16(0.5)² + 48(0.5) + 64

= −16(0.25) + 24 + 64

= −4 + 24 + 64

= 84

This means that 0.5 seconds after the object was launched, it was 84 feet above the ground.

Since the function represents the height of the object above the ground, the domain of the function would be the set of all real numbers x such that x represents the number of seconds after the object was launched.

This would include all positive and negative values of x, since the object could have been launched at any time in the past or future. However, if the problem specifies a specific range of time, then the domain would be limited to that range.

Therefore, the correct answer is as given above

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find formula for growth of city

y intercept of 300,000 because the function starts here

the slope is 1.08 because it grows by 8 percent each year

population at x year = 300,000(1.08)^x

you can better understand why the x is in the exponent by this example

in one year, it grows 8 percent

300,000 * 1.08 = 324,000

the next year, that previous year grows 8 percent

324,000 * 1.08 = 349,920

300,000 * 1.08 * 1.08 =349,920

300,000 * 1.08^2 = 349,920

in 2 years it grows to that

just do it to the 14th power now

300,000 * 1.08^14 = 881,158

hope this helps :)

if you got any questions just comment

The predicted value of the twin born first has an IQ of 104 is 106.2..

We have given that,

sample size n = 10

x = 98.13

y = 100.6

r = 0.904

p-value = 0.000

y'= 14.68 + 0.88x

significance level = 0.05

and we have to find predicted value of the twin born first has an IQ of 104.

We know that x represents the IQ score of the twin born first.

Therefore value of x is 104.

Hence the predicted value P will be,

P = 14.68 + 0.88(104)

  = 14.68 + 91.52

P = 106.2

Therefore the best predicted value of the twin born first has an IQ of 104 is 106.2.

The positive predicted value is the probability that a test gives result for a true statistic. The negative predictive value is the probability that a test gives a false result for a false statistic.

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201 numbers are less than 2017

If and only if it is odd, a number is the sum of two successive integers.

Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).

Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.

There are 201 numbers left.

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Elise only purchases the more expensive soft drinks. There is a linear demand curve. The relation is directly proportional is then the suitable compensation.

Linear demand curve

Elise only purchases the more expensive soft drinks. Her supply curve is straight.

Thus, the relation is directly proportional is then the suitable compensation.

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Answer:

q = -4

Step-by-step explanation:

0.0009 = 9 × 10^(-4)

q = -4

This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.

This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.

In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.

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The given set have two integers whose sum is 15 because if we selcet the element from the given set then there sum is equal to 15.

In the given question, let s = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. suppose six integers are chosen from s.

We have to check there be two integers whose sum is 15.

As we know that,

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The letter Z or the chalkboard Z is frequently used to represent the set of integers in mathematical terminology.

There are total 10 elements.

We have to choose two element from the given set which sum is equal to 15.

If we choose 3 and 12 then there sum is 15.

Similarly, if select (5,10), (6,9), (7,8) the sum of all these selection is 15.

So the given set have two integers whose sum is 15.

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convert 2.8hours to hours, minutes and seconds is 2.8 hours = 2 hours 48 minutes 0 seconds

The conversion of 2.8 hours into hours, minutes and seconds is relatively simple. To begin, we must first convert 2.8 hours into minutes. To do this, we multiply 2.8 by 60, which equals 168 minutes. Now, we need to convert those minutes into hours and seconds. To do this, we divide the 168 minutes by 60, which gives us 2 hours. We then take the remainder, which is 48 minutes, and divide it by 60, which gives us 0 seconds. Therefore, 2.8 hours is equivalent to 2 hours 48 minutes 0 seconds.

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Answer:

Step-by-step explanation:

fly

the sample mean is the point estimator of μ

Sample Mean:

The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.

Point Estimate:

p=x/

p is the point estimate for the population proportion, x is the number of

successes, n is the sample size

p= + /2

for the population proportion

x= + /2

for the population mean

= − /2

  is the margin of error

the sample mean is the point estimator of μ

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Answer:

Y=K1/x

K=6

Y=6

that's the process the answer is 6

Answer:

When using raitos you want to do P=2 +2+2+2

P=8

when L equals Ochoa

what will the answer be?

B2 + 62 + 25 gives us 169 - 25 and that gives us C Ronaldo

Step-by-step explanation:

Hope this helped! :)

Answer:

[tex]$\frac{x^{2}+12x-27}{x^{2}-x-6}$[/tex]

Step-by-step explanation:

See picture below :)

The relationship between the variables in terms of direction form and strength.

Given :

the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.

The straight line form with variables is :

y = mx + b is a straight line equation

here x and y are variables

m = slope

b = y - intercept

example :

y = 3x + 3

m = + 3 is a positive slope

y = -2x + 4

here

m = - 2 is a negative slope

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The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

The gradient vector field of a function

Suppose that  a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.

In which:

fx(x,y) is the partial derivative of f relative to variable x.

fy(x,y) is the partial derivative of f relative to variable y.

The function in this problem is defined as follows:

f(x,y) = xe^(9xy).

The partial derivative relative to x  as follows:

fx(x,y) = e^(9xy) + 9xye^(9xy) = (1 + 9xy)e^(9xy).

The partial derivative relative to y  as follows:

fy(x,y) = 9x²e^(9xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 9xy)e^(9xy) i + 9x²e^(9xy) j.

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The answer that is entirely correct based on the sales of popcorn is;

A: Jorge will raise more money because he is selling the popcorn for $3 per bag, and Alan is selling the popcorn for $2 per bag.

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, For Alan, we are told that her popcorn sales can be represented by the equation; y = 2x

where;

x is the number of bags of popcorn sold.

y is the amount of money raised.

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $2

Now, for Jorge, looking at the graph, we can see that;

y -intercept = 0

Slope = (15 - 6)/(5 - 2)

Slope = 3

Thus, if x is the number of bags of popcorn sold, then it means that the cost of each bag is $3.

Looking at the options, the correct one are Options A,

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Answer:

2/8, 3/12, 4/16 and etc

Step-by-step explanation:

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number

As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2

In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse

Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.

And we need to find is the square of the ratio of the short side to the long side of this rectangle

While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.

Therefore, the diagonal, according to the Pythagorean Theorem, is

√(a²+b²)

Now we can write the equation:

a / b = b /√ a² + b²

Then we have to find the square of the ratio of a to b.

Let us consider the answer, be k.

When we squaring the above equation,

a²/ b² = b² / a² + b² = k

When we solve this one then we get the value of  k = 1.

Now we have to Multiply each side of the equation by k,

=> k² = 1 - k.

And then adding each side by k,

k² + k − 1 = 0.

Now, we have to Solving for k using the Quadratic Formula,

= > k = -1 ± √[1² − 4(1)(−1)] / 2

=> k = -1±√5/2

As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.

Therefore, the resulting value is √5 - 1/2

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To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)

What is slope of a line?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tan.

When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.

To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.

When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.

To find y-intercept: set x = 0 and solve for y. The point will be (0, y).

To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).

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Step-by-step explanation:

Answer:About 155 results (0.47 seconds)

Tax and Tip - Illustrative Math Taskshttps://tasks.illustrativemathematics.org

Step-by-step explanation:

this may help

A general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as Probability sampling.

A probability sampling method is an any method of sampling that utilizes some from of random selection. Probability sampling refers to the selection of a sample from a population, when the selection is based on the principle of randomization, that is random selection or chance.

In simple random sampling each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.

The advantage of simple random sampling is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. In a simple random sample, every number of the population has an equal chance of being selected.

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Answer:

3753.20 ft

Step-by-step explanation:

tan 80° = 3400 ft/x

x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.

599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.

3400 ft is another leg of a right triangle.

(1589.51 ft)² + (3400 ft)² = y²

The hypotenuse, y, is the length of the cable.

y = 3753.20 ft

By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.

The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.

Here,

logₓy=logₐy/logₐx

log₇t=log₂t/log₂7

log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.

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