A normal population has mean 76 and variance 9. How large must be the random sample be if we want the standard error of the sample mean to be 1.1?

To find the 95% confidence interval for a sample of size 169 with 55 successes, we can use the following formula:

Confidence Interval = p-hat ± (Z * sqrt((p-hat*(1-p-hat))/n))

where p-hat is the sample proportion (successes/sample size), Z is the Z-score for a 95% confidence interval (1.96), and n is the sample size.

First, calculate p-hat:
p-hat = 55/169 ≈ 0.325

Next, calculate the margin of error:
Margin of Error = 1.96 * sqrt((0.325*(1-0.325))/169) ≈ 0.075

Finally, find the 95% confidence interval:
Lower Bound = 0.325 - 0.075 ≈ 0.250
Upper Bound = 0.325 + 0.075 ≈ 0.400

Thus, the 95% confidence interval is 0.250 ≤ p ≤ 0.400, expressed as a trilinear inequality with decimals accurate to three decimal places.

Answer:

3y(x + 2z)

Step-by-step explanation:

Both have 3 and y in common so you can take both those out

3y(x + 2z)

Answer:

No

Step-by-step explanation:

For three lengths to form a right triangle, the sum of the square of the two shorter sides (legs) must be equal to the square of the longest side (the hypotenuse)

This is not the case for 6, 8, and 9:

6^2 + 8^2 > 9^2

36 + 64 > 81

100 > 81

Had the longest side been 10 inches, the triangle would indeed by a right triangle as 10^2 = 100, but since this is not the case, you can't form a right triangle from the three lengths provided

Answer:

No.

Step-by-step explanation:

No, Alex is not correct.

760 mm = .760 m    .760 is less than 1.  To change mm to meters you need to move the decimal three places to the left.

Helping in the name of Jesus.

The probability that the servers will run for at least 56 days, given that they have been running for 16 days, is approximately 0.063.

Since the time between failures of the video streaming service follows an exponential distribution with a mean of 20 days, the parameter λ of the distribution can be calculated as:

λ = 1 / mean = 1 / 20 = 0.05

Let X be the time between failures of the video streaming service. Then X follows an exponential distribution with parameter λ = 0.05, and the probability density function of X is given by:

f(x) = λ e^(-λx)

We want to find the probability that the servers will run for at least 56 days, given that they have been running for 16 days. That is:

P(X > 56 | X > 16)

Using the conditional probability formula, we have:

P(X > 56 | X > 16) = P(X > 56 and X > 16) / P(X > 16)

Since X is a continuous random variable, we can use the cumulative distribution function (CDF) to calculate the probabilities:

P(X > 56 and X > 16) = P(X > 56)

= ∫56∞ λ e^(-λx) dx

= e^(-λx) |56∞

= e^(-0.05*56)

≈ 0.0284

P(X > 16) = ∫16∞ λ e^(-λx) dx

= e^(-λx) |16∞

= e^(-0.05×16)

≈ 0.4493

Therefore, P(X > 56 | X > 16) = P(X > 56 and X > 16) / P(X > 16)

= 0.0284 / 0.4493

≈ 0.0632

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The solution of the integral over general regions is ∫∫dA = [tex]\int ^\pi _0[/tex] π dx [tex]\int ^{sin x} _{2x/\pi}[/tex] dx

Let's consider a specific value of x, say x = a. Then we know that the y values that satisfy the inequalities for this x value are given by 0 ≤ 2a/π ≤ y ≤ sin a. We can represent this vertical slice as a rectangle with base length sin a - 2a/π and height dx (since we are integrating with respect to x).

The area of this rectangle is (sin a - 2a/π) dx, so the contribution to the total area from this vertical slice is given by the integral ∫(sin a - 2a/π) dx evaluated from 0 to π.

We can evaluate this integral using the Fundamental Theorem of Calculus, which tells us that the antiderivative of sin a is -cos a, and the antiderivative of -2a/π is -a²/π. Plugging in the limits of integration, we get:

∫(sin a - 2a/π) dx = [-cos a - (a²/π)] from 0 to π

= (-cos π - (π²/π)) - (-cos 0 - (0²/π))

= π + 0

So the contribution to the total area from this vertical slice is π. We need to integrate over all possible values of x to get the total area, so we set up the integral:

∫∫dA = [tex]\int ^\pi _0[/tex] π dx [tex]\int ^{sin x} _{2x/\pi}[/tex] dx

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the answer is A)determine if the combine length of any two sides a greater than the length of 3 sides

A. determine if the combined length of any two sides is greater than the length of the third side

To find the validity of a triangle with sides of lengths denoted as ∆ABC, one of the initial steps is to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:

For a triangle with sides of lengths a, b, and c:

a + b > c

a + c > b

b + c > a

If this condition is not met for any of the three pairs of sides, then the triangle with the given side lengths is not possible or valid.

Option A correctly suggests determining if the combined length of any two sides is greater than the length of the third side, which is a crucial step in determining the validity of a triangle. This is the most appropriate option for finding the incidence of ∆ABC among the given choices.

The estimated critical value for t given a 99% confidence interval and a sample size of 41 is approximately 2.704.

To estimate the critical value for t with a 99% confidence interval from a sample of size 41, you can follow these steps:

1. Determine the degrees of freedom: Since the sample size is 41, the degrees of freedom (df) will be 41 - 1 = 40.

2. Identify the confidence level: The confidence level is given as 99%, which corresponds to an alpha level (α) of 1% or 0.01.

3. Use a t-distribution table or calculator: With the degrees of freedom (40) and the alpha level (0.01), you can now consult a t-distribution table or use an online calculator to find the critical value for t.

Using a t-distribution table or an online calculator, the critical value for t with 40 degrees of freedom and a 99% confidence interval is approximately 2.704.

So, the estimated critical value for t given a 99% confidence interval and a sample size of 41 is approximately 2.704.

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The critical point of the function is x ≈ 0.889.

The indicated derivative for the function is f'(x), which represents the first derivative of the function f(x). To find this derivative, we need to take the derivative of each term separately using the power rule of differentiation:

f'(x) = 4 - 8x³ + 2

Therefore, the first derivative of the given function f(x) is f'(x) = 4 - 8x³ + 2.

Now, we are given that f''(x) = 0, which represents the second derivative of the function. This means that the rate of change of the function is not changing, i.e., the function is either at a maximum or a minimum point.

We can find the critical points of the function by setting f'(x) = 0 and solving for x:

4 - 8x³ + 2 = 0

-8x³ = -6

x^3 = 3/4

x = (3/4)^(1/3) or x ≈ 0.889

Therefore, the critical point of the function is x ≈ 0.889. Since the second derivative is zero at this point, we cannot determine whether it is a maximum or a minimum point without further analysis.

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The statement 'A nonzero scalar of F can be considered as a polynomial in P(F) having degree zero' is true because a scalar is a constant term with no variables, and a constant term is a polynomial of degree zero.

In polynomial algebra, a polynomial of degree zero is defined as a constant, which can be thought of as a special case of a polynomial. A scalar in F is a member of a field, which is a mathematical structure that satisfies certain axioms.

A constant scalar can be considered as a polynomial with degree zero in P(F). This is because a polynomial of degree zero is defined as a polynomial with the highest power of x equal to 0. Since there is only one scalar in F, the highest power of x in the polynomial representing the scalar is 0, and hence, the degree of the polynomial is 0.

Therefore, a nonzero scalar of F can be considered as a polynomial of degree zero in P(F).

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The geometric series converges when the absolute value of the common ratio (r) is less than 1. However, the harmonic series, which is a specific type of p-series, diverges since the sum of its terms does not have a finite limit.

Based on the information provided, it seems that the series represented by 27 1-1 JE SLI (b) b 3 is supposed to converge, but instead it diverges. This is indicated by the phrase "Diverges" in parentheses after the series. Additionally, it is noted that the geometric series represented by the same terms converges, while the harmonic series (a type of p-series) diverges. The phrase "Gemeia cene Diverceg" seems to be a misspelling or unrelated information.

The geometric series converges when the absolute value of the common ratio (|r|) is less than 1. However, the harmonic series, which is a specific type of p-series, diverges since the sum of its terms does not have a finite limit.

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The total number of subjects included in the study is the sum of positive and negative test results, which is 143 (positive) + 157 (negative) = 300 subjects.

To find the number of subjects with a true negative result, subtract the false negative results from the total negative results: 157 (negative) - 3 (false negative) = 154 true negative results. To calculate the probability that a randomly selected subject had a true negative result, divide the number of true negative results by the total number of subjects: 154 (true negative) / 300 (total subjects) = 0.5133, or approximately 51.33%.

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Answer:

red balls = 15

Step-by-step explanation:

It is given that The ratio of blue balls to red balls is 4: 5.

Let's assume

If there are 27 balls in total it means that sum of Blue balls and red is equal to 27.

Blue balls + red balls = 27.

[tex]:\implies \: \: [/tex] 4x + 5x = 27

[tex]:\implies \: \: [/tex] 9x = 27

[tex]:\implies \: \: [/tex]x = 27/9

[tex]:\implies \: \: [/tex] x = 3

Number of blue balls = 4x

[tex]:\implies \: \: [/tex] 4 × 3

[tex]:\implies \: \: [/tex] 12 balls

Number of red balls = 5x

[tex]:\implies \: \: [/tex] 5 × 3

[tex]:\implies \: \: [/tex] 15 balls.

Verification :

[tex]:\implies \: \: [/tex] Blue balls + red balls = 27.

[tex]:\implies \: \: [/tex] 12 + 15 27

[tex]:\implies \: \: [/tex] 27 = 27

Hence, Verified!

Therefore, The total number of red balls are 15.

On solving the provided question ,we can say that As a result, the pie chart's slice representing sleep has a 45 degree centre angle

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

We must first determine the percentage of the 24 hours that Burt slept in order to determine the size of the centre angle of the slice of the pie chart that represents sleep.

Burt slept for three hours out of a total of twenty-four, thus this is how much time he slept:

3/24 = 1/8

We need to multiply this ratio by 360 degrees (the total number of degrees in a circle) to determine the centre angle of the slice indicating sleep:

1/8 times 360 equals 45 degrees.

As a result, the pie chart's slice representing sleep has a 45 degree centre angle.

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The measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.

To calculate the measure of the central angle representing sleep in the pie chart, we need to determine what fraction of the 24 hours Burt spent sleeping.

Burt slept for 3 hours out of 24, so the fraction of time he spent sleeping is:

3 / 24 = 1 / 8

To convert this fraction into an angle, we use the formula:

angle = fraction * 360 degrees

So, the central angle representing sleep in the pie chart would be:

angle = (1 / 8) * 360 degrees = 45 degrees

Therefore, the measure of the central angle, in degrees, of the slice of the pie chart representing sleep is 45 degrees.

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The following equations show how the angle measurements in the figure relate to one another: D. a+b=180 and E. 180-a=b.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees.

KL is a segment of a straight line in the illustration.

This indicates that KL's angles are measured at 180 degrees.

This suggests that,

a + b = 180

or

180 - a = b

Thus, the following equations show how the angle measurements in the figure relate to one another: D. a+b=180 and E. 180-a=b.

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Complete question:

M is a point on line segment KL. NM is a line segment. Select all the equations that represent the relationship between the measures of the angles in the figure.

A. a=b

B. a+b=90

C. b=90−a

D. a+b=180

E. 180−a=b

F. 180=b−a

The probability of a z-score larger than 2 is approximately 0.0228, or 2.28%.

Therefore, the answer is (b) .0228.

To find the probability that the mean of a sample of 49 observations will be larger than 82, we need to calculate the standard error of the mean first. The standard error of the mean is equal to the standard deviation of the population divided by the square root of the sample size. Therefore, in this case, the standard error of the mean is 7 / sqrt(49) = 1.

Next, we need to convert the sample mean of 82 to a z-score. The formula for a z-score is:

[tex]z = (x - μ) / SE[/tex]

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean. Plugging in the values, we get:

[tex]z = (82 - 80) / 1 = 2[/tex]

To find the probability of a z-score larger than 2, we can use a standard normal distribution table or calculator. The probability of a z-score larger than 2 is approximately 0.0228, or 2.28%.

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the answer is: No, because for each input there is not exactly one output.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

To determine if the relation is a function, we need to check if for each input (x-value) there is exactly one output (y-value). We can do this by checking if any two points on the graph have the same x-value but different y-values.

Looking at the points given:

(-5, 1)

(-2, 0)

(-2, -2)

(0, 2)

(1, 3)

(5, 1)

We can see that (-2, 0) and (-2, -2) have the same x-value of -2, but different y-values. Therefore, the relation is not a function.

So the answer is: No, because for each input there is not exactly one output.

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We know that the point of intersection of the linear and quadratic functions lies on the xy-plane at coordinates ( ,v w). Since the vertex of the quadratic function is given as (4, 19), we can assume that the quadratic function is of the form

[tex]y = a(x-4)^2 + 19[/tex]

To find the value of v, we need to find the x-coordinate of the point of intersection. Since the linear function is also given, we can set y = mx + b (where m is the slope of the line and b is the y-intercept) equal to the quadratic function and solve for x. Once we have the value of x, we can substitute it back into either equation to find the value of v.

Regarding the second question, we know that there are 78 students and the dig site has 24 sections. Each section can be studied by a group of 2 or 4 students. Let the number of sections studied by a group of 2 students be x, and the number of sections studied by a group of 4 students be y.

We know that x + y = 24 and 2x + 4y = 78. Solving these two equations simultaneously gives us x = 9 and y = 15, which means that 9 sections will be studied by a group of 2 students.

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The tip was $2.11 and the sales tax was $0.44.

The sales tax is equal to 5% of the total amount due before tax and tip, or 0.05 x 8.75 = 0.4375.

The sales tax, rounded to the nearest cent, is $0.44.

We must first determine the entire cost of the bill after the sales tax is added before we can determine the tip:

8.75 + 0.44 = 9.19

Now that we have the entire amount, we can compute the tip:

0.23 x 9.19 = 2.1137

The tip total, rounded to the nearest cent, is $2.11.

So, the tip was $2.11 and the sales tax was $0.44.

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A sample that is larger than necessary will be better representative of the population and will hence provide more accurate results.

Research results are directly impacted by sample size calculations. Very tiny sample sizes compromise a study's internal and external validity. Even when they are clinically insignificant, tiny differences have a tendency to become statistically significant differences in very large samples.

Because they have smaller error margins and lower standard deviations, larger research produce stronger and more trustworthy results. Big samples, when properly gathered, produce more accurate results than small samples because the values of the sample statistic in a big sample tend to be closer to the true population parameter.

Each sampling distribution's variability diminishes as sample numbers grow, making them more and more leptokurtic.

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Given statement: The Central Limit Theorem says that if X does NOT have a normal distribution, X-Bar still has an approximate normal distribution if n is large enough (n > 30).

Statement is True,

Because The Central Limit Theorem (CLT) states that if X does NOT have a normal distribution, the sampling distribution of the sample mean (X-Bar) will still have an approximate normal distribution if the sample size (n) is large enough, typically when n > 30.

The statement is generally true.

The Central Limit Theorem (CLT) states that if we have a random sample of independent and identically distributed (i.i.d) variables X1, X2, ..., Xn from any distribution with mean μ and finite variance [tex]\sigma ^2[/tex], then the sample mean X-Bar (the average of the observations) will be approximately normally distributed with mean μ and variance σ^2/n, as n (the sample size) becomes large.

While the CLT assumes that the underlying population distribution of X does not have to be normal, it does require that the population distribution has a finite mean and variance. If the sample size is large enough (typically n > 30), the sample mean will be approximately normally distributed regardless of the shape of the population distribution.

However, it is important to note that there are some distributions where the CLT does not hold even for large sample sizes, such as heavy-tailed distributions like the Cauchy distribution.

In such cases, other techniques may be necessary to model the data.

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Answer: I can't be totally for sure but I'm pretty sure it's 18.

Step-by-step explanation:

Answer:

Add all the ages together and then divide by the total number of ages

Sorry I can't really view the numbers and on your dot plot so I can't help with that

Rolle's theorem applies and the point(s) guaranteed to exist is/are x = 1/3.

Since f(x) is continuous on [0, 3] and differentiable on (0, 3), Rolle's theorem applies.

To apply Rolle's theorem, we need to find a point c in (0, 3) such that f(c) = 0 and f'(c) = 0.

Let's find f'(x) first:

f(x) = x(x-3)^2

f'(x) = (x-3)^2 + x*2(x-3)

f'(x) = 3x^2 - 16x + 18

Now, we need to solve 3x^2 - 16x + 18 = 0 to find the critical points of f(x) in (0, 3).

Using the quadratic formula, we get:

x = (16 ± sqrt(16^2 - 4318)) / (2*3)

x = (16 ± 2) / 6

x = 3 or x = 1/3

Since x = 3 is not in (0, 3), the only critical point of f(x) in (0, 3) is x = 1/3.

Since f(0) = f(3) = 0 and f(1/3) = 4/27 ≠ 0, by Rolle's theorem, there exists at least one point c in (0, 3) such that f'(c) = 0.

Therefore, Rolle's theorem applies and the point(s) guaranteed to exist is/are x = 1/3.

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The value of the integral IdA is:

[tex]IdA = 2arc sin(\sqrt{(5)/4} ) - arcsin(\sqrt{(15)/4)[/tex]

To evaluate the integral IdA, we need to set up the integral in terms of the given region D.

The region D is defined by the inequalities:

1 < x < 4 (which implies x is positive)

-y < x - 1 < y

Rearranging the second inequality, we get:

1-y < x < 1+y

So, the region D can be described as:

D = {(x, y) : 1 < x < 4, [tex]- \sqrt{(16-y^2) }[/tex] < y < [tex]\sqrt{(16-y^2) }[/tex]}

To evaluate the integral IdA, we integrate over D as follows:

IdA = ∫∫D x dA

[tex]IdA = \int 1^4 \int -\sqrt{(16-y^2)} ^\sqrt{t(16-y^2)} x dy dx[/tex]

Integrating with respect to y, we get:

[tex]IdA = \int 1^4 x ∫-\sqrt{(16-y^2) } ^\sqrt{sqrt(16-y^2) } dy dx[/tex]

[tex]IdA = \int 1^4 x [arcsin(y/4)]^-\sqrt{(16-x^2)} ^\sqrt{(16-x^2) } dx.[/tex]

Evaluating the integral with respect to x, we get:

[tex]IdA = \int 1^4 [(x/2) * arcsin(y/4)]^-\sqrt{(16-x^2) } ^\sqrt{(16-x^2) } dx[/tex]

[tex]IdA = [(x/2) * arcsin(y/4)]_1^4[/tex]

[tex]IdA = (4/2 * arcsin(\sqrt{(5)/4)} ) - (1/2 * arcsin(\sqrt{sqrt(15)/4) } ).[/tex]

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The total cost function, C(x), is [tex]C(x) = (x^4 / 4) - (x^2 / 2) + 7000[/tex].

We have,

To find the total cost function, C(x), from the marginal cost function, C'(x), we need to integrate the marginal cost function.

The constant of integration will be the fixed cost, which is given as $7000.

So, integrating C'(x), we get:

C(x) = ∫ C'(x) dx = ∫ (x^3 - 2x) dx

C(x) = (x^4 / 4) - (x^2 / 2) + C

where C is the constant of integration.

Now, we know that the fixed cost is $7000, so we can set C(x) = 7000 when x = 0:

7000 = (0^4 / 4) - (0^2 / 2) + C

7000 = 0 - 0 + C

C = 7000

Therefore,

The total cost function, C(x), is:

[tex]C(x) = (x^4 / 4) - (x^2 / 2) + 7000[/tex]

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The same non-zero constant is an equivalent operation that preserves the solution of the equation.

Yes, in solving a system of linear equations, it is permissible to multiply an equation by any non-zero constant. This operation is known as scalar multiplication and it does not change the solution of the system of linear equations.

Let's consider a simple system of linear equations as an example:

Equation 1: 2x + 3y = 7

Equation 2: 4x + 5y = 9

To solve this system of linear equations, we can use the method of elimination or substitution. In the method of elimination, we need to eliminate one of the variables by adding or subtracting equations. To do this, we can multiply one of the equations by a constant to make it easier to eliminate a variable.

For instance, let's say we want to eliminate the variable y. We can multiply the first equation by -5 and the second equation by 3. This gives us:

Equation 1: -10x - 15y = -35

Equation 2: 12x + 15y = 27

Now we can add the two equations to eliminate the variable y:

-10x - 15y + 12x + 15y = -35 + 27

2x = -8

x = -4

We can then substitute this value of x back into one of the original equations to find the value of y:

2(-4) + 3y = 7

-8 + 3y = 7

3y = 15

y = 5

Therefore, the solution to the system of linear equations is x = -4 and y = 5.

As you can see, multiplying an equation by a constant did not change the solution of the system of linear equations. This is because multiplying both sides of an equation by the same non-zero constant is an equivalent operation that preserves the solution of the equation.

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Answer:

6

Step-by-step explanation:

The differential equation with initial condition that satisfied by B(t) = the body mass of a Guernsey cow t years after birth is k(B(t) - a)

In this context, the researchers presented a model in a paper published in 1996 that describes the relationship between the body mass of a Guernsey cow and the cow's age. This model is based on the assumption that the rate of change in body mass is proportional to how far the cow's current body mass is from the adult body mass, which is 486 kg.

To write the differential equation that represents this model, let B(t) be the body mass of a Guernsey cow t years after birth. The rate of change of body mass with respect to time t is given by dB/dt. According to the assumption, the rate of change of body mass is proportional to the difference between the current body mass and the adult body mass, which is B(t) - a. Therefore, we can write:

dB/dt = k(B(t) - a)

where k is a positive constant of proportionality. This is a first-order linear differential equation, which describes the growth of a Guernsey cow as a function of time.

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Complete Question:

A team of animal science researchers have been using mathematical models to try to predict milk production of dairy cows and goats. Part of this work involves developing models to predict the size of the animals at different ages. In a paper published in 1996 in the research journal Annales de Zootechnie, this team presented a model of the relationship between the body mass of a Guernsey cow and the cow's age. Suppose that a calf is born weighing 40 kg. Assumption: The body mass changes (with respect to age) at a rate proportional to how far the cow's current body mass is from the adult body mass (which is 486 kg),

a. (DE5) Write a differential equation with initial condition that satisfied by B(t) = the body mass of a Guernsey cow t years after birth. Use k as the constant of proportionality and write your equation so that k is positive.