You have a garden row of 20 watermelon plants that produce an average of 30 watermelons apiece. For any additional watermelon plants planted, the output per watermelon plant drops by one watermelon. How many extra watermelon plants should you plant?

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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Answer:

Step-by-step explanation:

Confidence Level - "P" values  

90% 1.645

Confidence Interval - "P" values  

(0.7119 , 0.8481 )  

The required inequality is x ≤ 22 and the variable showing the maximum number of players on the ground is x.

A relationship between two expressions or values that are not equal to each other is called inequality.

Given that, a condition that, the maximum number of football players allowed on the field is 11 players from one team.

Since, the number of team members in one team is 11 and there are two teams, therefore, the total numbers of players on the field can 22 but not more than that.

If we consider x to be the maximum number of players on the ground, then x should not be greater than 22,

Therefore, we can write it in inequality as,

x ≤ 22

Hence, the  required inequality is x ≤ 22 and the variable showing the maximum number of players on the ground is x.

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Answer:

44

Step-by-step explanation:

Answer: 44

Step-by-step explanation:

This is quite simple, Are you sure you can't do it on your own?

Answer:

2/5x = 3/20 or 2/5 *x = 3/20

Step-by-step explanation:

These are the same thing just different ways to write. The x represents the unknown number

The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

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Answer:

x= -3

Step-by-step explanation:

−2(8x−1)=5(1−3x)

Step 1: Simplify both sides of the equation.

−2(8x−1)=5(1−3x)

(−2)(8x)+(−2)(−1)=(5)(1)+(5)(−3x)(Distribute)

−16x+2=5+−15x

−16x+2=−15x+5

Step 2: Add 15x to both sides.

−16x+2+15x=−15x+5+15x

−x+2=5

Step 3: Subtract 2 from both sides.

−x+2−2=5−2

−x=3

Step 4: Divide both sides by -1.

−x

−1

=

3

−1

x=−3

SOLUTION

Given the question in the tab, the following are the solution steps to answer the question.

STEP 1: Write the given data

STEP 2: Write the formula for the are of a triangle

STEP 3: Substitute the given values

STEP 4: Cross multiply

Open the bracket

Subtract 90 from both sides

STEP 5: Solve the derived equations using quadratic formula

Since the value of the base of a triangle can not be negative, the base of the triangle is 6ft

STEP 6: Find the value of the height

Hence, the dimension of the triangle are:

base = 6ft

height = 15ft

To find what does Josiah weight now, solve the difference between 187.2 and 5 7/10.

To do this the first step is to convert the mixed number into a fraction and then into a decimal number. This will make things easier to us at the moment of solving the difference.

Finally, solve 187.2 minus 5.7

Josiah weights 181.5 pounds now.

Answer:6

Step-by-step explanation:

the correct answer would be 6. Step-by-step explanation: when 7 is multiplied by 6 it gives 42 ,then we have to add 8 to the product and it gives 50

Answer:

Area = 56.16 cm

Step-by-step explanation:

Area is b x h

b = 20.8

h = 5.2

bh =  56.16 = area

Answer:

a big pizza is a good pizza

Step-by-step explanation:

The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.

It follows from the task content that the equation which correctly represents the Given situation is to be determined.

Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;

Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.

Consequently, answer choice C; w = 5 × 15 is correct.

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I think the answer is C

c∥d by the converse of the same-side interior angles theorem.

If two parallel lines are cut by a transversal, then the same side interior angles are supplementary.

Given:

m∠3+m∠8=180°

As, we can see that <3 and <8 are lies on same side of transversal.

So, the line that are parallel are c and d converse of the same-side interior angles theorem.

Hence, c∥ d by the converse of the same-side interior angles theorem.

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Answer:

There should be points that you need to plot onto this graph, look around the paper you were given for them

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

Its easier to figure out since it is a prime number and not a compsite number.

The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

What is Elevation?

Elevation is distance above the sea.

Given that;

A stripes bass is swimming at an elevation of −3 feet.

And, A flounder is swimming at an elevation of −11 feet.

Clearly, The bass is at higher elevation than the flounder.

So, -3 > -11

Hence, The correct option is,

⇒ −3 > −11; the bass is at a higher elevation than the flounder.

Option B is true.

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EXPLANATION:

To convert degrees to radians, multiply by π / 180 °

since a full circle is 360° or 2π radians.

240°⋅π / 180° radians

Cancel the common factor of 60

4 × π / 3 radians

Combine 4 and π / 3.

4π / 3 radians

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The coordinates of the points on unit circle at the given angle 240 degrees is\((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)

\(radians= (degrees)\)×\(\frac{\pi }{180}\)

x=rcosθ

y=rsinθ           (where r is the radius of  circle for unit circle r=1)

According to the question

we have

θ = 240 degrees and, r =1

so,  240 degrees = 240×\(\frac{\pi }{180}\)

⇒240 degrees = \(\frac{4\pi }{3}\)   (in radians)

Therefore, the coordinates of the points on unit circle at angle \(\frac{4\pi }{3}\) is calculated as

\(x=(1)cos\frac{4\pi }{3}\)                    (for unit circle r=1)

\(x=\frac{-1}{2}\)

And,

\(y=(1)sin\frac{4\pi }{3}\)                 (for unit circle r=1)

\(y=\frac{-\sqrt{3} }{2}\)

Hence, the coordinates of the point on unit circle at angle 240 degrees is \((\frac{-1}{2} ,\frac{-\sqrt{3} }{2} )\)

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The mean of the given scores is 15.43

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Score       Mid-values       Frequency      Total score

1 - 7                  4                  19                 19 x 4 = 76

8 - 10               9                  16                  16 x 9 = 144

11 - 15              13                  6                   13 x 6 = 78

16 - 20            18                  14                  18 x 14 = 252

21 - 35            28                 15                  28 x 15 = 420  

36 - 50           43                  4                   43 x 4 = 172

Total                                     74                  1142

Mean = 1142 / 74 = 15.43

Thus,

The mean of the given scores is 15.43

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All tables that represent proportional relationship between x and y are:

B. table B.

E. table E.

In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = (20 - 15)/(10 - 5) = (5 - 4)/(1 - 0)

Constant of proportionality, k = 1.

Therefore, the required linear equation is given by;

y = kx

y = x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

43.6 has 3 significant figures.

Answer:

18 square units

Step-by-step explanation:

the area of a parallelogram is represented by length times width

or l * w

l is 3 and w is 6

when you multiply them you get 18

you have to add the square in front of your type of unit too

Answer:

x = 12

Step-by-step explanation:

We will label the unknown interior angle of the triangle d.

14x - 19 + d = 180

14x + d = 199

d = 199 - 14x

199 - 14x + 3x + 9x + 7 - 2 = 180

199 - 2x +5 = 180

204 - 2x = 180

204 = 180 + 2x

2x = 24

x = 12

The graph is attached below and reason is described.

The table is,

x                 (x, f(x))

-2                (-2, 4)

-1                 (-1, 1)

0                (0, 0)

1                 (1, 1)

2                (2, 4)

To graph the functions f(x) = x² and g(x) = x²-4,

Choose a set of integers for x from -2 to 2.

x = -2, -1, 0, 1, 2

Calculate the corresponding values of f(x) and g(x) for each value of x. For f(x) = x²:

f(-2) = 4

f(-1) = 1

f(0) = 0

f(1) = 1

f(2) = 4

Now For  g(x) = x²-4:

g(-2) = 0

g(-1) = -3

g(0) = -4

g(1) = -3

g(2) = 0

Plot the points on a graph with x on the horizontal axis and f(x) and g(x) on the vertical axis.

Analyze the graph of g(x) in relation to the graph of f(x).

From the graph,

We can see that the graph of g(x) is the same as the graph of

f(x) shifted down by 4 units.

In other words,

g(x) = f(x) - 4 for all values of x.

This is because the graph of g(x) is obtained by taking the graph of f(x) and shifting it down by 4 units.

Now the given function is,

f(x) = x²

Now the complete table be,

x          steps         (x, f(x))

-2          (-2)²          (-2, 4)

-1           (-1)²           (-1, 1)

0           (0)²          (0, 0)

 1           (1)²           (1, 1)

 2          (2)²          (2, 4)

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The additional 60 men, the provisions will last for approximately 20 weeks.

To determine how long the provisions will last with the additional 60 men, we need to consider the total number of people and the original duration the provisions were meant to last.

Originally, the provisions were intended to sustain 400 men for 23 weeks. This means that the provisions were estimated to be sufficient for a total of 400 * 23 = 9200 person-weeks.

Now, with the additional 60 men, the total number of men becomes 400 + 60 = 460.

To calculate how long the provisions will last with the increased number of men, we divide the total person-weeks by the new number of men:

Provisions last = Total person-weeks / Number of men

= 9200 / 460

≈ 20 weeks (rounded to the nearest whole number)

The additional 60 men will extend the supply's shelf life to around 20 weeks.

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Answer:

420 + 69 = 489

Step-by-step explanation:

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Answer:

489

Step-by-step explanation:

420 + 69 = 489