Sandy has 21 roses, 7 daisies, and 14 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?

The time-dependent temperature field T(r,0,t) in the disc of radius a is expressed in the form of an infinite series with coefficients expressed as definite integrals of known functions.

The solution of the two-dimensional problem at hand requires solving the heat equation in a disc with a fixed boundary temperature, using the separation of variables technique. The heat equation is given by:

\(\frac{\partial T}{\partial t}=k\left(\frac{\partial^2 T}{\partial r^2}+\frac{1}{r}\frac{\partial T}{\partial r}\right)\),

where T is the temperature, k is the thermal diffusivity, and r is the radius.

Using the separation of variables method, we assume a solution to the heat equation of the form:

\(T(r,0,t)=\sum\limits_{n=1}^\infty A_n(t) \cdot \phi_n(r)\)

where Aₙ are time-dependent coefficients and φₙ are the eigenfunctions of the Helmholtz equation, satisfying the boundary conditions

\(\phi_n(a)=0 \quad\) and \(\quad \phi_n'(a)=0.\)

These eigenfunctions are given by \(\phi_n(r)=\sin\Big(\frac{n\pi}{a}r\Big).\)

Substituting this form of T(r,0,t) into the heat equation and rearranging yields

\(\frac{dA_n}{dt}=k\frac{n^2 \pi^2}{a^2}A_n\)

which has the solution

\(A_n(t)=A_n(0)e^{\frac{n^2 \pi^2}{a^2}kt}\)

The initial condition of T(r,0,t) must also be considered. Initial temperature is zero everywhere for the given problem, hence

\(T(r,0,0) = \sum\limits_{n=1}^\infty A_n(0) \cdot \phi_n(r) = 0\)

This gives the initial conditions

\(A_n(0) \cdot \phi_n(r) = - \sum\limits_{m=1, m\neq n}^\infty A_m(0)\phi_m(r)\).

Allowing m to go to infinity, we obtain an expression for each of the A_n(0) coefficients in terms of the orthonormal basis functions:

\(A_n(0)= -\int_0^a \sum\limits_{m=1, m\neq n}^\infty A_m(0)\phi_m(r) dr\).

Now, using the boundary condition of T(a,0,t) = To(0), we obtain an expression for the Aₙ(0) coefficients in terms of definite integrals.

\(A_n(0) = \frac{1}{\phi_n(a)} \Big[\int_0^a T_0(r)dr - \int_0^a \sum\limits_{m=1, m\neq n}^\infty A_m(0)\phi_m(r) dr\Big]\)

Substituting the expression for A_n(0) back into the general solution, we get

\(T(r,0,t) = \sum\limits_{n=1}^\infty A_n(t) \cdot \phi_n(r)\)

\(= \sum\limits_{n=1}^\infty \Big[\frac{1}{\phi_n(a)} \Big(\int_0^a T_0(r)dr - \int_0^a \sum\limits_{m=1, m\neq n}^\infty A_m(0)\phi_m(r) dr\Big) \cdot e^{\frac{n^2 \pi^2}{a^2}kt}\Big] \cdot \phi_n(r)\)

Therefore, the time-dependent temperature field T(r,0,t) in the disc of radius a is expressed in the form of an infinite series with coefficients expressed as definite integrals of known functions.

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The quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

According to the question,

We have the following information:

0.03 is divided by 0.148

Now, we have the quotient as:

0.2027

Now, when rounding off the numbers we know that the digits from where we are rounding off we look at the right next to that digit and when that digit is greater than 5 then the digit should be increased by 1 and when that digit is less than 5 then the digit should be the same.

So, we will round it off by taking the underlined digit to be next to first 2:

So, the digit is 0.

Then, we have:

0.2

Hence, the quotient when 0.03 is divided by 0.148 after rounding it off is 0.2.

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Answer:

1

Step-by-step explanation:

Answer:

You didn't say what the question was

Answer: 3

Step-by-step explanation:

Answer:

250 in out to radical change

Answer:

Step-by-step explanation:

A negative number raised to an even exponent gives a positive result so it is the same as 3 raised to 6. That is 3 x 3 x 3 x 3 x 3 x 3 = 729

The (-3) to the sixth power, (-3)⁶, is equal to 729.

To express (-3) to the sixth power in exponential form, we write it as (-3)⁶.

Now, let's calculate (-3)⁶ properly:

(-3)⁶ = (-3) * (-3) * (-3) * (-3) * (-3) * (-3)

Multiplying -3 by itself six times:

(-3) * (-3) * (-3) * (-3) * (-3) * (-3) = 729

Therefore, (-3) to the sixth power, (-3)⁶, is equal to 729.

By raising -3 to the power of 6, we obtain the result of 729.

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The penguin swims half the circumference of the circular island, which is equivalent to half the distance around the circle.

The circumference of a circle can be calculated using the formula:

C = πd,

where C is the circumference and d is the diameter of the circle.

Given that the diameter of the island is 20 meters, the radius (r) of the island is half the diameter, which is 10 meters.

Substituting the value of the radius into the formula, we have:

C = π * 10 meters = 10π meters.

To find half the circumference, we divide the total circumference by 2:

Half circumference = (10π meters) / 2 = 5π meters.

Therefore, the penguin swims a distance of 5π meters.

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Answer:

A)

Step-by-step explanation:

just look at the picture.

what must have happened to figure A to turn into figure B ?

is B more to the right or to the left of A ?

well, right. isn't it obvious ?

and when you look at the coordinates of a vertex, it is 3 units to the right of A.

and if the shift to the right had not happened - the 2 figures would be a mirrored image of each other with the x-axis being the mirror.

that is why A) is the right answer.

The coordinates of the specified vertex after the given sequence of transformations is given by;

Q' = (3, -3).

In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.

Mathematically, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical expression g(x) = f(x) + N.

Where:

By translating the coordinate Q (1, 3) two (2) units to the right, we have the following:

Coordinate Q (1, 3) → Coordinate Q' (1 + 2, 3) = Q (3, 3)

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection over the x-axis is given by this transformation rule:

(x, y)      →       (x, -y)

Coordinate Q' (3, 3) → (3, -3).

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Answer:

34 bricks is the greatest amount Mary could have used

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Answer:

24+18 is 42.

Step-by-step explanation:

1

24

+18

____

 42

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Answer:

Step-by-step explanation:

x = -6

subtract 3 from both sides: x-3 = -9

reflexive identity: x-3 = -9, so -9 = x-3

multiply both sides by -100: 900 = -100(x-3)

commutative law for multiplication:  -100(x-3) = (x-3)(-100)

distributive rule:  (x-3)(-100) = -100x + 300

The components of a number are the numbers that divide evenly into it. To find the factors of 13, divide 13 by each number from 1 to 13 and check whether or not the result is an integer. 13 is made up of two factors: 1 and 13.

Division is one of the four fundamental arithmetic operations that allows integers to be connected to produce new numbers. Addition, subtraction, and multiplication are the other operations. Division is the process of dividing a given amount into equal pieces in mathematics. For example, a group of 20 people can be divided into four groups of five people each, or five groups of four people each, and so on. Splitting anything involves dividing it into two or more equal halves, such as an area, class, category, group, or division. To divide something simply is to cut it in half and give it to a group.

Here,

A number's components are the numbers that split equally into it. To determine the factors of 13, divide 13 by each number from 1 to 13 and see if the result is an integer or not. 13 has two factors: 1 and 13.

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Step-by-step explanation:

\( \sqrt{ - 81} = 9i \\ \sqrt{ - 11} = i \sqrt{11} \\ \sqrt{ - 20} = i \sqrt{20} \)

Answer:

$580000

Step-by-step explanation:

To find decrease we simply reverse the operations of increase

increase is x x 1.05 = 609000

x = 609000 / 1.05 = 580000  initial value

x= $580000

proof

580000 x 1.05 = 609000 new value

Answer:

a = 4

b = -2

Step-by-step explanation:

If the given function is continuous at x = 1

\(\lim_{x \to 1^{-}} f(x)=(x+1)\)

                     \(=2\)

\(\lim_{x \to 1^{+}} f(x)=ax+b\)

                     \(=a+b\)

\(\lim_{x \to 1} f(x)=ax+b\)

                   \(=a+b\)

And for the continuity of the function at x = 1,

\(\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)\)

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

\(\lim_{x \to 2^{-}} f(x)=ax+b\)

                     \(=2a+b\)

\(\lim_{x \to 2^{+}} f(x)=3x\)

                     \(=6\)

\(\lim_{x \to 2} f(x)=3x\)

                   \(=6\)

Therefore, \(\lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)\)

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2

Answer: its answer 3, most likely

Step-by-step explanation: i remember this question

You would need a total of 10 packages of C4 to complete the mission.

To answer your question, we need to calculate the total number of packages of explosives required.

Since you've already determined that you need one package of C4 for a single charge, we can use that information to calculate the total number of packages needed for the entire mission.

Let's say that you need to perform a total of 10 charges to complete the mission. Since you need one package of C4 for each charge, the total number of packages required would be 10 times the number of packages needed for a single charge, which is one.

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Answer:

sum of all angles of a triangle= 180°

Let angle A be x,

then 63°+90°+x=180°

x=17°

The first part:

Since the first number is 1 decimal place and second number is 2 decimals, we will round to 1 decimal.

Thus,

49.551 = 49.6

Next part of the problem becomes:

The calculation provides the answer: 0.4670...

The first number has 3 significant figures, that's the limit because next number has 5 significant figures. So, we round off our answer to 3 significant figures (3 decimal place, in this case)

Thus, the answer is:

0.467

To find the determinant of matrix B, we can use the formula for a 3x3 matrix: det(B) = (2 * (0 * 1 - 1 * 1)) - (2 * (1 * 1 - 0 * 1)) + (0 * (1 * 1 - 0 * 1))

Simplifying this expression, we get:

det(B) = (2 * (-1)) - (2 * (1)) + (0 * (1))

det(B) = -2 - 2 + 0

det(B) = -4

The determinant of matrix B is -4.

Since the determinant is non-zero, B is invertible.

To find the inverse of B, we can use the matrix equation B * X = I, where X is the inverse of B and I is the identity matrix.

B * X = I

Using the given values of B, we have:

|2 2 0| * |x y z| = |1 0 0|

|1 0 1| |a b c| |0 1 0|

|0 1 1| |p q r| |0 0 1|

Solving this system of equations, we can find the values of x, y, z, a, b, c, p, q, and r, which will give us the inverse matrix B^-1.

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Answer:

504 in²

Step-by-step explanation:

The area of a kite is given by :

(a * b) / 2

Where a and b are the width and height of the kite :

Width = 24 inches ; height = 42 inches

Hence,

Area of kite = (24 * 42) / 2

Area of kite = 24 * 21

Area of kite = 504 in²

Answer:

About 73.93 books. Round that to 73 books, because you can't place 93% of a book.

Step-by-step explanation:

You first calculate to dimensions of the bookcase, then you calculate the dimensions of the books. As a result, divide the calculation of the bookshelf by the calculation of the books, and you should have your answer.

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical. This can also imply that there is no skewness or bias in the data. Answer more than 100 words:When an instructor notes that the mean, median, and mode are all exactly 76.00, it can be inferred that the distribution of grades in the class is roughly symmetrical. This indicates that there are nearly equal numbers of students above and below the average grade.

The mean, median, and mode are three measures of central tendency that are used to summarize the distribution of a dataset. The mean is calculated by adding all the values in the dataset and dividing by the number of observations, while the median is the middle value when the dataset is ordered from smallest to largest. The mode is the value that occurs most frequently in the dataset. When all three measures of central tendency are equal, as in this case, it means that the dataset is roughly symmetrical and there is no skewness or bias. This can also indicate that the dataset is normally distributed, which means that it follows a bell-shaped curve.The instructor can conclude that the class performed around the average, as the mean, median, and mode are all 76.00.

However, it is important to note that this does not give any information about the spread of the dataset. In other words, the instructor cannot tell from this information alone whether the grades were tightly clustered around the average or widely dispersed. For this reason, it may be useful to calculate additional measures of spread, such as the range or standard deviation, to get a better understanding of the distribution.

The instructor can conclude that the class performed around the average and that the distribution of grades is likely to be symmetrical, with no skewness or bias. However, it is important to remember that this information alone does not provide any insight into the spread of the dataset. Additional measures of spread would need to be calculated to determine the degree of variability in the grades.

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The lower and upper bounds of c- d are 42.0 and 43.0 respectively.

For the given question;

A number, c, rounded to 1 decimal place is 47.3

Another number, d, rounded to 1 decimal place is 4.6

c- d = 47.3 - 4.6

c- d = 42.7

Lower bound = 42.0

Upper bound = 43.0.

Thus, the lower and upper bounds of c- d are 42.0 and 43.0 respectively.

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The silk density in g/cc if the specific gravity of the fiber is given as 1.32 is given as 1.32 g/cc.

Density is the mass of a material substance per unit volume. d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimetre are a typical unit of measurement for density.

For instance, whereas Earth has a density of 5.51 grammes per cubic centimetre, water has a density of 1 grammes per cubic centimetre. Another way to state density is in kilogrammes per cubic metre (in metre-kilogram-second or SI units). For instance, air weighs 1.2 pounds per cubic metre. In textbooks and manuals, the densities of typical solids, liquids, and gases are stated.

As we know that ,

Specific gravity = Density of object / density of water

1.32 = silk density / 1 g/cc

[Density of water is 1 g/cc]

Silk density = 1.32 x 1 g/cc

Silk density = 1.32 g/cc.

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Answer:

Angle 8

Step-by-step explanation:

consider the following image

Answer:

Step-by-step explanation:

The angles in matching corners are called Corresponding Angles.

The angle that corresponds with ∠4 is ∠8 as both of them are on the bottom right corner.

answer step by step:

hope this helps

Triangle congurent theorem is being applied if two triangles of one triangle are congruent to two angles of another triangle and the triangles are similar.

Angle-Side-Angle (ASA) theorem states that if two triangles are considered congruent, then the two corresponding angles equal to each other will include a corresponding side that is equal to each other.

By applying the Side Angle Side Postulate (SAS), you can also be sure your two triangles are congruent. Here, instead of picking two angles, we pick a side and its corresponding side on two triangles.

The SAS Postulate says that triangles are congruent if any pair of corresponding sides and their included angle are congruent.

Perhaps the easiest of the three postulates, Side Side Side Postulate (SSS) says triangles are congruent if three sides of one triangle are congruent to the corresponding sides of the other triangle.

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