Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y=0 and y=3,
y' > 0 for 0 y' < 0 for -inf < y < 0 and 3 < y < inf
dy/dx =

In the figure the area of circle is obtained as option C: 144π cm².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The area of the square is = 144 cm².

The formula for area of square is - (side)²

The equation is -

Area = (side)²

Substitute the value into the equation -

144 = (side)²

side = √144

side = 12 cm

The side of the square is the radius of the circle.

The area of circle is given as -

Area = πr²

Substitute the value into the equation -

Area = π(12)²

Area = 144π cm²

Therefore, the area of circle is 144π cm².

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Answer:

11.3

Step-by-step explanation:

13.3 - 2 = 11.3

Answer:

6(f-2)

Step-by-step explanation:

is a factor of 6f & 12

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1.

to get factors

write 1 to 10

to see if any of the factor numbers can be divided by any of the numbers between 1 thru 10 or sometimes even up to 20

2.

write

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

so 6 & 12 can be divided by

1 2 3 4 6 12

Answer:

6 pints of lemonade. here you go

The average atomic mass of the element in the data table is 39.95 amu.

The average atomic mass of the element in the data table is calculated by applying the following formula.

average atomic mass = ( 0.3365 / 100  x 35.97 amu ) + ( 0.0632 / 100  x 37.96 amu ) + ( 99.6 / 100  x 39.96 amu )

average atomic mass = ( 0.121 amu ) + ( 0.024 amu ) + ( 39.8 amu )

average atomic mass = 39.95 amu

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A function f(x) is said to have a jump discontinuity at x = a if:

3. The left and right limits are not equal.

The function has a jump discontinuity at x = 6 because:

The different lateral limits are the reason given for the jump discontinuity, as shown in the graph presented at the end of the answer.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

If the lateral limits are different, the limit does not exist and the function is not continuous at x = a, being said to have a jump discontinuity.

The function has a jump discontinuity at x = 6 because:

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The height of the school is 13.27 m.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have.

From the information given, we can draw the figure given below,

Now,

Triangle ABC and Triangle DCE are similar.

So,

x / 1.25 = 11.15 / 1.05

x = (11.15 x 1.25) / 1.05

x = 13.27 m

Thus,

The height of the school is 13.27 m.

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Answer:

975

Step-by-step explanation:

The largest number of pages the book can have is 975 because the maximum number of times the digit 7 can appear in the page numbers is 25. The maximum number of pages is obtained when the page numbers range from 100 to 999, inclusive, which would result in the digit 7 appearing 25 times.

The expected number of flips to get a string of r heads in a row, given that the probability of getting heads in each flip is p.

Probability is a scale between 0 and 1 that represents the possibility of an event happening. An event with probability 1 is guaranteed to happen, while an event with probability 0 is impossible. The number of favorable outcomes divided by the total number of potential outcomes in the sample space yields the probability of an event A, commonly denoted as P(A). The sample space, for a fair six-sided die, is the set of all potential outcomes, such as 1, 2, 3, 4, 5, and 6. The probability of rolling a 4 is 1/6. Numerous disciplines employ probability to make predictions, deduce conclusions, and make judgments in the face of uncertainty.

We can use a recursive formula to find the expected number of flips X.

Let X_i be the expected number of flips to get a string of r heads in a row, starting from the i-th flip. Then, X_i can be expressed in terms of X_{i+1}:

X_i = (1 - p) + p(1 + X_{i+1})

Here, (1 - p) represents the case where the i-th flip results in tails, and p(1 + X_{i+1}) represents the case where the i-th flip results in heads and we have to continue flipping until we get a string of r heads in a row.

To find the expected number of flips X, we need to sum over all X_i, starting from the first flip:

E[X] = X_1 = (1 - p) + p(1 + E[X])

Solving for E[X], we get:

E[X] = 1/(1 - p)

This formula gives us the expected number of flips to get a string of r heads in a row, given that the probability of getting heads in each flip is p.

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The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

What does the example set?

A set is a logically arranged group of items that can be represented in either set-builder form or roster form in mathematics.

                                 Sets are typically shown using curly brackets; for instance, A = 1, 2, 3, 4 is a set.

The given two sets are

            A = {x, j, a, m} and D = {x, a, b, y}

By definition,

The two sets A and B are equal sets if they contain the same elements.

Here,  j, m and b, y are different in two sets.

Thus, The set A and D does not contain the same elements.

Therefore, The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.

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Answer:

y = 3[tex]x^{4[/tex]

Step-by-step explanation:

given y varies directly as [tex]x^{4}[/tex] then the equation relating them is

y = k[tex]x^{4}[/tex] ← k is the constant of variation

to find k use the condition when x = 3 , y = 243 , then

243 = k × [tex]3^{4}[/tex] = 81k ( divide both sides by 81 )

3 = k

y = 3[tex]x^{4}[/tex] ← equation of variation

The missing side lengths are given as follows:

The three trigonometric ratios are defined as follows:

Considering the tangent of 30º, we can obtain the length y, as follows:

tan(30º) = y/12

y = 12 x tangent of 30 degrees

y = 6.93.

Applying the Pythagorean Theorem, we can obtain the length x, as follows:

x² = 6.93² + 12²

x = sqrt(6.93² + 12²)

x = 13.86.

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The coordinates of the vertices of the image include the following: (-1, 3), (-1, -1), (5, -1), and (7, 3).

In this exercise, we would have to dilate (enlarge) the coordinates of the pre-image by using a scale factor of 2 centered at the point (1, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate 1, we have;

Coordinate 1 = (2, 4)  →  (2(2 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (2, 4)  →  (2(-1) + 1, 2(-1) + 5)

Coordinate 1' = (-1, 3).

For coordinate 2, we have;

Coordinate 2 = (2, 2)  →  (2(2 - 1) + 1, 2(2 - 5) + 5)

Coordinate 2 = (2, 2)  →  (2(-1) + 1, 2(-3) + 5)

Coordinate 2' = (-1, -1).

For coordinate 3, we have;

Coordinate 3 = (3, 2)  →  (2(3 - 1) + 1, 2(2 - 5) + 5)

Coordinate 3 = (3, 2)  →  (2(2) + 1, 2(-3) + 5)

Coordinate 3' = (5, -1).

For coordinate 4, we have;

Coordinate 1 = (4, 4)  →  (2(4 - 1) + 1, 2(4 - 5) + 5)

Coordinate 1 = (4, 4)  →  (2(3) + 1, 2(-1) + 5)

Coordinate 1' = (7, 3).

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The value of the given expression is 64ab.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given a mathematical expression which includes the basic operations of multiplication and subtraction.

There are two terms for the expression, (-2a × 4b) and (-12a × 6b).

-2a × 4b = -8ab

-12a × 6b = -72ab

(-2a × 4b) - (-12a × 6b) = (-8ab) - (-72ab)

Two negatives become positive.

(-8ab) - (-72ab) = -8ab + 72ab

Both are like terms since the variables a and b are same. Just subtract it.

-8ab + 72ab = 64ab

Hence the solution of the difference of the expression is 64ab.

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Answer:frequency

Step-by-step explanation:

The graph of the function h is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Suppose that the function h is defined as follows.

h(x) = -1 if -2.5 < x ≤ -1.5

           0 if -1.5 < x ≤ -0.5

            1 if -0.5 < x ≤ 0.5

            2 if 0.5 ≤ x < 1.5

            3 if 1.5 ≤ x  < 2.5

The above function is a piecewise function

Next, we graph the individual functions in the function h according to their domain

See attachment for the graph of h

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X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

The number is said to be in variables its simplest form being divided in it's smallest equivalent fraction. When or how to find the most basic form. Look for common factors throughout the denominator and numerators. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two orthogonal axes and even an equal sign in the middle is called an equation in mathematics. The general form of any equation provides the degrees of all the  in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as assumptions or conditional equation.

given

(x²+3)+(x-1)

2x+3 / x = 1

X+1, R2 is the synthetic division of (x²+3)+(x-1) by In the divisor x + 5, change the constant's sign from 5 to -5 and bring it down.

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The solution will lie on the number line from (-∞ , 0)

An inequality is the representation of an algebraic statement with two non-equal values. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

One of the following options is available for resolving an inequality: Add the same amount to each side, deduct the same amount from each side, multiply each side by the same positive number, or split each side in half. If you multiply or divide each side by a negative value, the inequality sign must be reversed.

Given,

(x-0)(x-6)<0

⇒ x < 0 and x < 6

the solution will lie on the number line from -∞ to 0.

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On solving the provided question, we can say that the equation of inequality will be as follows 150x + 100y [tex]\leq[/tex] 300

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

A patient is not allowed to have more than 300 milligrams of cholesterol per day from a diet of eggs and meat.

Each egg provides 150 milligrams of cholesterol.

Each once of meat contains 100 milligrams of cholesterol

so, the equation of inequality will be as follows

150x + 100y [tex]\leq[/tex] 300

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The average rate of change of the function in the interval [ 4 , 9 ] is given by the equation m = -67

The average amount that a function changed per unit during that time period is the rate of change of that function. It is calculated using the slope of the line connecting the interval's endpoints on the graph of the function.

Rate of change = f ( b ) - f ( a ) / ( b - a )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 4 , -84 )

Let the second point be Q ( 9 , -419 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

The rate of change of the function = slope

Slope m = ( -419 - ( -84 ) ) / ( 9 - 4 )

On simplifying the equation , we get

Slope m = ( -419 + 84 ) / 5

Slope m = -335/5

Slope m = -67

Hence , the rate of change of function is m = -67

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The confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.

The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

The confidence interval is given as:

x' ± 1.96 s/√n

Substituting the value of x' = 60.5, s = 5, and n = 100.

60.5 ± 1.96 (5/ √√100)

60.5 ± 1.96 (5/10)

60.5 ± 0.98

Hence, the confidence interval: 59.5 to 61.5; margin of error: ± 1.0. Option B is the correct answer.

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the missing species in each nuclear equation are:

1.  ¹⁰₄Be ---> ¹⁰₅B + ⁰₋₁β

2. ³⁴₁₄Be ---> ³⁴₁₅P + ⁰₋₁β

3. ¹⁹²₇₈Pt -----> ¹⁹⁰₇₆Os + ⁴₂α

4.  ²⁸₁₂Mg ---> ²⁸₁₃Al + ⁰₋₁β

Nuclear equations represent the reactants and products in radioactive decay, nuclear fission, or nuclear fusion. Instead of chemical equations where it shows the different number of elements are conserved in a reaction, in a nuclear reaction the atomic mass and proton number are conserved.

1. In the first equation, the Beryllium-10 isotope undergoes beta decay, emitting a beta-particle to form the boron-10 isotope. The balanced nuclear equation is given below:

¹⁰₄Be ---> ¹⁰₅B + ⁰₋₁β

2. In this reaction, the silicon-34 isotope undergoes beta decay, emitting a beta-particle to form the phosphorus-34 isotope. The balanced nuclear equation is given below:

³⁴₁₄Be ---> ³⁴₁₅P + ⁰₋₁β

3. In this equation, the platinum-192 isotope undergoes alpha-particle decay emitting an alpha-particle to form the osmium-190 isotope. The balanced nuclear equation is given below:

¹⁹²₇₈Pt -----> ¹⁹⁰₇₆Os + ⁴₂α

4. In this equation, the magnesium-28 isotope undergoes beta decay, emitting a beta-particle to form the aluminum-28 isotope. The balanced nuclear equation is given below:

²⁸₁₂Mg ---> ²⁸₁₃Al + ⁰₋₁β

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answer: 39.5

Step-by-step explanation:

arrange numbers in ascending order....

5,22,31,38,41,55,75,69,80,83,89,91,96,97,100

then find median of the arranged list of numbers

which is 69

after that find the median between the arranged numbers starting from 5 to the median which we found as 69

which will be 38 and 41

So we add those two numbers together and then divide them by 2 .....which will give u 39.5

the following shaded-regions in the plane consists of all points whose polar coordinates satisfy the inequalities 0 ≤ r ≤ 3 and π/6 ≤ θ ≤ π/12.

It is referred to as a polar coordinate system when each point on a plane in a two-dimensional coordinate system is determined by a distance from a reference point and an angle measured from a reference direction. Pole: The object of comparison. The term "polar coordinates" refers to these new coordinates since you interpret the axes' intersection as a pole from which all other points radiate outward. change (degrees are measured in radians) (degrees are measured in radians).

Given that,

0 ≤ r ≤ 3

and π/6 ≤ θ ≤ π/12

In the given condition we can clearly see that the radius is not equal to 3 but it is less than 3. Thus graph number 1, 2, 4 and 6 do not match the given condition.

Now in the given condition 0 ≤ r ≤ 3 the angle is between 30° to 105°

In the graph number 3 radius varies from 0 ≤ r ≤ 3 but angle varies from 75° to 150°, so it is also incorrect.

Thus in the remaining graph number 5, the radius varies from 0  and angle also varies from 30° to 105°.

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The complete question is as follows:

Answer:

see below

Step-by-step explanation:

We need to solve the below two equations by graphing. We will plot the graph of the given equations and the point of intersection of line would be the solution to the equation.

[tex] 1. \begin{cases} y = -\dfrac{1}{2}x+2\\\\ y = -3x - 3 \end{cases}[/tex]

Firstly let's make a table;

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 1 \\ y & 2 & 1.5 \end{array}}[/tex]

Now plot the points , (0,2) and (1,1.5) .

Similarly make another table for second equation [tex] y = -3x - 3[/tex] as ,

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 1 \\ y & -3 & -6\end{array}}[/tex]

Now draw the lines joining the points. Hence from the graph the line intersects at (-2,3)

So the solution to equations are ,

_________________________________

Similarly we will solve the second set of equations as ,

[tex] 2. \begin{cases} x-4y=12\\\\ 7x-4y=12 \end{cases}[/tex]

make a table for plotting equation [tex] x-4y=-12[/tex]

[tex]\boxed{\begin{array}{c|c|c} x & 12 & 16 \\ y & 0 & 1\end{array}}[/tex]

make a table for plotting equation [tex] 7x-4y=12[/tex]

[tex]\boxed{\begin{array}{c|c|c} x & 0 & 2 \\ y & -3 & 0.5\end{array}}[/tex]

Now we see that the equations intersect at point (4,4) So the solution to the given equation is ,

________________________________

[tex] 3. \begin{cases} -8x-4y = 12 \dots (1)\\\\ x=y\dots(2)\end{cases}[/tex]

substitute value of equation 2 in 1

[tex]\longrightarrow -8x - 4x = 12 \\ [/tex]

simplify,

[tex]\longrightarrow -12x = 12[/tex]

Divide both sides by 12 ,

[tex]\longrightarrow\underline{\underline{ x = -1}} [/tex]

Substitute this value in equation 2 as ,

[tex]\longrightarrow x = y \\ [/tex]

[tex]\longrightarrow\underline{\underline{ y = -1}} [/tex]

Hence our required solution is ,

___________________________________

[tex] 4. \begin{cases} 2x + 4y = -10 \dots (1)\\\\ -7x -y = 22(2)\end{cases}[/tex]

Taking equation 2 ,

[tex]\longrightarrow y = -7x -22 [/tex]

substitute this value in equation 1,

[tex]\longrightarrow 2x + 4(-7x-22)=-10\\[/tex]

[tex]\longrightarrow 2x -28x -88 = -10\\ [/tex]

[tex]\longrightarrow -26x = 78\\[/tex]

divide both sides by 26,

[tex]\longrightarrow\underline{\underline{ x = -3}} [/tex]

Again, substitute this value in equation 2 , as ;

[tex]\longrightarrow y = -7(-3) -22\\ [/tex]

[tex]\longrightarrow y = 21 -22\\ [/tex]

[tex]\longrightarrow\underline{\underline{ y = -1}} [/tex]

hence our required solution is ,

And we are done!

A two-column table to prove that the triangles formed by the vertical support beam are congruent, (ΔAXB ≅ Δ(CXB) is presented as follows;

[tex]{}[/tex]  Statement                             Reasons

1. [tex]\overline{BX}[/tex] ⊥ [tex]\overline{AC}[/tex]; AB = CB    [tex]{}[/tex]                        Given

2. m∠BXA = m∠BXC = 90°[tex]{}[/tex]                   Definition of ⊥ segments

3. ΔABC is an isosceles triangle [tex]{}[/tex]         Definition

4. ∠BAC ≅ ∠BCA   [tex]{}[/tex]                               Base angles of an isosceles Δ

5. ΔAXB ≅ ΔCXB [tex]{}[/tex]                                 SAA congruence postulate

An indication that two triangles are congruent is if the corresponding sides on each of the triangles are congruent.

The details of the reasons used to prove that the triangles ΔAXB and ΔCXB are congruent, are presented as follows;

[tex]\overline{BX}[/tex] ⊥ [tex]\overline{AC}[/tex]; Perpendicular segments

Two segments are perpendicular if they intersect at right angles, such that the angles formed by the intersection of the segments are 90° angles

Isosceles triangles

An isosceles triangle is a triangle that has a pair of congruent sides (sides of the same length)

Base angles of an isosceles triangle are congruent

The sides of the same length in an isosceles triangle, according to the angle side relationship theorem, the angle opposite the congruent sides of an isosceles triangle which are the base angles of the triangle are congruent.

SAA congruence postulate

The Side-Angle-Angle, SAA, congruence postulate states that if in a triangle, two angles and a non included side are congruent to two angles and a non included side of another triangle, then the two triangles are congruent

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Answer:

564 inches is equivalent to 47 yards and 0 feet.

To maximize the store's profit, Hector should aim to sell as many lemons as possible while paying the lowest price possible for them. Since Hector estimates that he can sell a maximum of -2000p + 7540 lemons at price p, and Walt can supply at most 5000 lemons, Hector should buy all of the 5000 lemons from Walt.

To determine the price at which Hector should buy the lemons from Walt, we need to consider the average cost of the lemons. If Hector buys 5000 lemons at $1.60 per lemon, he will spend a total of 5000 x $1.60 = $8000 on lemons.

If he sells all 5000 lemons at the price p, his revenue will be (-2000p + 7540) x 5000 = -10,000,000p + 37,700,000.

His profit will be the difference between revenue and cost, which is given by:

Profit = -10,000,000p + 37,700,000 - $8000

To maximize profit, we need to take the derivative of the profit function with respect to p and set it equal to zero:

dProfit/dp = -10,000,000 = 0

Solving for p, we get:

p = $1.00

Therefore, Hector should buy 5000 lemons from Walt at $1.00 per lemon to maximize the store's profit.

The value of the equation is A = 50 ( n ) , where n is the number of employees

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the number of employees be n

So , A = product of 50 and the number of employees

A = 50 ( n )   be equation (1)

Therefore , the value of A is 50n

Hence , the equation is A = 50n

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