circles $\omega$ and $\gamma$, both centered at $o$, have radii $20$ and $17$, respectively. equilateral triangle $abc$, whose interior lies in the interior of $\omega$ but in the exterior of $\gamma$, has vertex $a$ on $\omega$, and the line containing side $\overline{bc}$ is tangent to $\gamma$. segments $\overline{ao}$ and $\overline{bc}$ intersect at $p$, and $\dfrac{bp}{cp}

The length, in units, of the rectangle is 9 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Length = x

Width = x - 8

Area = 9 square units

Now,

The area of the rectangle = length x width

9 = x (x - 8)

9 = x² - 8x

x² - 8x - 9 = 0

Solve for x.

x² - 8x - 9 = 0

x² - (9 - 1)x - 9 = 0

x² - 9x + x - 9 = 0

x(x - 9) + 1(x - 9) = 0

(x - 9) (x + 1) = 0

x - 9 =0 and x + 1 = 0

x = 9 and x = -1 (rejected)

Now,

Length = 9

Width = 9 - 8 = 1

Thus,

Length is 9.

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The Marginal Revenue MR(29) 11513 dollars per unit.

The velocity is v(t) = 24t² - 96t - 120.

The velocity equals zero at t = 5.

The acceleration of the particle is a(t) = 48t - 96.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

Suppose a product's revenue function is given by R(q) = -7q² + 600q,

where R(q) is in dollars and q is units sold.

We have to determine a numeric value for the marginal revenue at 29 units

As per the question we have

R(q) = -7q² + 600q

Substitute the value of q = 29, and we get

R(29) = -7(29)² + 600(29)

R(29) = 11513

Thus, the Marginal Revenue MR(29) 11513 dollars per unit

Let s(t) = 8t³ - 48t² - 120t be the equation of motion for a particle.

To find the velocity, we need to differentiate the equation for the position of the particle, s(t).

v(t) = ds/dt = d/dt (8t³ - 48t² - 120t) = 24t² - 96t - 120

To find the t-values where the velocity is equal to zero, we need to set v(t) equal to zero and solve for t.

0 = 24t² - 96t - 120

This is a quadratic equation, and we can solve for t by factoring the GCF

(t - 5)(t + 1) = 0

(t - 5) = 0 and (t + 1) = 0

t = 5 and t = -1

So the velocity equals zero at t = 5

To find the acceleration, we need to differentiate the velocity function, v(t).

a(t) = dv/dt = d/dt (24t² - 96t - 120) = 48t - 96

So the acceleration of the particle is a(t) = 48t - 96.

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The correct order of the assumptions used in the derivation is: A, B, C, D, E. A states that the population is large, B: random, C: representative, D: large, and E states that the sampling is done without replacement.

The derivation of the Central Limit Theorem was based on five assumptions: (a) The population is large, (b) The sample is random, (c) The sample is representative, (d) The sample size is large, and (e) The sampling is done without replacement. The first assumption used in the derivation is that the population is large, which means that the number of individuals in the population is much greater than the sample size. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases. The second assumption used is that the sample is random, which means that each individual in the population has an equal chance of being selected for the sample. This helps to ensure that the sample is representative of the population as a whole. The third assumption is that the sample is representative, which means that the characteristics of the sample are similar to those of the population. This is important because it allows us to make generalizations about the population based on the sample. The fourth assumption is that the sample size is large. This is important because the Central Limit Theorem states that the mean of the sample will approach the population mean as the sample size increases.

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The volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to the integral of the area of the cross-section of the solid from x=0 to x=1. The area of the cross-section is equal to the area of a circle with radius x, which is equal to πx. Thus, the volume of the solid is equal to the integral of πx from x=0 to x=1.

This integral can be solved using the formula for the area of a circle, which is equal to πr. Thus, the volume of the solid is equal to π∫x dx from x=0 to x=1. After solving the integral, the volume of the solid is equal to π/3. Thus, the volume of the solid formed by rotating the function f(x)=x about the x-axis from x=0 to x=1 is equal to 0.3333.

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the Total weight of the container that kept figs is 1.6 kg.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, 80 figs are kept in a container. Each fig weighs 0.02 kg.

Since,

One fig is weighing  = 0.02 kg

So,

80 figs will weigh = 0.02 * 80

80 figs will weigh =  1.6 kg

Therefore, the Total weight of the container that kept figs is 1.6 kg.

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B. II only. This initializes an 8 X 10 matrix with integer values that are perfect squares by looping through the rows and columns of the matrix and setting each element equal to the row number multiplied by itself.

II initializes an 8 X 10 matrix with integer values that are perfect squares. The initialization starts by declaring the matrix with the line int [][] mat = new int [8][10]; which creates the 8 X 10 matrix. The next step is to use a nested for loop to loop through the rows and columns of the matrix. The first loop, for(int r=0; r<mat.length; r++), begins by setting an integer variable r to 0 and looping through all of the rows in the matrix. The second loop, for(int c=0; c<mat[r].length; c++), begins by setting an integer variable c to 0 and looping through all of the columns in the matrix. Finally, the last line, mat[r][c] = r*r;, sets each element of the matrix equal to the row number multiplied by itself. This ensures that the values in the matrix are all perfect squares.

The complete question : Which of the following initializes an 8 X 10 matrix with integer values that are perfect squares? (0 is a perfect square.)

I. int [][] mat = new int [8][10];

II. int [][] mat = new int [8][10];

for (int r=0; r<mat.length; r++){

for(int c=0; c<mat[r].length; c++){

mat[r][c] = r*r; }}

III. int [][] mat = new int [8][10];

for (int c=0; c<mat[r].length; c++){

for(int r=0; r<mat.length; r++){

mat[r][c] = c*c; }}

A. I only

B. II only

C. III only

D. I and II

E. I, II, and III

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Answer: No, it is not proportional.

Step-by-step explanation: X will be the mystery number here. So first, we want to find a common denominator. 5 times x equals 20. We want to divide 20 by 5. 20/5 equals 4. X = 4. So now we want to multiply the 4 from 4/5 by 4. 4 times 4 equals 16.

4/5 = 16/20

Answer:

width of the flag is 440 feet and the length is 780 feet

Step-by-step explanation:

Let's call the width of the flag "w". Then the length of the flag can be represented as "w + 340".

The perimeter of the flag is the sum of all four sides, so we can write the following equation:

2w + 2(w + 340) = 2,440

Expanding the second term on the left side and simplifying:

2w + 2w + 680 = 2,440

4w + 680 = 2,440

Subtracting 680 from both sides:

4w = 1,760

Dividing both sides by 4:

w = 440

So the width of the flag is 440 feet and the length is 780 feet (440 + 340).

The length of the wing is, 12 inches.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The scale is,

⇒ 1 inch = 2 feet

And, Wing of airplane is 24 feet.

Now, We have;

The scale is,

⇒ 1 inch = 2 feet

Hence, The length of wing is,

⇒ 24 / 2 inches

⇒ 12 inches

Thus, The length of the wing is, 12 inches.

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The solution of the indefinite integral ∫ sin x cos x dx is (1 / 2) · sin² x + C.

There are integrals that can be solved by means of algebraic substitutions, which simplifies the expression and allow a quicker solution. Now we proceed to find the solution. First, define algebraic subtitution:

u = sin x

du = cos x dx

Second, simplify the integral by formulae defined in the previous step:

∫ sin x cos x dx

∫ u du

Third, integrate the resulting expression:

(1 / 2) · u² + C, where C is the integration constant.

Fourth, reverse the algebraic substitution:

(1 / 2) · sin² x + C

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A formula for the function g(x) obtained when the graph of f(x) = 1/x is shifted down 7 units and to the right 5 units is g(x) = 1/(x - 5) - 7.

In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image or function.

In Mathematics, a horizontal translation to the right is modeled by this mathematical expression g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

By translating the graph of f(x) = 1/x down 7 units and 5 units to the right , we have:

g(x) = f(x - 5) - 7

g(x) = 1/(x - 5) - 7

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Each piglet will receive 0.625 L of milk.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

Left to Right

We have 8 piglets that only have 5 liters of milk to share in between them. We need to split the milk between the 8 piglets.

We can divide the amount of milk we have already by the amount of piglets total:

5 liters of milk ÷ 8 piglets

Evaluating this, we should get 0.625 L of milk per piglet, assuming we don't lose a single drop while splitting the milk.

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Answer: 3

Step-by-step explanation:

2 1/4 cups of brown sugar + ¾ cup of white sugar.=the total amount of sugar in this recipe

2 1/4 + 3/4 =3

or

2 1/4=2.25 and 3/4=.75

2.25+.75=3

The minimum cost is $1500.

The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants of the parabola is at (h, k).

Given:

y =1/30 x²-2x+1530

y= 1/30 x² - 2x + 1530

comparing the above equation with y ax²+ bx +c we get

a = 1/30

b = -2

c = 1530

Now, the the x coordinate of the vertex

h = -b/(2a)

h = -(-2)/(2x(1/30))

h = 2/(2/30)

h = (2/1) x (30/2)

h = (2 x 30)/(1 x 2)

h = 60/2

h = 30

So, The x coordinate of the vertex is 30.

Now, we plug in x = 30 to find the y coordinate of the vertex.

y =1/30 x²-2x+1530

y =1/30 (30)²-2(30)+1530

y =1/30 (900)-60+1530

y= 1500

Thus, the minimum cost is $1500

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Answer: 2x-y=3

Step-by-step explanation: Search math w ay on the internet

The value of the functions are;

f(0) = 1

f(1) = 3

f(-1) = 4

A function can be described as a rule, law or expression explaining the relationship between two variables.

These variables are called;

From the information given, we have that;

F(x) = 2x + 1 when x is greater than or equal to zero

Also,

f(x) = -2x - 1 when x is less than zero

Then for f(0)

f(0) = 2(0) + 1

expand the bracket

f(0) = 1

For f(1) = 2(1) + 1

expand the bracket

f(1) = 3

f(-1) = -2(-1) + 1

expand the bracket

f(-1) = 4

Hence, the values are 1, 3 and 4

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The triangles are similar by SSS.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The sides of first triangle are, 6, 9.6, 12.3

And, The sides of second triangle are, 2, 3.2, 4.1

Now, The ratio of corresponding sides of triangle are,

⇒ 6 / 2 = 3

⇒ 9.6 / 3.2 = 3

⇒ 12.3 / 4.1 = 3

Thus, The triangles are similar by SSS.

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(a) Probability(3 white) = (19/52) * (18/51) * (17/50) = 0.027

(b) P(3 white, 2 tan, 1 pink, 1 yellow, 2 green) = (19/52) * (18/51) * (17/50) * (10/49) * (9/48) * (7/47) * (5/46) * (6/45) * (6/44) = 0.00004

(a) The probability of selecting three white hearts is calculated by multiplying the probability of selecting each heart. The probability of selecting one white heart is 19/52. The probability of selecting two white hearts is 18/51, and the probability of selecting three white hearts is 17/50. When multiplied together, the overall probability is 0.027.

(b) The probability of selecting three white hearts, two tan hearts, one pink heart, one yellow heart, and two green hearts is calculated by multiplying the individual probabilities for each heart. The probability of selecting one white heart is 19/52, the probability of selecting two tan hearts is 10/49, the probability of selecting one pink heart is 7/47, the probability of selecting one yellow heart is 5/46, and the probability of selecting two green hearts is 6/45. When multiplied together, the overall probability is 0.00004.

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The guidelines for developing the intervals are

An interval in math is calculated in terms of numbers. An interval comprises all the numbers that come between two particular numbers. This range includes all the real numbers between two numbers.

A closed interval is an interval that includes all its limit points and is denoted with square brackets. For example, [0, 1] means that greater than or equal to 0 and less than or equal to 1.

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The length of the three missing sides in the rhombus are x=75,y=75,z=75

Rhombus is a parallelogram whose all sides are of equal lengths.

Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).

Its vertex angles are bisected by its diagonals.

The triangles on either side of the diagonals are isosceles and congruent.

Given;

One side of rhombus= 75

Now, as we know that all sides of rhombus are equal

x=y=z=75

Therefore, the sides of rhombus will be x=75,y=75,z=75.

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0.23 as:

23% (0.23 * 100 = 23)

A decimal is a number that expresses fractional values with a base of 10. It uses the place value system where the position of a digit determines its value relative to other digits. Decimals are written using a decimal point to separate the whole number part from the fractional part. For example, 3.14 is a decimal representation of the fractional value pi.

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Answer:

523.3

Step-by-step explanation:

memorize this formula:

V = 4/3 π r³, where V = volume and r = radius.

so v=4/3π *5³ =125*4/3π =523.3

Option(a) is the correct answer.

The inequality is:

|X+6|- 12 < 13

Here we can add 12 to both sides:

|X+6| <13 + 12

⇒|X+6| <25

⇒|X+6| < 25

We can separate it into two equations:

if x > -6, then |X+6|  = x + 6

⇒ (x + 6) < 25

⇒x < 25 - 6

⇒ x <  19

if x < -6, then |X+6|  = -(x + 6)

⇒-(x + 6) < 25

⇒ -x < 31

 ⇒ x > -31      (changing the sign)

And with those two equations, we get the:

-31 < x < 19

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Answer:

A=587

B=-61

C=375

D=-375

Step-by-step explanation:

Nate is paid 16.50 dollars for each hour he works over 40.

We have that Nate's weekly pay is represented by the expression 16.50x + 24.75(a),

where x is the number of hours worked and a is a value such that 0 <= x <= 40.

We know that a mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

If  x > 40, the pay for each additional hour worked is given by the rate of change of the expression, which has it at 16.50 dollars per hour.

We therefor ca conclude that Nate is paid 16.50 dollars for each hour he works over 40.

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The solution to the algebraic expression (2*3)*5 using a*b= a+b -2ab is; 68

Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without truly specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as a, b, c etc. These letters are usually referred to as variables.

We are given the format for the algebraic expression as;

a*b = a + b - 2ab

Thus, we can solve the expression (2*3)*5 as;

(2*3) = 2 + 3 - 2(2*3)

= -7

(-7 * 5) = -7 + 5 - 2(-7 * 5)

= -2 + 70

= 68

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The matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.

A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that is used to represent a mathematical object or a characteristic of one.

Matrix representations of linear mappings without additional details enable explicit computations in linear algebra. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices.

The given equation is:

x1 + 2x₂ = 11

3x1 + 4x2 = 25

The equation is represented in matrix form as follows:

[tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex]

Hence, the matrix equation for the given is [tex]\left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{c}x1&x2\end{array}\right] = \left[\begin{array}{c}11&25\end{array}\right][/tex] and option B is the correct answer.

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Principal amount in each account is $200 for Account A and $600 for Account B. Simple interest is most earned for Account B.

Simple interest is defined as the interest obtained over the principal amount on a certain rate.

Simple interest is calculated by the formula,

SI = P × r × t,

where P is the principal amount, r is the interest rate and t is the time in years.

Account A :

t = 6 months = 0.5 year

S.I = $3.30

r = 3.3% = 0.033

Substituting in the formula,

3.30 = P × 0.033 × 0.5

P = 200

Principal amount in Account A is $200.

Simple interest earned in the first month = 200 × 0.033 × (1/12) = $0.55

Account B :

t = 30 months = 2.5 years

S.I = $37.50

r =  2.5% = 0.025

Substituting in the formula,

37.50 = P × 0.025 × 2.5

P = 600

Principal amount in Account B is $600.

Simple interest earned in the first month = 600 × 0.025 × (1/12) = $1.25

Account B earned more interest in the first month.

Hence Account B earned most interest in the first month with am amount of $1.25.

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