if 8 out of 12 marbles in a bag are green, what is the probability that a marble selected at random from the bag will NOT be green?​

The mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

A triangle is a three-sided polygon made up of three line segments that connect at three endpoints, called vertices. The study of triangles is an important part of geometry, and it has applications in various fields such as engineering, architecture, physics, and computer graphics.

The mass of a 2D region with variable density can be calculated using the double integral formula:

m = ∬R ρ(x,y) dA

where R is the region of integration, ρ(x,y) is the density function, and dA is the area element.

In this case, we have a triangular region with vertices (0, 0), (4, 0), and (0, 2), and the density function is ρ(x,y) = [tex]x^2 + y^2.[/tex]To set up the double integral, we need to determine the limits of integration for x and y.

Since the triangular region is bounded by the lines y = 0, y = 2, and x = (2/5)y, we can set up the integral as follows:

m = ∫0 ∫[tex]0^[/tex](2/5)y ([tex]x^2 + y^2)[/tex] dxdy

Integrating with respect to x first, we get:

m = ∫[tex]0^2 [(x^3/3) + xy^2]_0^(2/5[/tex])y dy

m = ∫[tex]0^2 [(8/375)y^5 + (4/15)y^3][/tex]dy

Evaluating the integral, we get:

m = [tex][(2/1875)y^6 + (2/5)y^4]_0^2[/tex]

m = (64/1875) + (16/5)

m = 136/375

Therefore, the mass of the triangular region with density function ρ(x,y) = [tex]x^2 + y^2 is 136/375.[/tex]

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The total volume of the wall units is 108 cubic feet

The volume of the wall is solved by dividing the figure to give the various dimensions represented in the form length x width x depth

The volume of each is solved then added to get the total volume

first division: 4 x 4 x 8 = 96

second division: 3 x 2 x 2 = 12

The total volume is

= 96 + 12

= 108 cubic feet

so the total volume is solved to be 108 cubic feet

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Answer:

d)367

Step-by-step explanation:

Given, Tn = 5n² - 4

To find the 5th term, substitute n = 5 in the equation Tn = 5n² - 4

T5 = 5(5)² - 4

T5 = 121

To find the 7th term, substitute n = 7 in the equation Tn = 5n² - 4

T7 = 5(7)² - 4

T7 = 241

Therefore, the sum of the 5th and 7th terms = T5 + T7 = 121 + 241 = 362.

Hence, the correct option is (d) 367.

The vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

The dimensions of the building can be represented by the variable h, whereas the proximity of Jeanna to the building in her initial stance can be identified as x. Utilizing the principles of trigonometry, it is feasible to express the following:

The trigonometric function involving the angle of 35 degrees and its corresponding acute triangle can be written as an equation in the form of tan(35) = h/x, which is denoted as equation 1.

Upon moving a distance of 100 feet from her initial position, Jeanna's distance from the building can be represented as x - 100. Additionally, the angle at which she must look up to view the top of the building is now 40 degrees. Through the application of comparable trigonometric reasoning, it is possible to articulate the following statement:

Equation 2 can be expressed as tan(40) = h/(x - 100), where h and x represent the height and horizontal distance, respectively.

Equation 1 can be manipulated in such a way as to express the variable x in terms of h. The value of x is obtained by dividing h by the tangent of 35 degrees.

The substitution of the given expression for variable x in equation 2 leads to the following result:

The equation tan(40) = h/(h/tan(35) - 100) is amenable for rephrasing in a more academic style of writing.

Upon performing reduction on this mathematical expression, it results in:

The given mathematical equation can be represented in an academic manner as follows: The equation tan(40) = tan(35)h/(h - 100tan(35)) holds true, where h denotes the height of an object located at an angle of 40 degrees to the horizontal plane. This equation specifies the relationship between the tangent values of two distinct angles, 40 degrees and 35 degrees, and the height of the object.

The present equation can be expressed in a more formal academic style as follows: "The function h is defined as the difference between the tangent of 40 degrees and the tangent of 35 degrees, i.e., h = tan(40) - tan(35). This formula can be simplified, resulting in h = -100tan(35)tan(40)."

By dividing each side of the equation by (tan(40) - tan(35)), we are able to obtain the following result:

The following expression denotes the value of h, computed using mathematical operations: h = -100tan(35)tan(40)/(tan(40) - tan(35)).

The value of h is approximately equal to 119.53 feet.

Hence, the vertical measurement of the structure corresponds to an estimated value of 119.53 feet.

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Answer:

251.2 in

Step-by-step explanation:

Circumference of circle = 2 · π · r

π = 3.14

r = 40 in

Let's solve

2 · 3.14 · 40 = 251.2 in

So, the circumference of the circle is 251.2 in

The simplest form of the expression "(14ab³)/(7a⁻²b⁻¹)" is represented by the expression (d) 2a³b⁴.

To simplify the expression (14ab³)/(7a⁻²b⁻¹), we first simplify the terms with the same base,

First, we simplify the coefficients "14" and "7" by dividing them to get:

⇒ (14ab³)/(7a⁻²b⁻¹) = 2ab³/a⁻²b⁻¹;

Next, we simplify the variables "a" and "b" by subtracting the exponents of "a" and "b" in the denominator respectively,

We get,

⇒ 2ab³/a⁻²b⁻¹ = 2a¹⁻⁽⁻²⁾b³⁻⁽⁻¹⁾ = 2a¹⁺²b³⁺¹ = 2a³b⁴,

Therefore, the simplest form of the expression (14ab³)/(7a⁻²b⁻¹) is 2a³b⁴, the correct option is (d).

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The given question is incomplete, the complete question is

Look at this expression. (14ab³)/(7a⁻²b⁻¹),

Which of the following is the simplest form of the expression above?

(a) 2a⁻²b⁻³

(b) 2a⁻¹b²

(c) 2[tex]a^{-\frac{1}{2} }[/tex]b⁻³

(d) 2a³b⁴.

Answer:

Step-by-step explanation:

1

The average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

To find the average height of each team, we'll sum up the heights and divide by the number of players on each team.

Soccer team average height:

Sum of heights: 60+61+...+87+88 = 2,246 inches

Number of players: 29

Average height: 2246 / 29 = 77.45 inches

Basketball team average height:

Sum of heights: 72+73+...+86+87 = 1,264 inches

Number of players: 16

Average height: 1264 / 16 = 79 inches

So, the average height of the soccer team is 77.45 inches, and the average height of the basketball team is 79 inches.

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Soccer team heights (in inches):

60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88

Basketball team heights (in inches):

72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87

Jason wants to find more information about the heights of players on his school's soccer team and his school's basketball team. Jason surveys 29 members of the soccer team and 16 members of the basketball team. The heights of the soccer team and basketball team players are given above. What is the average height of the soccer team and the basketball team?

Answer:

b

Step-by-step explanation:

b

Answer: 96 fifth grade students outside for exercise. 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Step-by-step explanation:

Let x be the total number of fifth grade students.

- 1/2x are on the soccer fields

- 1/4x are on the basketball courts

- 1/8x are jogging around the track

- 12 students are tossing footballs

x = 1/2x + 1/4x + 1/8x + 12

x = 4/8x + 2/8x + 1/8x + 12

x = 7/8x + 12

1/8x = 12

x = 12*8

x = 96

Therefore, there are 96 fifth grade students outside for exercise.

Soccer fields: 1/2x = 1/2 * 96 = 48 students

Basketball courts: 1/4x = 1/4 * 96 = 24 students

Jogging around the track: 1/8x = 1/8 * 96 = 12 students

Tossing footballs: 12 students (as given in the problem)

There are 48 students playing soccer, 24 students playing basketball, 12 students jogging around the track, and 12 students tossing footballs.

Answer:

96 students in general

Step-by-step explanation:

I drew an Euler circle to make it more clear. so we can see that 1/8 class = 12

so 1/4 class is 12×2=24

1/2 class is 12×4=48

12+12+24+48=96

I hope this helped

Therefore , the solution of the given problem of expressions comes out to be points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

Instead of using random estimates, shifting variable numbers should be employed instead, which can be growing, diminishing, or blocking. They could only help one another by transferring items like tools, knowledge, or solutions to issues. The explanations, components, or mathematical justifications for strategies like expanded argumentation, debunking, and blending may be included in the explanation of the reality equation.

Here,

Figure XYZ will be scaled down by 1/4, with the centres being X(-2,4), Y(-4,4), and Z(4,2)

=>  Old_x - Center_x - Scale_factor * New_x + Center_x

=>  Scale factor * (Old y - Centre y) + Centre y = New y

Regarding X:

=>  New_x = 1/4 * (-2 - (-2)) + (-2) = -2

=>  New_y = 1/4 * (4 - 4) + 4 = 4

Therefore, X'(-2,4) is the image of point X after dilation.

Regarding Y:

=>  New_x = 1/4 * (-4 - (-2)) + (-2) = -3

=>  New_y = 1/4 * (-4 - 4) + 4 = -1

Therefore, Y'(-3,-1) is the image of point Y following dilation.

Regarding Z:

=> New_x = 1/4 * (4 - (-2)) + (-2) = 0

=> New_y = 1/4 * (2 - 4) + 4 = 3

Therefore, Z'(0,3) is the image of point Z after dilation.

As a result, the image points for the dilated figure XYZ with the centre points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).

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The direct distance between Thom's house and his school, as the crow flies, is  7.21 miles.

To find the direct distance between Thom's house and his school, we can use the Law of Cosines.

The Law of Cosines is a formula used to find the length of one side of a triangle when the lengths of the other two sides and the angle between them are known. In this case, we have a triangle with sides of length 6 miles, 8 miles, and the angle between them is 60 degrees.

The Law of Cosines formula is:

c² = a² + b² - 2ab * cos(C)

where:

a and b are the lengths of the known sides of the triangle

C is the angle between those two sides

c is the length of the unknown side (the distance we want to find)

In this case:

a = 6 miles

b = 8 miles

C = 60 degrees

First, convert the angle from degrees to radians:

C (radians) = (60 degrees * π) / 180 = 1.047 radians

Now, apply the Law of Cosines:

c² = 6² + 8² - 2 x 6 x 8 x cos(1.047)

c² = 36 + 64 - 96 x cos(1.047)

c² ≈ 36 + 64 - 96 x 0.5

c² ≈ 36 + 64 - 48

c² = 52

Finally, find the square root to get the distance:

c = √52 = 7.21 miles

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Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.

A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.

The area of the rectangular patio is given by multiplying its length by its width, so the area is:

A = (1 + 2x)(2 - 3x)

Now using distributive property we get,

A = 2 - 3x + 4x - 6x²

Simplifying further, we get:

A = -6x² + x + 2

Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.

To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:

P = 2(1 + 2x) + 2(2 - 3x)

Simplifying this expression, we get:

P = 2 + 4x + 4 - 6x

P = 6 - 2x

Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.

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Answer:

76°

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°.

p = 360 - 60 - 134 - 90 = 76

Answer:

The molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound.

unit of measurement: g/mol.

A mole is the amount of substance that contains as many elementary entities as there are atoms in 12g of carbon-12.

Avogadro's number= 6.02*10^23 particles.

1/8

(1/2)^3 1^3 2^3 1/8 or:(1/2)^3 (1/2) (1/2)(1/2)1×1×1/2×2×1/8

Answer:

42, 41, 123

Step-by-step explanation:

3, 2, 6, 5, 15, 14

- 1 x3. - 1. x3. - 1

you just gotta look for the pattern thats the same in the sequence so the next three numbers would be x3, then - 1 then x3 again onto the numbers.

Answer:

The next three numbers are 42, 41, and 123

Step-by-step explanation:

3 - 1 = 2

2 * 3 = 6

6 - 1 = 5

5 * 3 = 15

15 - 1 = 14

The pattern is subtracting one and then multiplying by three.

14 * 3 = 42

42 - 1 = 41

41 * 3 = 123

The value of x in the expression is y + 3

The expression given is written as

3x + 3= 3y + 6

collect the like terms

3x - 3y= 6-3

3x - 3y= 3

3x= 3 + 3y

x= 3 + 3y/3

x= 3 + y

x= y + 3

Hence the value of x in the expression is y + 3

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The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

When you multiply an inequality by a positive number, the direction of the inequality does not change. So if 4 < 7, then:

what is inequality?

Inequality is a mathematical statement that describes a relationship between two values or expressions that are not equal. In an inequality, we use the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to) to indicate the relationship between the values or expressions.

For example, "x < 5" is an inequality that means "x is less than 5", and "y ≥ 10" is an inequality that means "y is greater than or equal to 10". Inequalities are often used in algebra and other branches of mathematics to express relationships between variables or to solve problems.

Multiplying both sides by

7 gives: 28 < 49

Multiplying both sides by

6 gives: 24 < 42

Multiplying both sides by

3 gives: 12 < 21

Multiplying both sides by

10 gives: 40 < 70

All of these inequalities are still true, because we are multiplying both sides by a positive number.

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Answer:

x=4

y=5

Step-by-step explanation:

The solution set is {(x, y) | x = y + 2}, which represents a straight line with a slope of 1 passing through the point (2, 0).

Therefore, the correct answer is option 2, infinite solutions.

Equations of the form ax2 + bx + c = 0, where a, b, and c are real numbers, and a 0, are known as polynomial equations in the variable x. Any equation that has the formula p(x) = 0, where p(x) is a polynomial of degree 2 with a single variable, is actually a quadratic equation.

The equation has the following form: ax2 + bx + c = 0, where x is the unknown variable and a, b, and c are constants, with "a" not equal to 0.

Numerous strategies, including factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations.

To solve the system of equations:

x - y = 2 ---(1)

-3x + 3y = -6 ---(2)

We can use the first equation to isolate x in terms of y:

x = y + 2

-3(y + 2) + 3y = -6

Simplifying the equation, we get:

-3y - 6 + 3y = -6

Solving for y, we get:

0 = 0

For all values of y this equation is true-

So,the equations has infinite solutions.

To find the solution set, we can substitute the value of y into the expression for x:

x = y + 2

x = y + 2, for all values of y

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An inequality that matches this graph include the following: B} x ≥ -5.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Since the closed circle is at point -5 and increases to the right, an inequality that matches this graph is x ≥ -5.

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Answer:

I got you

Step-by-step explanation:

c-11=25

c=25+11

c=36

Therefore, Postman Builders Inc’s new required rate of return is 23.7%1.

Rate might signify two different things. As a noun, it denotes an amount, frequency, or measure that is typically compared to another quantity or measure. Or, it can be used as a verb to indicate "assign a standard or value to" using a specific scale.

Postman Builders Inc. has a necessary return of 10.2% and a beta of 1.5, according to the information given.

We may get the new necessary rate of return as follows if Postman purchases risky assets that increase its beta by 65% and the predicted inflation rate and inflation premium increase by 2 percentage points.

New Required Rate of Return

= Risk-free rate + Beta * (Expected Market Return - Risk-free rate)

= 2% + (1.5 * (6% + 2% + (65% * 6%))) = 23.7%

New Required Rate of Return equals 8% plus 2.47 x (-2%) to 3.85%.

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The sportsman has a final distance with respect to his home equal to 305 meters.

In this problem we must the final distance of the sportsman with respect to his home. This can be determined by the following expression:

X = ∑ xₙ, for n = {1, 2, 3, ..., N}

Where the sportsman goes far away for his home for x > 0, in meters.

Now we proceed to determine the final distance:

X = + 350 m - 125 m + 80 m

X = + 305 m

The final distance of the sportsman with respect to his home is 305 meters.

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Answer:

y = (5/3)x + 2/3

Step-by-step explanation:

find slope

rise/run

(4--1)/(2--1)

(5)/(3)

M = 5/3

then plug in a point to get the y-intercept

4 = (5/3) * 2 + b

4 = 10/3 + b

subtract 10/3 on both sides

2/3 = b

in y =mx +b the equation is

y = (5/3)x + 2/3

Answer:

  C  ∫[-a,0] = -∫[0, a]

Step-by-step explanation:

You want an alternate representation of the given integral ...

  ∫(2x⁵ -5x³)dx

on the interval [-a, a].

The function f(x) = 2x⁵ -5x³ being integrated is an odd function. This means ...

  f(-x) = -f(x)   and   f(0) = 0

An even function is characterized by ...

  f(-x) = f(x)

The integral F(x) of this odd function f(x) is an even function, so the parts either side of x=0 have the integrals ...

  [tex]\displaystyle \int_{-a}^0{(2x^5-5x^3)}\,dx=F(0)-F(-a)=F(0) -F(a)[/tex]

  [tex]\displaystyle \int_0^a{(2x^5-5x^3)}\,dx=F(a)-F(0)[/tex]

As we can see, these integrals are the opposites of each other, matching answer choice C.

__

Additional comment

The second attachment shows a numerical value for a=2.