A game has a circular playing area in which you must hit a ball into a circular hole. The area of the playing area is 16pi ft squared. The hold has a diameter of 1ft. What is the probability of hitting a ball into the circular hole?

The expression in terms of x and/or y for

a) angle OAC = y

b) angle OBA = 2x

A circle is a shape consisting of all points in the plane that are at a specified distance from a specified point (center). Correspondingly, it is a curve drawn by points moving in the plane at a constant distance from a point. The distance from any point of the circle to the center is called the radius. Normally the radius should be a positive number.

Specifically, a circle is a simple closed curve that divides a plane into two regions inside and outside. In everyday use, the term "circle" can be used interchangeably to refer to the entire shape, including the boundary or interior of the shape. In strict technical usage the circle is just the boundary and the whole figure is called the disk.

In ΔOCA;

OC = OA  [Radius of circle]

So, m∠OCA = m∠OAC

y = m∠OCA

y = m∠OAC

Similarly in ΔAOB;

m∠OAB = 2x

m∠OAB = m∠OBA

2x = m∠OBA

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The complete question is as follows:

The diagram shows a circle with centre O.

Write an expression in terms of x and/or y for

a) angle OAC.

b) angle OBA.

Answer:

\( \frac{y {}^{7} }{z {}^{6}x {}^{5} } \)

I hope it helps you

please mark brainliest

When the spinner is divided evenly into eight parts with three colored blue, one colored orange, two colored purple, and two colored yellow, the likelihood that the spinner is spun once and the color is not blue is 62.5%.

Here,

number of possibility=8

number of sample case=5

Probability that spinner is spun once and color is not blue,

=5/8

=0.625

=62.5%

The probability that spinner is spun once and color is not blue is 62.5% when spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow.

Hence the correct option is B.

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If f(x, y) = f(x) · f(y) for all (x, y) such that f(x, y) > 0, then X and Y are not independent i.e. x ⊥⊥ y is false.

The given statement, "If f(x, y) = f(x) · f(y) for all (x, y) such that f(x, y) > 0, then x ⊥⊥ y" is false. What is the independence concept?

The independence concept is an important concept in probability theory. Independence is a mathematical concept that refers to a situation where knowledge of one event has no effect on the likelihood of another event. The independence concept is a key property of many probability distributions in statistics.

Two variables X and Y are said to be independent if the knowledge of one variable doesn't affect the distribution of the other variable, i.e. P(X|Y) = P(X).Given Definition:

By definition, x ⊥⊥ y iff f(x, y) = f(x) · f(y) for all (x, y).

Now we will check the statement's validity.

That is, If f(x, y) = f(x) · f(y) for all (x, y) such that f(x, y) > 0, then x ⊥⊥ y. This statement is false.

Let's check why?

Assume that X and Y are not independent i.e. P(X, Y) ≠ P(X)P(Y).

Then f(x, y) = P(X = x, Y = y) ≠ P(X = x)P(Y = y) = f(x) · f(y).

Therefore, f(x, y) = f(x) · f(y) is only true when X and Y are independent.

So, we can conclude that If f(x, y) = f(x) · f(y) for all (x, y) such that f(x, y) > 0, then X and Y are not independent i.e. x ⊥⊥ y is false.

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Answer:

Yes.

Step-by-step explanation:

Translating an image does not alter it. It only moves it somewhere else.

The original triangle will be identical to the final image because the translation changes the location.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The translation does not change the shape and size of the geometry. But changes the location.

The vertices of a triangle are A(0, -3), B(2, -1) and C(3, -3).

You translate the triangle 5 units right and 2 units down. Then you translate the image 3 units left and 8 units down.

Then the coordinate of the final image is given as,

A(0 + 5 - 3, -3 - 2 - 8) = (2, - 13)

B(2 + 5 - 3, -1 - 2 - 8) = (4, - 11)

C(3 + 5 - 3, -3 - 2 - 8) = (5, -13)

The original triangle will be identical to the final image because the translation changes the location.

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The total number of ways in which 4 questions can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

We are given;

Total number of objective questions = 5 questions

Number of choices of first 2 questions = 3 choices

Number of choices of last 3 questions = 4 choices

Number of ways of answering the first 2 questions = 3 * 3 = 9 ways

Number of ways of answering the last 3 questions = 4 * 4 * 4 = 64 ways

Total number of ways of answering the five questions = 9 * 64 = 576 ways

Now, she has to answer only 4 which means it can be either 2 of the first and 2 of the last of 1 of the first and 3 of the last.

Thus, total number of ways of answering 4 questions if it is fist 2 and last 2 = 9 * 16 = 144

Total number of ways of answering 4 questions if 1 of the first and 3 of the last = 3 * 64 = 192

The total number of ways in which they can be answered if the first 2 questions have 3 choices and the last 3 have 4 choices = 144 + 192 = 336

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Answer:

25x+100

Step-by-step explanation:

area of parallelogram = base*height

(x+4) * h = (5x+20)^2= 25x^2 + 200x + 400

h = 25x^2+200x+400/ (x+4)

= 25x + 100

Answer:

405

Step-by-step explanation:

divide 270 by 6 the multiply what you got with 9

:)

The flux of the vector field is -204800.

We are given that the cylinder is defined by the equation y =\(5x^2\) and the bounds of integration are 0 ≤ x ≤ 4 and 0 ≤ z ≤ 2. Let's parametrize the surface using u = x and v = z.

The parametric equations for the surface of the cylinder are:

x = u, y = \(5u^2\), z = v

To evaluate the flux, we need the surface normal vector. Since the normal vectors point in the general direction of the positive y-axis, the surface normal vector is given by n = <0, 1, 0>.

dS = (∂r/∂u) x (∂r/∂v)

  = <1, 10u, 0> x <0, 0, 1>

  = <10u, 0, 0>

The magnitude of dS is given by |dS| = |<10u, 0, 0>| = 10u.

The flux of F across the surface is given by the surface integral:

Flux = ∬S F · dS

Substituting F = <-y, x, 1> and dS = <10u, 0, 0>, we have:

Flux = ∫∫S <-y, x, 1> · <10u, 0, 0> dA

    = ∫∫S -10uy dA

Since the surface area element dA = |dS| dudv = 10u dudv, we can rewrite the flux integral as:

Flux = ∫∫S -10uy * 10u dudv

    = -100 ∫∫S \(u^2y\) dudv

Now we need to set up the limits of integration. Since 0 ≤ x ≤ 4 and 0 ≤ z ≤ 2, the corresponding limits for u and v are 0 ≤ u ≤ 4 and 0 ≤ v ≤ 2.

Flux = -100 ∫(v=0 to v=2) ∫(u=0 to u=4) \(u^2y\) dudv

To find the value of y in terms of u and v, we substitute the parametric equations for y = \(5u^2\):

Flux = -100 ∫(v=0 to v=2) ∫(u=0 to u=4) \(u^2(5u^2)\) dudv

    = -100 ∫(v=0 to v=2) ∫(u=0 to u=4)\(5u^4\)dudv

Now we can integrate the expression with respect to u and v:

Flux = -100 ∫(v=0 to v=2) [(5/5)\(u^5\)] from u=0 to u=4 dv

    = -100 ∫(v=0 to v=2) \(4^5\) dv

    = -100 (\(4^5\))(2)

    = -100 * 1024 * 2

    = -204800

Therefore, the flux of the vector field F across the cylinder is -204800.

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Answer:

45x*9

Step-by-step explanation:

Answer:

Your answer is 45x^9

Step-by-step explanation:

hope this helps!

The most likely thing Brooks will do with his increase in income is to increase his spending now that he can afford more.

It is common for people to adjust their spending habits to match their income. With a raise, Brooks may feel that he has more disposable income and therefore increase his spending. However, it is important to note that this may not always be the case for everyone.

The way individuals handle an increase in income can vary depending on their financial situation and personal beliefs about money management. In Brooks' case, it is likely that he will increase his spending because he now has more money available to him. This may mean he can afford to purchase more skateboard trucks and wheels or other items that he previously couldn't.  However, it is important for Brooks to consider his long-term financial goals before making any major purchases. While an increase in income may feel like an opportunity to spend more, it can also be a chance to save more or pay off debt. If Brooks has outstanding debt, he may want to consider using the extra income to pay it down faster. Alternatively, he may want to put some of the extra income into savings or investments to work towards longer-term goals like buying a house or planning for retirement.

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If Peter randomly surveys another 300 people, he would expect 117 people to live in an apartment, or option (B).

The prοbability οf an incident οccurring is defined by prοbability. There are many instances in real life where we may need tο make predictiοns abοut hοw sοmething will turn οut. The οutcοme οf an οccurrence may be knοwn tο us οr unknοwn tο us. When this happens, we state that there is a chance that the event will happen οr nοt. In general, prοbability has many great uses in games, in business tο make predictiοns based οn prοbability, and in this new branch οf artificial intelligence.

Tο answer this questiοn, we need tο use the infοrmatiοn given tο estimate the prοbability οf sοmeοne living in an apartment, and then use that prοbability tο calculate the expected number οf peοple whο live in an apartment οut οf the additiοnal 300 peοple that Peter surveys.

The proportion of people who live in an apartment in the sample that Peter already surveyed is:

14/(14+12+10) = 14/36 = 0.3889

So we can estimate that the probability of someone living in an apartment is 0.3889.

To calculate the expected number of people who live in an apartment out of the additional 300 people that Peter surveys, we can multiply the probability of living in an apartment by the total number of people that Peter surveys:

0.3889 x 300 = 132

So we can expect that Peter will survey approximately 132 people who live in an apartment out of the additional 300 people he surveys. Since we can't have a fraction of a person, we can round this number to the nearest whole number, which is 132.

Therefore, the answer is approximately 117, or option (B).

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Peter randomly surveys people at a shopping center about the type of home they live in. If Peter randomly surveys another 300 people, how many would he expect to live in an apartment?

Answer:

did u try looking it up lol?

Step-by-step explanation:

Answer:

21x^2 + 7x

Step-by-step explanation:

The formula for the area of a rectangle is L x W. The length in this case is 3x+1 and the width is x. Multiply those together and you get 3x^2 + x.

The formula for the area of a triangle is 1/2BH. When you plug in the numbers, the area of the triangle is 24x^2 + 6x.

Now, you want to subtract the area of the triangle from the area of the rectangle. When you do this, you get your answer: 21x^2 + 7x.

The store has 16 board games

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

Let x = number of legos

Let y =  number of board games

Given ratio: 9:6= 9/6

x/y = 9/6

substitute x=24

24/y=9/6

Do cross multiplication

(6*24)/9=y

16=y

or

y=16

So, the store has 16 board games

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Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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Answer:

a) two parallel lines

Step-by-step explanation:

Two parallel lines have the same slope

Let's take a concrete example:
y = 2x + 4        (slope =2, y-intercept = 4)
y = 2x + 10      (slope = 2, y-intercept = 10)

Lines are parallel to each other

If you try to solve this equation you get

2x + 4 = 2x + 10

Subtracting 2x on both sides gives you  the identity 4 = 10 (a contradiction)

This means the 2 line equations are inconsistent

Charles Horton Cooley and George Herbert Mead both contributed to the understanding of self-development, but their theories differ in terms of the primary influence on the formation of self.

Cooley's theory emphasizes the role of social interactions and the "looking-glass self," while Mead's theory focuses on the significance of language and symbolic interaction. Charles Horton Cooley's theory of self-development revolves around the concept of the "looking-glass self." Cooley argued that individuals develop their sense of self through social interactions and feedback from others.

According to Cooley, people imagine how they appear to others and interpret their reactions, forming their self-perception based on these social reflections. The looking-glass self emphasizes the influence of social relationships and the perception of others in shaping one's identity.

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Answer:

118

Step-by-step explanation:

The total area is the area of the large rectangle in the middle plus the areas of the two triangles.

The length of the entire rectangle is 5 cm + 5 cm + 4 cm = 14 cm.

The width of the rectangle is 7 cm.

Each triangle has a base of 4 cm and a height of 5 cm.

A = LW + 2 × (1/2)bh

A = (14 cm)(7 cm) + (4 cm)(5 cm)

A = 98 cm² + 20 cm²

A = 118 cm²

By using linear equation, the cost of the labor per hour turned out to be $45

A linear equation is a one-variable equation of a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax + b=0.

Given data:

Total cost = $290.75 …(1)

Cost of parts = $77.00.....(2)

subtracting 1 from 2

we get ,

$213.75

Let cost of labor per hour be A.

Here, A is a variable.

we get ,

4.75 x A = 213.75

A = 213.75/4.75

A = $45

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Expanded form is extracting the numbers from its standard form and setting it apart as individual numbers according to position then multiplying it -the numbers of zeros increase

Example:

110 x 10500

100 + 10 x 10000 + 500 =  1155000

Place value is arranging it according to the highest number place value to lowest

like,

10

* 5

-----

50

Answer:

9 boxes

Step-by-step explanation:

24 crayons each box

each child needs 12 crayons

1 box per 2 children

need to be 18 children

1 box per 2 chlidren

x boxes per 18 children

\(\frac{1}{2}=\frac{x}{18}\)

2x=18

x=9

9 boxes

Answer:

9 boxes

Step-by-step explanation:

1/2 = x/18

2x = 18

x = 9

9 boxes will be needed for 18 children.

To check:

18 * 12 = 216

9 * 24 = 216

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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The value of x = 93 degree and value of angle A and B is 72 , 108 degree

The pair of triangles that are supplementary and they add to form 180 degree angle are called Linear Pairs.

It is given that

∠ A = x -21

∠ B = x+15

also it is given that

angle  A and B form a linear pair

∠ A + ∠ B = 180 degree

To find the value of x

x -21 + x+15 = 180

2x - 6 = 180

2x = 186

x = 93 degree

so

∠ A = x -21 = 93 -21 = 72 degree

∠ B = x+15 = 93+21 = 108 degree

Therefore the value of x = 93 degree and value of angle A and B is 72 , 108 degree.

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Answer:

I think it is 2.............

Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2