and give simple working out :)

(x-4)²+(y+7)²=4² is the equation of the circle represented by the given figure.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the equation of the circle for the given figure.

(x-h)²+(y-k)²=r²

(h, k) is the centre of the circle.

From the image the centre is at (4, -7)

So h=4 and k=-7.

y+16=0

r=4

Substituting these values in the standard form we get

(x-4)²+(y+7)²=4²

Hence, (x-4)²+(y+7)²=4² is the equation of the circle represented by the given figure.

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The probability that a random sample of 150 bowlers will have an average score greater than 165 is 0

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to measure the likelihood or chance of an event occurring, ranging from impossible (0 probability) to certain (1 probability).

The basic concept of probability involves determining the ratio of the number of favorable outcomes to the total number of possible outcomes. This ratio is expressed as a fraction, decimal, or percentage.

For example, if you toss a fair coin, there are two possible outcomes: heads or tails. The probability of getting heads is 1/2 or 0.5 or 50%, and the probability of getting tails is also 1/2 or 0.5 or 50%.

To give the probability that a random sample of 150 bowlers will have an average score greater than 165

P( [tex]\bar X[/tex]> 165) = P(z > (165 - 157)/(12/√(150)))

= P(z > 8.16)

= 0 [since from z table]

= 0

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The solution to the given inequality w > 2w - 9 is w < 9.

Inequality is defined as mathematical pieces of information that have a minimum of two terms including variables or numbers that are not equal.

The "inequality" is given in the question, as follows:

w > 2w - 9

We have to solve the above inequality for w.

⇒ w > 2w - 9

Rearrange the term of variable w in the above inequality,

⇒ w - 2w > - 9

Apply the subtraction operation and solve for w:

⇒ - w > - 9

Multiply the negative sign and flip the sign of inequality:

⇒ w < 9

Thus, the solution to the given inequality is w < 9.

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The result of each length of the sides of a right triangle is as follows:

5, 12 and 13: Yes

12, 35 and 20√5: No

5, 10 and 5√5: Yes

8, 12 and 15: No

20, 99 and 101: Yes

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.

For 5, 12 and 13:

13² = 5² + 13²

169 = 169 (This is true)

YES

For 12, 35 and 20√5 :

(20√5)² = 12² + 35²

2000 = 1369 (This is false)

NO

For 5, 10 and 5√5 :

(5√5)² = 5² + 10²

125 = 125 (This is true)

YES

For 8, 12 and 15:

15² = 12² + 15²

225 = 369 (This is false)

NO

For 20, 99 and 101:

101² = 20² + 99²

10201 = 10201 (This is true)

YES

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The area of the figure can be expressed using the formula A = (x + 1)2.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

This formula is derived from the fact that the figure is a square with sides of length x + 1. Since a square is a special type of rectangle, the area of a square is simply equal to the product of its two sides, or (x + 1)2.

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The speed of the slower plane is 125 mph and the speed of the faster plane is 175 mph.

Let's call the speed of the slower plane "x" and the speed of the faster plane "x+50".

When two planes are flying in opposite directions, the distance between them increases at a rate equal to the sum of their speeds. So, we can set up the following equation:

2(x + x+50) = 600

Simplifying this equation, we get:

2(2x+50) = 600

4x + 100 = 600

4x = 500

Divide

x = 125

Therefore, the speed of the slower plane is 125 mph and the speed of the faster plane is x+50 = 175 mph.

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Yes, The y - intercept is zero because it cannot intercept at any point on y - axis.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of your model is,

⇒ y = 0.122x

Here, The y - intercept is zero.

Since, The slope intercept form of equation of line is,

⇒ y = mx + b

Where, 'm' is slope and 'b' is y - intercept.

By comparing with the given equation, We get;

The y - intercept is zero.

And, By graph it cannot intercept at any point on y - axis.

Hence, The y - intercept is zero because it cannot intercept at any point on y - axis.

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1) A(1,2),A'(-1,2) : a reflection across the y-axis

2) A(1,2), A'(-2,1): a rotation 270⁰ clockwise around the origin

3) A(1,2),  A'(-1,4):  a translation of 2 units left and 2 unit up

4) A(1,2),A'(-1,-2): a rotation 180⁰ around the origin

5) A(1,2),A'(-3,-7): a translation of 4 units left and 9 units down

What is the transformation of a point?

The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.

The given point is A(1,2).

The rule of a rotation 180⁰ around the origin is (x,y)→(−x,−y).

Therefore, A(1,2)→A'(-1,-2).

A rule of translation of 2 units left and 2 unit up is (x,y)→(x-2,y+2)

Therefore, A(1,2)→A'(1-2,2+2) = A'(-1,4).

The rule of a reflection across the y-axis is (x,y)→(−x,y).

Therefore, A(1,2)→A'(-1,2)

A rule of translation of 4 units left and 9 units down is (x,y)→(x-4,y-9)

Therefore, A(1,2)→A'(1-4,2-9) = A'(-3,-7).

The rule of a rotation 270⁰ clockwise around the origin is (x,y)→(-y,x)

Therefore, A(1,2)→A'(-2,1)

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Answer:

Step-by-step explanation:

The probability that both adults think most celebrities are good role models is  0.046

Probability is a branch of mathematics that deals with the study of random events or processes. It is the measure of the likelihood or chance of an event or outcome occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Given that the probability that the celebrities are good role models is 192/900

Then if we pick two adults without replacement; 192/900 * 192/899

= 0.046

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Missing parts;

In a sample of 900 U.S. adults, 192 think that most celebrities are good role models. Two U.S. adults are selected from this sample without replacement.Find the probability that both adults think most celebrities are good role models.

Answer:

x=5

Step-by-step explanation:

26=4x+6
20=4x

x=5

Are you more likely to see a twelve-pack from the local brewery or a twelve-pack from the large chain with an average fill of 327.9 ml?

Local brewery.

a. At the local brewery the middle 95% of six-packs will have an average fill between ml 326.828 and 329.572 ml

b. At the large chain brewery, the middle 95% of six-packs will have an average fill between 326.824 ml and 329.176 ml.

X ζ N (328.2, 0.7^2)

YζN (328, 0.6^2)

P (X> 327.9) = 0.6659

P (Y> 327.9) = 0.5662

Since, P (X> 327.9) > P (Y> 327.9)

We are more likely to see 12-pack from the local brewery.

a. To find a, b such that P(a<x<b) = 0.95

a= 326.828

b= 329.572

b. To find c, d such that P(c<Y<d) = 0.95

c= 326.824

d= 329.176

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Answer:

Slope = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Slope of a graph = [tex]\frac{rise}{run}[/tex]

Steps to follow:

1. Select two points along this linear graph by reading them:

For example (0, 3) and (8, 7)

2. Draw a vertical line from Point (8, 3) to Point (8, 7). This line is considered as the rise

3. Draw a horizontal line connecting (0, 3) with (8, 3). This line represents the run

4. Substitute the x and y coordinates of the two points mentioned in Step 1 in the formula below:

Slope = [tex]\frac{y_{2} - y_{1}}{x_{2} -x_{1}}[/tex]

          = [tex]\frac{7 - 3}{8 - 0}[/tex]

          = [tex]\frac{4}{8}[/tex]

Divide the numerator and denominator by the Highest Common Factor ‘4’ to simplify the fraction:

            = [tex]\frac{1}{2}[/tex]

Answer:

Let M be the minimum monthly payment and A be the additional monthly payment of $30. Let B be the balance on the store credit card.

From the problem, we have:B = M * 58 (if only minimum payments are made)

B = (M + A) * 24 (if an additional $30 is paid each month)

Simplifying these equations, we get:M = B / 58

M + A = B / 24

Substituting the first equation into the second equation, we get: B / 58 + A = B / 24

Solving for A, we get:A = B / 24 - B / 58

A = B * (58/24 - 1/58)

Simplifying, we get:A = B * 0.08275862

To find the percent of time that Haddad will save by paying the extra $30 per month, we need to find the difference in time between the two scenarios and divide by the longer time (58 months).

The time it takes to pay off the balance with only the minimum payments is 58 months, while the time it takes to pay off the balance with the additional $30 each month is 24 months.

The difference in time is:58 - 24 = 34

So Haddad will save 34 / 58 = 0.5862, or 58.62% of the time by paying the extra $30 per month.

Answer:

Step-by-step explanation:

4x-22.2=1.90

22.20-4x=1.90

4x + 1.90 = 22.20

By integration of monthly revenue we will get total revenue of the shop for a year is $51,600.

What is integration ?

Integration is a fundamental operation in calculus that involves finding the area under a curve, or the antiderivative of a function. It is the reverse operation of differentiation, which is used to find the rate of change of a function.

Integration is represented by the symbol ∫ (the integral sign), and the result of the operation is called the indefinite integral or antiderivative of the function. The antiderivative is a family of functions that differ only by a constant, known as the constant of integration.

Given by the question:

The monthly revenue can be calculated by multiplying the unit price and the quantity of goods sold in a given month. Therefore, the monthly revenue function is:

[tex]R(t) = P(t) * Q(t) = (t^2 + 9t + 36) * (t + 12)[/tex]

To find the total revenue over a year, we need to integrate the monthly revenue function over the interval [0,12] (since we are considering a year):

[tex]Total revenue = \int\limits^a_0 {R(t)} \, dt[/tex]

= [tex]\int\limits^a_b (t^2 + 9t + 36) * (t + 12) } \, dt[/tex]

= [tex]\int\limits^a_b {(t^3 + 21t^2 + 132t + 432) } \, dt[/tex]

=[tex][t^4/4 + 7t^3/3 + 66t^2 + 432t][/tex]evaluated from 0 to 12

=[tex](20736/4 + 12096 + 9504 + 5184) - (0 + 0 + 0 + 0)[/tex]

= [tex]51600[/tex]

Therefore, the total revenue of the shop for a year is $51,600.

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Answer:

3.00000000000

Step-by-step explanation:

2.77247497343 is closer to 3.00000000000 than 2.00000000000

The solution to the inequality is any value of X that is less than or equal to -69.

What is Inequality?

An inequality is a relationship that compares two numbers or other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.

The inequality X/(-3) ≥ 23 can be solved as follows:

We begin by multiplying both sides of the inequality by -3, which will reverse the direction of the inequality since we are multiplying by a negative number. This gives:

X ≤ -69

Therefore, the solution to the inequality is any value of X that is less than or equal to -69.

In interval notation, we can write the solution as:

(-∞, -69]

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Answer:

x=11.34

Step-by-step explanation:

We receive the ratio as follows:

7/17.5 = 12/x

We can cross-multiply and solve for x to determine x:

7x = 17.5 × 12

7x = 210

x = 210/7

x = 30

Hence, x has a value of 30 cm.

Measuring is a method that involves comparing an object's characteristics to a reference value to ascertain its attributes. The primary metric for expressing any quantity of items, things, and occurrences is measurement.

In a number of branches of mathematics, we work with several fundamental categories of measurement variables. As follows:

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently. Also, in that, it requires a specific number of items to complete a specific task. We frequently encounter many measurements kinds for length, weight, times, etc. in our daily lives.

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The types for each person are:

P1 belongs to type A

P2 belongs to type C

P3 belongs to type C

What is Statements?

Facts regarding a mixed company are key statements to add in the objective summary.

Let's assume that there are three possible types: A, B, and C. Then, we can use a process of elimination to determine the type of each person based on the given statements.

First, we know that P1 claims to belong to type A. Therefore, we can eliminate type A as a possibility for P2 and P3.

Next, P2 claims that P1 does not belong to type B. Since P1 has already claimed to be type A, we can eliminate type B as a possibility for P1. Therefore, we know that P1 belongs to type A and P2 does not belong to type B.

Finally, P3 claims that P2 does not belong to type B. Since we have already determined that P2 does not belong to type B, we can eliminate type B as a possibility for P3. Therefore, we know that P3 belongs to type C.

So the types for each person are:

P1 belongs to type A

P2 belongs to type C

P3 belongs to type C

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Answer:

Step-by-step explanation:

10.468 rounded to the nearest hundredth would be 10.47

4 = tenths place

6 = hundredths place

8 = thousandths place

8 >= 0.5 so 10.468 --> 10.47

Answer: 10.47

Step-by-step explanation: After the decimal, it goes tenths, hundredths, thousandths. So we're looking at the second place after the decimal, which is a 6, and the next number is 8. Think of it like 68, rounding up to the next ten, or 70. So that turns it into 10.470, and you get to drop the zero to make it 10.47.

The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.

Statistics in mathematics is the study of data gathering, organization, interpretation, analysis, and presentation. Planning the acquired data for experimental designs and statistical surveys is the major goal of employing statistics. A mathematical science that deals with numerical data is statistics. In short, statistics is an important process that aids in decision-making based on facts.

The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.

The most likely used method to compute the average commute time to work in Douglas County is: researchers collected a random sample of people in Douglas County who are employed and asked them for their commute time. They added up all of these commute times and then divided this number by the number of people in the sample.

To understand why the video describes certain companies as major employers in Douglas County, the most relevant statistic would be the number of employees of each of these companies.

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Orbital period of the planet is 2√2 earth years

According to Kepler's third law, the square of a planet's orbital period is proportional to the cube of its semi major axis.  

T² α a³

where, T is orbital period and a is length of semi-major axis.

Given,

Distance between the sun and the planet

= twice the distance of sun and earth

Let distance between sun and earth a₁ = d

then distance between planet and sun a₂= 2d

Orbital period of earth T₁ = 1 earth year

By Kepler's third law

T² α a³

(T₁/T₂)² = (a₁/a₂)³

(1/T₂)² = (D/2D)³

1/T₂² = 1/8

T₂ = 2√2 earth years

Hence, 2√2 earth years is the orbital period of other planet.

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Answer:

≈ 315

Step-by-step explanation:

To find the number that 105 is 33 1/3 of, we can use algebra.

Let x be the number we are looking for. Then we can write the equation:

105 = (33 1/3)% of x

To solve for x, we can first convert the percentage to a decimal by dividing by 100:

33 1/3% = 33 1/3 ÷ 100 = 0.3333

Substituting this in the equation, we get:

105 = 0.3333x

To solve for x, we can divide both sides by 0.3333:

x = 105 ÷ 0.3333

Using a calculator, we get:

x ≈ 315

Therefore, 105 is 33 1/3 of 315.

Answer:

112cm³

Step-by-step explanation:

Let us ignore the bottom part of the figure and first find only the volume of the cuboid at the top

from the figure we know that

length of the cuboid is 10 cm

Width is 2 cm

height is 5 cm

now the formula for Volume of cuboid is Length×Width×Height

so,

Volume of the Upper Cuboid = 10×2×5= 100cm³ ---(1)

Now we will ignore the cuboid on top and find the volume of the one at the bottom

From the figure, we know that its dimensions are

length = 2cm

height = 3cm

width = 2cm

Volume of the lower cuboid = 2×2×3 = 12cm³ ---(2)

Adding (1) and (2)

100cm³ + 12 cm³ = 112cm³

Therefore the volume of the given figure is 112cm³

The volume of the box is 112 cm³.

We have,

The figure can be considered as two boxes.

Now,

One box:

Volume.

= Length x Width x height
= 10 x 2 x 5

= 100 cm³

Another box:

Volume.

= Length x Width x height
= 2 x 2 x 3

= 12 cm³

Now,

The volume of the box.

= 100 + 12

= 112 cm³

Thus,

The volume of the box is 112 cm³.

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We can write tan(− 0.9) as -

tan(− 0.9) = -1.26.

Tangent function is defined as the ratio of perpendicular and base. Mathematically, we can write -

tan(Ф) = p/b

tan(Ф) = perpendicular/base

Given is to find the value of tan(− 0.9).

We know -

1 radian = 57.2958 degrees

0.9 radian = 57.3 x 0.9 = 51.57 degrees

0.9 radian = 51.57 degrees                           ... { 1 }

So, we can write -

tan(− 0.9) = tan( - 51.57°) = - 1.26

Therefore, we can write tan(− 0.9) as -1.26.

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Answer:

the total number of students on the honor roll increased by 13.8%.

Step-by-step explanation:

Last year, there were a total of 50 + 80 = 130 students on the honor roll.

This year, the number of boys on the honor roll increased by 20%, which means there are now 1.2 * 50 = 60 boys on the honor roll.

The number of girls on the honor roll increased by 10%, which means there are now 1.1 * 80 = 88 girls on the honor roll.

The total number of students on the honor roll this year is 60 + 88 = 148.

The percentage increase in the total number of students on the honor roll is (148-130)/130 * 100% = 13.8%.

Rounding to the nearest tenth, we get that the total number of students on the honor roll increased by 13.8%.

Therefore, the parameters of the binomial distribution in this scenario are:

p = 0.404

n = 21

Probability, or the probability that an event will occur, is calculated by dividing the number of favourable outcomes by the total number of potential possibilities. Indeed, a coin flip is the most simple illustration. When you flip a coin, only one of two outcomes—heads or tails—is possible.

A binomial distribution with p and n parameters is present in this situation.

The likelihood of making a free throw, p (a success).

The quantity n represents the attempted free throws.

p = 0.404, which is the probability of making a free throw.

1 - p = 0.596, which is the probability of missing a free throw.

n = 21, which is the total number of free throws attempted.

the probability that the player makes no more than 6 of the 21 free throws. This can be represented as P(X ≤ 6), where X is the number of successful free throws (or made free throws).

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