4b+9b simplified version

Answer:

1

Step-by-step explanation:

a) If Kristin has traveled 4 meters along the path of the Ferris wheel then the angle has swept out 0.5 radians.

b) If Kristin has traveled 45 meters along the path of the Ferris wheel then the angle has swept out 5.625 radians.

c) The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters is θ = s / r.

a. To determine the angle in radians, we can use the arc length formula for a circle. The formula is given by θ = s / r, where θ is the angle in radians, s is the arc length, and r is the radius of the circle.

In this case, Kristin has traveled 4 meters along the path of the Ferris wheel, and the radius is 8 meters.

Thus, the angle swept out is

θ = 4 / 8 = 0.5 radians.

b. Following the same approach, if Kristin has traveled 45 meters along the path of the Ferris wheel, the angle swept out is

θ = 45 / 8 ≈ 5.625 radians.

c. The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters Kristin has traveled since the ride started is given by

θ = s / r,

where θ is the angle in radians, s is the arc length traveled by Kristin, and r is the radius of the Ferris wheel.

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Answer:

It will take him 13 Months to save up $12 a month to buy the shoes.

Hope this helps

Step-by-step explanation:

The correct answer to the given question about colored congruent squares is option A) 0.4 < 0.6

This is because Raul shaded 40/100 of the squares yellow, which can also be written as 0.4 as a decimal. He shaded the other 60/100 of the squares green, which can also be written as 0.6 as a decimal. Therefore, we can compare the two decimals and say that 0.4 is less than 0.6. To show how we find the answer 0.4 < 0.6, we can follow these steps:

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Complete Question

Raul has a figure made up of 100 congruent squares. He shaded 40/ 100 of the squares yellow and the other 60/100 of the squares green. Select the decimal expression from the following

0.4 <0.6

0.04 < 0.06

0.4 = 0.6

0.04 = 0.06

0.4 > 0.6

0.04 > 0.06

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

A player would need to make a goal in less than 6.78 minutes to be sponsored by the puck company.

This is because 10% of goals are made in less than one standard deviation below the mean, which is 12.56 - (8.73 * 0.67) = 6.78 minutes. This is assuming that the distribution of goal times follows a normal distribution, which is a common assumption for many real-world data sets.

The standard deviation is a measure of how spread out the data is, and by multiplying it by 0.67, we can find the point that represents the 10th percentile of the data. In this case, the 10th percentile of goal times is less than 6.78 minutes, meaning that the top 10% of goal times fall below this threshold.

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Answer:

no

Step-by-step explanation:

sdfghgfdsadfghjgftdrsewdfghgfdsdfgdsfghj

In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Mathematical modeling of surfaces is the representation of two-dimensional manifolds using mathematical techniques, particularly in the context of Digital Terrain Modeling (DTM) where surfaces refer to the Earth's terrain or physical objects.

Mathematical modeling of surfaces plays a crucial role in various fields, including computer graphics, engineering, and geosciences. Surfaces are fundamental objects that can be represented and analyzed using mathematical techniques.

In this section, we will delve into the concept of surfaces, particularly in the context of Digital Terrain Modeling (DTM). Additionally, we will explore the distinction between 3D and 2D DTM.

1. The Concept of Surfaces:

In the realm of mathematics, a surface is defined as a two-dimensional manifold, meaning it is a topological space that locally resembles Euclidean space.

In simpler terms, a surface is a geometrical entity that can be thought of as a continuous collection of points, forming a boundary between a solid and its surrounding space. In the context of DTM, surfaces typically refer to the representation of the Earth's terrain or any other physical object using mathematical models.

2. Digital Terrain Modeling:

Digital Terrain Modeling involves the creation of digital representations of the Earth's surface or any specific region using computer algorithms. It serves as a crucial tool in various applications, such as urban planning, environmental analysis, and military simulations. DTM utilizes mathematical models to represent the terrain accurately, allowing for detailed analysis and visualization.

3. 3D Digital Terrain Models:

A 3D Digital Terrain Model (DTM) is a representation of the Earth's surface that captures three-dimensional information. It provides a detailed depiction of the terrain, including elevation data, contours, and topographical features.

3D DTMs are typically generated using techniques such as LiDAR (Light Detection and Ranging) or photogrammetry. These models enable precise analysis of the landscape, volumetric calculations, and visualization from different perspectives.

4. 2D Digital Terrain Models:

In contrast to 3D DTMs, 2D Digital Terrain Models represent the Earth's surface in two dimensions. They provide a simplified view of the terrain, focusing primarily on elevation data and contour lines. 2D DTMs are commonly used in cartography, where the terrain is represented on a flat surface, such as a map or a computer screen. While they lack the depth information of 3D DTMs, 2D models are still valuable for many applications, including geographic information systems (GIS) and land surveying.

5. Differences between 3D and 2D Digital Terrain Models:

The main distinction between 3D and 2D DTMs lies in the level of detail and the dimensionality of the representation. 3D DTMs provide a more comprehensive and realistic view of the terrain, capturing not only the elevation but also the shape, slopes, and other three-dimensional features. These models are highly suitable for applications that require a precise understanding of the terrain's topography, such as hydrological analysis or landscape design.

On the other hand, 2D DTMs offer a simplified representation of the terrain, primarily focusing on elevation data and contour lines. They are more commonly used for general visualization and analysis purposes where the third dimension is not critical. 2D DTMs are easier to create and process, making them more accessible for applications that do not require intricate three-dimensional modeling.

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According to Central Limit Theorem, Given Statement is false.

What exactly is Central Limit Theorem?

According to the central limit theorem, as long as the sample size is high enough, the sampling distribution of the mean will always be normally distributed.

This approach selects random samples of the population from a large population and estimates the mean. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or other distribution.

Now,

As The Central Limit Theorem states that the mean is always normallly

distributed.

so, the statement that the central limit theorem says that a histogram of the sample means will have a bell shape, even if the population is skewed and the sample is small is false.

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a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

Answer: Im not sure but have a wonderful day god bless you.

Step-by-step explanation:

a) the function y=x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, (x > 0).

b) The value of c for which the solution satisfies the initial condition y(8) = 6 is c = -3712.

a) To verify that the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2, we first need to find the derivative y' using algebra:
y = x^2 + c/x^2
y' = 2x - 2c/x^3

Now, plugging y and y' into the given differential equation:

x(2x - 2c/x^3) + 2(x^2 + c/x^2) = 4x^2

Next, simplify the equation:
2x^2 - 2cx^(-2) + 2x^2 + 2c/x^2 = 4x^2

Combine the like terms:
4x^2 = 4x^2

The equation holds true, so the function y = x^2 + c/x^2 is a solution of the differential equation xy' + 2y = 4x^2.

b) To find the value of c for which the solution satisfies the initial condition y(8) = 6, plug in x = 8 and y = 6 into the function y = x^2 + c/x^2:

6 = (8^2) + c/(8^2)

Solve for c:
6 - 64 = c/64
-58 = c/64
c = -58 * 64
So, the value of c is -3712.

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Answer:

Answer is C

(-2,3)

Step-by-step explanation:

Answer:

(-8, 18)

Step-by-step explanation:

To solve this system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the two equations.

One way to do this is to multiply the second equation by a constant that will make the coefficient of x the same as in the first equation. In this case, we can multiply the second equation by -5, which will give us:

-15x - 10y = -60

Now we can add this equation to the first equation:

5x + 2y = -4

-15x - 10y = -60

-10x - 8y = -64

Dividing both sides by -2, we get:

5x + 4y = 32

Now we have one equation with only x and y, so we can solve for either variable.

Let's solve for y by subtracting 5x from both sides:

5x + 4y = 32

-5x = -5x

4y = 32 - 5x

Dividing both sides by 4, we get:

y = (32 - 5x) / 4

Now we can substitute this expression for y into one of the original equations to solve for x. Let's use the first equation:

5x + 2y = -4

5x + 2[(32 - 5x) / 4] = -4

Multiplying both sides by 4, we get:

20x + 2(32 - 5x) = -16

Simplifying, we get:

20x + 64 - 10x = -16

10x = -80

x = -8

Now we can substitute this value of x into either of the equations to solve for y. Let's use the first equation again:

5x + 2y = -4

5(-8) + 2y = -4

-40 + 2y = -4

2y = 36

y = 18

Therefore, the solution to the system of equations is (x, y) = (-8, 18).

Answer:

200

Step-by-step explanation:

18 is double of 16 so you have to double the 100 and it makes 209

Answer:

300

Step-by-step explanation:

18/6 = 3

100 x 3 = 300

Have a nice day

Answer:

Step-by-step explanation:

diameter of each circle = 20/2 = 10 cm

rectangle is 20 cm by 10 cm

area of rectangle = 20×10 = 200 cm²

radius of each circle = 10/2 = 5 cm

area  of each circle = πr² = 25π cm²

shaded area = 200  - 2(25π) = 200 - 50π =42.92 cm²

The accumulated amount after 25 years is , $70,702.80.

Now, We can use the formula for compound interest to find the accumulated amount after 25 years:

A = P(1 + r/k)^(kt)

Where A is the accumulated amount, P is the principal , r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period.

In this case, we have:

P = $25,300

r = 0.045 (

k = 12 (monthly compounding)

t = 25

Substituting these values into the formula, we get:

A = $25,300(1 + 0.045/12)^(12 x 25)

A ≈ $70,702.80

Therefore, the accumulated amount after 25 years is ,

$70,702.80.

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8z + 7w;    z = 6;   w = 7

8z + 7w  

=(8x6) + (7x7)

=48 + 49

=97

The answer is 97.

Answer:

97

Step-by-step explanation:

BIG BRAIN

The probability of choosing all five white balls correctly from a bowl of 69 white balls and the probability of choosing the correct red ball from a bowl of 29 red balls is \({}^{69}C_5/29\) .

The probability of choosing all five white balls correctly can be calculated using the formula for combinations, where the order does not matter and the balls are chosen without replacement. The probability is given by:

P(Choosing all 5 white balls correctly) = (Number of ways to choose 5 white balls correctly) / (Total number of possible combinations)

The number of ways to choose 5 white balls correctly is 1, as there is only one correct combination.

The total number of possible combinations can be calculated using the formula for combinations, where we choose 5 balls out of 69. It is given by:

Total number of combinations = \({}^{69}C_5\)

Next, we need to calculate the probability of choosing the correct red ball from a bowl of 29 red balls. Since there is only one correct red ball, the probability is 1/29.

Finally, to find the likelihood of being the winner of the Powerball lottery, we multiply the probability of choosing all five white balls correctly by the probability of choosing the correct red ball:

Likelihood = P(Choosing all 5 white balls correctly) * P(Choosing correct red ball)

=\({}^{69}C_5 \times 1/29\\\)

This gives us the probability of being the winner of the Powerball lottery.

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The expected value of a ticket in this raffle is $12.50.

We have to given that;

1000 raffle ticket are sold for $1 each and there are ten $20, five $50, and one $100 prize.

Now, For the expected value of a ticket, we need to multiply the probability of winning each prize by the amount of each prize, and then add up those values.

Hence, In this case, there are a total of 16 prizes as,

⇒ (10 $20 prizes, 5 $50 prizes, and 1 $100 prize),

Thus, the probability of winning any one prize is,

⇒ 1/16

So, the expected value of a ticket would be:

= (10/16) $20 + (5/16) $50 + (1/16) x $100

= $12.50

Therefore, the expected value of a ticket in this raffle is $12.50.

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The answers to all parts are shown below.

1. 5a + 3 -4a² + 2a³

writing into standard form of polynomial

2a³- 4a² + 5a +3.

2. 7xy + x³ - y³ -5x²y²

writing into standard form of polynomial

= x³ - y³ - 5x²y² + 7xy

3. The degree of the polynomials are

3x+1 = 1 degree

5x² - 2 degree

10- 0 degree

3x³ -2x² + 10= 3 degree

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Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

9 / 63

    - 0

----------

     63

   - 63

----------

       0

Hope this helped :)

The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

Answer:

0.364

Step-by-step explanation:

Answer:

Independent = number of boxes bought

Dependent = cost

Step-by-step explanation:

       The cost will change depending on the number of cookie boxes bought. This means that the cost is dependent upon the number of boxes.

Answer:

x = 3 \(\frac{1}{3}\)

Step-by-step explanation:

Given

\(\frac{5+x}{x}\) = \(\frac{15}{6}\) = \(\frac{5}{2}\) ( cross- multiply )

5x = 2(5 + x) ← distribute

5x = 10 + 2x ( subtract 2x from both sides )

3x = 10 ( divide both sides by 3 )

x = \(\frac{10}{3}\) = 3 \(\frac{1}{3}\)

Answer:

1. .monthly payment

2. $276 club. $36 fee

3. you got this