The diameter of a circular of a field is 98 m. If a child walks at the rate of 14 M per minute how long will it take to walk around the field once ​

Therefore, the average speed in the simplest form is 6d² + 2d miles per hour.

In mathematics, an expression is a combination of symbols and values that can be evaluated to obtain a result. Expressions can contain variables, constants, operators, and functions, which can be combined using arithmetic or algebraic operations to form more complex expressions. Examples of expressions include 2 + 3, x + 5, and sin(θ) + cos(θ).

Here,

The given polynomial 90d² + 30d represents the miles traveled. We can find the average speed by dividing the distance traveled by the time taken. Since we have traveled for 15d hours, the total distance traveled is (90d² + 30d) miles. Thus, the average speed is:

=(90d² + 30d) miles / (15d) hours

= 6d² + 2d miles per hour

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Answer:

5 + 102x

Step-by-step explanation:

  5(-8+6x) - 9(-5-8x)

= -40 + 30x + 45 + 72x

= 5 + 102x

The negative correlation coefficient of -0.73 between consumption of vitamin A and the cancer rate of a particular type of cancer suggests that as vitamin A consumption increases, the cancer rate tends to decrease.

A correlation coefficient measures the strength and direction of the linear relationship between two variables.

In this case, a correlation coefficient of -0.73 indicates a negative correlation between consumption of vitamin A and the cancer rate.

Interpreting this correlation, it can be inferred that there is an inverse relationship between the two variables. As consumption of vitamin A increases, the cancer rate tends to decrease.

However, it is important to note that correlation does not imply causation.

It would be incorrect to conclude that consuming more vitamin A causes this type of cancer. Correlation does not provide information about the direction of causality.

Other factors and confounding variables may be involved in the relationship between vitamin A consumption and cancer rate.

To establish a causal relationship, further research, such as experimental studies or controlled trials, would be necessary. These types of studies can help determine whether there is a causal link between vitamin A consumption and the occurrence of this particular cancer.

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Answer:

XW = 134

Step-by-step explanation:

The fact that YZ bisects VW means that the angles VX and XW are supplementary, that is, they add to 180º. So

VX + XW = 180

We have that VX = 46. So

46 + XW = 180

XW = 134

Slope of change = 83 stores per year; Function model: S(x) = 83x + 788; Estimated number of Abercrombie and Fitch stores in 2014: S(10) = 1618 stores

(a) To calculate the rate of change in the number of Abercrombie and Fitch stores between 2004 and 2008, we use the formula:

rate of change = change in quantity / time period

= (new quantity - old quantity) / (new time - old time)

= (1125 - 788) / (2008 - 2004)

= 83 stores per year(approximately, rounding to two decimal places)

Therefore, the rate of change in the number of Abercrombie and Fitch stores between 2004 and 2008 is 83 stores per year.

(b) In 2004, the total number of Abercrombie and Fitch stores was 788, and in 2008, the total number of stores was 1125.

The function for the model that gives the number of Abercrombie and Fitch stores can be written in slope-intercept form: y = mx + b, where y = S(x) is the number of Abercrombie and Fitch stores, x is the number of years since 2004, m is the slope, and b is the y-intercept.

We can use the slope and one point on the line (the point (0, 788)) to find the y-intercept.

b = y - mx = 788 - 83(0) = 788

Therefore, the function for the model that gives the number of Abercrombie and Fitch stores is:

S(x) = 83x + 788.

(c) To estimate the number of Abercrombie and Fitch stores in 2014, we need to substitute x = 10 into the function:

S(10) = 83(10) + 788= 1618

Therefore, the estimated number of Abercrombie and Fitch stores in 2014 is 1618 stores (rounded to the nearest integer).

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In Problem 7, the total distance driven by the car is approximately 3.17 km. The car's overall displacement has a magnitude of approximately 1.84 km and is directed at an angle of approximately 45 degrees northwest.

In Problem 8, when a bicyclist travels around a circular track from the north side to the south side, their displacement is equal to the diameter of the track, which is 1000 m. When they make one complete circle around the track, their displacement is zero since they return to their starting point.

Problem 7:

To calculate the total distance driven, we sum up the distances traveled in each direction: 1 km + 2 km + 0.5 km = 3.5 km. So, the car has driven a total distance of approximately 3.17 km.

To find the car's overall displacement, we need to consider both the magnitude and direction. The first leg of the journey going north does not contribute to the displacement in the east-west direction. The second leg, driving 2 km at 30 degrees south of west, contributes to both the east and south directions. Using trigonometry, we can calculate the eastward component as 2 km * cos(30°) ≈ 1.73 km and the southward component as 2 km * sin(30°) ≈ 1 km. The third leg, driving 0.5 km northwest, contributes to both the east and north directions. Using trigonometry again, we can calculate the eastward component as 0.5 km * cos(45°) ≈ 0.35 km and the northward component as 0.5 km * sin(45°) ≈ 0.35 km. Adding up the eastward components (1.73 km + 0.35 km) and the northward components (1 km + 0.35 km), we find that the car's overall displacement has a magnitude of approximately 1.84 km and is directed at an angle of approximately 45 degrees northwest.

Problem 8:

When the bicyclist travels from the north side to the south side of the circular track, their displacement is equal to the diameter of the track. Since the track has a radius of 500 m, the diameter is 2 * 500 m = 1000 m. Therefore, the displacement when traveling from the north side to the south side is 1000 m.

When the bicyclist makes one complete circle around the track, they return to their starting point. Displacement is a vector that represents the change in position, and in this case, the change is zero since the starting and ending points coincide. Thus, the displacement when making one complete circle around the track is zero.

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The Laplace transform of the given differential equation is Y(s) = (B + C²)/(s(A - B - C + 1) + (B + C)).

The partial fraction expansion of Y(s) is Y(s) = A/(s - p) + B/(s - q), where p and q are the roots of the denominator polynomial.

Taking the Laplace transform of the given differential equation:

The Laplace transform of d²y/dt² is s²Y(s) - sy(0) - y'(0).

The Laplace transform of dy/dt is sY(s) - y(0).

The Laplace transform of A²dy/dt is A²sY(s) - A²y(0).

Substituting the given values A = 6, B = 4, C = 2 and assuming zero initial conditions (y(0) = y'(0) = 0), we get:

s²Y(s) - 6sY(s) + 36Y(s) - 4sY(s) + 24Y(s) = (4 + 4²)/(s(6 - 4 - 2 + 1) + (4 + 2)).

Simplifying the equation, we have:

s²Y(s) - 10sY(s) + 60Y(s) = (20)/(s).

Rearranging the equation, we get:

Y(s) = (20)/(s(s² - 10s + 60)).

To find the partial fraction expansion, we need to factorize the denominator polynomial:

s² - 10s + 60 = (s - p)(s - q), where p and q are the roots.

Solving the quadratic equation, we find the roots as p = 5 + √5 and q = 5 - √5.

The partial fraction expansion of Y(s) is given by:

Y(s) = A/(s - p) + B/(s - q).

Substituting the values of p and q, we get:

Y(s) = A/(s - (5 + √5)) + B/(s - (5 - √5)).

Therefore, the partial fraction expansion of Y(s) is Y(s) = A/(s - (5 + √5)) + B/(s - (5 - √5)).

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Taking out the equation of line in the given questions

What is Slope-Intercept?

One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis)

9) slope = 2/3 and points (-1, 2)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

2 = (2/3)(-1) + b

2 = (-2/3) + b

2 + 2/3 = b

(6 + 2)/3 = b

4/3 = b

so slope intercept form is y = (2/3)x + 4/3

10) slope = 5/4 and points (12,15)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

15 = (5/4)(12) + b

15 = (5)(3) + b

15 = 15 + b

15 - 15 = b

b = 0

so slope intercept form is y = (5/4)x + 0

11) slope = 4 points (0, -1)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

-1 = 4(0) + b

-1 = 0 + b

-1 = b

so slope intercept form is y = 4x - 1

12) slope = -1/4 and (1,-1)

Slope intercept form is y=mx + b. In this equation, m is the slope and b is the y-intercept. Point slope form is y-y1= m(x-x1). In this equation, m is again the slope and x1,y1 is where you plug in points from the line.

To solve this problem:

y=mx + b

-1 = (-1/4)(1) + b

-1 = -1/4 + b

1/4 - 1 = b

(1 - 4)/4 = b

-3/4 = b

so slope intercept form is y = (-1/4)x - 3/4

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Answers:

12.

Name: Octagon

Regular: Yes

13.

Name: Triangle

Regular: Yes

14.

Name: Rectangle

Regular: No

15.

Name: Pentagon

Regular: No

Answer:

5/4=1 1/4

Step-by-step explanation:

you have to turn the bottom number the same as the other one by multiplying it by 2,you have to do the for the top and it together to get your answer

Answer:

1 1/4

Step-by-step explanation:

1/2 + 2/4. 2/4 + 3/4 = 5/4 = 1 1/4

The range of allowable values 24; can vary by 3.5% is 0.9.

The difference between the highest and lowest values for a given data set is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3.

As a result, the range can also be thought of as the distance between the highest and lowest observation. The range of observation is the name given to the outcome. Statistics' range reflects the variety of observations.

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. That indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

24 × 3.5% =0.84

so round to nearest tenth is 0.9.

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Complete question:

Find the range of allowable values based on the given information. Round to the nearest tenth.

24; can vary by 3.5%

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8

The expressions are simplified to give;

7. 4n³(3n² + 4)

8. -3x(3x² - 4)

9. 5(k² - 8k + 2)

10. -10(6 + 6n² + 5n³)

11. 3(6n³ - 4n - 7)

12. 9(7n³ + 9n + 2)

Algebraic expressions are defined as mathematical expressions that are composed of variables, coefficients, terms, factors and constants.

These algebraic expressions are also made up of arithmetic operations, such as;

To factorize the expressions, we have;

12n⁵ + 16n³

Find the common term

4n³(3n² + 4)

-9x³ - 12x

find the common term

-3x(3x² - 4)

5k² - 40k + 10

find the common terms

5(k² - 8k + 2)

-60 + 60n² + 50n³

find the common term

-10(6 + 6n² + 5n³)

18n³ -12n - 21

find the common term

3(6n³ - 4n - 7)

63n³ + 81n + 18

Find the common term

9(7n³ + 9n + 2)

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MN = TS

5x -2 = 3x + 1

Add 2 to both sides:

5x = 3x + 3

Subtract 3x from both sides:

2x = 3

Divide both sides by 2

X = 3/2

Now you have x solve for TS

TS = 3x + 1 = 3(3/2) + 1 = 4 1/2 + 1 = 5 and 1/2

The smaller triangle is 2/3 the size ( 26/39 = 2/3)

5 1/2 x 2/3 =  3 2/3

The phase path provides insights into the behavior of the system, including the regions it can explore and the possible oscillations or movements it can undergo based on its energy.


Sure! Let's break down each step in detail.

1. Given the graph of the potential energy:
  a) The graph represents the potential energy of a system as a function of its position. The potential energy is typically denoted as U(x), where x represents the position of the system. The graph provides information about how the potential energy changes as the position of the system varies.
 
  For different values of energy, we can observe the following movements of the system:
  - When the energy of the system is lower than the potential energy at a particular position, the system will be confined to that region and will not have enough energy to move to other regions. It will oscillate back and forth around the minimum potential energy point(s) in that region.
  - When the energy of the system matches the potential energy at a specific position, the system will come to rest at that position since there is no net force acting on it. This position corresponds to an equilibrium point where the potential energy is minimized.
  - When the energy of the system is higher than the potential energy at a particular position, the system can move freely within the allowed region. It can move away from the equilibrium position and explore different regions of the potential energy graph.

  b) To plot the phase path (v against x), we need to relate the velocity (v) of the system to its position (x). The velocity is related to the potential energy by the equation:

     v = √(2/m * (E - U(x)))

  where m is the mass of the system and E is the total energy. This equation represents the conservation of energy, where the sum of the kinetic energy and potential energy remains constant.

  To plot the phase path, follow these steps:
  - Choose different values of energy (E) that correspond to different regions on the potential energy graph.
  - For each energy value, select a starting position (x) within the allowed region and calculate the corresponding velocity (v) using the above equation.
  - Plot the calculated velocity (v) on the y-axis and the corresponding position (x) on the x-axis. Repeat this process for various positions within the allowed region.
  - Connect the plotted points to obtain the phase path, which represents the trajectory of the system in the phase space (position-velocity space) for each energy value.

  It's important to note that the specific shape and features of the phase path will depend on the shape of the potential energy graph and the chosen values of energy. The phase path provides insights into the behavior of the system, including the regions it can explore and the possible oscillations or movements it can undergo based on its energy.

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Answer:

dont really understand your question but 20 months is

608.334 days and 86.9049 months

By rewriting a relation we will see that there are 0.5 fluid ounces in a tablespoon.

We know the relation between the different units:

1 fluid ounce = 2 tablespoons.

To see how many fluid ounces are in a tablespoon, we just need to work with the relation above and write "1 tablespoon" on the right side.

So if we take our relation:

1 fluid ounce = 2 tablespoons.

And we divide both sides by 2 then we will get:

1/2 fluid ounce = 2/2 tablespoons.

0.5 fluid ounces = 1 tablespoon.

then we can conclude that there is 0.5 fluid ounces in a tablespoon.

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Answer:

Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.

c + y = 2s ------ equation (1)

t + 4 = c ------ equation (2)

6t + 1 = y ------ equation (3)

Since Sofia is 38 years old, substitute s = 38 into equation (1):

c + y = 2(38)

        = 76 ------ equation (4)

Substitute equations (2) and (3) into equation (4):

t + 4 + 6t + 1 = 76

          7t + 5 = 76

                7t = 71

∴ t = 10 (to the nearest whole number)

∴Tony is 10 years old (to the nearest whole number).

Answer:

c. 8 cubes

Step-by-step explanation:

In this case if the original cube was divided into 27 equal smaller cubes, the way to do this is each top side divide it into 9 parts and then make 3 cuts down, so they would have 27 equal cubes.

The case that 3 faces are painted would be 8, because with this condition it would only be the corner cubes, the cube would have 4 lower corners and 4 upper corners, therefore 8 cubes would have 3 painted faces

Your classmate's score is higher than 130 because the 95th percentile represents the score below which 95% of the data falls.

The 95th percentile is a measure of relative standing in a data set. It represents the value below which 95% of the data points fall. In other words, if someone's score is at the 95th percentile, it means their score is higher than 95% of the scores in the data set.

Since your classmate scored at the 95th percentile, it implies that her score is higher than 95% of the scores. Therefore, her score is higher than the majority of scores, including the score of 130.

To further understand this, imagine arranging all the scores in ascending order. The 95th percentile corresponds to the score below which 95% of the scores lie. Since your classmate's score is at the 95th percentile, it means that only 5% of the scores are higher than hers, and the remaining 95% are lower. Therefore, her score is higher than 130 because it falls in the top 5% of scores.

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No, statistics and quantitative data are not necessarily more valid and objective than qualitative research.

While quantitative data can provide precise numerical measurements, it may not capture the full complexity of a particular phenomenon or experience. Qualitative research, on the other hand, can offer rich and nuanced insights into human behavior and attitudes. It allows for a deeper understanding of the context and meaning behind the data.

Ultimately, the choice between quantitative and qualitative research depends on the research question and the goals of the study. Both methods have their strengths and limitations, and it is important to consider them carefully when designing a study.

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The monthly profit for the company making decorative picture frames is given by the quadratic function f(p) = -93p^2 + 1,546p - 36,000, where p represents the price per frame.

The given quadratic function f(p) = -93p^2 + 1,546p - 36,000 represents the relationship between the price per frame (p) and the monthly profit (f(p)) of the company. The function is in the form of a quadratic equation, where the coefficient of p^2 is -93, the coefficient of p is 1,546, and the constant term is -36,000.

The coefficient of p^2 being negative (-93) indicates that the graph of the function is a downward-opening parabola. This means that as the price per frame increases, the profit initially increases but eventually starts decreasing.

The coefficient of p (1,546) represents the linear term, which determines the rate at which the profit changes with respect to the price. A positive coefficient implies that the profit increases linearly as the price per frame increases.

The constant term (-36,000) represents the initial profit when the price per frame is zero. In this case, it indicates that if the company gives away frames for free, it would experience a loss of $36,000 per month.

By analyzing the quadratic function and considering the coefficients, we can determine the optimal price per frame that maximizes the company's profit. This can be found by identifying the vertex (maximum point) of the parabolic graph, which corresponds to the price at which the profit is maximized.

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The problem wants us to solve for the area of the window.

As we can see the window is in the form of a SQUARE shape with a measurement of 0.25 in for 1/2 the side of the window.

Since 1/2 of the side of the window is 0.25, the full measurement of its side is just times two of its half. Therefore:

Side = 0.25(2) = 0.5 in

And we can see at the bottom of the picture the word SCALE. The SCALE shows the relationship between the measurement of something (in our case a cabin) in a model to the measurement of that something in the real life.

In our case we have a scale of 1 in = 8 ft, it means that 1 inch in the paper is actually 8 feet in real life. Therefore the side of the window which measures 0.5 in. in the paper is actually 4 feet in real life. Because 0.5 inch is half of 1 inch and 4 feet is half of 8 feet. To show it mathematically we have:

Since we now have a side of 4 ft. We can now solve for the area of our SQUARE WINDOW, using the formula of the area of the sqaure which is Area = Side x Side.

Therefore the area of the window is 16 square feet. LETTER C.

Answer:

2 Factors

Step-by-step explanation:

37 is a prime number

The solution for v in the equation (4)/(5v)=(1)/(10)-(3)/(2v) is v = 0.

To solve for v in the equation (4)/(5v)=(1)/(10)-(3)/(2v), we need to use the following steps:

Step 1: Multiply both sides of the equation by the common denominator of 10v to get rid of the fractions. This gives us:
(4)(10v)/(5v) = (1)(10v)/(10) - (3)(10v)/(2v)

Step 2: Simplify the equation by canceling out the common terms. This gives us:
8v = v - 15v

Step 3: Combine like terms on the right side of the equation. This gives us:
8v = -14v

Step 4: Add 14v to both sides of the equation to isolate v on one side. This gives us:
22v = 0

Step 5: Divide both sides of the equation by 22 to solve for v. This gives us:
v = 0/22

Step 6: Simplify the fraction to get the final answer. This gives us:
v = 0

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Answer:

126

Step-by-step explanation:

I = prt

I = (600)(0.07)(3)

I = 126

Answer: 126

Answer:

x = - 1, 6

Step-by-step explanation:

the denominator of h(x) cannot be zero as this would make h(x) undefined

equating the denominator to zero and solving gives the values of x that cannot be in the domain of h(x)

x² - 5x - 6 = 0

(x + 1)(x - 6) = 0

equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 6 = 0 ⇒ x = 6

then x = - 1, 6 are values not in the domain of h(x)

Answer:

Here is the equation in quadratic form:

x= 3±i√47/4