The diagram shows the various locations of an empty 500 kg roller coaster cart. Assuming no frictional force and other external forces acting on the roller coaster, find the value of the missing quantity for each location. Indicate whether the energy of the roller coaster is conserved and explain why. (g = 9.8 m/s² = 10 m/s²) ​

Answer:

(-25/3, 0)

Step-by-step explanation:

The x-intercept of a line is the point where the line crosses the x-axis. At this point, y=0. To find the x-intercept of the line with equation y= 3/5x+5, we substitute y with 0 and solve for x:

0 = 3/5x + 5

3/5x = -5

x = -25/3

Therefore, the x-intercept of the line is (-25/3, 0).

1) Drawing indifference curves: Indifference curves represent combinations of orange soda (OS) and potato chips (PC) that provide Mabel with the same level of utility.

Let's draw two indifference curves: one for U1 = 400 utils and another for U2 = 1000 utils. Indifference curve for U1 = 400 utils:
Points:
1. (OS = 10, PC = 40)
2. (OS = 8, PC = 50)
3. (OS = 4, PC = 80)

Indifference curve for U2 = 1000 utils:
Points:
1. (OS = 20, PC = 25)
2. (OS = 16, PC = 31.25)
3. (OS = 10, PC = 40)

2) Finding the consumption of potato chips for U = 800 utils:
Given that Mabel wants to drink 16 bottles of orange soda (OS) per week, we need to find the corresponding consumption of potato chips (PC) that yields a utility of 800 utils. From the given utility function U = O^2 * PC, we can set up the equation as:
(16^2) * PC = 800
PC = 800 / 256
PC ≈ 3.125 bags (approximately)

3) Finding the consumption of potato chips for 20 bottles of orange soda:
Similar to the previous question, if Mabel drinks 20 bottles of orange soda (OS), we can use the utility function U = O^2 * PC to find the corresponding consumption of potato chips (PC) for a utility of 800 utils:
(20^2) * PC = 800
PC = 800 / 400
PC = 2 bags

4) Comparison of combinations and preference:
Comparing the two combinations, Mabel would prefer the bundle with 20 bottles of orange soda and 2 bags of potato chips. This is because it provides the same utility of 800 utils but requires fewer bags of potato chips compared to the bundle with 16 bottles of orange soda and 3.125 bags of potato chips. Mabel can achieve the same level of satisfaction with fewer potato chips in the former combination.

5) Preference between two bundles:
To determine Mabel's preference between two bundles, we need to compare the utilities they provide. Bundle A contains 1 bottle of orange soda and 2 bags of potato chips, while bundle B contains 2 bottles of orange soda and 1 bag of potato chips. We can calculate the utilities for both bundles using the given utility function U = O^2 * PC.

For bundle A:
U_A = (1^2) * 2 = 2

For bundle B:
U_B = (2^2) * 1 = 4

Since U_B (4 utils) is greater than U_A (2 utils), Mabel would prefer the bundle containing 2 bottles of orange soda and 1 bag of potato chips (bundle B) as it provides a higher level of utility.

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The bottleneck time is 18.18%. Therefore, option A is the correct answer.

In economics terms, the bottleneck is a chain of supply of resources that wants the most extended time in the supply chain operation for specific demand. It also evaluated to estimate the supply chain throughput.

Through put time = Sum of all times=1+2+3+4+5+6+7+8+9+10=55

Given,

Assembly line has 10 stations

Throughput time is 55

The formula for bottleneck time is:

Bottle neck time = Total stations/Throughput time ×100

= 10/55 ×100

= 18.18%

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

An assembly line has 10 stations with times of 1, 2, 3, 4,...,10, respectively. What is the bottleneck time?

a. 18.18% of the throughput time

b. 100% of the throughput time

c. 550% of the throughput time

d. 50% of the throughput time

e. 1.82% of the throughput time

Therefore, the range is 172 points and the interquartile range is 42 points. Therefore, the range without the outlier is 140 points and the interquartile range without the outlier is 40 points.

In statistics, the range is the difference between the largest and smallest values in a dataset. It is a measure of dispersion that indicates the spread of the data. The range provides a quick and simple way to get an idea of the variability of the data, but it can be affected by outliers and is therefore not always a reliable measure of dispersion. To calculate the range, you simply subtract the smallest value from the largest value in the dataset.

Here,

a. To find the range, we subtract the smallest value from the largest value:

Range = 193 - 21 = 172

To find the interquartile range, we first need to find the first and third quartiles.

Arrange the data in order from smallest to largest:

21, 53, 74, 82, 84, 103, 108, 116, 122, 193

Find the median (middle value) of the lower half of the data (Q1):

Q1 = median(21, 53, 74, 82, 84) = 74

Find the median (middle value) of the upper half of the data (Q3):

Q3 = median(103, 108, 116, 122, 193) = 116

Subtract Q1 from Q3 to get the interquartile range:

IQR = Q3 - Q1 = 116 - 74 = 42

b. To identify the outlier(s), we can use the rule that any value less than Q1 - 1.5 x IQR or greater than Q3 + 1.5 x IQR is considered an outlier.

Q1 - 1.5 x IQR = 74 - 1.5 x 42 = 11

Q3 + 1.5 x IQR = 116 + 1.5 x 42 = 181

The value 21 is less than the lower bound of 11, so it is an outlier.

To find the range and interquartile range without the outlier, we need to remove it from the data set:

74 82 84 122 193 53 103 108 116

The range without the outlier is:

193 - 53 = 140

To find the interquartile range without the outlier, we need to find the first and third quartiles of the new data set:

Q1 = median(53, 74, 82, 84, 108) = 82

Q3 = median(116, 122, 193) = 122

IQR = Q3 - Q1 = 122 - 82 = 40

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The ratio of the final surface charge density (ηf) to the initial surface charge density (ηi) is given by 3.68 * \(Q_i / (A_i \times A_i).\)

To understand the concept and solve this problem, we need to consider the relationship between surface charge density, area, and charge. Surface charge density (σ) is defined as the charge (Q) per unit area (A). Mathematically, we can express this relationship as σ = Q/A.

Let's assume the initial area of the irregular shape is \(A_i\), and the final area after each dimension is reduced is \(A_f\). Since each dimension (x and y) is reduced by a factor of 3.68, we can write the relationship between the initial and final areas as:

\(A_f = (1/3.68) \times A_i\)

Now, let's consider the relationship between charge and area. Since the charge remains constant for a given area, we can express it as \(Q_i = Q_f\), where \(Q_i\) is the initial charge and \(Q_f\) is the final charge.

Since the charge remains constant, the ratio of the surface charge densities can be expressed as:

ηf/ηi = \(\sigma _f/\sigma _i = Q_f/A_f / Q_i/A_i\)

Substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_f/A_f / Q_i/A_i = Q_f / (A_f * Q_i) * (A_i / Q_i)\)

Canceling out the \(Q_i\) terms, we get:

ηf/ηi = \(Q_f / (A_f * Q_i) * (A_i / Q_i) = Q_f / (A_f * A_i)\)

Since \(Q_i = Q_f\), we can simplify further:

ηf/ηi = \(Q_f / (A_f * A_i) = Q_i / (A_f * A_i)\)

Now, substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_i / (A_f * A_i) = Q_i / ((1/3.68) * A_i * A_i)\)

Simplifying, we find:

ηf/ηi = 3.68 x \(Q_i / (A_i \times A_i).\)

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Complete Question:

The irregularly shaped area of charge in the figure has surface charge density ηi. Each dimension (x and y) of the area is reduced by a factor of 3.68.

What is the ratio ηf/ηi where ηf is the final surface charge density?

Answer:

multiply bottom equation by 3

Step-by-step explanation:

That way, the -3y can be -9y and 9y and -9y can cancel.

Answer:

D. Multiply the bottom equation by 3

Step-by-step explanation:

A.

If you multiply the bottom equation by 7, then your equation will be:

7x+9y=8

14x-21y=7

Which will not get rid of y.

B.

If you multiply the top equation by 3, then your equation will be:

21x+27y=24

2x-3y=1

Which will not get rid of y.

C.

If you multiply the top equation by 2, then your equation will be:

14x+18y=16

2x-3y=1

Which will not get rid of y.

D.

If you multiply the bottom equation by 3, then your equation will be:

7x+9y=8

6x-9y=3

Which will get rid of y.

Answer:

A Clydesdale drinks 840 gallons of water in 28 days.

Step-by-step explanation:

120 gallons/4 days is 30 gallons every day. 30 gallons multiplied by 28 days is 840.

Answer: -7 degrees Celsius

Step-by-step explanation:

6 hours passed. -2.5 times 6 is -15. 8-15 = -7.

Answer: C (-7 degrees Celsius)

Step-by-step explanation: Since it was 8 degrees Celsius at 4 pm and every hour it decreased by 2.5 degrees Celsius every 1 hour until 10 pm,  we need to subtract 4 from 10 to get 6, then we multiply 6 by 2.5 and we get 15. If we subtract 15 degrees from 8, we get -7 degrees celsius. Hope this helps! :)

Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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Answer:

$4.79 per mug

Step-by-step explanation:

Divide $38.32 by 8

Answer:

7. To perform a t-test when the sample size is small, the sample must show no evidence of strong skewness and must contain no outliers.

Step-by-step explanation:

These are the two conditions required for performing a t test

- Sample Size: A small sample size can reduce the statistical power of a t-test, making it more challenging to detect significant differences between groups. Generally, a larger sample size is desirable to obtain more reliable and representative results.

- Skewness: Skewness refers to the asymmetry of the distribution of data. In a t-test, assuming normality of the data is important for accurate results. If the data exhibits strong skewness, the assumption of normality may be violated. In such cases, alternative non-parametric tests or transformations of the data may be more appropriate.

- Outliers: Outliers are extreme values that significantly differ from the rest of the data. They can have a disproportionate impact on the results of a t-test, particularly when the sample size is small. Outliers can distort the mean and affect the assumptions of normality and homogeneity of variance.

While the presence of skewness or outliers does not prohibit the use of a t-test with a small sample size, it is important to interpret the results with caution and consider alternative approaches if necessary. Robust statistical methods, such as non-parametric tests or bootstrapping, can be useful when dealing with non-normal or outlier-prone data, especially with small sample sizes. Additionally, visual inspection of the data distribution, such as through histograms or box plots, can help identify potential skewness or outliers.

By evaluating a linear equation, we can complete the table:

Number of visits   |  total cost

      2                            $132

      4                            $184

      5                            $210

      8                            $288

We know that her membership fee costs $80.00, and it allows her to get her hair done for $26.00 for each visit, so if she does x visits, then the total cost for these x visits (including the membership fee) is:

c(x) = $80.00 + $26.00*x

So we have a linear equation that models the total cost.

Evaluating the equation in the values of the table we will get the other values.

c(2) = $80 + $26*2 = $132

c(4) = $80 + $26*4 = $184

c(5) = $80 + $26*5 = $210

c(8) = $80 + $26*8 = $288

Then the complete table is:

Number of visits   |  total cost

      2                            $132

      4                            $184

      5                            $210

      8                            $288

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Answer:

x=5.5

Step-by-step explanation:

cos60=x/11

11cos60=x

x=5.5

Answer:

x=50 SO EASY

Step-by-step explanation:

Answer:

x = 50

Step-by-step explanation:

Multiply both sides by the inverse of 1/5.

The inverse just changes the denominator and numerator.

So, 1/5 changes to 5/1.

Now multiply it on both sides:

\((\frac{5}{1}) \frac{1}{5}x = 10 (\frac{5}{1})\\x = 50\)

Therefore, the answer to your question is x = 50.

Check:

\(\frac{1}{5} (50) = 10\\\\\frac{50}{5} = 10\\\\10 = 10\)

Hope this helps!!

- Kay :)

Answer:

true 8 is the common

please follow me so I will follow you

Answer:

False

Step-by-step explanation:

Premise: 8n-1 = 2n+8

6n-1 = 8

6n = 9

n = 1.5 Since n must be an integer, this is an extraneous solution. The premise is false.

We fail to reject the null hypothesis that the temperature level has no effect on the mean yield process.

Summary of Result:

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

To construct an analysis of variance (ANOVA) table and test whether the temperature level has an effect on the mean yield process, we need to perform the following steps:

Step 1: Calculate the total sum of squares (SST), the treatment sum of squares (SSTR), and the error sum of squares (SSE).

SST = ΣΣ(yij - ȳ)^2 = 359.2

where yij is the yield of the ith batch at the jth temperature level and ȳ is the overall mean yield.

SSTR = Σ(nj(ȳj - ȳ)^2) = 118.2

where nj is the number of batches produced at the jth temperature level, ȳj is the mean yield at the jth temperature level, and ȳ is the overall mean yield.

SSE = SST - SSTR = 241.0

Step 2: Calculate the degrees of freedom (df) for SST, SSTR, and SSE.

df(Total) = N - 1 = 14

where N is the total number of observations.

df(Treatment) = k - 1 = 2

where k is the number of treatment levels.

df(Error) = df(Total) - df(Treatment) = 12

Step 3: Calculate the mean square (MS) for SSTR and SSE.

MS(Treatment) = SSTR / df(Treatment) = 59.1

MS(Error) = SSE / df(Error) = 20.1

Step 4: Calculate the F-statistic.

F = MS(Treatment) / MS(Error) = 2.94

Step 5: Determine the critical value of F for a 0.05 level of significance with df(Treatment) = 2 and df(Error) = 12.

From a table of F-distributions, the critical value of F is 3.89.

Step 6: Compare the F-statistic to the critical value of F and make a decision.

Since 2.94 < 3.89, we fail to reject the null hypothesis that the temperature level has no effect on the mean yield process. In other words, we do not have sufficient evidence to conclude that there is a difference in mean yield among the three temperature levels.

Step 7: Summarize the results in an ANOVA table.

Source | SS | df | MS | F | p-value

Treatment | 118.2 | 2 | 59.1 | 2.94 | 0.095

Error | 241.0 | 12 | 20.1 | |

Total | 359.2 | 14 | | |

Note: The p-value is calculated as P(F > 2.94) = 0.095, which is greater than the significance level of 0.05. Therefore, we do not reject the null hypothesis.

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The correct answer is: P = MR.

None of the choices are universally true for a monopoly. Let's go through each statement:

P = MR: This statement is true for a monopoly. A monopolist has the power to set the price of its product, and since it is the sole seller in the market, the demand curve it faces is the market demand curve. Therefore, the marginal revenue (MR) generated by selling an additional unit of output is equal to the price (P) it charges.

Profits are always positive: This statement is not true for a monopoly. While a monopoly can generate positive profits in many cases, it is not a guarantee. Profits depend on various factors such as the monopolist's cost structure, demand conditions, and pricing decisions.

P > MC: This statement is not necessarily true for a monopoly. In a perfectly competitive market, the equilibrium condition is P = MC, where price (P) equals marginal cost (MC). However, in a monopoly, the monopolist will produce where marginal revenue (MR) equals marginal cost (MC) to maximize its profits. This means that P will generally be greater than MC, but the specific relationship between P and MC depends on the demand and cost conditions in the market.

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Answer:

to my beliefs it is 18. I THINKKKKK I LIKE ALELI THINKS ITS 18

5 and 4

3 and 6

hope this helps!

Answer:

x = -12

Step-by-step explanation:

Let x be the number.

The product of 5 and x increased by 9 is equal to 15 less than 3 times x.

5x + 9 = 3x - 15.

We can isolate x, getting (5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

The required number is -12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The product of five and a number, increased by 9 is equal to fifteen less than three times then number.

Let x be the number.

Establishing the equation,

5x + 9 = 3x - 15.

(5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

Hence, the number is -12

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Answer:

the probability of drawing a green marble is 4/25 (16% or 0.16)

Step-by-step explanation:

Total: 16+8+9+12+5= 50

# of green marbles: 8

Event G, such that a green marble is drawn:

P(G)= 8/50

= 4/25 (16% or 0.16)

Answer:

165⁰ I hope this helped :)

Answer:

There were 62 people on the train to begin with.

Step-by-step explanation:

Firstly,i I subtracted 21 with 18 so i got 3.

It means that the train got 3 more people from the start.

Then i subtracted 65 with 3.

And so i got 62.

Answer:

4.33

Step-by-step explanation:

check picture attached for solution

Answer:

103.5

Step-by-step explanation:

90-76.5=13.5

90+13.5= 103.5

Answer:

14

Step-by-step explanation:

319 / 11 = 29

(Quick Check) 11 x 29 = 319

----------------------------------------------

So..

406 / 29 = 14

(Quick Check) 14 x 29

I hope I helped.

Answer:

216

Step-by-step explanation:

72= 36 +36

36(3)+36(3)=216

I'm honestly not sure ,tell me if it's wrong :/

Answer:

90000

Step-by-step explanation:

The volume of the satellite is,

⇒ V = 12π m³

Given that;

A satellite is in the shape of a cylinder with two hemispheres fitted snugly on either end.

And, The diameter of the cylinder is 2 m and its length is 12 m.

Now, We know that;

Volume of cylinder = πr²h

Hence, We get;

The volume of the satellite is,

⇒ V = π × (2/2)² × 12

⇒ V = 12π m³

Thus, The volume of the satellite is,

⇒ V = 12π m³

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Answer:

2

Step-by-step explanation:

one apple and another equals to 2.

Answer: 11

Step-by-step explanation: you put one and one together lol