"Imagine, you are solving a classification problems with highly imbalanced classes. The majority class is observed 90% of times in the training data. Which of the following is/are true in such a case? 1. Accuracy score is a good performance netric because it accounts for both positive and negative cases. 2. Precision and recall cannot be good performance metric because when one is high, the other will be low and vice versa.
3. fi score is a better performance metrix than accuracy although it is usually lower than accuracy score. A. Only 1 is true B. Only 2 is true C. Only 3 is true D. 1 and 2 are true E. 2 and 3 are true "
Answers
Precision and recall cannot be good performance metrics. fi score is a better performance metric.
The correct answer is: E. 2 and 3 are true.
In a classification problem with highly imbalanced classes where the majority class is observed 90% of the time, the correct statement(s) among the given options is/are:
1. Accuracy score is not a good performance metric in this case because it can be misleading due to the imbalance. A high accuracy might simply mean that the model is good at predicting the majority class but not necessarily good at predicting the minority class.
2. Precision and recall can be useful performance metrics in imbalanced classification problems. High precision means that there are fewer false positives, while high recall means there are fewer false negatives. In imbalanced problems, it is often important to balance these two metrics to find the best trade-off for the specific problem.
3. F1 score is a better performance metric than accuracy in imbalanced classification problems because it considers both precision and recall. It might be lower than the accuracy score, but it provides a more balanced view of the model's performance in both positive and negative cases.
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Related Questions
The team needs to choose a primary view for the part drawing. Three team members make suggestions:
- Team member 1 suggests an orthographic top view because that is how the plans for the part were submitted.
- Team member 2 suggests an isometric view showing side details that were documented within the submitted plans.
- Team member 3 suggests all three orthogonal views should be presented as the primary view.
What is the best way to proceed?
Answer choices below:
Answers
Answer:
Option 1
Explanation:
As the team has already submitted the plans for the part drawing, the best way to proceed would be how it was given in the plans. Hence, the option to be selected :
Team member 1 suggests an orthographic top view because that is how the plans for the part were submitted.Answer:
The first option
Explanation:
Team member 1 suggests an orthographic top view because that is how the plans for the part were submitted.
Tiny hydrogen bubbles are being used as tracers to visualize a flow. All the bubbles are generated at the origin (x = 0, y = 0). The velocity is unsteady and obeys the equations: u = 1 m/s v = 2 m/s 0 ≤ t < 2 s u = 0 m/s v = −1 m/s 2 s ≤ t ≤ 4 s Plot the pathlines of bubbles that leave the origin at t = 0, 1, 2, 3, and 4 s. Mark the locations of these five bubbles at t = 4 s. Use a dashed line to indicate the position of a streakline at t = 4 s
Answers
Answer:
for t = 1 : ( x1 , y1 ) = (1,2)
for t = 2 : ( x2, y2 ) = (2,4)
for t = 3 : ( x3, y3 ) = ( 0,-3)
for t = 4 : ( x4, y4 ) = ( 0,-4)
Explanation:
Attached below is the detailed solution and the sketch
we have to make assumptions for the various values of t and integrate accordingly
for t = 1 : ( x1 , y1 ) = (1,2)
for t = 2 : ( x2, y2 ) = (2,4)
for t = 3 : ( x3, y3 ) = ( 0,-3)
for t = 4 : ( x4, y4 ) = ( 0,-4)
Given data :
origin ( x = 0, y = 0 )
u = 1 m/s, v = 2 m/s,
\(0 \leq t < 2s\) where u = 0 m/s v = -1 m/s
Which of the following is the amount of torque a clutch can transmit before it starts to slip?A) Clutch capacityB) Clamp loadC) Clamp forceD) all above
Answers
Answer:
A. Clutch capacity
Explanation:
Hope this helps! :)
Happy Valentine's Day!
Brainliest, Please!
Weight, density, electrical conductivity, and coefficient of thermal expansion are examples of _______ properties.
Answers
Answer:
"Physical" would be the right approach.
Explanation:
Those properties would be that can be established without even any alteration throughout the identification of that same object. Property (whenever color, compressive strength, vapor pressure) of substance which does not require a biochemical alteration including its representation.So the answer here is just the perfect one.
Two blocks are joined by an inextensible cable as shown, if the system is released from rest, determine the velocity of block A after it has moved 4 m. Assume that the coefficient of friction between block A and the plane equal to 0.3 and the pulley is weightless and frictionless
Answers
To determine the velocity of block A after it has moved 4 m, we can use the principles of Newton's laws of motion and energy conservation. Here are the moves toward tackle the issue:
1. First, draw a free-body diagram for each block. Block A experiences weight (mg) downward, tension (T) upward, and friction (f) opposing its motion. Block B experiences weight (2mg) downward and tension (T) upward.
2. Apply Newton's second law of motion to both blocks. For Block A, we have the equation:
T - f = ma (Equation 1)
For Block B, we have:
2mg - T = 2ma (Equation 2)
3. The erosion power can be determined as:
f = μN
N = mg (normal force)
Therefore, f = μmg, where μ is the coefficient of friction.
4. Use the constraint equation due to the inextensible cable:
s = rθ
where s is the distance traveled by block A, r is the radius of the pulley (unknown), and θ is the angle in radians subtended by the arc on the pulley.
5. Apply conservation of energy:
The change in potential energy is equal to the change in kinetic energy for block A.
mgh = (1/2)mv^2
Solving for v, we get:
v = √(2gh)
6. Use the given information that block A has moved 4 m to determine the angle θ and the radius r using the constraint equation.
7. Substitute the values of μ, m, g, and h into the equation for v to calculate the velocity of block A after it has moved 4 m.
By following these steps, you can find the velocity of block A after it has moved 4 m. Remember to double-check your calculations and units to ensure accurate results.
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A picture showing the actual parts of a circuit and their connection is called_______ diagram
Answers
Answer:
a picture showing the actual parts of a circuit and their connection is call a Circuit diagram
.4- The wood structure panel roof diaphragm of a warehouse one-story building is shown in plan view. The calculated roof diaphragm shear capacity is 450 lb/ft in the east-west direction. The roof diaphragm is adequately anchored to the shear wall. a) Calculate the unit shear along the south shear walls b) Calculate the unit shear along the north shear wall c) Calculate the unit shear along the diaphragm in the direction of analysis 40'
Answers
The unit shear along the south shear walls is 450 lb/ft.
What is the shear capacity along the south shear walls?The unit shear along the south shear walls of the warehouse one-story building is 450 lb/ft in the east-west direction. Unit shear refers to the shear force per unit length, in this case, per foot, acting on the shear walls. Shear walls play a crucial role in resisting lateral forces and maintaining the structural stability of a building.
In this context, the calculated unit shear of 450 lb/ft indicates the maximum shear force that each foot of the south shear walls can withstand without experiencing excessive deformation or failure. It is important to ensure that the shear walls are designed and constructed to withstand these shear forces adequately.
The adequate anchorage of the roof diaphragm to the shear wall is another important aspect mentioned in the question. Proper anchoring ensures a strong connection between the roof diaphragm and the shear wall, allowing the transfer of shear forces effectively and enhancing the overall structural performance.
By calculating the unit shear, engineers and designers can assess the capacity of the south shear walls to resist the applied forces and ensure the stability and safety of the warehouse building. This information is crucial for designing and evaluating the structural integrity of the building to meet the required safety standards and codes.
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How much does 1 gallon of water weigh in pound given that the density of water is 1gram/ cm3
Answers
Explanation:
There are 8.35 pounds in a gallon of water. Water weighs 1 gram per cubic centimeter or 1 000 kilogram per cubic meter, i.e. density of water is equal to 1 000 kg/m³; at 25°C (77°F or 298.15K) at standard atmospheric pressure.
4. What do these expressions evaluate to? 1. 3 == 3 3. 3 != 3 4. 3 >= 4 5. not (3<4) 5. Complete this truth table: p q r (not (p and q)) or r F F F ?
F F T ? F T F ?
F T T ?
T F F ? T T F ?
T T T ? )
Answers
The expressions evaluate to: 1. True, 2. False, 3. False, 4. False.
The truth table is as follows: (p, q, r) -> (False, False, False): False, (False, False, True): True, (False, True, False): False, (False, True, True): True, (True, False, False): False, (True, False, True): True, (True, True, False): True, (True, True, True): True.
1. The expression "3 == 3" compares if 3 is equal to 3, which is true. Therefore, the result is True.
2. The expression "3 != 3" compares if 3 is not equal to 3, which is false. Therefore, the result is False.
3. The expression "3 >= 4" compares if 3 is greater than or equal to 4, which is false. Therefore, the result is False.
4. The expression "not (3 < 4)" checks if 3 is not less than 4. Since 3 is indeed not less than 4, the expression evaluates to False.
5. The truth table shows the evaluation of the expression "(not (p and q)) or r" for different values of p, q, and r. The "not" operator negates the result of the expression inside it, and "or" returns True if at least one of the operands is True. The table reveals that the expression is True when r is True or when both p and q are True. In all other cases, it evaluates to False.
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In real world, sampling and quantization is performed in an analog to digital converter (ADC) and reconstruction is performed in a digital to analog converter (DAC). Which of the following statements hold true (fs denotes the sampling frequency)?
a. the reconstruction filter can be found in the DAQ
b. the antialiasing filter removes all frequencies of the continuous-time analog input signal that are above fs/2
c. the DAC needs to know the sampling frequency of the ADC to correctly reconstruct the signal.
d. the reconstructed continuous-time signal only contains frequencies up to fs/2
Answers
Answer:
b
Explanation:
a) ADC is located on DAQ filter but not the reconstruction filter
b) to remove aliasing, the sampling rate must be greater than or equal ot twice the highest frequency component in the input signal. In other words, all frequencies in input sgnal are less than fs/2. Therefore, frequencies greater than fs/2 are removed by anti-aliasing filter
c) the DAC can have different sampling rate from ADC
The sections of piping immediately upstream and downstream of a primary flow measuring device are known as
Answers
The sections of piping immediately upstream and downstream of a primary flow measuring device are known as the "straight run."
The straight run refers to the lengths of piping that are required to be present immediately upstream and downstream of a primary flow measuring device. These sections of piping are necessary to ensure that the flow profile is fully developed and unaffected by any disturbances caused by bends, fittings, or obstructions in the pipe. The straight run allows the fluid to flow smoothly and uniformly before entering or exiting the flow measuring device, ensuring accurate and reliable measurements.
By providing sufficient straight run lengths, the flow profile becomes stable, minimizing turbulence and disturbances that could impact the accuracy of the flow measurement.
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Consider the following algorithm, which takes as input a
sequence of n integers a1, a2, . . . , an and produces as output
a matrix M = {mij } where mij is the minimum term
in the sequence of integers ai, ai+1, . . . , aj for j ? i and
mij = 0 otherwise.
initialize M so that mij = ai if j ? i and mij = 0
otherwise
for i := 1 to n
for j := i + 1 to n
for k := i + 1 to j
mij := min(mij, ak)
return M= {mij } {mij is the minimum term of
ai, ai+1, . . . , aj }
a) Show that this algorithm uses O(n3) comparisons to
compute the matrix M.
b) Show that this algorithm uses !(n3) comparisons to
compute the matrix M. Using this fact and part (a),
conclude that the algorithms uses"(n3) comparisons.
[Hint: Only consider the cases where i ? n/4 and
j ? 3n/4 in the two outer loops in the algorithm.]
Answers
The number of comparisons made by the algorithm is O(n^3).
a) To analyze the number of comparisons made by the algorithm, let's count the comparisons made in the innermost loop.
In the innermost loop, for each k from i + 1 to j, a comparison is made to update the value of mij if ak is smaller than the current value of mij. Since j can go up to n and k can go up to j, the innermost loop will execute j - (i + 1) + 1 = j - i times.
The outer two loops iterate over i from 1 to n and j from i + 1 to n. The total number of comparisons made in the innermost loop is the sum of j - i for all valid i and j.
Let's calculate the total number of comparisons:
∑(i=1 to n) ∑(j=i+1 to n) (j - i)
Rearranging the terms:
∑(i=1 to n) ∑(j=i+1 to n) j - ∑(i=1 to n) ∑(j=i+1 to n) i
Simplifying the expressions:
∑(i=1 to n) ( ∑(j=i+1 to n) j - ∑(j=i+1 to n) i )
The inner summations can be computed using the formulas for the sum of arithmetic series:
∑(j=i+1 to n) j = (n - i)(n + i + 1)/2
∑(j=i+1 to n) i = (n - i)(i)
Plugging in these values:
∑(i=1 to n) ( (n - i)(n + i + 1)/2 - (n - i)(i) )
Expanding and simplifying:
∑(i=1 to n) ( (n^2 + 2ni + n - i^2 - ni - i)/2 - (ni - i^2) )
∑(i=1 to n) ( n^2 + 2ni + n - i^2 - ni - i - ni + i^2 )
∑(i=1 to n) ( n^2 + n )
(n^2 + n) * n
n^3 + n^2
Therefore, the number of comparisons made by the algorithm is O(n^3).
b) The expression "!(n^3)" is not a valid notation in complexity analysis. I assume it was meant to be "Ω(n^3)" which represents the lower bound.
Since the algorithm uses O(n^3) comparisons (as shown in part a), and Ω(n^3) represents the lower bound, we can conclude that the algorithm uses Θ(n^3) comparisons.
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A chemist mixed two substances together: a colorless liquid with a strong smell and a white solid with no smell. The substances' repeating groups of atoms are shown above on the left. After they were mixed, the chemist analyzed the results and found two substances. One ending substance had the repeating group of atoms shown above on the right. Is the ending substance the same substance as the colorless liquid? What happened to the atoms of the starting substances when the ending substances formed? Be sure to explain your answers to both of these questions.
Answers
Answer:
[a]. It is the same substance as the colorless liquid with a strong smell.
[b]. the substance with colorless liquid with a strong smell and a white solid with no smell are being used up to produce the ending substance had the repeating group of atoms shown above on the right and the other ending substance.
Explanation:
Atoms are referred to be the smallest units of a substance although it can be sub-divided into smaller units such as proton, neutron and electron. When atoms combines in group they form a molecule.
From the question above it is seen that two substances were mixed together to give two ending substances that is:
substance A [ colorless liquid with a strong smell] + substance B[white solid with no smell] ---------> substance C[ repeating group of atoms shown above on the right] + substance D.
The ending substance that is, substance C is the same substance as substance A which is the colorless liquid with a strong smell.
When the substance A reacted with substance B, it gives substance C and D that is the ending substances are the products of the reaction between A and B.
Hence, the substance with colorless liquid with a strong smell and a white solid with no smell are being used up to produce the ending substance had the repeating group of atoms shown above on the right and the other ending substance.
Two added to four times a number, minus 3 times the number, equals 5.
Answers
x= 3.
Explanation:What is presented in this problem is basically an equation in verbal form.
1. Write the equation.
\(2+4x-3x=5\)
2. Solve for x.\(2+4x-3x=5\\ \\2+x=5\\ \\x=5-2\\ \\x=3\)
3. Express the result.x= 3.
You are designing a hydraulic power takeoff for a garden tractor. The hydraulic pump will be directly connected to the motor and supply hydraulic fluid at 250 psi for use by accessories. In order for the tractor to maintain normal operation, the maximum power the hydraulic system can use is limited to 11 hp. For what maximum hydraulic flow rate in gallons per minute (gpm) should you design
Answers
Answer:
required flow rate is 75.44 gal/min
Explanation:
Given the data in the question;
Power developed = 250 psi = 1.724 × 10⁶ Pa
hydraulic power W = 11 hp = 11 × 746 = 8206 Watt
now, Applying the formula for pump power
W = pgQμ
where p is density of fluid, Q is flow rate, μ is heat and W is power developed;
W = pgQμ
W = pgμ × Q
W = P × Q -------- let this be equ 1
so we substitute in our values;
8.2027 kW = 1.724 × 10⁶ Pa × Q
Q = 8206 / 1.724 × 10⁶
Q = 4.75986 × 10⁻³ m³/sec
We know that, 1 cubic meter per seconds = 15850.3 US liquid gallon per minute, so
Q = 4.75986 × 10⁻³ × 15850.3 gallon/min
Q = 75.44 gal/min
Therefore, required flow rate is 75.44 gal/min
an employee is having trouble with a current project and needs help.
Answers
Answer:
What ! you are an Engineer and I am a High school why are You in my feed..!!
Which business application uses passive (no power source) electronic tags and labels to identify objects wirelessly over short distances (up to 20 feet)?
a. Cellphone traffic monitoring
b. Global positioning systems
c. Location-based services
d. K-Band Satellite Internet Service
e. Radio-frequency identification
Answers
The business application that uses passive (no power source) electronic tags and labels to identify objects wirelessly over short distances (up to 20 feet) is radio-frequency identification (RFID).
RFID (radio-frequency identification) is a system that employs passive (no power source) electronic tags and labels to identify objects wirelessly over short distances (up to 20 feet).
The tags contain data that is transmitted by a reader that is also called a radio-frequency identification interrogator or transceiver.
An RFID tag is placed on the object to be identified, and when it comes into range of the reader, the reader sends a signal that activates the tag.
After that, the tag responds by transmitting the data encoded in its memory.
This data can include identification, status, location, and other information related to the object.
A conclusion may be that the radio-frequency identification (RFID) is an advanced technology that has been developed to improve the accuracy and efficiency of data collection and management.
It can be used in a variety of business applications, such as inventory management, supply chain management, and asset tracking.
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what improvement project stage have dr. gonsalvez and her team just completed?
Answers
but without any specific information about Dr. Gonsalvez, her team, or the nature of the improvement project, I cannot determine which stage they have just completed.
Improvement projects can have various stages depending on the methodology or framework being followed, such as DMAIC (Define, Measure, Analyze, Improve, Control) in Six Sigma or PDCA (Plan, Do, Check, Act) in continuous improvement. Each stage represents a specific phase of the project. If you provide more details or context, I might be able to assist you further. improvement project stage have dr. gonsalvez and her team just completed.
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the purpose of a diaphragm in a vane type fuel pump is to:___
Answers
And blank is a person who acts as an agent between two different groups, often result in conference
Answers
Answer:
mediator
Explanation:
A "mediator" has an important role of bridging the communication between parties/groups. He acts as a facilitator in order to hasten the process of making decisions or coming up with conflict resolutions in a timely manner. He does this by setting a schedule for the parties to meet–often resulting to a conference. This will allow each side of the party to voice out their opinion regarding a common concern. Such process is deemed to be a "cost-effective" way of handling matters/issues.
What is a Home Run terminology that is used in Electrical Wiring?
Answers
Answer:
Any circuit that goes directly from the fixture to the breaker panel. For dedicated outlets, isolated fixtures and high-load items, you would want them to be on their own breakers. Those would get a home run, a line that goes all the way back without stopping.
main circuit wiring is represented in a schematic by
A.the abbreviation mcw
B. A red line
C. A darker line
D.thicker line
Answers
Answer: a thicker line
Explanation:
In the construction of a timber-framed house, select and justify three timber based
materials used for the build.
Please help desperate
Brainiest-maybe
Answers
Timber frame construction uses timber studs and rails, together with a structural sheathing board, to form a structural frame that transmits all vertical and horizontal loads to the foundations.
Water is pumped steadily through a 0.10-m diameter pipe from one closed pressurized tank to another tank. The pump adds 4.0 kW of energy to the water and the head loss of the flow is 10 m. Determine the velocity of the water leaving the pump and discharging into tank B.
Answers
Complete Question
Complete Question is attached below.
Answer:
\(V'=5m/s\)
Explanation:
From the question we are told that:
Diameter \(d=0.10m\)
Power \(P=4.0kW\)
Head loss \(\mu=10m\)
\(\frac{P_1}{\rho g}+\frac{V_1^2}{2g}+Z_1+H_m=\frac{P_2}{\rho g}+\frac{V_2^2}{2g}+Z_2+\mu\)
\(\frac{300*10^3}{\rho g}+35+Hm=\frac{500*10^3}{\rho g}+15+10\)
\(H_m=(\frac{200*10^3}{1000*9.8}-10)\)
\(H_m=10.39m\)
Generally the equation for Power is mathematically given by
\(P=\rho gQH_m\)
Therefore
\(Q=\frac{P}{\rho g H_m}\)
\(Q=\frac{4*10^4}{1000*9.81*10.9}\)
\(Q=0.03935m^3/sec\)
Since
\(Q=AV'\)
Where
\(A=\pi r^2\\A=3.142 (0.05)^2\)
\(A=7.85*10^{-3}\)
Therefore
\(V'=\frac{0.03935m^3/sec}{7.85*10^{-3}}\)
\(V'=5m/s\)
True or False? although inductive current lags inductive voltage by 90°, both waves have the same frequency.
Answers
The answer to the question: "True or False? although inductive current lags inductive voltage by 90°, both waves have the same frequency."
True, although inductive current lags inductive voltage by 90°, both waves have the same frequency.
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Which of the following is iterative? *
Science
Engineering
Criteria
Infrastructure
Answers
How does critical reflection relate to Heuristics and
Engineered/Design solution
Answers
Critical reflection enhances the evaluation and improvement of heuristics and engineered/design solutions by identifying their effectiveness, biases, and areas for enhancement.
What is Critical reflection in relation to heuristics and engineered/design solutions?Critical reflection relates to heuristics and engineered/design solutions by providing a means to evaluate and improve upon them. Through critical reflection, one can assess the effectiveness and limitations of heuristics, which are mental shortcuts used for problem-solving, and engineered/design solutions, which are deliberate and planned problem-solving approaches.
It allows for a deeper understanding of their impact, potential biases, and areas for improvement, ultimately guiding the refinement and development of more effective problem-solving strategies.
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1. Calculate the surface deflection under the centre of a tyre (a = 152 mm, p = 552 kPa) for a 305 mm pavement having a 345 MPa modulus and subgrade modulus of 69 MPa from two-layer theory. Also calculate the interface deflection and the deflection that takes place within the pavement layer.
Answers
To calculate the surface deflection under the center of a tire, we can use the two-layer theory which considers the pavement layer and the subgrade layer. The formula for the surface deflection is given by:
δ = (P/a) * (1-v) * (h1/((E1/((1-v1^2) + (E2/((1-v2^2))))))
Where,
P = tire pressure = 552 kPa
a = contact area of the tire = 152 mm
v = Poisson's ratio
h1 = thickness of the pavement layer = 305 mm
E1 = modulus of elasticity of the pavement layer = 345 MPa
v1 = Poisson's ratio of the pavement layer
E2 = modulus of elasticity of the subgrade layer = 69 MPa
v2 = Poisson's ratio of the subgrade layer
Substituting the given values in the above formula, we get:
δ = (552/152) * (1-0.25) * (305/((345/((1-0.25^2) + (69/((1-0.3^2))))))
δ = 3.029 mm
The interface deflection can be calculated as:
δi = (P/a) * ((h2 * (E1/((1-v1^2) + (E2/((1-v2^2))))))
Where,
h2 = thickness of the subgrade layer
Substituting the given values in the above formula, we get:
δi = (552/152) * ((0.0 * (345/((1-0.25^2) + (69/((1-0.3^2))))))
δi = 0 mm
As there is no thickness of subgrade layer given, the interface deflection is zero.
The deflection that takes place within the pavement layer can be calculated as the difference between the surface deflection and the interface deflection:
δp = δ - δi
δp = 3.029 - 0
δp = 3.029 mm
Therefore, the surface deflection under the center of a tire is 3.029 mm, the interface deflection is 0 mm, and the deflection that takes place within the pavement layer is 3.029 mm.
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\(\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}\)
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A doctor is deciding how to treat a given disease. the doctor will precribe one medication, one dietary change, and one type of vitamin supplement. there are five medications, five dietary changes, and five types of vitamins the doctor might prescribe. how many combina-tions are possible?
Answers
The total combinations are possible is 125 combinations.
We need to know about math combinations to solve this problem. The combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed. It can be written as
nCr = n! / (r!(n-r)!)
where n is object and r is a sample
From the question above, we know that
1 vitamin supplement chosen has combination
5C1 = 5! / 1!(5-1)! = 5 combination
1 meditation chosen has combination
5C1 = 5! / 1!(5-1)! = 5 combination
and 1 dietary chosen has combination
5C1 = 5! / 1!(5-1)! = 5 combination
Hence, the total combination is
C = Cvitamin x Cmeditation x Cdietery
C = 5 x 5 x 5
C = 125 combinations
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Write 3 important things learned about oxyfuel cutting and welding system.
Answers
Answer:
see and make me brainlist
Explanation:
What is oxy fuel cutting used for?
Oxy-fuel cutting is used for the cutting of mild steel. Only metals whose oxides have a lower melting point than the base metal itself can be cut with this process. Otherwise as soon as the metal oxidises it terminates the oxidation by forming a protective crust.