Answer:
2
hope this helps :)
The formula currently used for calculating the correlation coefficient wasdeveloped by ____.a.Galton b.Thorndike c.Cattell d.Binet e.Pearson
The formula currently used for calculating the correlation coefficient was developed by e. Pearson.
Sir Karl Pearson, a British mathematician and statistician, introduced the formula for the Pearson correlation coefficient in the early 20th century. The Pearson correlation coefficient, also known as the Pearson's r, is a measure of the strength and direction of the linear relationship between two variables. The coefficient ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 implies no correlation.
Pearson's correlation coefficient formula has been widely adopted in various fields, such as psychology, finance, and biology, to determine the extent of the relationship between two sets of data. This valuable statistical tool has paved the way for further development and understanding of correlations and their significance in research and data analysis. So therefore the correct answer is e. Pearson is the developer formula currently used for calculating the correlation coefficient.
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What was the name of the first oil well in the UAE?
A.Murban
B.ADNOC
C.Murhabba
D.OLPEC
Answer:
B.ADNOCExplanation:
the Abu Dhabi Petroleum Company
The first commercially viable oil discovery was made at Bab in 1960. In 1962, the company was renamed the Abu Dhabi Petroleum Company. Exports began to flow from the Jebel Dhanna terminal on December 14, 1963.
Answer:
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the temperature of a 2.0 kg block increases by 5 degrees celsius when 2000j of thermal energy are added to the block. what is the specific heat of the block?
Specific heat is quantity of heat required to increase the temperature of a substance by one degree celsius.
The formula to calculate heat energy is
Q=mc∆T
How to calculate specific heat capacity using heat energy formula?We know, Q=mc∆T
Where Q = heat energy
m = mass
c= specific heat capacity
∆T= change in temperature
Thus,
According to above formula
c= Q/m∆T
Here m= 2 kg
∆T= 5 degrees
Q= 2000 joules
c= 2000/2×5
c= 200
Thus, the specific heat capacity of the block is 200.
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You are pushing a box toward your friend with a force of 15 N, and your friend is pushing the box toward you with a force of 30 N. What is the net force? What direction will the box move (toward you or toward your friend)?
Answer:
A. Net force is 15 N.
B. The answer is given below.
Explanation:
The following data were obtained from the question:
Force applied by you (Fᵧ) = 15 N
Force applied by your friend (Fբ) = 30 NForce applied by you (Fᵧ) = 15 N
Force applied by your friend (Fբ) = 30 N
Net force (Fₙ) =?
A. Determination of the net force.
Force applied by you (Fᵧ) = 15 N
Force applied by your friend (Fբ) = 30 N
Net force (Fₙ) =?
Fₙ = Fբ – Fᵧ
Fₙ = 30 – 15
Fₙ = 15 N
Thus, the net force acting on the box is 15 N.
B. From the question given above, we can conclude that the box will move towards you because the force applied by your friend is greater than yours.
if someone feels intent on fighting with you, what should you do to prevent getting into a fight?
Answer:
avoid verbal argument and walk away
how much does a change in mass affect the kinetic energy of two balls of comparable diameter?
Answer:
Mass and kinetic energy have a positive relationship, which means that as mass increases, kinetic energy increases, if all other factors are held constant.
In this state, Kinetic energy is equal to half of the product mass and velocity. SI unit is joules. So it's if the mass is doubled then the kinetic energy also gets doubled.
An echo is a reflection of sound against another surface. Suppose you are standing on one side of a canyon and you
yodeled. Suppose the temperature is 20°C and the canyon is 750 m wide, how long does it take for you to hear the echo
of your yodel?
Answer:
10-1 Temperature and Expansion. 135 ... text, the laboratory work that you do, or your physics teacher. ... Assume that the speed of sound in air is 340 m/s. How.
Explanation:
hope that helps
In a physics lab, you apply a 34.5 N rightward
force to a 4.52 kg cart to accelerate it across a
horizontal surface at a rate of 1.28 m/s/s.
Determine the friction force acting upon the cart
and coefficient of friction.
Answer:
Explanation:
The frictional force is
=
28.71
N
Explanation:
Let
F
r
=
frictional force
and
F
=
the force applied
The net force acting on the object is
(
F
−
F
r
)
By Newton's second Law
(
F
−
F
r
)
=
m
a
where,
a
=
the acceleration
and
m
=
mass of the cart
So,
F
−
F
r
=
m
a
F
r
=
F
−
m
a
=
34.5
−
4.52
⋅
1.28
=
28.71
N
in simple harmonic motion, when is the speed the greatest? (there could be more than one correct choice.) question 2 options: when the magnitude of the acceleration is a maximum when the displacement is a maximum when the magnitude of the acceleration is a minimum when the potential energy is a maximum when the potential energy is a zero
The correct choice is "when the displacement is a zero". In simple harmonic motion, the speed is greatest when the displacement is zero, i.e., at the equilibrium position.
In simple harmonic motion, the speed of an oscillating object is the greatest when the displacement is zero, and the magnitude of the acceleration is zero. This occurs when the object passes through its equilibrium position.
At this point, the potential energy is at its minimum and the kinetic energy is at its maximum. As the object moves away from the equilibrium position, the potential energy increases while the kinetic energy decreases, resulting in a decrease in speed.
As the object approaches the maximum displacement, the potential energy is at its maximum while the kinetic energy is at its minimum, resulting in a decrease in speed. Therefore, the speed is greatest when the object passes through its equilibrium position.
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What is the difference between abiotic and biotic factors?
Answer:
Abiotic referfers to non-living and biotic factors are living or once living
Explanation:
A student conduct an activity using concave mirror with focal length 10 cm. He placed an object 15 cm from the mirror. Where is the image likely to be formed
When a student conducts an activity using a concave mirror with a focal length of 10 cm and places an object 15 cm away from the mirror, the image is likely to be formed behind the mirror at a distance of -30 cm.
When a student conducts an activity using a concave mirror with a focal length of 10 cm and places an object 15 cm away from the mirror, the image is likely to be formed behind the mirror. The distance of the image from the mirror is calculated using the mirror equation, which states that 1/f = 1/u + 1/v, where f is the focal length, u is the distance of the object from the mirror, and v is the distance of the image from the mirror. Substituting the values given in the question, we get 1/10 = 1/15 + 1/v. Solving this equation gives us v = -30 cm. The negative sign indicates that the image is formed behind the mirror, which is expected since the mirror is concave. The magnification of the image can be calculated using the formula m = -v/u, which gives us m = -30/15 = -2. This means that the image is inverted and its size is twice that of the object. The image is inverted and its size is twice that of the object.
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A certain Diesel engine performs 372 of work in each cycel wth an efficieny of 33.0 percent.How much energy is transferred from the engine to the exhaust and cooling system as heat
Answer:
122.76J
Explanation:
Given data
work done= 372 Joules
efficiency= 33%
Required
We want to compute the value of the work that is 33%
= 33/100* 372
= 0.33*372
= 122.76J
Hence 122.76J of work is transferred from the engine to the exhaust
Why should you choose why should you choose wire with a thinner insulation?
Answer:
Because of the given stranded wires is that it's thinner there are even more air gaps and a greater surface area in the individual stranded wires then therefore it carries less current than similar solid wires can with each type of wire , insulations technologies can greatly assist in reducing power dissipation.
Un diapasón vibra a 140 [Hz] y la onda emitida por él se propaga con una rapidez de 340 m/s.Considerando lo anterior, se puede afirmar correctamente que la longitud de onda de la onda emitida por el diapasón es
The question is: A tuning fork vibrates at 140 [Hz] and the wave emitted by it propagates with a speed of 340 m / s. Considering the above, it can be correctly stated that the wavelength of the wave emitted by the tuning fork is
Answer: Wavelength of the wave emitted by the tuning fork is 2.43 m.
Explanation:
Given: Frequency = 140 Hz
Speed = 340 m/s
wavelength = ?
Formula used to calculate the wavelength is as follows.
\(\lambda = \frac{v}{f}\)
where,
\(\lambda\) = wavelength
v = speed
f = frequency
Substitute the values into above formula.
\(\lambda = \frac{v}{f}\\= \frac{340 m/s}{140 Hz} (1 Hz = 1 s^{-1})\\= 2.43 m\)
Thus, we can conclude that wavelength of the wave emitted by the tuning fork is 2.43 m.
During the 4.0 min a 5.0 A current is set up in a wire, how many
(a) coulombs and
(b) electrons pass through any cross section across the wire’s width?
a) The amount of Coulombs that passed through any cross-section across the wire's width would be 1200 coulombs.
b) The number of electrons that passed through any cross-section across the wire's width would be7.5 × \(10^{21\) electrons.
Current and charges(a) Coulombs can be calculated using the formula:
Q = I × t
where Q is the charge in coulombs, I is the current in amperes, and t is the time in seconds.
Converting the time to seconds, we have:
t = 4.0 min × 60 s/min = 240 s
Substituting the given values, we get:
Q = 5.0 A × 240 s = 1200 C
Therefore, 1200 coulombs of charge pass through any cross-section across the wire's width during the 4.0 min.
(b) The number of electrons can be calculated using the formula:
n = Q / e
where n is the number of electrons, Q is the charge in coulombs, and e is the elementary charge, which is approximately 1.6 × 10^-19 C.
Substituting the given value of Q, we get:
n = 1200 C / (1.6 × 10^-19 C) ≈ 7.5 × \(10^{21\)
Therefore, approximately 7.5 × \(10^{21\) electrons pass through any cross-section across the wire's width during the 4.0 min.
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I will give you more points if you want!!! :)
But first please answer the following question!
Answer:
thank you very much for giving me points.
Explanation:
I really appreciate it so muchhhhh so muchhhh thanks again
an organic compound was analyzed and found to contain 70.6% carbon, 5.9% hydrogen, and 23.5% oxygen by mass. additionally, the molar mass of the compound was experimentally determined to be 136 g/mole. what is the molecular formula for the compound? how many grams of mgcl 2 would be required to prepare 250 ml of a 0.8 m solution of that solute in water? please report your answer to two digits after the decimal place.
This substance's chemical formula is C₈H₈O₂ and To create the 0.8 M solution, 19.04 g of MgCl₂ must be dissolved in 250 mL of water.
How is a molecular formula composed?The chemical formula for a chemical compound's molecular formula lists the variety of atoms that make up the molecule.
Briefing:Assuming we have 100 g of the molecule, the masses of its constituent parts are as follows in order to get its molecular formula:
-70.6 g of carbon
-5.9 g of hydrogen
-23.5 g of oxygen
We next divide these masses by the molar masses of the constituent components to obtain the moles:
-carbon: 70.6 g / 12 g/mol = 5.88 mol
-hydrogen: 5.9 g / 1 g/mol = 5.9 mol
-oxygen: 23.5 g / 16 g/mol = 1.47 mol
To get the molar ratio, divide the moles by the least number (1.47 mol for oxygen):
-carbon: 5.88 mol / 1.47 mol = 4
-hydrogen: 5.9 mol / 1.47 mol = 4
-oxygen: 1.47 mol / 1.47 mol = 1
As a result, we have the empirical formula:
This empirical formula's molar mass is
4 x 12 g/mol + 4 x 1 g/mol + 16 g/mol = 68 g/mol
In order to arrive at our final result, we divide the molar mass of our compound by the molar mass of the empirical formula.
136 g/mol / 68 g/mol = 2
We multiply the index numbers by 2 to get the molecular formula C₈H₈O₂.
The following equation is used to determine how much MgCl2 is required to make a 0.8 M solution of it in 250 mL (0.250 L):
c = n/V ⇒ n = c * V
c - molarity of the solution (0.8 M)
n - number of moles of solute
V - the volume of the solution
Now we plug in the values we have:
n = 0.8 M * 0.250 L
n = 0.2 mol
Now, we can determine the mass of the solute using the molar mass of MgCl2 (M = 95.211 g/mol):
n = m/M ⇒ m = n * M
m - the mass of the substance
m = 0.2 mol * 95.211 g/mol
m = 19.04 g
Therefore, 19.04 g of MgCl2 are required to create a 0.8 M solution in 250 mL.
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why doesn't the repulsive electric force of protons in the atomic nucleus cause the protons to fly apart?
The strong nuclear force overcomes the repulsive electric force of protons in the atomic nucleus because it is a much stronger force. It is able to act over very short distances and is mediated by particles that are much heavier than electrons and photons.
The repulsive electric force of protons in the atomic nucleus does not cause the protons to fly apart because of the strong nuclear force. The strong nuclear force is an attractive force between nucleons that overcomes the repulsion between protons due to the electromagnetic force. This force is responsible for holding the nucleus of an atom together.
We will explain the physics behind why the strong nuclear force overcomes the repulsive electric force. The protons in the nucleus are positively charged and would normally repel each other due to the electrostatic force. The reason why they do not is because they are held together by a stronger force, the strong nuclear force. This force acts between nucleons, which are particles found in the nucleus of an atom. The strong nuclear force is a short-range force that acts over distances of less than a femtometer. It is much stronger than the electrostatic force, which is why it is able to hold the nucleus together. The reason for this is that the strong nuclear force is mediated by particles called mesons, which are much heavier than electrons and photons. The strong force is able to overcome the repulsion between protons because it is much stronger than the electromagnetic force, which is what causes the repulsion in the first place.
The strong nuclear force overcomes the repulsive electric force of protons in the atomic nucleus because it is a much stronger force. It is able to act over very short distances and is mediated by particles that are much heavier than electrons and photons. This force is responsible for holding the nucleus of an atom together and is what allows for the existence of matter as we know it.
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What is the main reason that the gravitational attraction between Earth and the Moon changes each day?
(1) Earthâs axis is tilted at 23.5°.
(2) Earthâs rotational speed varies with the seasons.
(3) The Moon has an elliptical orbit.
(4) The Moon has a spherical shape.
The main reason that the gravitational attraction between Earth and the Moon changes each day.
Option b is correct.
what does the gravitational attraction between the Earth and the moon cause?Tides are the result of the gravitational tug from the Moon and Sun that the Earth feels. If we disregard the Sun for now, the Earth's oceans facing the Moon bulge up in response to the lunar gravitational force: a high tide.
Why is the gravitational attraction of the moon to Earth greater than the attraction of Earth to sun?Even though the sun is much more massive and therefore has stronger overall gravity than the moon, the moon is closer to the earth so that its gravitational gradient is stronger than that of the sun.
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A girl and a boy are riding on a merry-go-round that is turning at a constant rate. The girl is near the outer edge, and the boy is closer to the center. Who has greater angular displacement?
A. both the girl and the boy have zero angular displacement
B. both the girl and the boy have the same non zero displacement
C. the boy has greater
D. the girl has greater
Option B. is correct. Both the girl and the boy have the same non-zero displacement.
Angular displacement is the angle covered by an object moving along a circular path in a particular direction, usually measured in radians or degrees. It represents the change in the object's position relative to its starting point on the circle. For example, if an object moves along a circular path from an initial point at an angle of 30 degrees to a final point at an angle of 60 degrees, its angular displacement would be 30 degrees (i.e., the difference between the final and initial angles). The direction of the angular displacement is determined by the direction of rotation.
Angular displacement is the angle through which an object moves on a circular path, measured in radians. In this case, both the girl and the boy are riding on a merry-go-round that is turning at a constant rate, so they both have a non-zero angular displacement. Since they are both on the same merry-go-round, the magnitude of their angular displacement is the same. Therefore, option B is correct.
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What are combined vectors that go in one direction?
A. equal in magnitude
B. one-dimensional
C. two-dimensional
D. displacements
Answer:
One-dimensional
Explanation:
The 0.100-kg sphere in Fig. below is released from rest at the position shown in the sketch, with its center 0.400 m from the center of the 5.00-kg mass. Assume that the only forces on the 0.100-kg sphere are the gravitational forces exerted by the other two spheres and that the 5.00-kg and 10.0-kg spheres are held in place at their initial positions. What is the speed of the 0.100-kg sphere when it has moved 0.400 m to the left from its initial position? 10.0 kg 5.00 kg 0.100 kg 0.400 m 0.600 m
The speed of the 0.100-kg sphere when it has moved 0.400 m to the left from its initial position can be determined using the principle of conservation of energy. The speed is found to be approximately 0.894 m/s.
To find the speed of the 0.100-kg sphere, we can analyze the system's energy before and after the sphere has moved. Initially, the sphere is at rest, and its gravitational potential energy is given by U-initial = mgh, where m is the mass of the sphere, g is the acceleration due to gravity, and h is the height of the sphere above its lowest position. In this case, h = 0.600 m - 0.400 m = 0.200 m.
When the sphere moves 0.400 m to the left, it loses height and gains speed. At its new position, its gravitational potential energy is U-final = mgh', where h' is the new height above its lowest position. In this case, h' = 0.200 m - 0.400 m = -0.200 m (negative because the sphere has moved to the left).
According to the principle of conservation of energy, the initial potential energy must be equal to the final kinetic energy. Therefore, we have \(mgh = (1/2)mv^2\), where v is the final speed of the sphere. Solving for v, we get \(v = \sqrt{(2gh)}\)
Plugging in the values, where g is approximately \(9.8 m/s^2\), and h = 0.200 m, we find \(v = \sqrt{(2 \times 9.8 m/s^2 \times 0.200 m)} = 0.894 m/s\). Therefore, the speed of the 0.100-kg sphere when it has moved 0.400 m to the left is approximately 0.894 m/s.
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give reason
2- The wheel barrow is a liver.
Answer:
In a wheelbarrow, the load is in the middle. The fulcrum is at the end where the wheels touch the ground. The effort is applied at the other end where we hold the wheelbarrow. So, it is classified as a class 2 lever.
Explanation:
Btw, you spelled liver, not lever. Anyway, hope this helped you! The answer is underlined.
what can be respresented by a force arrow weight or mass
Answer:
Force arrows are used to represent both the magnitude and direction of forces. The length of the arrow corresponds to the magnitude of the force, with longer arrows indicating forces with larger magnitudes. The direction of the arrow corresponds to the actual direction that the force is being exerted. Force arrows are used by scientists and engineers to predict the motion of an object based on the forces that are applied to it.
Let's go back to Amil and his box for a moment. To represent the force that he is exerting on the box, we can draw the box and then show the force using a force arrow, like this:
Explanation:
How would our force arrow change if he pushed the box with twice as much force? Because the magnitude of the force is doubled, the length of the force arrow should also be doubled.
Now, what if he didn't push directly to the right, but instead his arms made a 30-degree angle with the ground? In that case, the direction of the force arrow needs to change to show the direction in which the force is applied.
identify the type of plate boundary along the path that you created for question 1, then define the type of fault that you would expect to occur and the type of forces involved (compression, tension, shear). justify your choices in 1-4 clearly worded sentences.
It appears that the plate boundary is a transform boundary. This is because the path appears to cut across the boundary between two tectonic plates. As for the type of fault that can be expected to occur, it would most likely be a strike-slip fault, given the horizontal movement observed along the path.
The forces involved in this type of fault are mainly shear forces, which cause the rocks on either side of the fault to slide past each other in opposite directions. This is consistent with the observed movement along the path, where one side appears to be moving toward the north while the other is moving toward the south.
In summary, the observed path suggests a transform boundary with a strike-slip fault and predominantly shear forces.
Different types of plate boundaries, faults, and forces.
There are three main types of plate boundaries: convergent, divergent, and transform. Convergent boundaries occur when two plates move towards each other, resulting in compression forces. Divergent boundaries involve plates moving away from each other, creating tension forces. Lastly, transform boundaries have plates sliding past each other, leading to shear forces.
The type of fault associated with each boundary is as follows: convergent boundaries typically produce reverse or thrust faults; divergent boundaries create normal faults; and transform boundaries result in strike-slip faults.
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Rock X is released from rest at the top of a cliff is on earth. A short time later, Rock y is released from rest from the same point as rock X. Both rocks fall for several seconds before landing on the ground directly below the cliff. Frictional forces are considered to be negligible. Which of the following graph correctly shows the vertical velocity of rock X as a function of time? Take the positive direction to the upward.
Answer:
The graph that correctly shows the vertical velocity is B. since the velocity is negative and increases linearly over time
Explanation:
When an object is dropped from rest its movement is ruled only by the effect of gravity.
The acceleration of gravity \(g=9.8\ m/s^2\) makes the object gain speed with a linear relation as shown:
vf = g.t
If we take the positive direction to be upward, then the speed will always be negative since the object will go against the positive direction.
Thus, the graph that correctly shows the vertical velocity is B. since the velocity is negative and increases linearly over time
From the given graphs, only the second graph (option B) started from rest (0) and later increased with time.
The given parameters;
Rock XRock yinitial velocity of Rock X = 0The final vertical velocity of the rock X after a short time "t" is calculated as follows;
\(v_y_f = v_y_i + gt\\\\v_y_f = 0 + 9.8t\)
The vertical velocity of the rock x will increase with time as it moves downwards.
Therefore, we can conclude that, from the given graphs, only the second graph (option B) started from rest (0) and later increased with time.
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A student places two horseshoe magnets next to each other, and the poles of the magnets attach to each other. How does the kinetic energy of the system change?
The kinetic energy of the system does not change.
When two horseshoe magnets are placed next to each other, then they either attract or repel each other, depending on the position of their poles. if the poles are opposite they attract, if they are same they repel with other.
In case, if the poles of two horseshoe magnets are attracted to each other, indicating poles are opposite to each other. when the magnets are brought together then the work must be done to oppose the magnetic field between poles. This increases the potential energy of the system.
However, the question is about the kinetic energy of the system, which is related to the motion of the objects in the system. In this case, once the magnets are brought together they attract each other, they will have zero potential. Therefore, the kinetic energy will not change.
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What is the current in a 120V circuit if the resistance is 20Ω?
We have: \(I=\frac{U}{R}=\frac{120}{20}=6A\)
ok done. Thank to me :>
Answer:
The Current is 6 Ampere.
Step-by-step explanation:
Given :
\(\small\red\bull\) Voltage = 120V\(\small\red\bull\) Resistance = 20ΩTo Find :
\(\small\red\bull\) CurrentUsing Formula :
\( \star{\small{\underline{\boxed{\sf{ I = \dfrac{V}{R}}}}}}\)
\(\small\blue\star\) I = Current\(\small\blue\star\) V = Voltage\(\small\blue\star\) R = ResistanceSolution :
Substituting all the given values in the formula to find Current :
\({\dashrightarrow{\pmb{\sf{ I = \dfrac{V}{R}}}}}\)
\({\dashrightarrow{\sf{ Current = \dfrac{Voltage}{Resistance}}}}\)
\({\dashrightarrow{\sf{ Current = \dfrac{120}{20}}}}\)
\({\dashrightarrow{\sf{ Current = \cancel{\dfrac{120}{20}}}}}\)
\({\dashrightarrow{\sf{ Current = 6A}}}\)
\({\star{\underline{\boxed{\sf{\red{ Current = 6A}}}}}}\)
Hence, the Current is 6 Ampere.
\(\rule{300}{1.5}\)
A concrete parking garage has a 6-in concrete slab at each level. The 6-in slab weighs 75 psf (NOTE : psf =lb/ft∧2). If the columns are placed on a rectangular grid with 25−ft spacing in the long direction and 20 - t spacing in the short direction. What is the concentrated reaction to the column due to the weight of the slab on a single level? Assume all framing is simply supported, with a regular spacing, and equal reactions at each end . ( 25 Points) 37,500lb 30.000lb 225,000fo 46675lb
The concentrated reaction to the column due to the weight of the slab on a single level is 37,500 lb.
To calculate the concentrated reaction to the column, we need to determine the total weight of the slab on a single level.
Given that the weight of the 6-inch concrete slab is 75 psf (pounds per square foot), we first convert it to pounds per square inch (psi) by dividing by 144 (since 1 square foot is equal to 144 square inches).
Weight of slab per unit area = 75 psf / 144 = 0.5208 psi
Next, we calculate the area of the slab on a single level by multiplying the spacing in the long direction (25 ft) by the spacing in the short direction (20 ft).
Area of slab = 25 ft * 20 ft = 500 sq. ft
Finally, we multiply the weight per unit area by the area of the slab to find the total weight of the slab on a single level.
Total weight of slab = 0.5208 psi * 500 sq. ft = 260.4 lb
Therefore, the concentrated reaction to the column due to the weight of the slab on a single level is 37,500 lb.
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A physicist needs to estimate the density of a cube (all sides of the cube have equal length). Density (in kg/m3) can be found by D= M/L^3
where M is the mass of the object (in kg) and L is the length of a side of the cube (in meters). Assume the mass M~(um = 1.0, om = 0.022) (i.e. 1.0=0.02) and assume the length L~.(u = 0.1, 02 = 0.0052) (i.e. 0.1+0.005). Assume M and L are independent. (a) Approximate ud. (b) Approximate od. (c) Write the estimate of the density, along with the estimated error, in engineering (i.e. =) notation. Be sure to state the units.
ud = 0.511kg
od = 0.0525m
density = 4396.77 kg/m^3
(a) The approximate value of the mass, ud, is (1.0+0.022)/2 = 0.511 kg.
(b) The approximate value of the length, od, is (0.1+0.005)/2 = 0.0525 m.
(c) The estimated density can be calculated using the formula D = M/L^3.
D = 0.511/(0.0525)^3 = 4396.77 kg/m^3.
To calculate the estimated error, we can use the formula for the propagation of errors, which states that the error in a function of two independent variables is the square root of the sum of the squares of the individual errors. In this case, the error in the density is given by:
error = sqrt((dD/dM * error in M)^2 + (dD/dL * error in L)^2)
where dD/dM = 1/L^3, dD/dL = -3M/L^4, error in M = (0.022-1.0)/2 = 0.489 kg, and error in L = (0.0052-0.1)/2 = 0.0474 m.
Substituting the values, we get:
error = sqrt((1/(0.0525)^3 * 0.489)^2 + (-3*0.511/(0.0525)^4 * 0.0474)^2) = 256.88 kg/m^3.
Therefore, the estimated density with the error in engineering notation is:
D = 4400 +/- 260 kg/m^3.
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