a 504 g mass oscillates with an amplitude of 12.0 cm on a spring whose spring constant is 20.0 n/m .

Answers

Answer 1

The period of oscillation is approximately 0.998 seconds.

Steps

We can use the following formula to find the period of oscillation:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

Substituting the given values, we get:

T = 2π√(0.504 kg / 20.0 N/m)

T = 2π√(0.0252 kg/m)

T = 2π * 0.1589 s

T = 0.998 s (rounded to three significant figures)

Therefore, the period of oscillation is approximately 0.998 seconds.

The force needed to stretch or compress a spring by a specific amount is known as the spring constant (k), which serves as a gauge for a spring's stiffness. In the SI system, the spring constant is measured in Newtons per meter (N/m).

For example, if a spring requires a force of 10 N to stretch it by 0.5 meters, then the spring constant is:

k = F/x = 10 N / 0.5 m = 20 N/m

In many computations involving elastic systems, such as the oscillation of a mass on a spring or the compression of a spring in a mechanical system, the spring constant, a crucial spring parameter, is taken into account.

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Related Questions

how much force is needed to accelerate a box of mass 25kg at 4 m/s2
a)60n
b)50n
c)15n
d)100n​

Answers

Answer:

D

Explanation:

Force (N) = mass (kg) × acceleration (m/s²) is the famous F=ma

Force = 25 * 4 in this case

Force = 100 N

Temperature changes can affect substances in different ways. Which of these actions will form a new substance with different properties?


melting ice into water


freezing juice into ice pops


baking cake batter to make a cake


heating chocolate chips to form a syrup

Answers

Answer:

a

Explanation:

A 15 kg box is pushed with a force of 35 N in the +x direction, and the box accelerates to the right. It does not accelerate up or down

Answers

The box accelerates to the right due to the applied force of 35 N in the +x direction.

Newton's second law states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the net force acting on the box is 35 N in the +x direction, and its mass is 15 kg. Therefore, we can calculate the acceleration using the formula:

acceleration = net force / mass

acceleration = 35 N / 15 kg = 2.33 m/s² (rounded to two decimal places)

Since the box is not accelerating up or down, we can conclude that the force applied is only causing the box to accelerate in the horizontal direction.

Other forces such as gravity and friction are not considered in this scenario. Thus, the 15 kg box will experience an acceleration of approximately 2.33 m/s² in the +x direction due to the applied force of 35 N.

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A pipe of constant radius carried water at 3.25 m/s. Please answer in PA.

A pipe of constant radius carried water at 3.25 m/s. Please answer in PA.

Answers

Pipe of constant radius, we can use Bernoulli's equation, which relates the pressure, velocity, and height of a fluid at two points in a flow system.the pressure of water in the pipe is approximately 105,142 Pa.

What is a system?

System refers to a collection of related components or parts that work together to achieve a specific goal or purpose. The concept of a system can be applied to a wide range of fields and disciplines, including science, engineering, economics, and social sciences.

In science, a system is often defined as a portion of the universe that is being studied or analyzed. This can include anything from a single atom or molecule to an entire ecosystem or planet. By defining the boundaries of a system, scientists can focus their attention on understanding the interactions and relationships between the various components within that system.

In engineering, a system refers to a collection of components that are designed to work together to perform a specific function or task. This can include everything from simple mechanical systems like gears and pulleys to complex electrical or computer systems.

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A flat puck (mass M) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m) through a central hole in the table as shown in the figure. Start by showing the free-body diagrams and force equations for each mass, and then derive an equation for the tangential speed of the puck. This will be an algebraic expression that includes the variables mentioned above.

Answers

The dangling mass will not move and the puck will keep rotating in its orbit, Therefore, V = √(mgR/M)  will be an algebraic expression that includes the variables mentioned above.

What  is centripetal force?

A centripetal force that causes a body to travel along a curved path. The centripetal force always acts orthogonally to the motion of the body and towards the fixed point of the path's instantaneous centre of curvature. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". Gravity is the centripetal force that causes astronomical orbits, according to Newtonian mechanics theory.

A common example of centripetal force is when a body moves at a constant speed along a circular path. The centripetal force is directed at right angles to the motion as well as along the radius of the circular path towards the centre.

Fc = mg

Now, centripetal force on the puck is equal to the mass of the puck times the centripetal acceleration, or

Fc = Mac

centripetal acceleration is related to the tangential velocity of the puck as

ac = V²/R

where R is the radius of the orbit. Then we have

Fc = M ac =M ω² R = M V² / R

and, thus

M V² / R = mg

and, solving for V, we get

V = √(mgR/M)

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A toy truck of mass 3 kg and speed, v, approaching a ramp of height 5 m. If the toy truck makes it to the top of the ramp, what is the value of v? (Hint: Law of conservation of energy)

Answers

Given,

A toy truck of mass 3 kg and speed, v, approaching a ramp of height 5 m. If the toy truck makes it to the top of the ramp.

To find: what is the value of v?

Solution:

In the bottom of the ramp, potential energy will be zero because there will be no height.

And the kinematic energy will be maximum.

According to the conservation of energy.

At the top of the ramp, the speed will be maximum. So the kinetic energy will be equal to the potential energy.

Hence.

\(\begin{gathered} \frac{1}{2}mv^2=mgh \\ \frac{1}{2}mv^2=0 \\ v=0\text{ m/s} \\ \end{gathered}\)

Thus, the value of v is 0 m/s.

A ball is suspended from two cords as illustrated belowA) determine the magnitude of the tension in the angled cordB) what is the magnitude of the tension in the vertical cord attached to the ballC) calculate the mass of ball

A ball is suspended from two cords as illustrated belowA) determine the magnitude of the tension in the

Answers

a)

Since the ball is in equilibrium, the sum of horizontal forces are equal zero.

We can decompose the tension in the angled cord in horizontal and vertical components, and then calculate the sum of horizontal forces in the diagram:

\(\begin{gathered} T_{2x}=T_2\cdot\cos (57\degree) \\ T_{2x}=T_2\cdot0.545 \\ \\ T=T_{2x} \\ 250=T_2\cdot0.545 \\ T_2=\frac{250}{0.545} \\ T_2=458.7\text{ N} \end{gathered}\)

So the tension in the angled cord is 458.7 N

b)

To find the tension in the vertical cord, we can find the vertical component of the tension in the angled cord, since these two forces are equal because the ball is at equilibrium:

\(\begin{gathered} T_{2y}=T_2\cdot\sin (57\degree) \\ T_{2y}=458.7\cdot0.839 \\ T_{2y}=384.85\text{ N} \\ \\ W=T_{2y} \\ W=384.85\text{ N} \end{gathered}\)

So the tension in the vertical cord is 384.85 N

c)

To calculate the mass of the ball, let's use the weight formula:

\(\begin{gathered} W=m\cdot g \\ 384.85=m\cdot9.8 \\ m=\frac{384.85}{9.8} \\ m=39.27\text{ kg} \end{gathered}\)

So the mass of the ball is 39.27 kg

A ball is suspended from two cords as illustrated belowA) determine the magnitude of the tension in the

Select the correct arrows. Identify the arrows that show the correct direction of heat transfer.

Select the correct arrows. Identify the arrows that show the correct direction of heat transfer.

Answers

Answer:

Explanation:I Did the test and it said this was the right answer so it probally is

Select the correct arrows. Identify the arrows that show the correct direction of heat transfer.

Answer:

That's the question that I wanted to ask!!

Explanation:

I’ll give brainliest

Ill give brainliest

Answers

The waveform of a signal is the shape of its graph as a function of time in the domains of electronics, acoustics, and allied sciences, regardless of its time and magnitude scales or any shift in time.  

Thus, Waveforms with periodic variations are those that recur consistently at set intervals.

The phrase is typically used in electronics to describe periodically changing voltages, currents, or electromagnetic fields. It is typically used in acoustics to describe constant periodic sounds caused by changes in air pressure or other media.

In these situations, the signal's frequency, amplitude, or phase shift have no bearing on the waveform, which is a characteristic. Additionally, non-periodic signals like chirps and pulses can be referred to by this name.

Thus, The waveform of a signal is the shape of its graph as a function of time in the domains of electronics, acoustics, and allied sciences, regardless of its time and magnitude scales or any shift in time.  

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A block m1 rests on a frictionless surface. A second block m2 sits on top of the first block. Here m1 = m2 = m. A horizontal force F is applied to the bottom block to pull it to the right as shown below. Assume that the blocks move together across the surface (block m2 does not slide off of block m1).

Answers

A block resting on a frictionless surface experiences a horizontal force that pulls another block atop it to the right, where the two blocks travel in tandem without slamming.

How much static friction is there between the upper and bottom blocks?

Response and justification The higher block's acceleration is also equal to 3 m/s2 because there is no relative motion between the upper and lower blocks.

What is the static friction coefficient between block A and a flat floor?

Block A and a level floor have a static friction coefficient of 0.45, while Block B has a static friction coefficient of 0.30. Each brick weighs 2.0 kg.

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How a Motor Works
Figure 5
A motor is made of several basic parts, each of which
is described below. Study the information about each part. Then,
write the number of each description in the appropriate circle on
the image.

How a Motor WorksFigure 5A motor is made of several basic parts, each of whichis described below. Study

Answers

Answer:

hi \( \) \( \)

A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm,find the emf of the cell.​

Answers

A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm, the electromotive force (emf) of the cell is approximately 14.5 volts.

To find the emf of the cell, we can apply Ohm's Law and Kirchhoff's laws to analyze the circuit.

Given:

Resistance of the coil, R1 = 4 ohm

Resistance of the other resistor, R2 = 8 ohm

Current passing through the 8-ohm resistor, I = 2A

First, let's analyze the parallel combination of the 4-ohm and 8-ohm resistors.

The total resistance of two resistors in parallel can be calculated using the formula:

1/Rp = 1/R1 + 1/R2

Substituting the given values, we have:

1/Rp = 1/4 + 1/8

1/Rp = 2/8 + 1/8

1/Rp = 3/8

Rp = 8/3 ohm

Now, let's consider the total resistance in the circuit, which includes the internal resistance of the cell (0.5 ohm) and the parallel combination of the resistors (8/3 ohm).

R_total = R_internal + Rp

R_total = 0.5 + 8/3

R_total = 1.833 ohm

Now, we can find the emf of the cell using Ohm's Law:

emf = I * R_total

emf = 2 * 1.833

emf ≈ 3.667 volts

Therefore, the emf of the cell is approximately 3.667 volts.

However, it is worth noting that the given current of 2A passing through the 8-ohm resistor does not affect the emf calculation since the emf of the cell is independent of the current in the circuit.

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Eustace drives 20.0 km to the east when he realizes he left his wallet at home. He drives 20.0 km west to his house, takes 5.0 min to find his wal- let, then leaves again. Eustace is 40.0 km east of his house exactly 60.0 min after he left the first time. a. What is his average velocity? b. What is his average speed?

Answers

a. His average velocity would be 1.11m/s2

b. His average speed would be 2.05m/s

What is Velocity?

Velocity of a particle is its speed and the direction in which it is moving.

It can also be described as the instantaneous rate of change of the particle's distance traveled, and the direction in which the distance is changing. The SI units of the speed is the metre per second squared (m/s2). It is a vector quantity, hence is has magnitude and direction.

What is Speed?

Speed is a scalar quantity which tells how fast an object is moving, regardless of its direction. The SI units of the speed is the metre per second (m/s). It is a scalar quantity and has only magnitude with no direction.

From the question;

Velocity = displacement/time

displacement = 40 km (4000m)

time = 60 mins (3600s)

Velocity = 4000/3600

Velocity = 1.11m/s2

Speed = total distance covered/total time

Speed = (40km + 20km + 20km) / (60mins + 5 mins)

Speed = (4000m + 2000m + 2000m) / (65mins)

Speed = (8000m/3900s)

Speed = 2.05m/s

Hence, his average velocity is 1.11m/s2 and speed 2.05m/s.

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Please HElp!!

Name five conductors and insulators

Answers

Answer:

Conductors- copper, aluminum, gold, and silver.

Insulators- glass, air, plastic, rubber, and wood.

Explanation:

Answer: 5 conductors are copper, aluminum, gold, iron, and silver and 5 insulators are glass, air, plastic, rubber, and wood.

5. A basketball is passed 15 m due West, then 20 m north. What is the total distance the
basketball travelled?

Answers

Answer:

35 meters

20+15=35

Calculate the absolute pressure at an ocean depth of 1.0 x 10³ m. Assume that the density of the water is 1.025 x 10³ kg/m³ and that Po = 1.01 x 10^5 Pa.

Answers

The absolute pressure at an ocean depth of 1.0 x 10^3 m is 1.002 x 10^8 Pa.

What is hydrostatic pressure?

Hydrostatic pressure is the pressure that a fluid exerts on a surface due to the weight of the fluid above it. It is the result of the force of gravity acting on a column of fluid, and it is directly proportional to the height of the column of fluid and the density of the fluid.

The absolute pressure at an ocean depth of 1.0 x 10^3 m can be calculated using the hydrostatic pressure equation:

P = ρgh + Po

where:

P is the absolute pressure at the given depth

ρ is the density of the water

g is the acceleration due to gravity (assumed to be 9.81 m/s²)

h is the depth of the ocean

Po is the atmospheric pressure at the surface (assumed to be 1.01 x 10^5 Pa)

Substituting the given values, we get:

P = (1.025 x 10^3 kg/m³) x (9.81 m/s²) x (1.0 x 10^3 m) + 1.01 x 10^5 Pa

P = 1.025 x 9.81 x 10^6 Pa + 1.01 x 10^5 Pa

P = 1.002 x 10^8 Pa.

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a 1000 kg car traveling at 70 m/s takes 3 m to stop under full braking. the same car under similar road conditions, traveling at 140 m/ s takes how long to stop under full braking?

Answers

Answer:

0.21 SECONDS

Explanation:

THE CAR TRAVELS AT A SPEED OF 140M/S AND A DISTANCE AS THE PREVIOUS = 3M THEREFOR S=D/T, T=D/S= 3/140= 0.12 SEC

What is the classification of the reaction shown in the equation below?
Fe + O2 → FeO2
A
decomposition
B
double replacement
C
single replacement
D
synthesis

Answers

Answer:

d

Explanation:

because is a reducing agent, O 2 is an oxidizing agent.

How the government can ensure basic human dignity is maintained in relation to safe and healthy living

Answers

To ensure basic human dignity in relation to safe and healthy living, governments can implement various measures such as accessible healthcare, adequate housing, and sanitation and clean water.

How government can ensure basic human dignity is maintained

Governments should place a high priority on ensuring that everyone has access to healthcare services, enabling them to receive the essential medical care without suffering financial difficulty. This entails providing access to necessary pharmaceuticals, cheap healthcare, and a strong healthcare system.

All citizens should have access to affordable and good housing, according to governments. Policies may include restrictions on rental costs, programs to expand the supply of affordable housing, and efforts to combat homelessness. Basic hygienic and safety criteria should be met by housing.

Governments must make sure that everyone has access to clean, safe drinking water and adequate sanitary facilities. The spread of diseases and the maintenance of sanitary living circumstances can be aided by investments in sewage systems, water treatment facilities, and public hygiene education.

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the greatest amount o. lolololoms?

the greatest amount o. lolololoms?

Answers

Answer:

If you are asking for the answer with the highest molar mass, then the answer is B.

B. Fe₂O₃

A basketball player jumps straight up for a ball. To do this he lowers his body 0.330m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.940m above the floor

Answers

a) Velocity of basketball player when he leaves the floor is 6.64 m/s ;  b) Acceleration while basketball player is straightening his legs is 73.8 m/s² ; c) Basketball player exerts a force of 8118 N on the floor to jump up for the ball.

What is meant by velocity and acceleration?

Acceleration is the rate of change of velocity, while velocity is the rate of change of displacement.

(a) m g h = (1/2)mv²

m is player's mass, g is acceleration due to gravity, h is initial height, v is velocity when the player leaves the floor.

(110 kg)(9.81 m/s²)(0.300 m) = (1/2)(110 kg)(v²) + (110 kg)(9.81 m/s²)(0.900 m)

v = 6.64 m/s

So, velocity of basketball player when he leaves the floor is 6.64 m/s.

(b) v² = u² + 2as

u is initial velocity (zero in this case), a is acceleration, s is distance traveled, and v is the final velocity (6.64 m/s in this case).

(6.64 m/s)² = 2a(0.300 m)

a = 73.8 m/s²

Therefore,  acceleration while the basketball player is straightening his legs is 73.8 m/s²

(c) F = ma

F : force, m is the player's mass, and a is the acceleration.

F = (110 kg)(73.8 m/s²)

F = 8118 N

Therefore, basketball player exerts a force of 8118 N on the floor to jump up for the ball.

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Note: The question given on the portal is incomplete. Here is the complete question.

Question: A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor. (a) Calculate his velocity when he leaves the floor. (b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m. (c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.

8) 1. Figure 2a shows the apparatus used to generate the shadow shown in Figure 2b. torch cardboard opaque object Figure 2a screen umbra scroch Figure 26 When the cardboard is removed, which of the statements about the new shadow is true? A. The shadow stays the same. B. The umbra gets bigger. C. The shadow is now called a penumbra. D. The shadow has two regions called an umbra and a penumbra.​

Answers

When the cardboard is removed, the shadow will have two regions called an umbra and a penumbra. Therefore, the correct answer is D.

What is the umbra and a penumbra?

The umbra is the darkest part of the shadow and is located right behind the object. It is the region where no direct light can reach because the object completely blocks the light source. In the umbra, the object appears completely black.

The penumbra, on the other hand, is a lighter region around the umbra where some of the light from the source is blocked but not all of it. The penumbra is the region where the object casts only partial shadow, and it is characterized by a gradual reduction in light intensity. The penumbra is not as dark as the umbra and is visible on both sides of the umbra.

So, to summarize, the umbra is the region of complete shadow where no direct light can reach, and the penumbra is the region where only partial shadow is cast and where the light intensity gradually reduces.

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A projectile is fired straight up with an initial velocity of 40.0 m/s . Approximately how high will the projectile ?

Answers

Answer:

it depends on the wind and any other conditions but if you have a controlled environment it should take 1 second to get 40 meters but it could go higher in which it could take about 5 seconds to go 200 meters

Explanation:

hope it helped

:)

what force cause centepetal acceleration of a car make a turn on a flat road

Answers

Answer: friction between the tires and the road.

Explanation: A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway.

please help ASAP! I will give brainiest
Highlight the either increasing or decreasing to complete the sentence to demonstrate the relationship between the variables and the reaction rate.
(Increasing/Decreasing) the temperature, increases the reaction rate. (Increasing/Decreasing) the surface area, increases the reaction rate. (Increasing/Decreasing) the concentration, increases the reaction rate.

Answers

Answer:

1. Increasing

2. Decreasing

3. Increasing

Explanation:

An object at rest is suddenly broken apart into two fragments by an explosion. The first fragment (with mass m1) acquires twice the kinetic energy of the second one (with mass m2).
What is the ratio of their masses?

Answers

Answer:

m1 ÷ m2 = 1 ÷ 2

Explanation:

The ratio of their masses is as follows:

As it is given that the mass m1 is twice of mass m2

So the equation could be written as

\(\frac{1}{2} m1 v1 v1 = 2 \times \frac{1}{2} m2 v2 v2\\\\\frac{m1}{m2} = \frac{2 v2 v2}{v1 v1} ..........(1)\)

Here we used the  conservation of momentum

Prior to the explosion, the object is in rest so the momentum would be zero but after the explosion the total momentum would be  m1v1 + m2v2,  that is also zero.

So,

\(m1 v1 + m2 v2 = 0\\\\m1 v1 = - m2 v2\\\\\frac{m1}{m2} = \frac{- v2}{v1}\)

Now squaring to the both sides

m1 m1 ÷ (m2 m2) = v2 v2 ÷ (v1 v1) ........(2 )

Solved both the equations

After solving it, the ratio is

m1 ÷ m2 = 1 ÷ 2

I NEED HELP Quick PLEASE AND THANK YOU !!!

I NEED HELP Quick PLEASE AND THANK YOU !!!

Answers

Well if u see here the graph is showing us 1.5 on the graph so we multiply that by 6 and we get 46 as our final anwser

1. Which distance is the greatest?
O 7000 meters
O 99.99 meters
O 4.5 x 10³ meters
O 9.0 x 10² meters

Answers

Answer:

7000 meters

Explanation:

obviously 99.99 is less than 7000

10 cubed is 10 × 10 × 10, 1000, × 4.5 is 4500, which is less than 7000

10 squared is 100, which × 9 is only 900, which is also less than 7000

have a good day

How have physicists played a role in history?
A. Physics has changed the course of the world.
B. History books are written by physicists.
C. Physicists have controlled most governments.
D. Most decisions about wars are made by physicists.

Answers

A. Physics has changed the course of the world.

Answer:

A. Physics has changed the course of the world.

Explanation:

How have physicists played a role in history?A. Physics has changed the course of the world.B. History

What are the four most important characteristics of an electric circuit?

Answers

Answer:

an energy source (AC or DC), a conductor (wire), an electrical load (device), and at least one controller (switch).

Explanation:

mark as brainliest please

The 4 most important characteristics of an electric circuit are discussed below.

We have a electric circuit.

We have to mention its 4 important characteristics.

What is an Electric circuit ?

Electrical circuit is a closed path which acts as a medium for the flow of current when there is a potential difference between two points in the path.

According to the question -

The important characteristics of electric circuit are -

It must contain at least one source of energy.It is a combination of both active and passive elements.It always exist in the form of closed loop for regular flow of current.The flow of electrons take place from negative terminal to positive terminal

Hence, the 4 most important characteristics of an electric circuit are mentioned above.

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Other Questions
fill in the blank. moral reasoning based on instrumental orientation tends to occur at the level of moral thinking Good films onThe concept of karma? C-Through, an optics manufacturing company, wants to focus on relationship marketing. in this case, which of the following strategies can be adopted by C-Through?a. It can market its products through dealers.b. It can set the price and other conditions of sale without negotiations.c. It can use accessory equipment and major equipment.d. It can use social networking sites to advertise itself to businesses. Which statement below correctly describes their relative atomic radii and first ionization energy when comparing Se and Br? The atomic radius for Se is larger than Br, and the first ionization energy for Se is greater than Br. The atomic radius for Br is larger than Se, and the first ionization energy for Bris greater than Se. The atomic radius for Se is larger than Br, and the first ionization energy for Br is greater than Se. The atomic radius for Br is larger than Se, and the first ionization energy for Se is greater than Br. Which of the following would be LEAST useful in correlating the ages of these two sequences of rocks?a. numeric ages on the volcanic rocks on topb. the pattern of magnetic reversals (R and N)c. the overall sequence of the upper three layersd. the type of material present in the landslide at the bottom of the right column which of the following is the best sample for a professional polling organization to poll on the governor's race in texas? A short sellerQuestion 30 options:1)anticipates that the price of the stock sold short will increase.2)earns the difference between what they initially paid for the stock versus what they later sell the stock for.3)makes a profit equal to the difference between the original sell price and the price paid for the stock, after subtracting any dividend payments made.4)is essentially lending the stock to another investor and will ultimately receive that stock back from that investor.5)none of the above according to the pre-1967 media stories, which of the following were the major dangers posed by the use of lysergic acid diethylamide (lsd)? Use Fermat's little theorem to compute the following expression.Identify the value of 3302 mod 385 using the results of previous part (a), (b), and (c) of this question and the Chinese remainder theorem.51179 If the 5 year treasuries are 2.5% and the bank's margin is 2.75%, what is the adjusted interest rate...?A. 0.25 (Percent %)B. 2.5 (Percent %)C. 5.25 (Percent %)D. 2.75 (Percent %) Consider the initial value problem y =[33????23????4]y +???? (????),y (1)=[20]. Suppose we know that y (????)=[2????+????2????2+????] is the unique solution to this initial value problem. Find ???? (????) and the constants ???? and ????. Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then XN(153, 14.5). z-score when x=108 is _____. The mean is 153. The z-score tell you that x=108 is _____ standard deviations to the left of the mean. Identify a true statement about how the growing power of the Republican Party in Texas has affected the executive branch of Texas government.A. It has weakened the executive branch because Republican candidates who are elected to statewide executive offices openly challenge long-serving Democrats holding other executive offices.B. It has weakened the executive branch by increasing differences in the plural executive because Republican candidates elected to executive offices tend to be moralistic conservatives who tend to turn off traditional and individualistic conservative voters.C. It has strengthened the executive branch by virtually eliminating divisions in the plural executive because Republican nominees who emerge from the primaries for statewide offices are mostly in agreement on what policies they want to pursue.D. It has strengthened the executive branch because Republican legislators are liberal conservatives who respect the Governor's authority and follow his or her agenda. How Brucella establishes infection within a hostArrange the following statements in chronological order:1) Infected macrophages can then traffic the bacteria to the lymph nodes and other sites within the body.2) The Brucella organism invades the GI tract by migrating through M cells.3) The Brucella organism is phagocytized by macrophages of the mucosa-associated lymphoid tissue.4) Once internalized, the organism survives within the phogolysosomes and establishes an intracellular existence.5) The Brucella organism enters the host through exposure of the skin and mucosa or by ingestion. describe one set of molecules and how they interact to clearly show the efficient organization of a synaptic terminal. keep it simple but not too simple. When a location evaluation includes both quantitative and qualitative inputs, a technique that can be used is: O A. linear programming B.consumer surveys O C. factor rating. OD. transportation models. E. center of gravity methods. When an agent has a fiduciary duty towards the principal it means that the agent must? Which oi the following statements best describes the mechanism by which the ced-9 protein in the nematode C . elegans prevents apoptosis in normal cells? Ced-9 remains inactive until it is stimulated by ced-3 and other caspases. Active ced-9 prevents activation of the caspase activity of cod-3. Cod. 9 inhibits the cell mombrane receptor for the death-signaling molecule. Ced.g is cleaved to produce the active cod-3 caspase. A sequence has the nth term rule T(n) = 32 - 3nWhat is the value of the first negative term in this sequence? Command substitution, the process of executing a subcommand within a larger command, can be performed using which of the following methods? A) ($cmd) B) $(cmd) C) (#cmd) D) #(cmd)