The angle between the vectors is 0.59 radians.
Calculationcos(ϕ)=[tex]\frac{u.v}{|u|.|v|}[/tex]
cos(ϕ)= [tex]\frac{4}{\sqrt{5}\sqrt{6}}[/tex]
ϕ= 43.09°
or 0.59 in radians
Angle between vectorsThe angle that is created at the intersection of two vector tails is called as the angle between the two vectors.
If the vectors are not joined tail-to-tail, we must shift one of the vectors using parallel shifting in order to join them from tail to tail.
Between Two Vectors AngleThe angle between the tails of two vectors defines the distance between them. Either the cross product or the dot product (scalar product) can be used to find it (vector product).
The angle between two vectors always ranges from 0° to 180°, as you should be aware of.
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What’s an example of potential energy? I WILL CROWN YOU PLS HELP
A
Water behind a dam
B
A dart stuck in a dartboard
C
Plants using photosynthesis
D
A cow chewing grass
A. Water behind a dam an example of potential energy
What are some illustrations of kinetic and potential energy?The energy an individual or an item has as a result of motion—in this case, the motion of the falling apple—is known as kinetic energy. Potential energy, which exists in a bike that is parked on top of a hill, is converted to kinetic energy when you start riding it downhill.
Kinetic energy may be observed in anything that moves around the house. This might happen when a glass breaks after falling off the counter, a fan circulates air on a warm day, or a cue ball rolls on a pool table. Kinetic energy is used by on-turning electrical equipment as well as by individuals moving around the house.
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he atmosphere exerts a pressure of 14.7 lbf/in.2 on top of the 6-in.-diameter piston. the absolute pressure of the air inside the cylinder is 16 lbf/in.2 the local acceleration of gravity is g
The absolute pressure of the air inside the cylinder is 16 lbf/in
1.3psig.
A straightforward idea is pressure—the measurement of force in a certain space.
There are several approaches of comprehending the strain, nevertheless, depending on the query.
Here are some tips for differentiating pressure measurement types and units when describing when and why such pressure measurements are employed.
Calculate the mass of the piston by applying the equilibrium condition.
∑F_y=0
p_(air)A_(piston)- p_(atm)A_(piston)-m_(piston)g=0
(p_(air)-p_(atm))A_(piston)-m_(piston)g=0
m_(piston)=(p_(air)-p_(atm))A_(piston)/g ______(1)
Calculate the area of the piston,
A_piston= πD^2/4
=π×D^2/4
=π×6^2/4
=28.274 in^2
By substituting the value in m_(piston)=(p_(air)-p_(atm))A_(piston)/g
=(16.14.7 lbf/in.^2)(28.274 in.^2)/32.2 ft/s^2(32.2 ft/s^2/1lbf)
=36.756 lbm
b)
Calculate the gage pressure if the air,
p_(gage) = p_(abs)-p_(atm)
p_(gage)=16-14.7
=1.3psig
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The brakes are applied to a moving vehicle, causing it to uniformly slow down. While slowing, it moves a distance of 40.0 m in 7.45 s to a final velocity of 1.50 m/s, at which point the brakes are released.
What was its initial speed (in m/s), just before the brakes were applied?
What was its acceleration (in m/s2) while the brakes were applied? (Assume the initial direction of motion is the positive direction. Indicate the direction with the sign of your answer.)
The acceleration is 1.03m/s^2 and initial velocity is 6.1735m/s
As it is given that motion is in positive direction and in one dimension, we will use the formulas of motion in one dimension
It is given to us that while slowing vehicle moves 40m
time taken to halt is 7.45s
final velocity is 1.5 m/s
We are required to find initial speed and acceleration
Using the equation v = u + at
v=1.5 , t = 7.45
1.5 = u + a x 7.45
u + 7.45a= 1.5
u =1.5 -7.45a
Now using the equation v^2 -u^2 =2aS
1.5 x 1.5 -u^2 = 2 x a x 40
2.25 - u^2 = 80a`
2.25- 80a = u^2
Now squaring for u in first equation and equation with second ,we get:
(1.5 -7.45 a)^2 = 2.25 -80a
2.25 + 55.50a^2 -22.35a =2.25 -80a
55.5a^2+57.65 a =0
a(55.5a +57.65)=0
a= 57.65 /55.5 =1.03 m/s^2
u = 1.5 - 7.45 x 1.03
=-6.1735 m/s
negative sign implies that initial speed is in opposite direction
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Select all of the following that are vector quantities.
A acceleration
B. force
C. mass
D. speed
E. velocity
F. volume
drivers must slow down from 60 to 40 mph to negotiate a severe curve on a rural highway. a warning sign for the curve is clearly visible for a distance of 200’. how far in advance of the curve must the sign be located in order to ensure that vehicles have sufficient distance to safely decelerate? use the standard reaction time and deceleration rate recommended by aashto for basic braking maneuvers.
The sign needs to be placed 292.07 feet in advance of the curve in order to provide cars enough room to safely slow down.
Prior to putting up a sign board to slow down traffic, we first calculate the distance.
d is the safe stopping distance, Si is the initial speed (60 mph), t is the time reaction (2.5 seconds), Sf is the end speed (40 mph), and G is the grade (0).
Therefore, we replace d = (1.47 60 2.5) + [(602 - 402) / 30(0.348 0) = 220.5 + (2000/10.44) = 220.5 + 191.57 = 412.07 ft Now that we know that a warning sign is clearly visible at a distance of 120 ft, the ideal safe distance will be d = minimum distance - sign visible distance d = 412.07 ft.
d = 412.07 - 120
d = 292.07 ft
In order to ensure that vehicles have enough room to safely slow down, the sign must be placed 292.07 feet ahead of the bend.
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timing of excessive ultraviolet radiation and melanoma: epidemiology does not support the existence of a critical period of high susceptibility to solar ultraviolet radiation-induced melanoma
The existence of a 'critical period' early in a life characterized by high susceptibility to melanoma initiation due to excessive ultraviolet (UV) radiation has been suggested by various authors based on epidemiological findings from migration studies and some case-control studies.
Objective To compare the increase in melanoma risk due to excessive UV radiation between different periods in life.
We found a very similar upward gradient of melanoma risk in exposure categories related to the frequency of sunburns during both periods in life. More than five sunburns doubled the melanoma risk, irrespective of their timing in life.
The hazardous impact of sunburns seems to persist lifelong and thus activities concerned with melanoma prevention should be directed to the entire population rather than being focused only on younger age groups.
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at the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/s2 . at the same instant a truck, traveling with a constant speed of 22.0 m/s , overtakes and passes the car.
The distance at which the car meets the truck after the traffic light turns green is at 302.5 m
We know that,
s = ut + 1/2 a[tex]t^{2}[/tex]
v = s / t
where,
s = Distance
u = Initial velocity
t = Time
a = Acceleration
Given that,
The car has with a constant acceleration of 3.2 m / [tex]s^{2}[/tex]
Initial velocity of car = 0
Velocity of truck = 22 m / s
After the traffic signal distance travelled by the car and truck are equal and time taken is also equal.
For the truck,
s = v * t
For the car,
s = ut + 1/2 a[tex]t^{2}[/tex]
vt = ut + 1/2 a[tex]t^{2}[/tex]
22 * t = 0 + 1/2 * 3.2 * [tex]t^{2}[/tex]
t = 13.75 s
s = v * t = 22 * 13.75
s = 302.5 m
Velocity is the distance travelled by an object with respect to time. It is denoted by V.
Therefore, the distance at which the car meets the truck after the traffic light turns green is at 302.5 m
The given question is incomplete. The complete question is
At the instant the traffic light turns green, a car that has been waiting at an intersection starts ahead with a constant acceleration of 3.20 m/[tex]s^{2}[/tex] . at the same instant a truck, traveling with a constant speed of 22.0 m/s , overtakes and passes the car. How far beyond the traffic signal will the car overtake the truck?
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One of the pieces of evidence supporting energy quantization was the line spectra of elements. Why does this demonstrate energy quantization?.
The line spectra supports the quantization of energy, because there are sharp emission lines demonstrating discrete energy levels.
What is emission of radiation by elements?When an element emits energy in the form of radiation, it produces a spectrum of colors on a photographic plate.
This spectrum can either be continuous or discrete.
In continuous spectrum the spectrum continues without any discrimination between two regions.
Also, the line spectrum consists of discrete and sharp lines, which shows the emission of radiation in a certain amount in a certain time, with a break between emission.
Thus, the line spectra supports the quantization of energy, because there are sharp emission lines demonstrating discrete energy levels.
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The end of the film includes interviews with several “elite” athletes. List at least 3 of the benefits of a vegan diet that these elite athletes say they’ve experienced.
Veganism is the practice of avoiding using animal products, especially in your diet, and an ideology that supports this practice that rejects treating animals as a commodity.
The end of the film includes interviews with several “elite” athletes. List at least 3 of the benefits of a vegan diet that these elite athletes say they’ve experienced.
A vegan is someone who adheres to the ideology or diet. Numerous health advantages of a vegan diet exist.
A vegan diet can be beneficial for those trying to lose weight. Consuming vegan food may also keep your heart healthy. Additionally, this diet might provide some defense against type 2 diabetes and some malignancies.
Vegan diets typically contain higher levels of fiber, antioxidants, and healthy plant chemicals. Additionally, they seem to contain higher amounts of potassium, magnesium, folate, and vitamins A, C, and E.
Since plant-based meals are bursting with phytochemicals, especially the potent antioxidants found in fruits and vegetables, eating vegan can help lower our risk for disease. Researchers discovered that compared to non-vegans, vegans had higher amounts of saturated fatty acids, a higher proportion of total omega-3 fatty acids, and antioxidant carotenoids, all of which are associated with better health.
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At your annual physical exam the nurse takes your blood pressure and records it as 130/110. why is the diastolic pressure a concern but systolic is not?
Heart attacks, heart failure, kidney disease, and overall mortality are all associated with systolic blood pressure. Aortic disease risk is increased by a high diastolic reading.
What is systolic blood pressure?Two figures are used to calculate blood pressure: the first, systolic blood pressure, represents the force exerted on your arteries as your heart beats.
The second number, or diastolic blood pressure, measures the pressure in your arteries between heartbeats.
Systolic blood pressure, the highest reading, gauges the force the heart applies to the artery walls with each beat. The bottom reading, or diastolic blood pressure, gauges the pressure the heart places on the artery walls between beats.
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a bicyclist traveled from 15.6 m/s to 21.1 m/s over a distance of 30 meters
a) what is the acceleration of the bicyclist?
b) How much time does it take the bicyclist to travel the 30 meters
The acceleration of the bicyclist is 3.35 m / s². It takes the bicyclist 1.64 s to travel the 30 meters
We know that,
a = ( v - u ) / t
s = ut + 1 / 2 at²
where,
a = Acceleration
v = Final velocity
u = Initial velocity
t = Time taken
s = Distance travelled
Given that,
u = 15.6 m / s
v = 21.1 m / s
s = 30 m
a = ( 21.1 - 15.6 ) / t = 5.5 / t
s = ut + 1 / 2 at²
30 = 15.6 t + 1 / 2 ( 5.5 t )
30 = 15.6 t + 2.75 t
t = 30 / 18.35
t = 1.64 s
a = 5.5 / t = 5.5 / 1.64
a = 3.35 m / s²
Equations of motion are used to describe the position of an object using the motion of the object with respect to time. It is done using speed, acceleration, distance and time.
Therefore,
a) The acceleration of the bicyclist is 3.35 m / s²
b) Time taken by the bicyclist =
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a 60kg person walks from the ground to the roof of a 80m tall building. what is the person's potential energy once they get to the top?
The potential energy is 47040 joules.
We need to know about potential energy to solve this problem. The potential energy is the object's energy caused by its position. Potential energy can be determined as
PE = m . g . h
where PE is potential energy, m is mass, g is the gravitational acceleration (9.8 m/s²) and h is height.
From the question above, we know that
m = 60 kg
h = 80 m
By substituting the given parameters, we can calculate the potential energy
PE = m . g . h
PE = 60 . 9.8 . 80
PE = 47040 joules
Hence, the potential energy is 47040 joules.
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What is efficiency of petrol engine of a train
a ball is thrown directly downward with an initial speed of 8.35 m/s from a height of 29.6 m. after what time interval does it strike the gro
A ball is thrown directly downward with an initial speed of 8.35 m/s from a height of 29.6 m is 2.59s
What is speed?Speed is the time rate at which an object is moving along the path, while the velocity is the rate and direction of an object’s movement. Put the another way, speed is a scalar value, while the velocity is a vector.
The mathematical calculation for the speed is relatively straightforward, wherein the average speed of an object is calculated by dividing the distance traveled by the time it took the object to travel the distance. Velocity, on other hand, is more complicated mathematically and can be calculated in different ways, depending on what information is available about the object’s motion. In its simplest form, the average velocity is calculated by dividing change in position (Δr) by change in time (Δt)
a ball is thrown directly downward with an initial speed of 8.35 m/s from a height of 29.6 m. The equation for the height of the ball as a function of time is
y f =y i +v i -1/2g[tex]t^{2}[/tex]
0=29.6+(-8.35)-4.90[tex]t^{2}[/tex]
Solving for t,
t=[tex](+8.35± \sqrt{(-8.35)^{2}-4(-4.90(29.6)}) /2(-4.90)= (+8.35± \sqrt{69.72-580.16})/(-2.9)[/tex]
t=2.59s
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On holiday a family travels from meyerville 10 miles away to sprytown 70 miles away in 3 hours. Find their speed
On holiday a family travels from meyerville 10 miles away to sprytown 70 miles away in 3 hours, their speed is 20 miles per hour.
Equation :To find speed using formula,
s = d / t
s = 70 - 10 / 3
s = 60 / 3
s = 20 miles / hours
Speed :Speed is defined as the rate of change of position; what we mean by speed is the magnitude with which an object moves, or, more scientifically, the rate at which an object changes its position is per unit time.
Speed is calculated as speed = distance / time. To figure out what the units for speed are, you must first understand the units for distance and time. Because distance is measured in metres (m) and time is measured in seconds (s), the units will be metres per second (m/s).
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A reaction occurs in which carbon combines with oxygen to form carbon dioxide is this a chemical reaction or nuclear reaction
The part of river's current moves at a 1.486 m/s speed.
the distance between two points, objects, lines, etc. Remoteness is the quality of being physically separated from another thing or person. a line drawn in the universe. To walk seven miles in one hour would be too time-consuming.
The difference between the change in distance and the change in time is used to compute the rate of change.
Rate: times the distance Time
The distance is 16.5 miles, and the time is 5.5 hours.
If we enter this into the formula above, it yields:
16.5 - 5.5 / 10.9 - 3.5 = 11/7.4 = 1.486 m/s is the rate of change.
Calculations show that the constant rate of change is 1.486 m/s.
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Can an object have zero velocity and nonzero acceleration at the same time give examples.
Yes, an object can have zero velocity and non-zero acceleration at the same time.
Let's take an example of a tennis ball. If we throw the tennis ball vertically upward, the ball will have zero velocity at the highest point. At that point, the gravity is still acting downwards on the tennis ball. At this point, the ball has zero velocity and accelerates downward with gravitational acceleration = 9.8m/s.
Another example is oscillatory motion. In oscillatory motion, the acceleration is always opposite to the velocity. When the velocity becomes zero at the extreme position the body has non-zero acceleration.
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the magnitude of the unit is the same between the and scales. they differ in the position of the zero point.
The magnitude of the unit is the same between the interval and ratio scales. The location of the zero point varies amongst them.
What are interval and ratio scales?Both interval scales and ratio scales are made up of tangible, uniformly sized units like millimetres or seconds. The difference between three and four seconds, for example, is the same as the difference between four and five seconds since seconds are all the same size.
The distinction between interval and ratio scales is that the former has significant zero points while the latter does not.
How is the interval scale different from the ratio scale?The data gathered can be added, subtracted, and multiplied on an interval scale. The scale makes it possible to calculate the degree of the difference but not the ratio. A ratio scale allows for division in addition to addition, subtraction, and multiplication. In other words, you can figure out how the values compare.
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Tyler wants to learn about the types of insects in the soil near his house. Which would be a benefit of carrying out a descriptive investigation?
He could collect a large amount of data for a low cost.
He could control most of the variables affecting the insects.
He would get results that might change after the investigation.
He would be able to study cause-and-effect relationships.
Tyler wants to learn about the types of insects in the soil near his house. He could collect a large amount of data for a low cost.
Types of investigation :Descriptive investigation, comparative investigation, and experimental investigation are the three types of investigations that scientists use to research and create explanations for events in nature.
What is the benefit of carrying out a descriptive investigation?Providing descriptions is the aim of descriptive research. It should describe phenomena in a factual, precise, and organized manner without attempting to infer their causes. It does not provide an explanation for the how, when, or reasons why a specific phenomenon occurred.
Methods of investigation :In various situations, scientists employ a variety of investigational techniques. These techniques include fair testing, identifying and classifying, modeling, pattern seeking, and researching (in no particular order). According to research, fair testing dominates science instruction.
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A satellite in orbit around Earth is in uniform circular motion. What is the angle between the velocity vector and acceleration vector at any given point on the orbit?
A. 90°
B. 45°
C. 180°
D. 0°
The angle between the velocity vector and acceleration vector at any given point in the orbit would be 90 degrees, therefore the correct answer is option A.
What is acceleration?The rate of change of the velocity with respect to time is known as the acceleration of the object. Generally, the unit of acceleration is considered as meter/seconds².
As given in the If a satellite in orbit around Earth is in a uniform circular motion then we have to find the angle between the velocity vector and acceleration vector.
In a uniform circular motion, the angle between the velocity vector and acceleration vector is always π/2.
The angle between the velocity vector and acceleration vector at any given point in the orbit would be 90 degrees.
Thus, the correct answer is option A.
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a team of engineers is asked to help a community improve local air quality what must the team do before it can begin to identify possible solutions
The team must first take action before looking for potential answers. Improve the solution by iterating.
Why do you mention Teams?A team is described as a collection of individuals who collaborate to complete interdependent activities in support of a common goal or mission. A good team can be created by having open communication, patience, respect for one another, and shared, compatible goals.
How do you build a team?From the start, establish expectations.Respect your team members as individuals. Engender connections within the team. Develop your emotional intelligence.Encourage others with optimism.Be in constant communication.Find ways to honor good effort.Diversify.To know more about Team visit:
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A light microscope with an objective lens numerical aperture of 0.65 is capable of allowing two objects 320 nm apart to be distinguished when using light with a wavelength of 420 nm.
a. true
b. false
It is false to conclude that a light microscope with an objective lens numerical aperture of 0.65 is capable of allowing two objects 320 nm apart to be distinguished when using light with a wavelength of 420 nm.
Given,
Numerical aperture of lens = 0.65
Wavelength (λ) = 420 nm
Now,
0.61 × λ / numerical aperture = resolving power
Or, 0.61 × 420 / 0.65 =394.15 nanometers
Therefore, the least distance between two things that can be distinguished as two independent objects is 394.15 nm, which means two objects separated by 320 nm can not be distinguished as two separate objects with this microscope.
Hence, as a result, the statement is false.
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an aircraft is flying not worth at 300 km per hour yesterday wind is blowing West was at 80 km per hour what is the actual Direction the aircraft travels over the ground
Answer:
220km
Explanation:
In an rlc series circuit, the voltage amplitude and frequency of the source are 100 v and 500 hz, respectively, and , l = 0.20 h, and . (a) what is the impedance of the circuit?
The impedance of the series RLC circuit which have the voltage amplitude and frequency of the source as 100 v and 500 hz, respectively, and l = 0.20 h is 686 ohms.
What is impedance?
The opposition to alternating current presented by the combined effect of resistance and reactance in a circuit is called impedance.
Given,
Voltage (V₀) = 100 v
Frequency (f) = 500 Hz
Inductance (L) = 0.20 h
Angular frequency,
ω = 2πf = 2π(500) = 1000π rad.
Since there is no capacitor and resistance present in the circuit, the impedance will solely depends on the inductance.
Inductive reactance,
[tex]X_L = (w)(L) = (1000)(3.4)(0.20) = 628 ohms[/tex]
By equation,
[tex]Z = \sqrt{R^2 + (X_L - X_C)^{2} }[/tex]
[tex]Z = \sqrt{0 + (628 + 0) ^{2} }[/tex]
Z = 628 ohms.
Hence, the impedance of the circuit is 628 ohm.
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Find the caloric content of 100g of fruit salad containing 20g of apple, 25g of strawberry, 15g of grapes, 30g of banana, and 10g of honey.
90 caloric content of 100g of fruit salad containing 20g of apple, 25g of strawberry, 15g of grapes, 30g of banana, and 10g of honey.
energy are the strength that a meals or beverage includes.
On food merchandise, energy are normally noted, and wearables just like the first-class health trackers assist you to hold-song of how many calories you burn even as undertaking numerous sports. greater energy are usually found in positive ingredients, together with those which are fatty, fried, or processed. clean fruit and veggies, as an instance, have fewer calories on average than different foods. Conversely, low-calorie objects like food regimen soda don't have any dietary value while some nutritious culmination and vegetables might have a high-calorie content.Find out more information about Calories.
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A gas with initial state variables p1, v1, and t1 is cooled in an isochoric process until p2=13p1.part aby what factor does the volume change?
If the volume is held constant, a process is said to be isochoric (or iso-volumetric). The work that the system performs in any isochoric process is always zero.
In thermodynamics, a condition in which a system's volume doesn't change is referred to as an isochoric process. A pressure volume diagram serves as the model for this operation (PV diagram). Consequently, Q1 / Q2 = T1 / T2 or Q1 / Q2 = Q2 / T2 as these two equations are equivalent. The term "lower amount of heat" refers to the proportion of heat to temperature. The total of the reduced amount of heat is therefore zero for the Carnot heat engine. As a result, we can see that in an isochoric process, the volume is constant, and no work is being done. The gas's intrinsic energy is the only thing that changes.
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Hydrogen fusion in the sun requires a temperature (in kelvin) of:_____.
Hydrogen fusion in the sun requires a temperature of more than 100 million kelvin.
so that you can fuse two hydrogen atoms things are required: excessive temperature and excessive pressure. The minimum temperature required to fuse hydrogen is set a hundred million Kelvin, which is set six times the temperature in the middle of our sun.
What temperature does fusion get up inside the sun?
The gravity of the solar, which is sort of 28 times that of Earth, ''traps'' hydrogen from its environment and this hydrogen fuels the Hydrogen fusion reaction. At temperatures of 15 million diploma Celcius within the solar's center, hydrogen gasoline becomes plasma, the fourth country of depend.
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What is the width of the 90 confidence interval for true population proportion if there are 12 successes in a sample of 25?
width of the 90 confidence interval for true population proportion if there are 12 successes in a sample of 25 is around 0.164
We use the following formula to determine the value of the approximate breadth or margin of error:
width is about equal to z [p (1 - p) / n]
^0.5
Consequently, at a 90% confidence level, the z score can be calculated using normal distribution tables. P = likelihood of success and N = 25 samples. According to the standard distribution tables, z = 1.645 is the value of z at the 90% level. There is a 12 out of 25 chance of success, therefore
p = 12 / 25 = 0.48 As a result, the width is approximately:
width is roughly equal to 1.645 [0.48 (1 - 0.48) / 25]
^0.5
width is around 1.645. (0.0999)
width is around 0.164.
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What is tmaxtmaxt_max, the longest time after the dragster begins to accelerate that you can possibly run into the back of the dragster if you continue at your initial velocity?
The correct answer is t_max=V_0/a.
Here, we must apply the motion equation v=u+at to both the first and second conditions. Next, determine the entire time that can be determined using the law of motion. The next thing is our velocity.
Dynamic and kinematic motion descriptions are the two different categories. Dynamics covers a wide range of phenomena since it takes into account the momenta, forces, and energy of the particles.
Let the time be t_max when you collide with the dragster,
speed of dragster at time t_max is at_max .
If at_max = v_0(speed of years) i.e., both have the same speed you will collide with dragster.
t_max = (v-u)/a
=(v_0 - 0)/a
=v_0/a
Hence t_max=V_0/a.
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What is nature's heat tax, and how does it relate to energy use? drag the terms on the left to the appropriate blanks on the right to complete the sentences.
As per second law of thermodynamics, The amount of energy that must be lost to the environment for the process to take place is known as nature's heat tax.
What is second law of thermodynamics?
The second law of thermodynamics is a physical principle founded on the knowledge of how heat and energy are transformed throughout the world. Explanation of the law is that, without energy input to change the direction of heat flow, heat always goes "downhill," or from hotter to colder objects. The phrase "not all heat energy can be turned into work in a cyclic process" is another definition.
Every energy exchange is subject to the inevitable energy reduction known as "nature's heat tax." The majority of energy transactions lose some energy to the environment, making each transaction only marginally efficient. As a result, the energy is used most effectively when there are fewest number of transactions.
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