The Gaussian (0, 1) random variable is also known as the standard normal distribution, where the mean (µ) is 0 and the standard deviation (σ) is 1. The notation E[X] represents the expected value of X, which is the mean of the probability distribution of X.
Now, let's break down the expression E[ XIX >= E[X]]. The symbol IX >= E[X] means that we are considering only those values of X that are greater than or equal to the expected value of X. In other words, we are looking at the right tail of the distribution.
To calculate E[ XIX >= E[X]], we need to find the expected value of X, given that X is greater than or equal to the expected value of X. This is also known as the conditional expected value.
One way to approach this problem is to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
In our case, A represents the event XIX, and B represents the event X >= E[X].
We know that X is a standard normal distribution, which means that its probability density function (PDF) is given by:
f(x) = (1 / sqrt(2π)) * e^(-x^2/2)
Using this PDF, we can calculate the probabilities of the events A and B:
P(A) = ∫x=0^∞ f(x) * x dx = 1/2
P(B) = ∫x=0^∞ f(x) dx = 1/2
P(A and B) = ∫x=0^∞ f(x) * x dx = 1/2
Therefore, the conditional probability P(A|B) = P(A and B) / P(B) = 1.
This means that the expected value of X, given that X is greater than or equal to the expected value of X, is equal to 1.
Therefore, E[ XIX >= E[X]] = 1 * P(X >= E[X]) = 1/2, since the probability of X being greater than or equal to its mean is 1/2 for a standard normal distribution.
In summary, E[ XIX >= E[X]] = 1/2 for a standard normal distribution.
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Since X is a standard Gaussian, we know that E[|X|] = √(2/π). Therefore,
E[Y] = 2 √(2/π) ≈ 1.5958.
6.2.2)
Let's start by finding the CDF of Y = IXI.
For any given value of y, we have two cases:
1. If y < 0, then P(Y <= y) = 0 because Y can only take non-negative values.
2. If y >= 0, then P(Y <= y) = P(-y <= X <= y) = F_X(y) - F_X(-y), where F_X is the CDF of X.
Since X is a standard Gaussian, we know that F_X(x) = Φ(x), where Φ is the standard Gaussian CDF. Thus,
P(Y <= y) = Φ(y) - Φ(-y) for y >= 0.
To find the expected value of Y, we use the definition of the expected value:
E[Y] = ∫(-∞ to ∞) y f_Y(y) dy, where f_Y is the PDF of Y.
To find f_Y, we can differentiate the CDF we just found:
f_Y(y) = d/dy [Φ(y) - Φ(-y)] = φ(y) + φ(-y), where φ is the standard Gaussian PDF.
Thus,
E[Y] = ∫(0 to ∞) y (φ(y) + φ(-y)) dy
= ∫(0 to ∞) y φ(y) dy + ∫(0 to ∞) y φ(-y) dy
= 2 ∫(0 to ∞) y φ(y) dy (by symmetry)
= 2 E[|X|]
Since X is a standard Gaussian, we know that E[|X|] = √(2/π). Therefore,
E[Y] = 2 √(2/π) ≈ 1.5958.
7.1.2)
We start by finding E[X], which is the expected value of a discrete uniform random variable on the interval [0,5]. Since the distribution is uniform, we have E[X] = (a+b)/2 = (0+5)/2 = 2.5.
Next, we need to find E[ XIX >= E[X]]. This is the expected value of X given that X is greater than or equal to its expected value. Using the definition of conditional expectation, we have:
E[ XIX >= E[X]] = ∑(i=0 to 5) xi P(X = xi | X >= 2.5)
Since X is discrete uniform, we know that P(X = xi) = 1/6 for all i from 0 to 5. To find P(X = xi | X >= 2.5), we note that X >= 2.5 if and only if X takes on the values 3, 4, or 5. Thus,
P(X = xi | X >= 2.5) =
{ 1/3 if xi = 3, 4, or 5
{ 0 otherwise
Substituting these values into the above expression, we get:
E[ XIX >= E[X]] = (3/6)(3) + (1/6)(4) + (1/6)(5) = 17/6 ≈ 2.8333.
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A centrifugal pump levers water
to a boiter at the rate of 0.05mls
pressure rises across the
is 7 bar, the suction pipe 100m
I'm diameter, and delivering pipe
the
ритр
is 15mm diameter, the outlet
being 0.5m above the intet.
Calculate the efficiency of
the pump
the
kipe, it
power delivered to
the driving shaft is 45 kWatt
Answer:
Industrial users can select from numerous pump technologies for water supply and the handling of other liquid media. A particular favorite is the centrifugal pump. How do centrifugal pumps work? What different delivery principles are there? For which applications are centrifugal pumps especially well-suited?
Here we provide you an overview of the different types of centrifugal pumps. In addition, the operating principles are explained, and typical applications are listed also.
Explanation:
Water enters a vertical jet with low velocity and a pressure of 350 kPa. What is the maximum height that the water can rise above the jet
The maximum height that the water can rise above the jet is; 35 m
How to find the height pressure of water?
The formula for pressure here is;
P = P₀ + ρgh
where;
P₀ is the pressure at the fluid's surface.
ρ is the density of the fluid. (density of water = 1000 kg/m³)
g is the acceleration due to gravity = 10 m/s².
h is height of rise of fluid
Now, the pressure at water surface is zero because the pressure the atmosphere exerts on the water is equal to the pressure the water exerts on the atmosphere. Thus, P₀ = 0 Pa
We are given P = 350 kPa = 350000 Pa. Thus;
350000 = 0 + (1000 * 10 * h)
350000 = 10000h
h = 350000/10000
h = 35 meters
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Water enters a vertical jet with low velocity and a pressure of 350 kPa. What is the maximum height that the water can rise above the jet
The maximum height that the water can rise above the jet is: 35 meters.
Maximum height that the water can rise above the jetGiven:
P = 350 kPa = 350000 Pa
We would use pressure(p) formula to determine the maximum height that the water can rises above the jet by solving for h (height).
Using this formula
Pressure(P) = P₀ + ρgh
Where;
P₀ represent Pressure at the fluid's surface
ρ represent Density of the fluid = 1000 kg/m³
g represent acceleration due to gravity = 10 m/s².
h represent height
Solving for h (height)
350000 = 0 + (1000 × 10 ×h)
350000 = 10000h
Divide both side by 10000h
h = 350000/10000
h = 35 meters
Therefore the maximum height that the water can rise above the jet is: 35 meters.
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Determine the carburizing time necessary to achieve a carbon concentration of 0.30 wt.% at a position of 4 mm into an iron-carbon alloy that initially contains 0.10 wt.% C. The surface concentration is to be maintained at 0.90 wt.% C, and the treatment is to be conducted at C. Use the diffusion data for -Fe in Table 5.2
Answer:
the carburizing time necessary to achieve a carbon concentration is 31.657 hours
Explanation:
Given the data in the question;
To determine the carburizing time necessary to achieve the given carbon concentration, we will be using the following equation:
(Cs - Cx) / (Cs - C0) = ERF( x / 2√Dt)
where Cs is Concentration of carbon at surface = 0.90
Cx is Concentration of carbon at distance x = 0.30 ; x in this case is 4 mm = ( 0.004 m )
C0 is Initial concentration of carbon = 0.10
ERF() = Error function at the given value
D = Diffusion of Carbon into steel
t = Time necessary to achieve given carbon concentration ,
so
(Cs - Cx) / (Cs - C0) = (0.9 - 0.3) / (0.9 - 0.1)
= 0.6 / 0.8
= 0.75
now, ERF(z) = 0.75; using ERF table, we can say;
Z ~ 0.81; which means ( x / 2√Dt) = 0.81
Now, Using the table of diffusion data
D = 5.35 × 10⁻¹¹ m²/sec at (1100°C) or 1373 K
now we calculate the carbonizing time by using the following equation;
z = (x/2√Dt)
t is carbonizing time
so we we substitute in our values
0.81 = ( 0.004 / 2 × √5.35 × 10⁻¹¹ × √t)
0.81 = 0.004 / 1.4628 × 10⁻⁵ × √t
0.81 × 1.4628 × 10⁻⁵ × √t = 0.004
1.184868 × 10⁻⁵ × √t = 0.004
√t = 0.004 / 1.184868 × 10⁻⁵
√t = 337.5903
t = ( 337.5903)²
t = 113967.21 seconds
we convert to hours
t = 113967.21 / 3600
t = 31.657 hours
Therefore, the carburizing time necessary to achieve a carbon concentration is 31.657 hours
When performing a vertical analysis which income statement item do you use to determine the cost contribution for each expense category? (What is the denominator?)
Review Later
Net income
Sales
Gross profit
Operating expenses
Sales represent the income statement item used in verticla analyses in order to determine the cost contribution for each expense category (Option C).
What is a vertical analysis?In business, a vertical analysis represents a methodology used to examine financial statements that are ordered as specific points.
A vertical analysis analyzes numbers for only one period, conversely to the horizontal analyses that generally involve many different periods.
In conclusion, sales represent the income statement item used in verticla analyses in order to determine the cost contribution for each expense category (Option C).
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What frequency bands are used primarily for short range distances select all the nearby?
The frequency bands that are used primarily for short-range distances include the following:
The upper portion of the VHF band (225 MHz to 300 MHz).The lower portion of the UHF band (300 MHz to 400 MHz).What is GSM?GSM is an abbreviation for global system for mobile communication and it can be defined as an open and digital cellular network technology that is designed and developed to be used for the transmission of both mobile voice and data services at the same time.
In Computer technology and networking, the global system for mobile communication (GSM) is typically designed and developed to operates at the following bands of frequencies:
850 MHz900 MHz1800 MHz1900 MHzIn this context, we can infer and logically deduce that the frequency bands that are used primarily for short-range distances such as PAN, include the following:
The upper portion of the VHF band (225 MHz to 300 MHz).The lower portion of the UHF band (300 MHz to 400 MHz).Read more on frequency bands here: https://brainly.com/question/19097094
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What advanced safety features are now standard on 2023 Z?
The advanced safety features that are now standard on 2023 Z are:
The above is the short name or nickname for the All New 2023 Nissan Z coupe Sports car.
The care also features Advanced driver assist and safety technology which relieves the driver's everyday workload, allowing you to focus on what matters most.
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A______solid-state relay is an electronic device that performs the same function as an electromechanical relay.
Answer: Non-programmable
Explanation:
A non-programmable solid-state relay is an electronic device that performs the same function as an electromechanical relay.
What is a solid-state relay?An SSR is an electrical switching device that turns on or off when an external voltage (AC or DC) is applied across its control terminals. They perform the same job as an electromechanical relay, but because they include no moving parts, they have a longer operational lifetime.
Solid-state relays are the semiconductor analogs of electromechanical relays and can thus control electrical loads. When energized, the solid-state relay is a fairly complex device with a simple purpose: to activate a single output load.
Therefore, a non-programmable solid-state relay is a type of electrical device that functions similarly to an electromechanical relay.
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Consider fully developed flow in a circular pipe with negligible entrance effects. If the length of the pipe is doubled, the pressure drop will _____.
Waterbutt filtration system for pond. Water pressure principles, help needed?
I have water butt 1 and 2 working perfectly but as soon as I add another to the system water butt 1 and 2 start rising and overflowing.
Is there something I'm missing or doing wrong here? How does water leveling work?
Thanks all.
Water pressure principles is known to state that the amount of Fluid pressure is said to be perpendicular to the surface on which it it exert or works on.
Note that principle is shown by a vessel that is said to be having flat sides and has water. The pressure exerted by the weight of the water is therefore known to be perpendicular to the walls of the storage.
What is a Waterbutt used for?A water butt is known to be a container that is made and also used to store a lot of rainwater.
Note that Water pressure principles is known to state that the amount of Fluid pressure is said to be perpendicular to the surface on which it it exert or works on.
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For some alloy, the yield stress is 345-MPa (50,000-psi) and the elastic modulus (E) is 103-GPa (15x106 psi). What is the maximum load that may be applied to a specimen with a cross-sectional area of 130-mm2 (0.2-in2) without plastic deformation
The maximum load that may be applied to a specimen with a cross-sectional area of 130 mm² is; 35535 N
How to find Elastic Modulus?We are told that for an alloy, the yield stress is 345-MPa and the elastic modulus (E) is 103-GPa.
Now, we want to find the maximum load that may be applied to a specimen with a cross-sectional area of 130-mm² without plastic deformation. Thus;
We are given the parameters;
Yield Stress; σ = 345 Mpa = 345 * 10⁶ Pa
Elastic Modulus; E = 103 GPa = 103 * 10⁹ Pa
Cross sectional Area; A = 130 mm² = 103 * 10⁻⁶ m²
Formula for stress without Plastic deformation is;
σ = F_max/Area
where;
σ is stress
F_max is maximum force
Area is Area
Thus making maximum force the subject of the formula gives;
F_max = σ * A
Plugging in the relevant values for stress and area gives us;
F_max = 345 * 10⁶ * 103 * 10⁻⁶
F_max = 35535 N
The maximum load that may be applied to a specimen with a cross-sectional area of 130 mm² is gotten to be 35535 N
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Explain any three ways research can facilitate the work of building technicians
According to the research, research can facilitate the work of building technicians in the conception, materials to use and planning of the project.
What are building technicians?They are experts in construction projects, supporting the design of plans, estimating costs, planning work methods, etc.
Research can facilitate the work of building technicians in the following ways:
Conception, design and planning of the project.Selection of materials for floor, wall and ceiling systems.Carry out the programming of works, budgets and analysis of unit prices.Therefore, we can conclude that according to the research, research can facilitate the work of building technicians in the conception, materials to use and planning of the project.
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A cantilever beam has a length L and is loaded by a triangularly distributed load of maximum intensity q0 at B. (Solve this problem by integration the differential equations of the deflection curve. The beam has constant flexural rigidity E I.)
The Deflection due to Triangular load is 11q₀L⁴/120EI
What is deflection due to triangular load?The deflection due to the triangular load is usually given as:
σ₁ = 11q₀L⁴/120EI
Deflection due to reaction (R[tex]_{b}[/tex])(σ₂) =
R[tex]_{b}[/tex]L³/3EI
⇒ σ₁ = σ₂⇒ 11q₀L⁴/120EI
= R[tex]_{b}[/tex]L/3EI= R[tex]_{b}[/tex]
= 11q₀L/40
What is the significance of deflection in a beam?In terms of structural engineering, a beam or node moving from its initial location is referred to as deflection.
It occurs as a result of the loads and forces that are placed on the body.
Deflection, also known as displacement, can result from the weight of the body structure itself or from externally applied stresses.
What is the relevance of deflection due to triangular load?A structure's deflection must be taken into account during design, and the consequences of not doing so can be disastrous.
Deflections may be caused by various loads. These include, among others,
ground pressureearthquakeswind loadsshear loadspoint loadsevenly distributed loads and uniformly distributed loads.Learn more about similar solutions at;
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different lever designs can be engineered to alter the brake pedal effort required of the driver by using different levels of ?
Different lever designs can be engineered and developed to alter the brake pedal effort required of the driver by using different levels of mechanical advantage.
What is mechanical advantage?Mechanical advantage can be defined as a ratio of the output force of a lever to the force acting on it (input force or effort), assuming no losses due to wear, flexibility, tear or friction.
This ultimately implies that, different lever designs can be suitably engineered and developed to alter the brake pedal effort (input force) that is required of the driver, especially by using different levels of mechanical advantage.
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A flexible hydraulic hose identified as mil-h-8788 will have a stripe running the length of the hose. This stripe?
Answer: This a system of equations question. What you will do is make an equation comparing the two lengths then make another one as the sum of the lengths. H1 will stand for hose 1 and H2 will stand for hose 2.
so our first equation is H1=4*(H2)-20. We know this because H1 is 20 less than 4 times H2.
After landing equipment, a hydraulic flexible hose has been removing the everlasting form of a hose because of stress is called a save you high strain from extruding the seal among the transferring and desk-bound parts.
What are Hydraulics?Hydraulics is a mechanical characteristic that operates via the pressure of liquid pressure. In hydraulics-based totally structures, mechanical motion is produced with the aid of contained, pumped liquid, normally via hydraulic cylinders transferring pistons.
Hydraulic structures paintings through using pressurized fluid to energy an engine. these hydraulic presses position pressure on a small amount of fluid for you to generate a massive amount of power. Hydraulic structures are capable of shifting heavier loads in addition to offering greater force than mechanical, electrical, or pneumatic systems. The fluid energy gadget approach can without difficulty address a huge weight variety without having to use gears, pulleys, or heavy leavers.
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A +7.5% grade meets a horizontal grade on a section of a rural mountainous highway. If the length of the crest vertical curve formed in that section is 300 ft long, determine the safe operating speed on the highway.
Using the formula of comfort condition it is possible to determine the safe operating speed on the highway.
What is a deflection angle?In physics, we define angular deviation as the angle resulting from the deflection of light when reflected from a prism. A prism has the ability to separate white light into several other colors, which are reflected by the object.
The comfort condition formula is given by: [tex]L=2(\frac{NV^{3} }{C} )^{\frac{1}{2} }[/tex]
Where, L is the length of the vertical curve, N is the grade, V is the safe speed operation and assuming the standart value for C (0,6 m/s3) it is possible to calculate:
[tex]C = 0,6 m/s^{3} = 1,968 ft/s^{3}\\ N= N1 - N2 = 7,5-0 = 7,5% = 0,075[/tex]
Changing the values in the formula:
[tex]L=2(\frac{NV^{3} }{C}){\frac{1}{2} } \\300 = 2(\frac{0,075.V^{3} }{1,968})^{\frac{1}{2} } \\V = 83,89 ft/s[/tex]
So, the safe operating speed on the highway is 83,89 ft/s.
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True or false? if i were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit.
Answer: True
Explanation:
True or false? if i were to hook up an ac voltage source to a resistor, the voltage drop across the resistor would be in phase with the current in the circuit.
Answer: True
Explanation:
When a system is in deep vacuum;
a. never add refrigerant to the system.
b. never use a micron gauge.
c. never energize the compressor.
d. never energize system fans and blowers.
When a system is in a deep vacuum, never energize the compressor. The correct option is a.
What is a deep vacuum?A deep vacuum is a system in which the boiling point of liquid lowers down and the temperature lowers for outgassing. They help in freeze drying, metallurgy, distillation, etc. It used 500 or less than 500 microns for deep vacuum.
Vacuum tubes, such as cathode ray tubes, and electron microscopes are made possible by the electronic resistivity of the vacuum. Torr is the unit used to measure vacuums.
Thus, the correct option is a. never energize the compressor.
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g wastewater is to be treated with aerated lagoons. You are considering two different design options: A) A single lagoon with a surface area of 180 m2 B) Two lagoons in series with surface areas of 90 m2 each. All ponds have a depth of 2 m. The flow rate of wastewater is 5000 L/day. The waste contains 600 mg/L of organic material that is readily biodegradable with a first-order rate constant of 0.35 day-1. What final effluent concentration of organic material would you expect for each design
Steam at 75 kPa and 8 percent quality is contained in a spring-loaded piston–cylinder device, as shown in Figure, with an initial volume of 2 m3 . Steam is now heated until its volume is 5 m3 and its pressure is 225 kPa. Determine the heat transferred to and the work produced by the steam during this process.
The heat transferred to and the work produced by the steam during this process is 13781.618 kJ/kg
How to calcultae the heat?
The Net Change in Enthalpy will be:
= m ( h2 - h1 ) = 11.216 ( 1755.405 - 566.78 ) = 13331.618 kJ/kg
Work Done (Area Under PV curve) = 1/2 x (P1 + P2) x ( V1 - V2)
= 1/2 x ( 75 + 225) x (5 - 2)
W = 450 KJ
From the First Law of Thermodynamics, Q = U + W
So, Heat Transfer = Change in Internal Energy + Work Done
= 13331.618 + 450
Q = 13781.618 kJ/kg
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A certain sine wave has a positive-going zero crossing at 0° and an rms value of 20 V. Calculate its instantaneous value at each of the following angles
Based on the positive-going zero crossing at 0° of the sine wave, the instantaneous value at 15° is 7.321V.
What is the instantaneous value?At 15°, the instantaneous value is:
= 20√2 x Sin(angle)
Solving gives:
= 20√2 x Sin(15°)
= 7.321V
At angel 33°, the instantaneous value is:
= 20√2 x Sin(angle)
= 20√2 x Sin(33)
= 15.405V
At angle 70°:
= 20√2 x Sin(angle)
= 20√2 x Sin(70)
= 26.579V
The full question is:
A certain sine wave has a positive-going zero crossing at 0° and an rms value of 20 V. Calculate its instantaneous value at each of the following angles: a. 15° b. 33° c. 70°
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When you approach an uncontrolled intersection, you should treat it as though which sign is present?
Answer: A yield sign
Explanation:
If a dielectric material, such as teflon®, is placed between the plates of a parallel-plate capacitor without altering the structure of the capacitor, how is the capacitance affected?.
The capacitance is affected is that the capacitance increases because of the insertion of Teflon.
What is capacitance?A capacitance is known to be a form of a device that is said to be used to save some measures of charges in any kind of an electrical circuit.
Note that the capacitor functions on the principle that the capacitance of a conductor is said to go up if an earthed conductor is taken close to it.
Therefore, The capacitance is affected is that the capacitance increases because of the insertion of Teflon and so the teflon tends to widen the capacitance.
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How are new slip rings attached to the rotor core during alternator rebuilding?
The new slip rings is been attached to the rotor core during alternator rebuilding by b. Soldered on.
What Soldering ?Soldering serves as the way of joining different types of metals together by melting solder.
This is been used on new slip rings to get it attached to the rotor core during alternator rebuilding .
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CHECK THE COMPLETE QUESTION BELOW:
How are new slip rings attached to the rotor core during alternator rebuilding?
a. Machine clamped
b. Soldered on
c. Crimped on
d. epoxy glue
3) Explain how dc machines Can work as motor and generator
The working principle of a DC machine is when electric current flows through a coil within a magnetic field, and then the magnetic force generates a torque that rotates the dc motor. The DC machines are classified into two types such as DC generator as well as DC motor.
It is possible to design a reactor where the scy conductor and the nitrogen/ammonia electrode operate at different temperatures. Which combination of temperatures is expected to give the best results?.
The combination of temperatures that is expected to give the best result is option A: SCY temperature higher than electrode temp.
Why the case above?The answer is option A because the proton conductivity of SCY is known to be one that often goes up along with increasing temperature, and the favorability of reaction goes down or reduces with total temperature.
Hence, It is said to be good for one to to keep the SCY conductor at a higher temperature and as such, The combination of temperatures that is expected to give the best result is option A: SCY temperature higher than electrode temp.
See options below
. Which combination of temperatures is expected to give the best results?
A.
SCY temperature higher than electrode temperature
B.
SCY temperature lower than electrode temperature
C.
SCY temperature the same as electrode temperature
D.
The temperature of the components does not make a difference.
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The high-pressure fuel pumps used in gasoline direct-injection (GDI) systems are powered by ________.
Answer:
Camshaft
Explanation:
In order to live and grow, bacteria need moisture, food, the right temperature, and ______? Fill in the blank
Answer:
acidity, time,oxygen
Explanation:
These are some conditions for the growth of bacteria
What dimensions are used when measuring the area of a building
Answer:According to NEC 220.12,
“the floor area shall be calculated from outside dimensions of the buildings, dwelling unit, or other area involved.
The area should not include open porches, garages or unused or unfinished spaces not adaptable for future use”.
pa brainliest plss..thankss
Explanati