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29 days ago

Which of the following ranges depicts the 2% tolerance range to the full 9 digits provided?

Engineering

1 answer:

Mrrafil [253]29 days ago

4 0

Answer:

Only option C fulfills the criteria.

Explanation:

A quantity's tolerance defines the allowable range of variation for that quantity.

To calculate this, we need to know the magnitude, with the closest value being the average. This average may be provided or can be found using the formula

x_average = ∑ $x_{i}$ / n

The error or tolerance is determined by comparing the current value with the average expressed as a percentage

Δx₁ = x₁ / x_average

tolerance = | 100 - Δx₁ 100 |

where bars denote absolute values

Let’s compute these values for each option.

x_average = (2.1700000 + 2.258571429) / 2

x_average = 2.2142857145

For x₁, we compute the fluctuation

Δx₁ = 2.17000 / 2.2142857145

Tolerance = 100 - 97.999999991

Tolerance = 2.000000001%

For x₂, we analyze the fluctuation

Δx₂ = 2.258571429 / 2.2142857145

Δx₂ = 1.02

tolerance = 100 - 102.000000009

tolerance = 2.000000001%

x_average = (2.2 + 2.29) / 2

x_average = 2.245

For x₁, we evaluate fluctuation

Δx₁ = 2.2 / 2.245

Δx₁ = 0.9799554

tolerance = 100 - 97.999

Tolerance = 2.00446%

For x₂, we measure fluctuation

Δx₂ = 2.29 / 2.245

Δx₂ = 1.0200445

Tolerance = 2.00445%

x_average = (2.211445 + 2.3) / 2

x_average = 2.2557225

Δx₁ = 2.211445 / 2.2557225 = 0.9803710

tolerance = 100 - 98.0371

tolerance = 1.96%

Δx₂ = 2.3 / 2.2557225 = 1.024624

tolerance = 100 - 101.962896

tolerance = 1.96%

x_average = (2.20144927 + 2.29130435) / 2

x_average = 2.24637681

Δx₁ = 2.20144927 / 2.24637681 = 0.98000043

tolerance = 100 - 98.000043

tolerance = 2.000002%

Δx₂ = 2.29130435 / 2.24637681 = 1.0200000017

tolerance = 2.0000002%

x_average = (2 + 2.3) / 2

x_average = 2.15

Δx₁ = 2 / 2.15 = 0.93023

tolerance = 100 - 93.023

tolerance = 6.98%

Δx₂ = 2.3 / 2.15 = 1.0698

tolerance = 6.97%

Examining these outcomes, it is evident that result E does not fall within the specified tolerance range, while the remaining values could align with the desired tolerance based on the required degree of precision. Thus, under stringent precision requirements, option C stands out as the only choice that meets the criteria.

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You want to determine whether the race of the defendant has an impact on jury verdicts. You assign participants to watch a trial

grin007 [219]

Response:

The confidence scale is an ordinal measurement scale

Clarification:

An ordinal measurement scale is utilized for assessing attributes that can be ranked or ordered, yet the intervals in between attributes lack quantitative meaning. In this scenario, the scale utilized was from 1 to 7, where "1" signifies that the defendant's race has little impact on jury verdicts, and "7" indicates a strong impact of race on such verdicts. For instance, in a survey measuring customer satisfaction for a product, a "1" indicates great dissatisfaction, while "10 " denotes highest satisfaction. In the first instance, it would be incorrect to assert that the difference between a rating of 1, which implies "not at all," and perhaps a 3, is equivalent to the gap between a 5 and a 7, as these numbers merely serve as labels devoid of quantifiable value.

Other types of measurement levels include:

1. Nominal: This is the most straightforward measurement level, employed primarily for categorizing attributes. An example would be gathering data on gender, with categories such as male, female, and transgender.

2. Interval: An interval scale is used when the distances between two attributes hold meaning, but a true zero point is absent from the scale.

3. Ratio: This level combines all three previously mentioned measurements, serving to categorize, show ranking, maintain meaningful distances between attributes, and possess a true zero point. A typical example is measuring temperature using a Celsius thermometer, which has a true zero at 0°C, and the intervals between 5°C and 10°C are equivalent to those between 10°C and 15°C.

6 0

4 days ago

A bar of 75 mm diameter is reduced to 73mm by a cutting tool while cutting orthogonally. If the mean length of the cut chip is 7

mote1985 [204]

Answer:

r=0.31

Ф=18.03°

Explanation:

Provided:

Original diameter of bar = 75 mm

Diameter post-cutting = 73 mm

Average diameter of the bar d= (75+73)/2=74 mm

Average length of uncut chip = πd

Average length of uncut chip = π x 74 =232.45 mm

Thus, cutting ratio r

$Cutting\ ratio=\dfrac{Mean\ length\ of cut\ chip}{Mean\ length\ of uncut\ chip}$

$r=\dfrac{73.5}{232.45}$ r=0.31

Therefore, the cutting ratio equals 0.31.

Now, the shearing angle is given as

$tan\phi =\dfrac{rcos\alpha }{1-rsin\alpha }$

Next by substituting the values

$tan\phi =\dfrac{rcos\alpha }{1-rsin\alpha }$

$tan\phi =\dfrac{0.31cos15 }{1-0.31sin15 }$ \

Ф=18.03°

Concluding, the shearing angle is 18.03°.

4 0

1 month ago

The rate of flow of water in a pump installation is 60.6 kg/s. The intake static gage is 1.22 m below the pump centreline and re

mote1985 [204]

Answer:

The power of the pump is 23.09 kW.

Explanation:

Parameters

gravitational constant, $g = 9.81 m/s^2$

mass flow rate, $\dot{m} = 60.6 kg/s$

flow density, $\rho = 1000 kg/m^3$

efficiency of the pump, $\eta = 0.74$

output gauge pressure, $p_o = 344.75 kPa$

input gauge pressure, $p_i = 68.95 kPa$

cross-sectional area of output pipe, $A_o = 0.069 m^2$

cross-sectional area of input pipe, $A_i = 0.093 m^2$

height of discharge, $z_o = 1.22 m - 0.61 m = 0.61 m$ (evaluated at pump’s maximum height of 1.22 m)

input height, $z_i = 0 m$

hydraulic power of the pump, $P =? kW$

Initially, the volumetric flow (Q) needs to be determined

$Q = \frac{\dot{m}}{\rho}$

$Q = \frac{60.6 kg/s}{1000 kg/m^3}$

$Q = 0.0606 m^3/s$

Next, compute the velocity (v) for both input and output

$v_o = \frac{Q}{A_o}$

$v_o = \frac{0.0606 m^3/s}{0.069 m^2}$

$v_o = 0.88 m/s$

$v_i = \frac{Q}{A_i}$

$v_i = \frac{0.0606 m^3/s}{0.093 m^2}$

$v_i = 0.65 m/s$

Subsequently, the total head (H) can be calculated

$H = (z_o - z_i) + \frac{v_o^2 - v_i^2}{2 \, g} + \frac{p_o - p_i}{\rho \, g}$

$H = (0.61 m - 0 m) + \frac{{0.88 m/s}^2 - {0.65 m/s}^2}{2 \, 9.81 m/s^2} + \frac{(344.75 Pa-68.95 Pa)\times 10^3}{1000 kg/m^3 \, 9.81 m/s^2}$

$H = 28.74m$

Finally, the computation of pump power is done as follows

$P = \frac{Q \, \rho \, g \, H}{\eta}$

$P = \frac{0.0606 m^3/s \, 1000 kg/m^3 \, 9.81 m/s^2 \, 28.74m}{0.74}$

$P = 23.09 kW$

6 0

25 days ago

Steam flows at steady state through a converging, insulated nozzle, 25 cm long and with an inlet diameter of 5 cm. At the nozzle

iogann1982 [279]

Answer:

The velocity at exit U_2 is 578.359 m/s

The exit diameter d_e is 1.4924 cm

Explanation:

Provided data includes:

Length of the nozzle L = 25 cm

Inlet diameter d_i = 5 cm

At the nozzle entrance (state 1): Temperature T_1 = 325 °C, Pressure P_1 = 700 kPa, Velocity U_1 = 30 m/s, Enthalpy H_1 = 3112.5 kJ/kg, Volume V_1 = 388.61 cm³/gAt the nozzle exit (state 2): Temperature T_2 = 250 °C, Pressure P_2 = 350 kPa, Velocity U_2, Enthalpy H_2 = 2945.7 kJ/kg, Volume V_2 = 667.75 cm³/g To determine:a. Exit Velocity U_2b. Exit Diameter d_e

a.The Energy Equation can be represented by:ΔH + ΔU² / 2 + gΔz = Q + WAssuming Q = W = Δz = 0Substituting the values yields:

(H_2 - H_1) + (U²_2 - U²_1) / 2 = 0From which we can derive U_2 = sqrt((2* (H_1 - H_2 )) + U²_1) with the calculations leading to U_2 = sqrt ( 2 * 10^3 * (3112.5 -2945.7) + 900) yielding U_2 = 578.359 m/s

Using mass balance approach, we have U_1 * A_1 / V_1 = U_2 * A_2 / V_2

Here, A = π*d² / 4

This leads to U_1 * d_i² / V_1 = U_2 * d_e² / V_2, thus d_e = d_i * sqrt((U_1 / U_2) * (V_2 / V_1)). Hence, d_e = 5 * sqrt((30 / 578.359) * (667.75 / 388.61)) computes to d_e = 1.4924 cm

6 0

5 days ago

3/63 A 2‐kg sphere S is being moved in a vertical plane by a robotic arm. When the angle θ is 30°, the angular velocity of the a

Kisachek [217]

Answer:

Ps=19.62N

Explanation:

A thorough explanation of the answer can be found in the attached files.

5 0

29 days ago