It is true that the polynomial is divisible by 6
How to prove the division of the polynomial?From the question, we have the following polynomial that can be used in our computation:
Polynomial = x^3+15x^2+74x+120
Divisor = 6
Rewrite the given parameters as
P(x) = x³ +15x² + 74x + 120
x = -6
Substitute x = -6 in the equation P(x) = x³ +15x² + 74x + 120
P(-6) = (-6)³ +15(-6)² + 74(-6) + 120
Evaluate
P(-6) = 0
because the result is 0, the polynomial is divisible
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consider the experiment of tossing a fair coin 7 times. find the probability of getting a prime number of heads given that heads occurs on at least 6 of the tosses
The probability of getting a prime number of heads given that heads occurs on at least 6 of the tosses is 0.0078
The number of observations n is 7
Here the success is heads
The probability of heads is 1/2
We need to find the the probability of getting a prime number of heads.
Heads occurs on at least 6 of the tosses
prime number greater than equal to 6 and less than equal to 7 is 7
So, X = 7
P(X = 7) = 7C7(1/2)⁷(1/2)⁰
P(X = 7) = 1 x (1/2)⁷ x
P(X =7 ) = 1/128
= 0.0078
Therefore, the probability of getting a prime number of heads given that heads occurs on at least 6 of the tosses is 0.0078
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ERROR ANALYSIS Describe and correct the error ir
solving for one of the variables in the linear system
The first set of steps solving 5x-y = 4 to get y = 5x-4 is correct.
The second set of steps are incorrect since it involves circular logic. Notice we're plugging y = 5x-4 back into the original equation we just solved. It would be like plugging an extension cord into itself, and somehow expecting electricity to magically come out of nowhere.
Instead we should plug that y expression into the first equation and solve for x like so:
8x+2y = -12
8x+2(5x-4) = -12
8x+10x-8 = -12
18x-8 = -12
18x = -12+8
18x = -4
x = -4/18
x = -2/9
Then we use this to find the value of y.
y = 5x-4
y = 5(-2/9)-4
y = -10/9-4
y = -10/9 - 36/9
y = (-10-36)/9
y = -46/9
In summary we have the solution (x,y) = ( -2/9, -46/9 )
0.15w+0.35=0.22w-0.14
Answer: w = 7
Step-by-step explanation:
Isolate the variables by dividing each side with the constants.
Hope this helps!
a new car purchased for $20.000 decreases by 10% each year. Write an exponential decay
model for the car. Then determine how long it will take the value of the car to decrease to $7000.
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=years\\ \end{cases} \\\\\\ A=20000(1 - 0.1)^{t} \implies A=20000(0.9)^t[/tex]
how long till it's $7000?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &7000\\ P=\textit{initial amount}\dotfill &20000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ t=\textit{elapsed time} \end{cases} \\\\\\ 7000=20000(1 - 0.1)^{t} \implies \cfrac{7000}{20000}=0.9^t\implies \cfrac{7}{20}=0.9^t[/tex]
[tex]\log\left( \cfrac{7}{20} \right)=\log(0.9^t)\implies \log\left( \cfrac{7}{20} \right)=t\log(0.9) \\\\\\ \cfrac{\log\left( \frac{7}{20} \right)}{\log(0.9)}=t\implies 9.96\approx t \qquad \textit{about 9 years and 11 months}[/tex]
Model Real Life 212 students and
89 teachers are attending a leadership
conference. Each table can seat
16 people. Only one table does not
have 16 people seated. What fraction
of the table is full?
The fraction of table filled is 285/301 or in decimal as 0.946
What is FractionsFractions are expressed in mathematics as a number value that defines a part of a whole or group of objects. Fraction is a component or sector of a given quantity taken from the whole, which might be a number, a specified value, or an item.
In a given fraction, the value on the top is called the numerator, while the value on the bottom is known as the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
In this question, we have to add the total number of attendees first
212 + 89 = 301
But each seat except 1 is filled by 16 people
Let's subtract 16 from the total number
301 - 16 = 285
The fraction of table filled is 285 ÷ 301 = 285/301 = 0.946
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Mr. William thi $40 a month for 7 gallon of water Mr. William pay $40 a month for city water, no matter how many gallon or water he ue in a given month. Let x repreent the number of gallon of water ued per month. Let y repreent the monthly cot of the city water in dollar. What i the equation of the line that repreent thi information? What i the lope of the line? ued in the number of gallon of water ued per month
Answer: y = 40, slope is 0, the line is horizontal
Step-by-step explanation:
the perimeter of a certain isosceles right triangle is 16 plus 16 the square root of 2 what is the length of the hypotenuse of the triangle?
The perimeter of 2nd right isosceles triangle is 16(√2 + 2).
If a is the equal sides of a right isosceles triangle,
Then its hypotenuse is √2 a and perimeter is √2a (√2 + 1 )
The perimeter of 1st right isosceles triangle is 16(√2 + 1)
= √2a (√2 + 1 )
= 16 (√2 + 1 )
a = 8√2
The hypotenuse of 1st triangle = √2 a
= √2 * 8√2
= 16cm
Let A be the equal sides of 2nd right isosceles triangle
Then its hypotenuse is √2 a and perimeter is √2a (√2 + 1 )
According to the question,
A = 16 cm
The perimeter of 2nd right isosceles triangle is √2 * 16(√2 + 1)
= 16(√2 + 2)
Hence, The perimeter of 2nd right isosceles triangle is 16(√2 + 2).
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A survey of 34 students at the Wall College of Business showed the following majors:
Accounting 10
Finance 5
Economics 3
Management 6
Marketing 10
Suppose you select a student and observe his or her major.
(a) What is the probability he or she is a management major? (Round your answer to 3 decimal places.)
Probability (b) Which concept of probability did you use to make this estimate?
Empirical
Classical
The probability he or she selects a management major is 0.176. This is estimated using empirical probability.
Probability is a branch of mathematics that deals with numerical probabilities of events. It is expressed in a range from 0 to 1, not below or above this range. The probability formula is P(E) = (number of favorable outcomes)÷(total number of outcomes).
a) Here, given the total number of outcomes is 34. The favorable outcome is 6. Therefore, the probability he or she selecting the management major is,
P(E)=6/34=0.176.
b) The empirical probability employs numerous trials to calculate likelihood using real observed frequencies. It is an experimental probability that is based on previous or past data.
In the given question, we used past data to estimate the probability. Therefore, it is empirical.
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To determine how American college students feel about commuting, 100 students at a private university were randomly chosen by selecting 50 men and 50 women to participate. They were asked how far they commute each day (in minutes) to campus.
The results of this survey are unreliable primarily because of
voluntary response bias
sampling bias
the absence of a control group
response bias
None of the above
The key reason why this investigation's findings are erroneous is sampling bias. In statistics, sampling bias refers to a bias during which a sample is constructed in a way that makes some members of the intended population less likely than others to be included.
A private university's 100 students, 50 men, and 50 women were randomly chosen to participate in a study on how American college students felt about commuting. They were questioned about their daily commuting distance (in minutes) to college. The key reason why this investigation's findings are erroneous is sampling bias.
When certain individuals of a population are consistently more likely to be chosen in a sample than others, this is known as sampling bias. In the medical sciences, it is also known as ascertainment bias. Because sampling bias jeopardizes external validity, particularly population validity, it restricts the generalizability of findings.
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Finding Angles with Justification
Answer:
m<D = 108
Step-by-step explanation:
m<ACD = 28 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent.
m<CAD = 44 degrees. This is because if a transversal cuts through two parallel lines, Alternate Interior Angles are Congruent. (Same reasoning.)
Now, since the sum of all angles in a triangle is 180 degrees, we can use the two angles that we know as well as angle D to add up to 180 and figure out how much D is. (All of the angles in triangle ADC)
<CAD + <ACD + <D = 180
Substitute the values in.
44 + 28 + <D = 180
72 + <D = 180
Subtract on both sides
<D = 108
The measure of angle D is 108 degrees.
Guide
A chemist mixes Chemical A and Chemical B to make a solution. She uses the same ratio of chemicals for each batch she
makes.
Drag numbers to complete the table.
?
4
6
12
Chemical A (ML) Chemical B (mL)
3
36
48
84
36
96
108
132
168
7
9
When chemist mixes Chemical A and Chemical B to make a solution
Part A
When the quantity of chemical B = 48 ml, then the quantity of chemical A = 4 ml
Part B
When the quantity of chemical A = 9 ml, then the quantity of chemical B = 108 ml
A chemist mixes Chemical A and Chemical B to make a solution
She uses the same ratio of chemicals for each batch
The solution A and B are in linear relationship
y = kx
Where y is the quantity of chemical A
x is the quantity of chemical B
k is the constant
Substitute the values in the table and find k
36 = k × 3
k = 36 /3
k = 12
Part A
When chemical B = 48 ml
48 = 12 × x
x = 48 / 12
x = 4 ml
Part B
When chemical A = 9 ml
y = 12 × 9
y = 108 ml
Therefore, when Chemical B = 48 ml, chemical B is 4ml . When chemical A = 9 ml, Chemical B = 108 ml
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243 divided by 15 and I need to show my work
Answer:
16.2
Step-by-step explanation:
use long division so:
What is the slope of the line in this graph?
Answer:
it is b 5/7
Step-by-step explanation:
bc you rise 5 and run 7
hope this helps
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Express 9 inches of rain in 72 hours as a unit rate
The unit rate of rainfall for 72 hours of rain will be equal to u = 8 inches/hour.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the provided data in the question,
Total time, t = 72 hours and,
The total amount of water in inches, w = 9 inches.
Then unit rate, u will be,
u = 72/9
u = 8 inches/hour.
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please help fast i dont understand
Does the following relation represent a function? \displaystyle \left\{\left(-12, -21\right), \left(-21, -22\right), \left(22, -12\right), \left(21, 22\right), \left(17, -22\right)\right\}{(−12,−21),(−21,−22),(22,−12),(21,22),(17,−22)} Yes No There is not enough information to answer this question.
Yes, The relation represent a function.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The points are,
{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) }
Now,
Since, The points are,
{ (- 12, - 21) , (- 21, - 22) , (22, - 12) , (21, 22) , (17, -22) }
Clearly, All inputs having exactly one output.
Thus, The relation represent a function.
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Help! 20 points if u answer it it’s due tomorrow:(
Step-by-step explanation:
390 ft² (aka 390 ft. squared)
bh times 1/2
13 times 5 divided by two is 37.5 but sine you have two just skip the division and say 75
and then multiply 12 by 10 for the square and get 120
(120+75)*2=390
so the answer is 390 ft. squared
construct a confidence interval for at the given level of confidence. 374 506 439 491 90% confidence g
The confidence interval for the given data be,
(144.83 , 155.17).
On Subtracting 1 from your sample size, we get
150 – 1 = 149.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 149 and α = 0.025
from the table at df = 149 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(150) = 2.28
Now, 2.262 × 2.28 = 5.17
So, the confidence interval be,
(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)
Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17).
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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After 888 months, he weighed 138138138 kilograms. He started at 909090 kilograms. Let yyy represent the sumo wrestler's weight (in kilograms) after xxx months. Complete the equation for the relationship between the weight and number of months.
The required relationship between weight and number of months is given as y = 6x + 90.
As of the given data, assume the relationship on the graph,
Initially ordered pair (0, 90) and instantaneous ordered pair (8, 138)
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
The slope of the relationship,
M = (y₂ - y₁) / (x₂ - x₁)
m = 138 - 90 / 8 - 0
m = 48 / 6
m = 6
Now,
Equation of the relationship,
y - y₁ = m (x - x₁)
y - 90 = m{x - 0}
y = 6x + 90
Thus, y = 6x + 90 is the needed relationship between weight and the number of months.
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A college admissions director states that the age of a typical student currently enrolled has increased from 19 years old. In a random sample of 20 students that are currently enrolled, the mean age is found to be 22.9 years. Assume the distribution of ages is normal with the standard deviation of 1.5 years. Use the significance level of 0.05. Which of the following is the appropriate Decision and Conclusion? Reject the null hypothesis. Sample data did not provide evidence to support that the average age of all students currently enrolled has increased from 19 years old. Reject the null hypothesis. Sample data provided evidence to support that the average age of all students currently enrolled has increased from 19 years old. Do not reject the null hypothesis. Sample data provided evidence to support that the average age of all students currently enrolled has increased from 19 years old. None of these Do not reject the null hypothesis. Sample data did not provide evidence to support that the average age of all students currently enrolled has increased from 19 years old.
The required 90% confidence interval for population mean age is (22.35,23.45)
Given,
Sample size, n = 20
Sample mean, μ = 22.9 years
Standard deviation, σ = 1.5 years
Significance level, α = 0.05
We have to find the 90% confidence interval;
Here,
x ± z(critical) σ/√n
Substituting the values;
z(critical) at α₀.₀₅ = ±1.64
22.9 ± 1.64 (1.5/√20)
= 22.9 ± 0.55
= (22.35, 23.45)
That is,
(22.35,23.45) is the required 90% confidence interval for population mean age.
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Find the 96th term of the arithmetic sequence -30, -32, -34
The 96th term of the given arithmetic sequence is -220
The nth term of an arithmetic sequenceFrom the question, we are to determine the 96th term of the given arithmetic sequence.
The given arithmetic sequence is
-30, -32, -34
The nth term of an arithmetic sequence is given by
aₙ = a + (n - 1)d
Where a is the first term
and d is the common difference
From the sequence,
a = -30
d = a₂ - a₁ = -32 - (-30)
d = -32 + 30
d = -2
Thus,
The 96th term is
a₉₆ = -30 + (96 -1)-2
a₉₆ = -30 + (95)-2
a₉₆ = -30 + (-190)
a₉₆ = -30 - 190
a₉₆ = -220
Hence, the 96th term is -220
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HCF and LCM of two numbers are 15 and 180 respectively. If they are in the ratio 3;4,find the numbers
I WILL OPEN MY ALT AND ANSWER AND GIVE YOU A BRINLIST OPEN IF YOU SHOWED YOUR WORK!!! OPEN THE IMAGE
Answer:
x = 0
Step-by-step explanation:
1. Distribute
2. Add the numbers
3. Rearrange terms
4. Subtract 19 from both sides
5. Simplify
6. Add 5x to both sides
7. Simplify
8. Divide both sides by the same factor
9. Simplify
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 9 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
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Step-by-step explanation:
Find the two whole numbers that are the closest to square root 42. Explain your reasoning.
Answer: 6 and 7
Step-by-step explanation:
Find the square root of 42 = 6.48
Closest whole numbers to 6.48 are 6 and 7
Need help getting this done by today.
The equation of the line perpendicular to given equation is 3x - y + 2 = 0
what is perpendicular line?
A straight line that forms a right angle of 90 degrees with another line is known as a perpendicular in mathematics. Alternatively stated, two lines are perpendicular to one another if they cross at a right angle.
solution:
The slope for the perpendicular line is - ( 1/m )
Then the given line has the slope y = (1/3)x - 2 is 1/3
substitute 1/3 in perpendicular equation, Then the slope for the perpendicular line is - ( 1/m ) is -3
The line equation is y = mx +c, ( -2, -4 )
Then c = -2
substitute slope for the perpendicular line is - ( 1/m ) is -3 and c = -2 in line equation
then the equation is 3x - y + 2 = 0
Therefore the equation of line perpendicular to given equation is 3x - y + 2 = 0
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What is the 91st term in the sequence? 1,1.01,1.02
The 91st term in the sequence is 1,1.01,1.02 is 1.9.
How to calculate the sequence?An arithmetic sequence is a set of numbers that are ordered and have a common difference between each consecutive term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence. We use the formula for finding the nth term to find a specific term in an arithmetic sequence. Step 1: An arithmetic sequence's nth term is given by a = a + (n - 1)d.
Based on the information given, it should be noted this is an arithmetic sequence.
The formula t calculate the nth term will be:
= a + (n - 1)d
where
a = first term = 1
n = 91
d = common difference = 0.01
The 91st term will be:
= a + (n - 1)d
= 1 + (91 - 1) × 0.01
= 1 + (90 × 0.01)
= 1 + 0.9
= 1.9
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Suppose that you have data recording the body weight and the running speed for each of several different jackrabbits. To summarize this data, it suffices to note the mean and SD for each of these two variables. a. True b. False
I think that it is true because it is asking for a summary of the data and finding the mean and standard deviation of the speeds and weight would give you the summary of all the data.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
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what is the equation based on the focus and vertex
Check the picture below, so the parabola looks more or less like so.
keeping in mind the vertex is always half-way between the focus point and the directrix, let's also notice the "p" distance.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-4\\ k=2\\ p=-1 \end{cases}\implies 4(-1)(y-2)=( ~~ x-(-4) ~~ )^2\implies -4(y-2)=(x+4)^2 \\\\\\ y-2=-\cfrac{1}{4}(x+4)^2\implies {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x+4)^2 + 2 \end{array}}[/tex]
you have 700 ft of fencing to make a pen for hogs. if you have a river on one side of your property, what are the dimensions (in ft) of the rectangular pen that maximiz
The dimension of the rectangular pen that maximizes the area is 61,250ft.
What is a dimension?
Something's size, including its breadth, height, and depth: She took exact measurements of the room's dimensions in one direction, like the distance from the ceiling to the floor. The room was surprisingly small, in terms of length, width, and height.
Here, we have
L+2W = 700
Area = A= LW = (700-2W)W = 700W -2W²
Take the derivative, set it equal to zero, and solve for W
-4W + 700 = 0
W = 175 feet
L = 700-2(175) = 350 feet
350 by 175 ft maximizes area = 61,250 square feet
Hence, the dimension of the rectangular pen that maximizes the area is 61,250ft.
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Brawdy Plastics, Inc. produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. If required, enter negative values as negative numbers.
a. Select a scatter diagram with the line speed as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation (to 1 decimal). = + x d. Predict the number of defective parts found for a line speed of 25 feet per minute.
a) scatter diagram made using the provided data is attached.
b) According to the scatter diagram, the number of defective parts discovered rises with line speed.
c) Y = 27.5 - 0.3 X is the regression model.
What does statistics mean in plain English? a field of mathematics concerned with the gathering, examination, presentation, and interpretation of vast amounts of numerical data. a compilation of numerical data
20 faulty pieces are anticipated to be present when the line speed is 25 feet per minute.
Detailed explanation:
The given information is displayed as follows:
Line Speed; 20, 20, 30, 30, 40, 40, 50, 50
Number of Defective; 23, 21, 19, 16, 15, 17, 14, 11
Parts located
a. The scatter diagram made with Microsoft Excel is attached.
b. The scatter figure appears to show a relationship between increased line speed and the quantity of detected defective parts.
c. The following equation is given for linear regression using the least squares approach;
Y = a + b·X
Where;
b= N∑XY - (∑X)(∑Y)/N∑X^2 - (∑X)^2
a= ∑Y - b∑X / N
We have data from Microsoft Excel;
∑X = 280, ∑Y = 136, ∑X² = 10,800, ∑XY = 4,460, (∑X)² = 78,400, N = 8
By entering the values, we obtain;
b = (8×4,460 - 280×136)/(8×10,800 - 78,400) = -0.3
a = (136 - (-0.3)×280)/8 = 27.5
As a result, we have the following linear regression;
Y = 27.5 - 0.3·X
Consequently, we have when the line speed is 25 feet per minute;
Y = 27.5 - 0.3 × 25 = 20
When the line speed is 25 feet per minute, Y = 20 faulty components should be expected to be identified.
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an airport escalator is designed to move 42 people, 75 kg each, upward at a constant speed of 0.6 m/s at 45o slope. determine the minimum power input needed to drive this escalator.
The minimum power input needed to drive this escalator is
15.59 kw.
What is escalator?
A moving staircase that transports people between floors of a building or other structure is called an escalator. It is made up of a motor-driven chain of separately linked steps on a track that rotates on two other tracks, keeping them horizontal.
Given:
[tex]N_p = 50\\m_p = 7.5 kg\\V = 0.6m/s\\[/tex]
θ = 45°
Total mass = 50 x 75 = 3750 kg
The energy required = Change in potential energy
ΔE = mg ΔZ
Power = ΔE/t = mg(ΔZ/t)
ΔZ/t = vsinθ = 0.6 sin(45°) = 0.4247
Power = mg x 0.4243 = 3750 x 9.8 / 100 x 0.4243
P = 15.59 kw
Hence, the minimum power input needed to drive this escalator is
15.59 kw.
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