The brass strip AB has been attached to a fixed support at A and rests on a rough support at B. Knowing that the coefficient of
1 answer:
Answer:
Decrease in temperature = 4.6714°C
Step-by-step explanation:
We know that the formula fro deflection is:
δ = PL/AE + LαΔT
As deflection is equal to zero in this case, the formula becomes
ΔT = -P/αAE -------------- equation (1)
Now,
we see that only vertical force acting is weight
W = mg = 100*9.81
W = 981N = ∑ where 1N = 1kgm/s²
Now,
for horizontal forces
As we know that, Sum of all horizontal forces = 0
P - μN = 0
P - μW = 0
P = μW
P = 0.6 * 981
P = 588.8N or 589N
Now we need to calculate the area
area = width * thickness = 20 * 3
area = 60 mm²
Now by substituting all these values in equation 1, wee get
ΔT = -P/αAE = - 588.6/(20*10⁻⁶*60*10⁻⁶*105*10⁹)
ΔT = - 4.6714°C (negative sign indicates decrease)
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Answer:
Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because
Step-by-step explanation:
The complete question in the attached figure
we know that
If the length sides of a triangle, satisfy the Pythagorean Theorem, then is a right triangle
where
c is the hypotenuse (the greater side)
a and b are the legs
In this problem
The length sides squared of the triangle are equal to the areas of the squares
so
substitute
----> is not true
so
The length sides not satisfy the Pythagorean Theorem
therefore
Based on the converse of the Pythagorean Theorem, the triangle is not a right triangle, because
Answer:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:Step-by-step explanation:
A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12. Find the probability that the sample mean is in the interval 47<=X<53. Is the assumption of normality important. Why?
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
We can find the probability required like this:
And using a calculator, excel ir the normal standard table we have that:
And we can calculate the probability like this:
Answer:
a)
b)
c)
Step-by-step explanation:
Data given
Assuming the following data:
Method A: 18.0, 18.0, 18.0, 20.0, 22.0, 22.0, 22.5, 23.0, 24.0,24.0,25.0,25.0, 25.0,25.0,26.0,26.4
Method B: 18.8, 18.9, 18.9, 19.6, 20.1, 20.4, 20.4, 20.4, 20.4,20.5, 21.2. 22.0,22.0, 22.0,22.0,23.6
Method C: 20.2, 20.5, 20.5, 20.7, 20.8, 20.9, 21.0, 21.0,21.0,21.0, 21.0, 21.5,21.5,21.5,21.5,21.6
Method D: 20.0, 20.0, 20.0,-20.0, 20.2, 20.5, 20.5, 20.7, 20.7,20.7, 21.0, 21.1, 21.5, 21.6, 22.1,22.3.
Part a
The sample mean is defined as:
If we apply this formula for the four methods we got:
Part b
Since the total number of points for each method is 16 and this is an even number we need to calculate the median as the average between the 8th and the 9th position of the data ordered from the smallest to the largest. If we do this we have that:
Part c
The trimmed mean by 20% means that we need to calculate removing the 20% from each of the tails, the 20% of 16 is 3.2, so we need to remove 3 observations from both ends of the data like this:
Method A: 20.0, 22.0, 22.0, 22.5, 23.0, 24.0,24.0,25.0,25.0, 25.0
Method B: 19.6, 20.1, 20.4, 20.4, 20.4, 20.4,20.5, 21.2. 22.0,22.0
Method C: 20.7, 20.8, 20.9, 21.0, 21.0,21.0,21.0, 21.0, 21.5,21.5
Method D: 20.0 20.2, 20.5, 20.5, 20.7, 20.7,20.7, 21.0, 21.1, 21.5.
If we calculate the mean for each method we got: