The moment of inertia for rotation about the z axis is [tex]I & =\frac{a^2 M}{3}[/tex].
A triangular prism of mass m, whose two ends are equilateral triangles.
Two ends are equal.
The xy plane with side 2a, is centered on the origin with its axis along the z axis.
Find the moment of inertia for rotation the z-axis.
It is divide into 4 triangles with side 'a' k one side is 3cm.
[tex]$$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$[/tex]
It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.
Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.
[tex]$$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$[/tex]
[tex]$$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$[/tex]
⇒ Now, by using the [tex]$I_{\text {Big }}=I$[/tex]
⇒[tex]I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\[/tex]
⇒[tex]4 I & =I+a^2 m[/tex]
⇒[tex]4 I-I & =a^2 m \\[/tex]
⇒[tex]3 I & =a^2 M . \\[/tex]
⇒[tex]I \quad & =\frac{a^2 M}{3}[/tex]
Therefore, the moment of inertia is [tex]I & =\frac{a^2 M}{3}[/tex].
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In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 190 pounds in the summer, including clothing and carry‑on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 35 pounds. Weights are not normally distributed, especially when the population includes both men and women, but they are not very non‑Normal. A commuter plane carries 22 passengers. What is the approximate probability P that the total weight of the passengers exceeds 4500 pounds? Use the four‑step process to guide your work. Give your answer as a percentage precise to two decimal places. P=___?
The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Total of 22 is more than 4500 is equivalent to average of 22 is more than [tex]$\frac{4500}{22}[/tex]=204.545
[tex]$$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$[/tex]
= 1 - 0.8997
= 0.1003
= 10.03%
Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.
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please help me will give u extra points :)
•
From the graph, the compound inequality represented is x < -2 and x > 5
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequalities shows the non equal comparison of two or more numbers and variables. Compound inequality is an inequality that is composed of more than one inequality.
From the graph, the inequality is not a solid circle, so it is either > or < sign.
From the graph, the inequality shown is x < -2 and x > 5
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how to solve that and what is the answer
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let 's' be the cost of the skirt. Then the equation is given as,
3/4(18 + s) = 31.50
The equation that represents the cost of the skirt will be 3/4(18 + s) = 31.50. Then the correct option is D.
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Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
x-7=-2
scores on the mathematics part of the sat exam in a recent year were roughly normal with mean 515 and standard deviation 114. you choose an srs of 100 students and average their sat math scores. suppose that you do this many, many times. which of the following are the mean and standard deviation of the sampling distribution of a) Mean =515,SD=114 (b) Mean =515,SD=114/√100 (c) Mean =515/100,SD=114/100 (d) Mean =515/100,SD=114/√100 (e) Cannot be determined without knowing the 100 scores.
The mean and standard deviation of the sampling distribution of the sample mean (average) of the SAT math scores are:
(b) Mean = 515, SD = 114/√100
SAT Math Scores Mean, SDThe mean of the sampling distribution of the sample mean is equal to the population mean (515), because the expected value of the sample mean is equal to the population mean. The standard deviation of the sampling distribution of the sample mean is called the standard error, and it is equal to the population standard deviation divided by the square root of the sample size (114/√100).
The result (b) is determined based on the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is 515 and the population standard deviation is 114, so the standard deviation of the sampling distribution of the sample mean is equal to 114/√100. This result can be mathematically proven using the formula for the standard deviation of the sample mean:
SD of sample mean = σ/√n, where σ is the population standard deviation and n is the sample size.
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two letters without replacement from the three letters a b and c how many ways can this be done if the order of choice is taken into consideration how many ways can this be done if the order of the choices is not taken into consideration
Answer:
If order is considered = 6
If order is not considered = 3
Step-by-step explanation:
If order is to be taken in consideration then the following values can be taken:
a, b
a, c
b, a
b, c
c, a
c, b
Total = 6 ways
If order is not taken in consideration then the following values can be taken:
a, b
a, c
b, c
Total = 3 ways
Point P is on line segment O Q . Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾ . PQ
Answer: PQ is 9 units.
Step-by-step explanation:
The length of PQ can be found using the proportion of OQ and OP.
(PQ / OQ) = (OP / OQ)
PQ = (OP / OQ) * OQ
Substituting in the given values:
PQ = (9 / 11) * 11
PQ = 9
Therefore, the length of PQ is 9 units.
Given the following diagram what can you conclude?
Answer:
YXZ=AXZ
because if you see the letters they form triangle
Find the value of M and N
Answer: n=110, m=110
Step-by-step explanation: I think m=110 because of vertical angles. m might also equal 70.
Which solution for the value of x is right? 4x - 2 = 3x + 6 or 4x - 2 +3x+6=180
Answer:
Step-by-step explanation:
4x+3x=6+2
7x/7=8/7
=1.143
Answer: X=22
According to equation given :-
4x-2=3x+6 ----------------------(1)
4x - 2 +3x+6=180 -------------(2)
hence put equation (1) in (2) which that
4x - 2 +4x-2=180
2* ( 4x-2 ) = 180
4x-2 =90
4x = 88
x= 22 (answer)
A 9 footbpiece of twine costs $8.64. What is the price per inch?
Answer: 0.08 dollars
Step-by-step explanation:
8.64 divided by 9 = 0.96
0.96 divided by 12 = 0.08
A jar contains 7 poker chips: 4 blue, 2 red and 1 white. You randomly select two chips from the jar. What is the probability that your selection includes two different colored chips? Report your answer to three decimal places.
The probability of selecting two different coloured chips is the fraction 14/49.
What is probability?Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.
total possible outcome = 7
blue chips = 4
red chips = 2
white chips = 1
probability of selecting blue chips = 4/7
probability of selecting red chips = 2/7
probability of selecting white chips = 1/7
probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7
probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49
probability of selecting two coloured chips at random = 14/49
Therefore, the probability of selecting two different coloured chips is the fraction 14/49
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Every day, Patrick's orange juice stand uses 3/4 of a bag of oranges. How many days will 1 1/2 bags of oranges last?
Answer:
2 days
Step-by-step explanation:
We want to divide 1 1/2 by 3/4
1 1/2 ÷ 3/4
Change the mixed number into an improper fraction.
3/2 ÷ 3/4
Copy dot flip
3/2 * 4/3
Rewrite
3/3 * 4/2
1 * 2
2
It will last 2 days
my’s Annual Expenditures
Rent $ 8,580.00
Utilities $ 3,480.00
Internet & Phone $ 1,896.00
Entertainment $ 2,232.00
Student Loan Payment $ 4,116.00
Home & Auto Insurance $ 1,164.00
Food $ 6,000.00
Car Payment & Gas $ 2,820.00
Travel $ 1,200.00
Savings $ 1,200.00
Personal Expenses $ 1,847.00
Pet Expenses $ 965.00
Business Expenses $ 4,800.00
Q1. Amy’s day job is as a secretary at a law firm. After taxes and health insurance, she nets $1550 bi- weekly. How much does Amy net in a year from her day job?
Q2. Based on her net income and annual expenditures summary, by how much did Amy over or under spend this year?
Part a: Amy's net amount in a year from her day job is found as $40411.
Part b: Amy under spend this year by amount $8331.
Define the term annual expenditure?Just before annual contribution margin, all expense items in the profit and loss statement, including operating costs including finance charges, are referred to as annual expenditure.Part a:
The calculation is done bi- weekly.
Total days = 2*7 = 14.
Net amount = $1550.
Net amount for the year = (1550/ 14)*365
Net amount for the year = $40411
Thus, Amy's net in a year from her day job is found as $40411.
Part b:
Total amount spend : Sum of all expenditures.
Total amount spend : $32,080
Difference = $40,411 - $32,080
Difference = $8331
Thus, based on her net income as well as annual expenditures summary,
Amy under spend this year by amount $8331.
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i need help solving rhis problem please show your work
The length of the GH is 4, when H is the midpoint of GI.
What is midpoint of a line?An area of a line that connects two distinct locations is referred to as a line segment. It is the least path between two places that can be determined to have a length.
A line segment's midpoint is the point on the segment when it is divided into two similar segments. The point on a line segment that is equally spaced from the two terminating points is known as the midpoint of the segment.
Given that H is the midpoint of GI.
Then we can say that,
GI / 2 = GH
Substitute the equations of the length of GH and GI as given:
(9x - 19) / 2 = 3x - 5
9x - 19 = 2(3x - 5)
9x - 19 = 6x - 10
9x - 6x = -10 + 19
3x = 9
x = 3
Substitute the value of x in the equation of the length of the segment GH thus:
GH = 3x - 5
GH = (3)(3) - 5
GH = 4
Hence, the length of the GH is 4, when H is the midpoint of GI.
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If you spent $20,750 for goods, service and housing in 2000, what would the same purchase have cost in 1984?
Answer:
below
Step-by-step explanation:
20750 is to 172.2 as x is to 103.9
20750 /172.2 = x / 103.9
x = $ 12519.89
3. A dilation is represented in the following table. Determine the scale factor for the dilation.
Express your answer in function notation (x,y) → (kx,ky).
Pre-Image
Image
I
(2,4)
(1, 2)
(1, 0)
(0.5, 0)
(-4,-1)
(-2,-0.5)
The scale factor of the dilation, expressed in function notation, (x, y) → (k·x, k·y), is (x, y) → (0.5·x, 0.5·y)
What is a dilation transformation?A dilation transformation is a transformation in which the dimensions of the image are obtained by multiplying the dimensions of the pre-image by a value, known as a scale factor of the dilation.
The possible table, based on the similarities of the coordinate points can be presented as follows;
Pre-Image [tex]{}[/tex] Image
(2, 4) [tex]{}[/tex] (1, 2)
(1, 0) [tex]{}[/tex] (0.5, 0)
(-4, -1) [tex]{}[/tex] (-2, -0.5
The specified formula for the image, following the dilation of the point (x, y) by a scale factor of k is; (x, y) → (k·x, k·y)
Therefore, we get;
k = k·x/x = k·y/y
The comparison of the points in the table with the points (x, y), and (k·x, k·y), indicates that we get;
When (x, y) = (2, 4) and (k·x, k·y) = (1, 2)
Therefore;
k = k·x/x = k·y/y = 1/2 = 2/4 = 0.5
The scale factor of the dilation , k = 0.5, therefore;
(x, y) → (0.5·x, 0.5·y)
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Determine the value of h such that the matrix is the augmented matrix of a consistent linear system.
[1 h 4
3 6 8]
The value of h can be any value other than 2.
Value of h for Consistent SystemThe augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.
For the given matrix, the coefficient matrix is:[1 h
3 6]
The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.
For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.
Therefore, the value of h can be any value other than 2.
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if monique wanted to run 7/8 mile and she went to the school track which was one quater of a mile long how lany laps would she have to run
Which of the following questions could I use to find the answer check all that apply.
A. L x 1/4=7/8. YES OR NO
B. 7/8 x 1/4 = L. YES OR NO
C. 7/8 X 4=L. YES Or NO
D. L/ 7/8 = 1/4. YES OR NO
hURRY
if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is
C. 7/8 X 4 = L. What is a lap in race?One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.
A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows
assuming the number of laps is L
1 lap = 1/4 mile
L laps = 7/8 miles
cross multiplying
1 * 7/8 = L * 1/4
multiplying by 4 for each side
1 * 7/8 * 4 = L * 1/4 * 4
1 * 7/8 * 4 = L * 1
7/8 * 4 = L
hence option C is correct
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A radio tower is located 300 feet from a building. From a window in the building, a person determines that
the angle of elevation to the top of the tower is 38° and that the angle of depression to the bottom of the
tower is 29°. How tall is the tower?
Round your answer to 2 decimal places
The height of the tower is 600 feet
What is angle of elevation and the angle of depression?
Angle of elevation: The angle of elevation is the angle produced by the line of sight with the horizontal when the item is above the horizontal level.
Angle of depression: The angle of depression is the angle produced by the line of sight with the horizontal when the item is below the horizontal level.
Let's call the height of the tower "h".
Using trigonometry, we can set up equations based on the angles of elevation and depression:
tan 38° = h / 300
tan 29° = (h - 300) / 300
Solving for h,
h = 300 * tan 38°
h = 300 * 0.8192
h = 245.76
Now,
300 * tan 29° = (h - 300) / 300
300 * 0.5672 = (h - 300) / 300
h - 300 = 300 * 0.5672 / 0.5672
h - 300 = 300
h = 600
So, The height of the tower is 600 feet, rounded to 2 decimal places.
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You roll two six-sided dice numbered from one through six. What is the probability that the maximum of the two dice is greater than or equal to six? Report your answer to three decimal places.
The probability that the maximum of the two dice is greater than or equal to six is 0.722.
What is probability?
Probability is a way of calculating how likely something is to happen. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.
We are given that two six-sided dice numbered from one through six are rolled.
The sample space of the event is
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Probability that the maximum of the two dice is greater than or equal to six is
26 out of 36 i.e. 26/36
This is equal to 0.722.
Hence, the probability that the maximum of the two dice is greater than or equal to six is 0.722.
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which of the following statements are true of an event listener's callback function? (select all that apply) A.It will be called every time the event listener is triggered B.Idon't know It must always define a parameter for the event object C.It must be passed to the event listener as the second argument D.It can be either an anonymous or a named function
Out of the following statements A)It will be called every time the event listener is triggered, C. It must be passed to the event listener as the second argument and D.It can be either an anonymous or a named function that is true of the event listener's callback function.
An event listener's callback function is a function that is triggered when an event is fired and the callback function is responsible for handling the event. A callback function must be passed to the event listener as the second argument, and it can be either an anonymous or a named function.
The callback function will be called every time the event listener is triggered, and it must always define a parameter for the event object. This allows the callback function to access the event object's properties and methods to handle the event accordingly. The event object contains information about the event, such as the type of event, the target element, and more. By accessing this information, the callback function can determine how to handle the event.
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Traveling 120km total, 1st 59km are 90km P/h. Remaining km are 50km P/h. How long does the trip take total?
The total trip took a total of 1.87 hours.
What is the speed of an object?Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time
Given here: Total distance=120 km and 59 km at 90 km/hr and the remaining distance at 50 km/hr
Remaining distance= 120-59
=61 km
Thus for the first 59 km the time it took was
Time= Distance/ Speed
= 59/90
=0.65 hr
Similarly time taken for the second part of the journey is = 61/50
=1.22
Hence, total time taken for the trip is 1.22+0.65=1.87 hr.
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Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + [1/(32√2)] + [1/(243√3)] + [1/(1024√4)] + [1/(3125√5)] + ….
p = _____
A. converges B. diverges
The answer is B. diverges.
Theorem 9.11 states that if the sequence of positive terms (an) satisfies the condition 1/an^p converges, then the p-series ∑an converges if p > 1 and diverges if p ≤ 1. In this case, the positive terms of the sequence are given by [1/(n^(3/2))]. So, [1/an^p] = [1/(n^(3/2))^p] = [1/n^(3p/2)].
For the series to converge, we need [1/an^p] to converge, or [1/n^(3p/2)] to converge.
If 3p/2 > 1, then [1/n^(3p/2)] converges and the series converges.
If 3p/2 ≤ 1, then [1/n^(3p/2)] diverges and the series diverges.
So, to determine the value of p, we need to find the value of p such that 3p/2 = 1. Solving for p, we find that p = 2/3.
Since 2/3 ≤ 1, the series diverges. Therefore, the answer is B. diverges.
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show that if xt x is not invertible, then at least one column of x is a linear combination of the others. this implies that there is only one way in which problem with invertibility of xt x may arise'
If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.
This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.
If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:
c = k1a + k2b
where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.
This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.
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Your question is incomplete, but most probably, the full question was:
Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise
What is the volume of the cube shown?
WILL GIVE BRAINLEST
Answer:
11.390625 in^3
Step-by-step explanation:
2.25^3 = 11.390625 in^3
Evaluate the limit.
A farmer wants to build a fence around the edge of a field shaped like a right-angled triangle, as shown below. The fence costs £1.26 per metre.
Calculate the total cost of the fence.
Give your answer to the nearest pound.
To calculate the total cost of the fence, we need to know the length of the fence.
In a right-angled triangle, the length of the fence can be calculated using the Pythagorean theorem, which states that the length of the hypotenuse (the fence) is equal to the square root of the sum of the squares of the other two sides (the base and the height of the triangle).
So, the length of the fence (C) = square root of (A^2 + B^2), where A is the base and B is the height of the triangle.
If the base of the triangle is x and the height of the triangle is y, then the cost of the fence can be calculated using the formula:
Cost = (length of fence) x (cost per meter)
Cost = (square root of (x^2 + y^2)) x 1.26
In order to calculate the cost, the farmer needs to know the values of x and y.
The total cost of the triangular shaped fence is A = £ 530
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AB = 145 m
Now , the measure of ∠BAC = 59°
From the trigonometric relations
tan θ = opposite / adjacent
tan 59° = BC / 145
Multiply by BC on both sides , we get
BC = 241.320524941 m
Now , the hypotenuse of the triangle is
H = √ ( 145 )² + ( 241.320524941 )²
H = √ ( 21,025 + 58,235.595757
H = √79,260.595757
H = 281.53258 m
Now , the total perimeter of triangle is P = 281.53258 + 241.320524941 + 145
P = 667.85310877 m
Now , fence costs £1.26 per meter
A = 667.85310877 m / £1.26
So , the total cost is A = £ 530
Hence , the total cost is A = £ 530
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Please help me with this question.
The solution to the system of equations in this problem is given as follows:
X = [28571
14286].
How to solve the system of equations?The system is defined by the following equation:
X = DX + E.
The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:
0.2A + 0.3B = 10000.0.5A + 0.4B = 20000.Inserting this system into a calculator, the solution is given as follows:
A = 28571.B = 14286.Hence the matrix X is given as follows:
X = [28571
14286].
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5y+8-2y=4y-y+5
Can someone please help im failing math (like explain the steps pls)
Answer: false
Step-by-step explanation: 1st we collect the Like Terms which would make the new equation 3y + 8 = 3y + 5 then we can cancel the 3y's bc they're equal and leaves us with 8 = 5 which we could see is false, so this equation is false
