5 flight attendants are required.
The number of flight attendants required on an aircraft is determined by regulatory agencies such as the Federal Aviation Administration (FAA) in the United States and the European Aviation Safety Agency (EASA) in Europe.
The number of flight attendants depends on several factors, including the type of aircraft, the number of passenger seats, the length of the flight, and the number of passenger exits.
The number of flight attendants required can be determined by the following formula:
The minimum number of flight attendants = (N / 50) + 1 where N is the number of passenger seats.
So, for an aircraft with 275 seats and 249 passengers:
(249 / 50) + 1
= 5 flight attendants are required.
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When Kyle doesn't study for his tests, he has a 45% chance of passing. If Kyle didn't study for15 tests this semester, what is the probability he passed at this semester?
The probability that Kyle will pass all 15 tests if he does not study for them is approximately 0.0017.
This is because the probability of passing each individual test without studying is 0.45, and the probability of passing all tests without studying is equal to 0.45 multiplied by itself 15 times, which is 0.0017. This means that the odds of Kyle passing all 15 tests without studying are very slim.
Even if he has a good understanding of the material and has been able to recall the information without studying, it is very unlikely that he will be able to do so for all 15 tests. It is therefore recommended that Kyle studies for his tests in order to increase his chances of passing them.
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(exercise 2: find the critical points of the gompertz equation (1). (is y = 0 a critical point? does it solve the algebraic equation you get?).dy = ry In(K/y
y = k asymptotically stable critical point because f'(k) < 0 and f'(0) > 0. So y = 0 is an an asymptotically unstable critical point.
The Gompetz equation is dy/dt = ry In(K/y).
In order to find critical points equate dy/dt equal to zero
dy/dt = 0
ry In(k/y) = 0
Here, k and r are constants
y In(k/y) = 0
y = 0
In (k/y) = 0
Eliminating In
k/y = e^0
k/y = 1
Multiply by y on both side, we get
k = y
y = 0 and y = k
The critical points are 0 and k
Since zero is a critical point
dy/dt = f(y)
dy/dt = ry In(k/y)
Differentiation on both side
f'(y) = ry In(k/y) - ry × y/k × k/[tex]y^2[/tex]
f'(y) = r In(k/y) - r
f'(k) = r In(k/k) - r
f'(x) = -r < 0
So that, y = k asymptotically stable critical point because f'(k) < 0
f'(0) > 0
That means y=0 is asymptotically unstable critical point.
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the vector a2 is in w if and only if a2 can be written in the form c1a1 c2a2 c3a3 with
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
What is vector ?
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.
Let W be a subspace of a vector space V and let a1, a2, and a3 be vectors in V. The vector a2 is in the subspace W if and only if it can be written as a linear combination of the vectors a1, a2, and a3. That is, there exist scalars c1, c2, and c3 such that:
a2 = c1 * a1 + c2 * a2 + c3 * a3
This equation can be written in matrix form as:
[a2] = [a1 a2 a3] * [c1; c2; c3]
where [a2] is the column vector representation of a2, [a1 a2 a3] is the matrix with a1, a2, and a3 as columns, and [c1; c2; c3] is the column vector of scalars c1, c2, and c3.
Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.
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Trapezoid HRNB is shown with midsegment MS.
HM = (5x-3),
MB = (x + 5)
HR=(2y+3).
MS (4y - 3). and
BN= (10x+1)
What is the value of a?
What is the value of y?
the value of x=2 and y =5, for the given trapezoid.
What is trapezoid?
A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.
Given, HM =5x-3
BM = x+5
So 5x-3 = x+5
4x = 8
x = 2.
and (4y - 3) =(2y+3)+(10x+1) /2
8y-6 = 2y+3 + 10x+1
6y = 10+20
y =5
Hence the value of x=2 and y =5, for the given trapezoid.
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How do I find the measure of angle ABE?? 43
The required measure of supplementary angle ∠ABE is 137°.
What are the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
The measure of a supplementary angle to an angle with measure x is defined as 180°-x. Therefore, the measure of the supplementary angle ∠ABE to an angle with a measure 43° is:
∠ABE = 180° - 43° = 137°
Thus, the required measure of supplementary angle ∠ABE is 137°.
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sandeep, hee, sara, and mohammad play euchre with a standard deck consisting of 24 cards (a, k, q, j, 10 , and 9 from each of the four suits of a regular deck of playing cards). in how many ways can the deck be dealt so that each player receives 5 cards, with 4 cards left in the middle, one of which is turned face-up? the order of the 3 cards that are left face-down in the middle does not matter, but who receives a particular set of 5 cards (for example, sara or sandeep) does matter.
There are 23,311,945,600 possible ways to deal the cards to the four players and choose one card to be turned face-up in the middle.
We can calculate the number of ways to deal the cards to the four players and then multiply by the number of ways to choose which card is turned face-up in the middle.
First, there are 24 choose 5 ways to deal the first hand, since each player receives 5 cards. Then, there are 19 choose 5 ways to deal the second hand, since there are now 19 cards left. Similarly, there are 14 choose 5 ways to deal the third hand and 9 choose 5 ways to deal the fourth hand.
So, the number of ways to deal the cards to the four players is:
24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!))
Now, we need to multiply this result by 4, since there are 4 possible cards to turn face-up in the middle. So, the final answer is:
4 * 24 choose 5 * 19 choose 5 * 14 choose 5 * 9 choose 5 = 4 * (24! / (5! * 19!)) * (19! / (5! * 14!)) * (14! / (5! * 9!)) * (9! / (5! * 4!)) = 4 * 5,827,986,400 = 23,311,945,600.
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we plan to turn over the first 3 cards in a well-shuffled deck of 52 cards. compute the probability that both the second and third cards are the same suit.
Answer is 1/104. Probability is a branch of mathematics that deals with numerical descriptions of the probability of an event occurring or the probability that a statement is true.
What is the probability that both the second and third cards are the same suit?
Probability that the first card is a club = 1/4. (There are 13 club cards in the deck, and 13/52 = 1/4). Probability that the second card is a 3 = 1/13. (There are four 3 cards in the deck, and 4/52 = 1/13). Probability that the third card is red = 1/2. (There are 26 red cards in the deck, and 26/52 = 1/2). The probability of an event is a number between 0 and 1, where 0 represents approximately an impossibility and 1 represents a certainty. The higher the probability of an event, the more likely the event will occur. A simple example is mining a fair (impartial) coin. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely; the probability of heads is equal to the probability of heads; and since no other outcome is possible, the probability of "heads" or "heads" is 1/2 (which can also be written as 0.5 or 50%).
Probability that the first card is a club, the second card is a 3, and the third card is red = 1/4 * 1/13 * 1/2
= 1/104
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as an architect, you are designing a new house. a window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. what are the smallest and largest areas that the window could be?
The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of rectangle .
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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The smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
This problem is based on the area of a rectangle.
Here, since the height and the width of the window are distinct, so the window can be assumed to be of rectangular shape.
Now, the area of a rectangle is given by = l x b where l and b are respectively the height and the width of the window respectively.
The area would be smallest when both the height and width are least i.e. 140 cm and 70 cm .
So, smallest area = lxb = 140 x 70 = 9800 sq. cm = 9.8 sq. m.
Similarly, the largest area would be when both the height and the width are maximum i.e. largest area = lxb = 150x 74 = 11,100 sq cm. =11.1 sq metres.
Therefore, the smallest and the largest area of the window will be 9.8 and 11.1 sq. metres respectively.
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pls help I can't figure out the problem and I need help it worth a lot of points in my grade
Answer:
Perimeter 18.42
Area 20.13
Step-by-step explanation:
Perimeter:
This is the distance around the figure.
The distance around the triangle is 9.
The distance around the 1/2 circle
c= 2[tex]\pi[/tex]r
c [2(3.14)(3)]/2
c = 9.42
9.42 + 9 = 18.42
Area:
triangle
a = 1/2(bh)
a - 1/2 (3)(4)
a = 6
circle
a = 1/2([tex]\pi r^{2}[/tex])
a = 1/2(3.14)(9)
a = 14.13
6 + 14.13 = 20.13
Please help need this done asap
A. KP = ST is given
B. Given as PR = TV is known
C. KP + PR = ST + TV using the addition property.
D. Segment addition in KP + PR = KR
E. ST + TV = SV
F. Segment addition has obtained this answer
G. KR = SV by substitution property
The solution has been obtained by using the concept of mathematical reasoning.
What is mathematical reasoning?
In mathematics, reasoning entails making logical deductions from data or presumptions.
A. For this, we are stated a reason that it is given.
So, the statement is KP = ST.
B. We are given the statement as PR = TV
The reason is that it is given.
C. For this, we are stated a reason that it is obtained by addition property.
So, the statement is KP + PR = ST + TV.
D. We are given the statement as KP + PR = KR
The reason is that it is obtained by segment addition.
E. ST + TV = SV is the statement
F. The reason for the statement is that it is obtained by segment addition.
G. For this, we are stated a reason that it is obtained by substitution property.
So, the statement is KR = SV.
Hence, the statements and their respective reasons have been arranged.
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Se conoce el peso ideal de un niño de 5 años en Colombia es de 20Kg. Escriba una frase que indique a cuántos kilogramos está cada niño, por debajo, por encima del peso ideal.
a. Juan pesa 22kg b. Mario pesa 18Kg c. Pedro pesa 26kg d. Alfredo pesa 20Kg
a) Juan, 2 kg de encima
b) Mario, 2 kg por debajo
c) Pedro, 5 kg por encima
d) Alfredo, Tiene el peso preciso
Qué se entiende por diferencia en matemáticasOperaciones aritméticas incluyen suma, resta, multiplicación y división
La diferencia en matemáticas es una operación aritmética de resta entre dos números grandes con un número pequeño para que el resultado sea siempre positivo.
La diferencia en matemáticas es también la diferencia de valor entre dos números
Ejemploa) la edad de Dewi = 25 años
edad de Adi = 51 años
entonces
Diferencia de edad entre A y B
= (51 – 25) años
= 26 años
Entonces la diferencia en sus edades es 26 años
b) El dinero de A = IDR 13,000.00
Dinero de B = IDR 10,500.00
entonces diferencia en su dinero es
= 13.000,00 IDR – 10.500,00 IDR
= 2.500,00 IDR
Entonces, la diferencia o la diferencia en su dinero es IDR 2,500.00
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When the p-value is used for hypothesis testing, the null hypothesis is rejected ifa)p-value ≤ αb)α < p-valuec)p-value ≥ αd)p-value = 1 - α
If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .
In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.
The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.
If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.
Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .
The given question is incomplete , the complete question is
When the p-value is used for hypothesis testing, the null hypothesis is rejected if
(a) p-value ≤ α
(b) α < p-value
(c) p-value ≥ α
(d) p-value = 1 - α
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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.
The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.
If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.
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Explain why each of the following expressions makes no sense. (dot product )(a) u\bullet(v\bulletw)(b) (u\bulletv)+w(c) ?u\bulletv?(d) k\bullet(u+v)
All the given statements does not make sense by the definition of dot product.
(a) (dot product)(a): The dot product is a mathematical operation and doesn't take any arguments or values, so this expression doesn't make sense as written.
(b) u\bullet(v\bulletw): The dot product is associative, meaning that u\bullet(v\bulletw) = (u\bullet v)\bullet w. However, the expression itself is not well defined, since the inner expression v\bullet w doesn't specify what values v and w represent.
(c) (u\bullet v) + w: The dot product is an scalar product, meaning it results in a scalar value, and adding a scalar to a vector does not make sense mathematically.
(d) k\bullet(u+v): The dot product is between two vectors, and the expression k\bullet(u+v) implies that the dot product is between a scalar (k) and a vector (u+v). This does not make mathematical sense, as the dot product is only defined between two vectors of the same dimension.
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write an equivalent expression to the following: 5y + 35 HINT: think distributive property.
Answer:
5(y+7)
Step-by-step explanation:
Answer:
5(y + 7)
Step-by-step explanation:
Need some help ASAP!
Given: AD, BE and FC intersect at point P. AD⊥FC.
Write at least 6 algebra equations to relate different pairs of angles. Justify your statements with the correct definition or theorem.
The required six algebraic equations to relate the given different pairs of angles are in the solution part.
What are supplementary angles?The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.
Given: AD, BE and FC intersect at point P.
AD⊥FC.
According to the given figure, the required equations would be as:
m∠APB = m∠EPD (vertical angles)
m∠FPD = m∠APC (right angles are congruent)
m∠EPC + m∠EPF = 180 degrees (linear pair)
m∠BPC = m∠EPD (vertical angles)
m∠APB + m∠BPC = 90 degrees (complementary angles)
m∠FPB + m∠BPC = 180 degrees (linear pair)
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in the standard normal curve, what percent of data lies between 0 and 1 standard deviation?
About 68% of the data in a typical normal curve is within one of the mean's standard deviation. Accordingly, 68% of the data should fall between -1 and 1 if the data's mean was 0 and its standard deviation was 1.
A theoretical continous probability distribution known as the "standard normal curve" depicts a bell-shaped, symmetrical curve. The normal distribution or the Gaussian distribution are other names for it. The standard normal curve, which serves as a benchmark for other normal distributions, has a means of 0 and a variance of 1. For simpler analysis and comparison, data sets can frequently be translated into the normal form standards. The distributions of many real-world events, including IQ scores, length, weight, and heart rate, to mention a few, is described by the curve, which is significant in statistics. Among other uses, the normalised curve is employed in statistical inference, quality control, and hypothesis testing.
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Determine the value of the variable that makes the equation true.
1=-10c
The value of the variable that makes the equation true -1/10
What is an equation?An equation is a mathematical statement that shows the equality of two or more things. that is An equation is a mathematical statement that shows that two mathematical expressions are equal
The given equation is 1=-10c
To make the statement true, we have to determine the value of the variable c
this is done by making the variable c the subject of the relation
Now, 1/-10 = -10c/-10
Therefore c = -1/10 makes the equation true
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Whats the slope and y-intercept
2x-6y=24
I think I know the intercept I just don't know the slope.
Answer:
x-6y=-24
Step-by-step explanation:
do it
Answer:
Step-by-step explanation:
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope and y-intercept of the equation 2x - 6y = 24, you can first isolate y by adding 6y to both sides and then dividing both sides by -6. This gives you: y = (-1/3)x + 4
So, the slope is -1/3 and the y-intercept is 4.
Tramaine is using a carton of chicken stock that contains 4 1/2 pints of chicken stock. He will use the 3/5 carton to make a stew and he will use the rest of the carton to make rice. How many pints of chicken
stock with Tramaine use for each dish?
Using the given fractions, we can see that for the stew they use (27/10) pints and for the rice (18/10) pints.
How many pints of chicken stock with Tramaine use for each dish?
We know that the carton has a volume of:
(4 + 1/2) pints of chicken stock.
He uses 3/5 of the carton to make a stew, so he uses:
(3/5)*(4 + 1/2) pints = (12/5 + 3/10) pints
= (27/10) pints.
And the rest, (2/5) of the carton, is used to make rice, then:
(2/5)*(4 + 1/2) pints = (8/5 + 2/10) pints = (18/10) pints.
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Two teams need to raise $100 each for their end-of-the-year field trips. Team A wants to sell popcorn at the Spring Fling Carnival, and Team B wants to sell cotton candy. It costs $15 to rent a popcorn machine and it costs $25 to rent a cotton candy maker. The cost of additional supplies for the popcorn is $0.05 per bag. The additional cost for the cotton candy is $0.10 per stick. Team A will sell the bags of popcorn for $0.50 each. Team B will sell the cotton candy for $0.75 per stick.
What is the least number of items Team B will need to sell to avoid losing money?
Team B will need to sell at least 192 candies to avoid losing money.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given total amount to be raised by each team is $100,
Team B wants to sell cotton candy,
rent of candy machine = $25
total cost to be earned for team B = $100 + $25 = $125
let the number of candies sold be x
cost used in candy sticks = $0.10 per stick
cost used in x candy sticks = $0.10x
the selling price of each candy = $0.75
the selling price of x each candy = $0.75x
total gain = $0.75x - $0.10x
total gain = $0.65x
minimum candies to be sold for no loss
$0.65x = $125
x = 125/0.65
x = 192.30
x = 192
Hence for no loss, at least 192 candies are to be sold.
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What is the value of x in this triangle?
Enter your answer in the box.
Answer:102+31-180 = 47
so x = 47
Step-by-step explanation:
this is very simple
You'll earn 95 points! ASAP please
Suppose you bought 8 mangoes and four apples for $20 and 3 mangoes and 6 apples for $16.50. What is a system of equations that represents the situation? how much does each mango and each apple cost?
Answer: Apples: $2 Mangos: $1.50
Step-by-step explanation:
8m+3a = 183m+5a=14.5
Multiply the first equation by 5 and multiply the second equation by 340m+15a=909m+15a=43.5
Subtract the equations
31m=46.5m=46.5/31m=1.5
Substitute to find the price of apples
8(1.5)+3a=1812+3a=183a=18-123a=6a=2
Apples cost $2.00 each mangoes cost $1.50 each
Write an equation for this line.
Answer:
y = -2
Step-by-step explanation:
The equation is y = mx + b
But this line has no slope, but it has a y-intercept at (0,-2), so the equation is
y = -2
solve for x: x 2a-b=3(x a)-2(2a-b)
The expression x 2a-b=3(x a)-2(2a-b) has the result x = 2a / (2a + 3).
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
To solve for x, we can simplify the equation first:
x * 2a - b = 3(x + a) - 2(2a - b)
Expanding the right side:
x * 2a - b = 3x + 3a - 2 * 2a + 2b
Combining like terms:
x * 2a - b = 3x + 3a - 4a + 2b
x * 2a - b = 3x - a + 2b
Now, we can isolate x on one side of the equation:
x * 2a - 3x = a - b + 2b
x * 2a - 3x = a + b
Multiplying both sides by -1:
-x * 2a + 3x = -a - b
Adding 2a to both sides:
x * 2a + 3x + 2a = -a - b + 2a
Combining like terms:
x * 2a + 3x + 2a = -a + 2a
x * 2a + 3x + 2a = 2a
Finally, collecting all x terms on one side:
x * (2a + 3) = 2a
Dividing both sides by (2a + 3):
x = 2a / (2a + 3)
The value of x for the expression x 2a-b=3(x a)-2(2a-b) is x = 2a / (2a + 3).
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how many turning points does -3x^{3} 2 have
The polynomial -3x^3 + 2 has only one turning point.
A turning point is a point on a curve where the curve changes direction, either from going up to going down or vice versa. In other words, it is a point where the first derivative of the curve changes sign.
For the polynomial -3x^3 + 2, the first derivative is given by:
d/dx (-3x^3 + 2) = -9x^2
Since the first derivative is a monotonically decreasing function (that is, its slope is always negative), the polynomial -3x^3 + 2 has only one turning point.
Slope of first derivative
d²(-3x^3 + 2)/dx² = -18x
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which of the following is the midpoint riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width?
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980
The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.
The formula for the midpoint Riemann sum is given by:
Sum = (width of interval) * (height of midpoint)
For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:
Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)
Substituting the values for each midpoint, we get the following equation:
Sum = 4 * (1 + 4^3 + 8^3 + 12^3)
This simplifies to:
Sum = 4 * (1 + 64 + 512 + 1728)
Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:
Sum = 4 * (2495)
Sum = 9980
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If AE=6x-55 and EC=3x-16, find DB quetion 8 6. 3 polygon and quadrilateral geometry
The length of side DB can be expressed as [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
To solve this, we can use the Pythagorean theorem:
[tex]DB^2 = AE^2 + EC^2[/tex]
Substituting the values of AE and EC:
[tex]DB^2 = (6x - 55)^2 + (3x - 16)^2[/tex]
[tex]DB^2 = 36x^2 - 720x + 3025 + 9x^2 - 96x + 256[/tex]
[tex]DB^2 = 45x^2 - 816x + 3281[/tex]
[tex]DB =[/tex] [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]
Key points:
The Pythagorean theorem states:
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.Symbolically, this can be expressed as [tex]a^2 + b^2 = c^2[/tex], where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.The theorem can be used to find the length of one side of a right triangle if the lengths of the other two sides are known.It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery and proof.The theorem has many applications in mathematics, physics, engineering, and construction, among others.Learn more about the Pythagorean theorem here:
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The complete question is:
In a quadrilateral ABCD, the length of sides AB and CD are equal and measure x units. If AE = 6x - 55 and EC = 3x - 16, find the length of side DB.
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2/3 - 5/9=
in simplest form
Answer:
Step-by-step explanation:
2/3 - 5/9 = 1/
9
≅ 0.1111111
Answer: 1/9
Step-by-step explanation:
find the inverse of the matrix, if it exists. use the algorithm for finding by row reducing i]
The matrix is now in row echelon form. The inverse is the right side of the augmented matrix: [tex]$$\begin{bmatrix}1 & 1 & 0 \\2 & 1 & 3 \\0 & 1 & 2\end{bmatrix}$$[/tex]
We will use the algorithm for finding the inverse of a matrix by row reducing.
Step 1: Augment the matrix with the identity matrix.
[tex]$$\begin{bmatrix}1 & 1 & 0 & | & 1 & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
Step 2: Use row operations to transform the matrix into the identity matrix.
1. Multiply the first row by [tex]$\frac{1}{2}$[/tex] to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
2. Subtract two times the first row from the second row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]
3. Subtract the first row from the third row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 2 & | & -\frac{1}{2} & 0 & 1\end{bmatrix}$$[/tex]
4. Multiply the third row by [tex]$\frac{1}{2}$[/tex] to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 1 & | & -\frac{1}{4} & 0 & \frac{1}{2}\end{bmatrix}$$[/tex]
5. Subtract [tex]$\frac{3}{2}$[/tex]times the second row from the third row to get:
[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 0 & | & \frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]
Step 3: The matrix is now in row echelon form. The inverse is the right side of the augmented matrix:
[tex]$$\begin{bmatrix}1 & 0 & 0\\-1 & 1 & 0\\\frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]
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if you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of: (a) < 0.25 inch (b) > 0.125 inch (c) < 0.125 inch (d)
The best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius of (b) > 0.125 inches.
The choice of fillet radius is an important factor in determining the surface tolerance and finish of a machined part. A fillet radius is a rounded corner between two flat surfaces. A fillet radius that is too small can result in a rough surface, while a fillet radius that is too large can weaken the part.
In this scenario, a 1/4 inch diameter mill is being used, so the best surface tolerance and finish would be achieved if the fillet radius is greater than 0.125 inch, but less than 0.25 inch. This will ensure that the part is not weakened and the surface is smooth. The exact value of the fillet radius will depend on the specific requirements of the machining process.
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Complete Question:
If you must use a 1/4 inch diameter mill, then the best surface tolerance and finish would be gotten if all inside vertical corners had a fillet radius with the minimum requirement of:
(a) < 0.25 inch
(b) > 0.125 inch
(c) > 0.25 inch
(d) = 0.25 inch
(e) = 0.125 inch
(f) < 0.125 inch