A translation is a mapping of a figure in a direction and distance without changing its orientation. The rule for a translation is of the form (x, y) -> (x + h, y + k), where h and k are the horizontal and vertical distances of the translation, respectively.
A reflection is a mapping of a figure across a line, called the line of reflection, without changing its size or orientation. The rule for a reflection is of the form (x, y) -> (x, -y) or (x, y) -> (-x, y), depending on whether the line of reflection is horizontal or vertical, respectively.
A rotation is a mapping of a figure around a point, called the center of rotation, by a certain angle. The rule for a rotation is of the form (x, y) -> (x', y'), where x' and y' are the coordinates of the rotated point, and are given by x' = xcos (theta) - ysin(theta) and y' = xsin(theta) + ycos(theta), where theta is the angle of rotation.
A glide reflection is a composition of a translation and a reflection. The rule for a glide reflection is of the form (x, y) -> (x + h, -y) or (x, y) -> (x, -y + k), depending on whether the line of reflection is horizontal or vertical, respectively, and h or k is the distance of translation.
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M109) solve
cos²x + 2 cosx + 1 = 0
Answer:
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \huge \color{green}{ \fbox \colorbox{black}{ \fbox{ \green {Answer} \: }}}[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + 2 \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{2} (x) + \cos(x) + \cos(x) + 1} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos {}^{} (x) ( \cos(x) + 1)+ 1(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( \cos(x) + 1)(\cos(x) + 1} )= 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{2} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ ( (\cos(x) + 1} {}^{} ) {}^{} = 0[/tex]
[tex] \longrightarrow \sf \color{teal}{ \cos(x) {}^{} }= - 1[/tex]
[tex]\longrightarrow \sf \color{teal}{ x{}^{} }= \cos {}^{ - 1}( - 1)[/tex]
[tex]\longrightarrow \sf \color{teal}{ x = (2n + 1) \pi \: \: \: \: rad}[/tex]
where, [tex]{ n \in \{whole \:\; number\}} [/tex]
Principle value -
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \cos {}^{ - 1} ( - 1) [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2n + 1) \pi \: \: \: \: rad \: [/tex]
put n = 0
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (2(0) + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = (0 + 1) \pi \: \: \: \: rad \: [/tex]
[tex] \longrightarrow \sf \color{teal}{ x} {}^{} {}^{} = \pi \: \: \: \: rad \: = 180 \degree[/tex]
-2(3n+6) = 3(-n+12)
Solve for n
Please explain each step
Answer: n = -16
Step-by-step explanation:
1) Distribute
—2(3n +6) = 3(-n + 12)
—6n - 12 =3(-n + 12)
2) Distribute
—6n - 12 = 3(-n + 12)
—6n — 12 = —3n +36
3) Add 12 to both sides
—6n — 12 = -3n +36
-6n = 12+ 12 = - 3n + 36 + 12
4) Simplify
----Add the numbers
—6n = -3n +48
5) Add 3n to both sides
—6n = -3n +48
—6n + 3n = —3n + 48 + 3n
6) Simplify
- Combine like terms
—3n = 48
7) Divide both sides by the same factor
—3n = 48
-3n ÷ -3 = 48 ÷ -3
8) Simplify
- Cancel terms that are in both the numerator and denominator
- Divide the numbers
n = —16
Please give brainliest
The volume of a cylinder is 90 cm³. If the radius is 3 cm, what is the height of the cylinder? OA. 10 cm OB. 30 cm C. 15 cm D. 5 cm 3 cm
Answer:
3 cm
Step-by-step explanation:
Volume of a cylinderThe formula of a cylinder is given by:
[tex]\pi r^{2} h[/tex]
where r is the radius and h is the height of the cylinder.
SolutionGiven information from the question:
Volume of cylinder = [tex]90cm^{3}[/tex]
Radius of cylinder = 3cm
We can derive an equation to find the height:
[tex]90=\pi 3^{2} h\\9\pi h=90\\h = \frac{90}{9\pi } \\h = 3.18cm[/tex]
Given the height is 3.18cm, we will choose the closest answer which is 3 cm.
olve the differential equation by variation of parameters. Y" + y = sin?(x) y(x) =
The provided statement indicates that the differential equation's solution will be y = c₁ + c₂ e⁻ˣ - 1/2 cos x
With examples, define differential equation:Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variable x and y are related because y is an unidentified function of x. The component of y is also on the equation's left-hand side.
The analytical solution is, given that.
⇒ y'' + y = sin x
Now,
The system of equations as follows:
The difference between these two is,
⇒ y'' + y = sin x
Find its auxiliary equation as;
⇒ m² + m = 0
⇒ m (m + 1) = 0
⇒ m = 0 or m = - 1
Therefore, the auxiliary equation is c1 e0 + c2 ex.
= c₁ + c₂ e⁻ˣ
And, Particular integral = 1/(D² + D) (sin x)
= 1/2D (sin x)
= 1/2 (- cos x)
= - 1/2 cos x
Consequently, the differential equation's solution will be;
⇒ y = A.E + P.I
⇒ y = c1 + c2 e x - cos x / 2
As a result, the differential equation's solution is;
⇒ y = c1 + c2 e x - cos x / 2
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The complete question is-
Solve the differential equation by variation of parameters.
y'' + y = sin x
Q: Find (i) The area and (ii) The perimeter of the shaded region in each of the following figures given that all arcs are either quadrant or semicircles.
(please help me solve this and tell me how to solve it properly!)
Answer:
Step-by-step explanation:
ask if you don't understand my answer
Answer:
Shaded area = 42.1 cm^2
Shaded perimeter = 44 cm
Step-by-step explanation:
See the attached worksheet. The approach is the subtract the 4 semicircle areas from the total quare area to obtain the area of the shaded region. The perimeter is calculated by the perimeter of one complete circle. Since all four semicircles are 1/4 of the full circle, the total perimeter is equivalent to one full circle.
Pls help with theseeeeeeee
Yes, you can assume both statements. In the diagram, planes W and X intersect at the line KL.
Determine whether you can assume the statement?This means that the points K, L, M, and N lie on the same plane, making them coplanar.All four points are contained within the same plane and are connected by lines, so it is clear that they all lie on the same plane.This means that statement 11 is true and statement 12 is also true.Yes, you can assume the statement in Exercises 11 and 12.The statement in Exercise 11 is true because it is shown in the diagram that Planes W and X intersect at KL.The statement in Exercise 12 is true because the points K, L, M, and N all lie on the same plane, which is Plane W.This type of reasoning is called deductive reasoning.Deductive reasoning is a logical process in which a conclusion is drawn based on the evidence that is given.In this case, the evidence is the diagram and the conclusion is the statement in the exercise.
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z is a standard normal random variable. the p(z ≥ 2.11) equals
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
To calculate the p(z ≥ 2.11), you can use a z-table to look up the z-score. This z-score falls in the area of the tail of the distribution, which means it is the area to the right of 2.11.
The area of the tail is 1 minus the area to the left of 2.11. So, you can look up the area to the left of 2.11 in the z-table, which is 0.9823, and subtract it from 1 to get the area of the tail, which is 0.0177.
The p(z ≥ 2.11) is 0.0177.
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Find the lengths of AC and BC in cm to the nearest hundredth
Answer:
Step-by-step explanation:
Which function includes the data set {(2,4), (6,6) (12,9)}?
The function that includes the data-set {(2,4), (6,6) (12,9)} is given as follows:
D. y = x/2 + 3.
How to obtain the points of the data-set?The points of the data-set follow the format given as follows:
(x,y).
Hence the meaning of each point is given as follows:
(2,4): when x = 2, y = 4.(6,6): when x = 6, y = 6.(12,9): when x = 12, y = 9.Then the correct option is given by option D, that is:
y = x/2 + 3.
As we obtain the numeric values of y for the input x as follows:
x = 2: y = 2/2 + 3 = 1 + 3 = 4.x = 6: y = 6/2 + 3 = 3 + 3 = 6.x = 12: y = 12/2 + 3 = 6 + 3 = 9.Which are the three points that compose the data-set.
Missing InformationThe options are given by the image presented at the end of the answer.
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what do i do if the there is a number in a set of numbers that is much lower than the other when finding the average
Answer: Keep it in the calculation
Step-by-step explanation:
Inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles
Therefore ,2.113 is the deemed appropriate of the greatest square that could be inscribed with in area between the square and the triangle.
Describe the triangle.A triangle is considered a polygon since it has four vertices or segments. It is a basic geometric form. Triangle ABC refers to a triangle the with ends A, B, and C. In Euclidean geometry, a singular plane plus square are produced when the sides are not collinear. A triangle is a polygon if it has three parts and three corners. The points where the three sides of the triangle meet are known as its corners. Three triangle angles add up to 180 degrees.
Here,
The midpoint of foot FE, G, is where we start by measuring the side length of the equilateral triangle.
Given that DE=GB and G is the midpoint, let GE equal x.
As a result, DGGB=x3 using fundamental trigonometry.
DB=2x3 follows.
We may then construct the equation 2x3=102 because DB is the orthogonal of ABCD and has length 102. Thus, the triangle's side length is
2x=(10√2)/√3.
Now, observe the diagonal AC. It is composed of the triangle's side length and the little square's diagonal multiplied by two. Let the little square's side length be y:
Let the little square's side length be y:
AC=y√2 + [(10√2)/√3]+y√2=10√2.
How to find y?
=>y√2+y√2 + (10√2√3)/3=10√2
=>y√2+y√2 + (10√6)/3=10√2
=> [3y√2+3y√2 + (10√6)] /3=10√2
=>6y√2+10√6=30√2
=>6y√2 = 30√2-10√6
=>y√2 = (30√2-10√6)/6
=>y = (30√2-10√6)/6√2
=>y = (60-20√3)/12
=>y= 5(3−√3)3 or 2.113
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please answer my revision q xx
Answer:
k - 2n = x
Step-by-step explanation:
4^n = 2 ^ 2n
2^k/2^2n = 2^(k-2n) = 2^x
k - 2n = x
Thanks
Answer:
x = k - 2n
Step-by-step explanation:
The main exponent properties
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] ........ (1)
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] ........ (2)
[tex](a^{m} )^{n}[/tex] = [tex]a^{m*n}[/tex] = [tex]a^{mn}[/tex] ........ (3)
~~~~~~~~~~~~~~~~~~
[tex]\frac{2^{k} }{4^{n} }[/tex] = [tex]2^{x}[/tex]
Let apply (3) and (2) exponent properties
L.H. = [tex]\frac{2^{k} }{(2^2 )^{n} }[/tex] = [tex]\frac{2^{k} }{2^{2n} }[/tex] = [tex]2^{k-2n}[/tex]
[tex]2^{k-2n}[/tex] = [tex]2^{x}[/tex] ⇒ x = k - 2n
if the heights of 99.7 of american men are between 5 and 7 what is the estimate of the standard deveiation of the height of american men
The value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
What is the empirical rule?
If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.
It is given that the heights of a large population of ostriches are normally distributed. The percentage of these heights is within 3 standard deviations of the mean.
As we know from the empirical rule:
It is the rule of 68-95-99.7.
From the data given in the question: The height of a large population of ostriches is normally distributed.
X ~ (u, б²)
Normal distribution.
P{u - 3б < X < u + 3б}
From the distribution table:
P{u - 3б < X < u + 3б} = 99.7%
Thus, the value of 99.7% is the closest to the percentage of these heights that is within 3 standard deviations of the mean.
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The following set of ordered pairs, represents a power inverse variation. Find the value of r given that k=5. ( 1/2,20)(1,5)(2,5/4) : a. r=5 b. r=2 c. r=-5 d. r=2
The correct value of r is 2.
What is the power inverse variation?
Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
The equation for a power inverse variation is y = kx^r,
where k is a constant, x is the independent variable, y is the dependent variable, and r is the power.
We have given the set of ordered pairs,
we can find the value of r by substituting in the known values of x and y and solving for r.
(1/2,20) => 20 = 5 * (1/2)^r => r = log(20)/log(1/2) = -2
So the answer is:
r = 2
Hence, the correct value of r is 2.
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(9-12)x5+13-2=
explanation please
Step-by-step explanation:
(9-12)×5+13-2
=(-3)×5+13-2, (frist bracket )
=-15+13-2
=-4
Answer:
(9-12)x5+13-2= -4
Step-by-step explanation:
1. Solve the equation in parenthesis. 9-12 is -3. If you use a number line and add 9, then subtract twelve, you'll be three behind zero!
2. Then multiply -3 by five which is -15. -15+13 is -2, (since the thirteen is positive, it cancels out thirteen negative ones, and leaves us with two negative ones)
3. -2 -2=-4 (Negative two, subtracted by positive two, is negative four) subtracting a positive number, is the same as adding its opposite. Example. 8-5=3 (as we all know). And 8+-5=3. Numbers that have the same absolute value are opposites. AKA Numbers that are the same distance away from zero. -5 and 5 are both 5 spaces from zero!
A 9-kilogram bag of rice costs $12.96. What is the unit price?
Answer:
$1.44
Step-by-step explanation:
9kg costs $12.96
1kg costs ($12.96*1kg)÷9kg
=$1.44
Josh graphs a system of equations to determine the roots of the polynomial equation x Superscript 5 Baseline
The statement 2 is true i.e. He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be root multiplicities or complex.
Understanding the fundamental theorem of algebra, the number of roots of a polynomial equation must be equal to the degree of the equation. While been given any polynomial in factored form, we must expand the parentheses to find the highest-degree term.
For the equation provided, simplified form could be x⁵ + 2x² = 0, and as looking at this polynomial and graphing it, it is evident that the total roots or solutions is equal to the highest exponent of the term x which is 5. Hence, Josh makes an incorrect statement.
The multiplicity of a root is the number of occurrences of the said root in the entire complete factorization of the polynomial, as by the means of the fundamental theorem of algebra. The root multiplicities are thus the repeated roots as involved in the full factorization process of a single equation of a polynomial.
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The correct question is:
Josh graphs a system of equations to determine the roots of the polynomial equation x⁵ = -2x² . From the graph, he determines that there are two solutions to the equation. Which statement is true?
He is correct because the least exponent of the system is two so there must be two solutions.He is not correct because the greatest exponent of the system is five so there must be five solutions, three of which must be multiplicities or complex.He is correct because the graph shows two intersection points.He is not correct because the difference of the exponents is three, so there must be three solutions, one of which is a multiplicity.5. Find the distance between (-1, -1) and (1, 1). Round to the nearest tenth if needed.
A. 6
B. 2.9
C. 2.8
D. 31
Answer: C. [tex]2.8[/tex]
Step-by-step explanation:
Using the distance formula, [tex]\sqrt{(-1-1)^2 +(-1-1)^2} \approx 2.8[/tex].
big box have 1/4 of 20
gigabytes of ram
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
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.
Big boxes have 1/4 of 20 gigabytes of ram.
Then the multiplication of the numbers 1/4 and 20 will be given by putting a cross sign between them. Then we have
⇒ (1/4) x 20
⇒ 20 / 4
⇒ 5 gigabytes
Big boxes have 1/4 of 20 gigabytes of ram will be 5 gigabytes.
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ANDY DALTON THREW 18 TOUCHDOWn
PASSES LAST SEASON. In 2016 He
THREW 25 TOUCHDOWN PASSES. WHAT
WAS HIS PERCENT OF CHANGE?
The percentage change in the Touchdown passes is 28 %
What is percentage ?A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
Andy Dalton's throw is 18 touchdaown
In last saeson he threw 25 touchdown
So, the percentage change = (25-18)/25 * 100 = 28 %
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What is an equation of the line that passes through the point (1, 7) and is parallel to the line 32 -y= 1?
The general form of a linear Equation in two variables is ax + by + c = 0.
32-y=1
0.x+y+32 = 0
Hence Proved.
same has 4 times as many nickels as dimes. he had 0.90 in all. how many coins of each type does he have>
The number of dimes are 2 and number of nickels are 8 according to the sum and number of coins.
Let the number of dimes be x. The number of nickels will be 4x. Also, as per the known fact, the value of dimes is 0.1 and value of nickels is 0.05. Keeping the values in formula -
0.05x + 0.1×4x = 0.90
0.05x + 0.4x = 0.90
Performing addition on Left Hand Side of the equation
0.45x = 0.9
Rewriting the equation
x = 0.9/0.45
Performing division on Right Hand Side of the equation
x = 2
Number of dimes = 2
Number of nickels = 4×2
Performing multiplication
Number of nickels = 8
Thus, there 2 dimes and 8 nickles.
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How many integers fall between $\sqrt5$ and $\sqrt{50}$ on a number line?
Answer:
We can start solving this problem by finding the two numbers that bound the range of integers we're looking for.
First, we can approximate $\sqrt{5}$ to the nearest integer by finding the square root of 5. We know that 2^2 = 4 and 3^2 = 9, so 2 < $\sqrt{5}$ < 3. Therefore, $\sqrt{5}$ is a little bit more than 2 and a little bit less than 3.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
Step-by-step explanation:
Similarly, we can approximate $\sqrt{50}$ to the nearest integer by finding the square root of 50. We know that 7^2 = 49 and 8^2 = 64, so 7 < $\sqrt{50}$ < 8. Therefore, $\sqrt{50}$ is a little bit more than 7 and a little bit less than 8.
Now we know that the range of integers we are looking for is between 2 and 7, inclusive. There are 7-2+1 = 6 integers between 2 and 7: 2, 3, 4, 5, 6, 7.
Therefore, there are 6 integers that fall between $\sqrt{5}$ and $\sqrt{50}$ on a number line.
Solve the triangle. Round each angle to the nearest degree and round each side to the nearest hundredth. Do not use rounded answers In Your calculations to find missing measures
Rounded answers In Your calculations to find missing measures is given below.
Given: a = 8.72, b = 11.1, c = 11.7
Using the Law of Cosines, we can calculate angle A:
A = arccos((b2 + c2 - a2)/2bc)
A = arccos((11.12 + 11.72 - 8.722)/(2*11.1*11.7))
A = arccos(2.61/265.57)
A = arccos(0.00984)
A = 89.8°
Using the Law of Sines, we can calculate angle B:
Using the Law of Cosines, we can calculate side c:
c2 = a2 + b2 - 2abcos(C)
c2 = 8.722 + 11.12
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in a stem-and-leaf display, . a. a single digit is used to define each stem, and one or more digits are used to define each leaf b. one or more digits are used to define each stem, and a single digit is used to define each leaf c. a single digit is used to define each stem, and a single digit is used to define each leaf d. one or more digits are used to define each stem, and one or more digits are used to define each leaf
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
What is stem-and-leaf plot?A stem and leaf plot, often known as a stem plot, is a method for categorizing discrete or continuous data. Data are organized as they are gathered using a stem and leaf plot. A stem and leaf plot resembles a bar graph in appearance. As each integer throughout the database is divided into a stem and a leaf, thus the name fits.
The last digit of each data point serves as the "leaf" in a stem and leaf plot, which divides the data into numerical points (the leading digit or digits).
Thus, in this case, correct option is:b
in a stem-and-leaf display: b. one or more digits are used to define each stem, and a single digit is used to define each leaf
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The function cox) models the number of cookies sold each day by a bakery
during a 10-day period
between which days did the number of cookies sold by the bakery increase?
a between days 5 and 6
b. between days 3 and 4
c.between days 2 and 3
d. between days 6 and 7
The function c(x) models the number of cookies sold each day by a bakery during a 10-day period between (c) days 02 and 03 did the number of cookies sold by the bakery increase.
Cox Proportional hazards Model:
Sir David Cox observed that if the proportional hazards assumption holds (or, is assumed to hold) then it is possible to estimate the effect parameter (s), denoted β₁ below, without any consideration of the full hazard function. This approach to survival data is called application of the Cox proportional hazards model, sometimes abbreviated to Cox model or to proportional hazards model. However, Cox also noted that biological interpretation of the proportional hazards assumption can be quite tricky.
Let Xi = ([tex]X_i1[/tex] , … , [tex]X_in[/tex]) be the realized values of the covariates for subject i. The hazard function for the Cox proportional hazards model has the form:
λ (t I [tex]X_i[/tex]) = λ₀(t) exp( β₁[tex]X_i1[/tex] +...... + βₙ[tex]X_in[/tex])
= λ₀ (t) exp( [tex]X_i . \beta[/tex])
This expression gives the hazard function at time t for subject i with covariate vector (explanatory variables) Xi. Note : that between subjects, the baseline hazard is identical (has no dependency on i). The only difference between subjects' hazards comes from the baseline scaling factor exp [tex](X_i . \beta)[/tex].
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What is a 1-factor graph theory?
A 1-factor graph is a graph that can be decomposed into one or more 1-factors. In other words, a 1-factor graph is a graph that can be partitioned into disjoint perfect matchings.
In graph theory, a 1-factor is a subgraph of a graph that forms a perfect matching, or 1-factorization. A perfect matching is a set of edges in a graph such that each vertex is incident to exactly one edge in the set. A 1-factorization of a graph is a collection of perfect matchings such that every vertex is included in exactly one perfect matching.
The study of 1-factors and 1-factorizations is an important area of graph theory because of its connections to other areas of mathematics such as algebra, combinatorics, and statistical physics. It has various applications including coding theory, scheduling, and transportation networks.
1-factor graph theory is the study of graphs that can be decomposed into 1-factors and the properties of such graphs. This field of study helps to understand the conditions under which a graph can be decomposed into 1-factors and the properties of such graphs.
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if In = 5 x"" (1+x)0.5 dx ,n= 0,1,2.... where the integral is for x e [0,1]. By first finding a bound on the integrand, which of these is an upper bound on In? Pick ONE option O 1/(n+1) O 1/2(n+1) O 1/(n+1) + 1/(n+2) O N^N
On solving the provided question we cans ay that the upper bound for the integral is 1/(n+1).
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas. The main goal of calculus is to work with derivatives and integrals. Primitives and inverse derivatives are other terms for integral. Integration is essentially utilized to determine the area of 2D space and determine the volume of 3D objects. As a result, calculating an integral of a function with respect to x entails calculating the area between the curve and the x-axis.
The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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the length of the three sides of a a triangke is 2.92 meters, 7.67 meters and 8.82 meters what is the cosine
Answer: The cosine of angle C is -0.0168.
Step-by-step explanation: To find the cosine of the angle opposite the side of length 2.92 meters, you can use the cosine law which states that:
c^2 = a^2 + b^2 - 2ab * cos(C)
where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides, and C is the angle opposite side c.
So in this case,
c = 8.82 m
a = 2.92 m
b = 7.67 m
then we can substitute the values into the equation and solve for cos(C):
(8.82)^2 = (2.92)^2 + (7.67)^2 - 2(2.92)(7.67) * cos(C)
cos(C) = (a^2 + b^2 - c^2) / (-2ab)
cos(C) = (2.92^2 + 7.67^2 - 8.82^2) / (-22.927.67)
cos(C) = -0.0168
What is the difference between a class boundary and a class limit? (Select all that apply.)
A. Class limits specify the span of data values that fall within a class.
B. Class boundaries are values halfway between the upper-class limit of one class and the lower class limit of the next.
C. Class boundaries specify the span of data values that fall within a class.
D. Class boundaries are not possible data values.
E. Class limits are not possible data values.
F. Class limits are possible data values.
G. Class limits are values halfway between the upper-class boundary of one class and the lower-class boundary of the next.
H. Class boundaries are possible data values.
Class limits indicate the largest and smallest data values that can be included in the class. Class limits are referred to actual data values. On the other hand, class boundaries give values that remove gaps between the classes in the frequency distribution. Class boundaries are considered to be one decimal place more accurate in comparison to the data. Options A, B, D, and F correctly describe differences between a class boundary and a class limit.
Following are the potential differences between a class boundary and a class limit.
Class limits define the span of data values that fall within a class.Class boundaries are referred to the values halfway between the upper-class limit of one class and the lower-class limit of the next.Class boundaries are not possible data values.Class limits are possible data values.You can learn more about class boundary and a class limit at
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