The probability of rolling two ones in a row is equal to P = 1/36
How to find the probability?
We want to find the probability of rolling two ones in a row.
Remember that a dice has 6 sides, so the probability of randomly rolling a 1 is just:
p = 1/6
And if we want to do that two times then we need to have that probability twice:
q = 1/6
And the joint probability (probability of rolling two ones) is equal to the product between the individual ones:
P = p*q = (1/6)*(1/6)
P = 1/36
That is the probability.
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Type the expression that results from the following series of steps: Start with x , subtract 4, divide by 5, then add 9.
Answer:
Step-by-step explanation:
x-4/5+9
5. give an example of tangents in the real world that have not been presented in this lesson. explain how you know the tangent and the radius in your example are perpendicular.
Part A: The path of the ball in relation to the curved path of the thrower
Part A: The path the ball takes is perpendicular to the hand, bat, or feet at the point of last contact
Part A:
A real-world example of tangents is the direction of a ball immediately after it is released and the circular path of the motion, that provides the force input that is given to the ball to cause it to move in the required direction
The tangent is the path the ball takes immediately after it is moving without contact with the bat, hand, or feet that causes it to move.
The circular path is the motion of the hand, leg, bat, or feet that makes before the ball is released.
The radius is the hand, leg, or bat that rotates in a circular path, so as to move the ball
Part B:
The radius, such as the leg kicking a ball is perpendicular to the tangent which is the path of the ball because a kick sends the ball into the air, the orientation of the leg at the point the ball leaves is perpendicular to the angle of elevation with which the ball is launched.
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The multiplicative inverse of -7/9 is
Answer:
9/-7
Step-by-step explanation:
the reason is all you have to do is reverse the fraction
Answer:
-9/7
Step-by-step explanation:
The multiplicative inverse of -7/9 is_____?
The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1
-7/9 × (- 9/7) = 1
. MATHEMATICS: 1. Given that x + y =3/4 and x - y =5/2 find the value of 2y + x
Step-by-step explanation:
[tex]x = \frac{13}{8} \\ y = \frac{ - 7}{8} \\ 2y + x = - \frac{14}{8} + \frac{13}{8} = - \frac{1}{8} [/tex]
Answer:
-1/8
Step-by-step explanation:
x + y = 3/4
x -y = 5/2
2x = 13/4 3/4 + 5/2 = 3/4 + 10/4 = 13/4 Next divide both sides by 2
[tex]\frac{2x}{2}[/tex] = [tex]\frac{\frac{13}{4} }{2}[/tex] [tex]\frac{13}{4}[/tex] ÷[tex]\frac{2}{1}[/tex] = [tex]\frac{13}{4}[/tex] x [tex]\frac{1}{2}[/tex] = [tex]\frac{13}{8}[/tex]
x = [tex]\frac{13}{8}[/tex]
plug in 13/8 for x in either of the two original equations.
x + y = 3/4
13/8 + y = 3/4 Subtract 13/8 from both sides
y = -7/8 3/4 - 13/8 = 6/8 - 13/8 = -7/8
Check:
substitute x = 13/8 and y = -7/8 back into the original two equations to see if the equations ae true
x + y = 34
13/8 - 7/8 = 3/4
6/8 = 3/4
3/4 = 3/4 Checks
x - y = 5/2
13/8 - (-7/8) = 5/2
13/8 + 7/8 = 5/2
20/8 = 5/2
5/2 = 5/2 Checks
Find the value of 2y + x
2(-7/8) + 13/8
-14/8 + 13/8
-1/8
1. You are the manager of a small store that specializes in hats, sunglasses, and other accessories. You are considering a sales promotion of a new line of hats and sunglasses. You will offer the sunglasses only to those who purchase two or more hats, so you will sell at least twice as many hats as pairs of sunglasses. Moreover, your supplier tells you that, due to seasonal demand, your order of sunglasses cannot exceed 100 pairs. To ensure that the sale items fill out the large display you have set aside, you estimate that you should order at least 210 items in all. Assume that you will lose $3 on every hat and $2 on every pair of sunglasses sold. Given the constraints above, how many hats and pairs of sunglasses should you order to lose the least amount of money in the sales promotion? [Using Graphic method]
Graphical techniques are widely used to assess whether the data support the fractionation of a single source or the mixture of two putative sources.
For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
What is meant by Graphic method?To determine if the data support the mixing of two potential sources or the fractionation of a single source, graphical approaches are frequently used.
To better interpret their data, researchers now employ a variety of graphical tools, including scatterplots, box plots, and histograms. Graphs are excellent for illustrating trends, patterns, and correlations between variables as well as for displaying and summarizing vast volumes of numerical data.
We generate a graph for each equation in order to solve systems of equations or simultaneous equations graphically. Then, we search for the intersection of the two graphs. The system of equations would have a solution at the coordinates of the point of intersection.
Let x be the number of hats and y be the number of pairs of sunglasses.
The constraints exists:
2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)
y <= 100 (because the supplier can only provide 100 pairs of sunglasses)
x + y >= 210 (because you want to sell at least 210 items in total)
x, y >= 0 (because the number of items sold cannot be negative)
Lose in every hat is $3 and in Pair of Sunglasses is $ 2
Total loss in promotion or cost of promotion is
3x + 2y
For least purchase,
x + y = 210
⇒ x + x/2 = 210
⇒3x/2 = 210
⇒ x =140
y = 140/2 = 70
So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
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For 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
What is meant by total?
Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totalled in an accident is irreparably damaged.the outcome of addition. For instance, adding 3 and 2 balls results in a total of 5 balls. Another illustration: The result of 12 + 4 + 6 = 22 is 22. Math is enjoyable.When you add up or count up all of something's components, you obtain the entire number or cost of that thing.Let x be the number of hats and y be the number of pairs of sunglasses.
The constraints exists:
2y = x (because for every 2 hats sold, 1 pair of sunglasses is sold)
y <= 100 (because the supplier can only provide 100 pairs of sunglasses)
x + y >= 210 (because you want to sell at least 210 items in total)
x, y >= 0 (because the number of items sold cannot be negative)
Lose in every hat is $3 and in Pair of Sunglasses is $ 2
Total loss in promotion or cost of promotion is
3x + 2y
For least purchase,
x + y = 210
⇒ x + x/2 = 210
⇒3x/2 = 210
⇒ x =140
y = 140/2 = 70
So, for 210 items in total there will be 140 number of hats and 70 number of pairs of sunglasses.
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Prove that ROS is an equivalence relation if and only if RoS= So R.
Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb.
How to find the calculation?R and S should be two equivalence relations on X.
I want to demonstrate that the relationship RS is equivalent, but I am unable to demonstrate that it is transitive and reflexive.
regarding transitivity
There are random x and y with (x,y)RS, z with (x,z)R and (z,y)S, and what else?
Do I need to use R=S=S=R somewhere else?
As opposed to (x,y)R, I use the notation xRy. For some a, the term "xRSy" specifically refers to "xRaSy." Additionally, writing (xRy and yRz) is more convenient than writing xRySz. I would generally suggest drawing these relationships as graphs, with the vertices representing the points and the edges denoting the relationship.
assumption R=S=R.
Transitivity: Assume that for some a, b, xRSy and yRSz, or xRaSy and yRbSz, exist. After that, aSRb, abbreviated as aSyRb. In light of the fact that SoR=RoS, we obtain aRSb, or, to use an example, aRcSb. Then, as R,S are equivalence relations, xRcSz follows from xRaRcSbSz, and xRSz follows.
I'm sure you can now independently demonstrate reflexivity.
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What is an equivalent way to write the expression without grouping symbols?
3(4x−5)
Drag and drop the values into the boxes to create an equivalent expression.
30POINTS! please answer!!!
The equivalent way to write the expression is 12x-15. The solution has been obtained by simplifying the expression.
What is simplified expression?
Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.
We are given 3(4x-5).
There are no like terms in the given expression.
Therefore, as the next step, we need to solve the bracket for simplifying the expression.
Thus, we obtain
⇒ 3*4x - 5*3
⇒ 12x -15
Hence, the equivalent way to write the given expression is 12x-15.
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Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept
f(x) = (x + 1)(x - 5)(x - 1)^2
The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.
What is polynomial function?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses non-negative integer powers or only positive integer exponents of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5. A polynomial is a function that has the formula f(x) = anxn + anxn + anxn+1 +... + a2x2 + a1x + a0. The highest power of x in the formulation of a polynomial is its degree. Constant (non-zero) polynomials, linear polynomials, quadratics, cubic, and quartics, respectively, are polynomials of degree 0, 1, 2, 3, and 4.Given
f(x) = x²(x+2)
To find the x-intercepts ⇒ f(x) = 0
∴ x²(x+2) = 0
∴ x² = 0 OR x+ 2 = 0
∴ x = 0 or x = -2
So, the x-intercepts will be at x = 0 , -2
We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)
The attached figure represents the graph of f(x)
As shown in the figure:
1) The graph crosses the x-axis at x = -2
2) The graph touches the x-axis and turns around at x = 0
The complete question is,
Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.
f(x) = x2(x + 2)
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Chris buys 1.6 pounds of almonds and 2.8 pounds of cashews. Emily buys 0.7 pound of almonds and 1.5 pounds of cashews.
The total cost of the nuts that Chris and Emily buy can be found using the expression: (1.6a) + (2.8c) + (0.7a) + (1.5c) You can also use the expression (10.6a) + (2.8c) for the total cost of nuts that Chris buy.
What is pounds?pound, unit of avoirdupois weight, equal to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The Roman ancestor of the modern pound, the libra, is the source of the abbreviation lb. In medieval England several derivations of the libra vied for general acceptance.
Among the earliest of these, the Tower pound, so called because its standard was kept in the Royal Mint in the Tower of London, was applied to precious metals and drugs and contained 5,400 grains, or 0.350 kg, whereas the mercantile pound contained 6,750 grains, or 0.437 kg. The troy pound, believed to have originated in Troyes, France, superseded the lighter Tower pound in 1527 as the gold and silver standard. Increased trade with France led also to the adoption of the 16-ounce avoirdupois pound in the 16th century to replace the mercantile pound.
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A three-column table is given.
Part 8 B D
Part 10 15 45
Whole A C 72
What is the value of C in the table?
18
24
27
71
The value of C in the table will be 24.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, a table of proportional data below,
Part 8 B D
Part 10 15 45
Whole A C 72
Since the two-part will be proportional to the whole.
thus,
=> c /72 = 15/45
=> C = 72/3
=> C = 24
Therefore, the value of C in the given table will be 24 as pe the proportionality.
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consider the following set of requirements for a university database that is used to keep track of students' transcripts. the university keeps track of each student's name, student number, social security number, current address and phone, permanent address and phone, birthdate, sex, class (freshman, sophomore, ..., graduate), major department, minor department (if any), and degree program (b.a., b.s., ..., ph.d.). some user applications need to refer to the city, state, and zip of the student's permanent address, and to the student's last name. both social security number and student number have unique values for each student. each department is described by a name, department code, office number, office phone, and college. both name and code have unique values for each department. each course has a course name, description, course number, number of semester hours, level, and offering department. the value of the course number is unique for each course. each section has an instructor, semester, year, course, and section number. the section number distinguishes different sections of the same course that are taught during the same semester/year; its values are 1, 2, 3, ..., up to the number of sections taught during each semester. a grade report has a student, section, letter grade, and numeric grade (0, 1, 2, 3, 4 for f, d, c, b, a, respectively). using a modeling tool, complete the following. design a conceptual schema for this company (see chapter 1, page 13 for an example) draw an er diagram for that schema. specify key attributes of each entity type and structural constraints on each relationship type. note any unspecified requirements and make appropriate assumptions to make the specification complete. what to submit submit a word or pdf document containing both the conceptual schema and the er diagram. additional resources summary of the notation for er diagrams try one of the following er modeling tools to complete this assignment. gitmind - free online mind mapping diagrams.net dbdiagram.io start date jan 9, 2023 7:00 pm due date jan 23, 2023 11:59 pm
The conceptual schema and the E-R diagram are attached.
(i) Before making the E-R diagram we discuss the entity relational model for the given problem. So the E-R diagram is the graphical representation of different entities and attributes.
Assumptions for the given problem:
(i) University: a university has its name, address, email id, and mobile number
the university gives admission to students and also university and different departments.
(ii) Student: a student has attributes name, contact number, and social security number as the primary number, address, student number, birth date has its name, department, sex, class, department, and degree program.
(iii) Department: the department has its name, department code, office number, phone
(iv) Courses: each course has its name, description, course number, number of semester hours, level, and offering department.
(v) Section: section has an instructor, semester, year, course, section number
(vi) Grade report: a grade report contain a student section, letter grade, and numeric grade
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How do you solve this please
The number of students in the population would be:
Wear glasses - 165 students Wear contact lenses - 60 students No vision problem diagnosed - 525 students How to find the population ?The sample is directly related to the population of students so parts of the students can be found using the sample.
Students in population who wear glasses :
= Sample who wear glasses / Total sample x Total population
= 11 / 50 x 750
= 165 students
Students who wear contacts:
= 4 / 50 x 750
= 60 students
Students with no vision problems :
= 35 / 50 x 750
= 525 students
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which correctly explains the number of solutions of the following system of linear equations -2x+2y=10
y=x+5
For the system of equations, there are infinitely many solutions exist.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equations are,
⇒ - 2x + 2y = 10 .. (i)
⇒ y = x + 5 .. (ii)
Here, From (i) equation,
⇒ - 2x + 2y = 10
Take 2 as common,
⇒ 2 (- x + y) = 10
⇒ - x + y = 5
⇒ y = x + 5
Which is same as equation (ii).
Hence, There are infinitely many solutions exist.
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Please help, thank you in advance! 15 POINTS!!!
The value of the probability of event C is 0.30.
How to determine the probabilityThe law of total probability states that
P(A U B U C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C).
Substitute the known values in the above equation, so, we have the following representation
P(A U B U C) = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02.
Also are given:
P(A U B U C)' = 0.33,
This implies that
P(A U B U C) = 1 - 0.33 = 0.67.
Substituting the values, we get:
0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02
0.67 = 0.24 + 0.26 + P(C) - 0.15 + 0.02
0.67 = 0.50 + P(C) - 0.13
0.80 = 0.50 + P(C)
P(C) = 0.80 - 0.50 = 0.30.
Hence, the probability is 0.30
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What is the equation of the line that passes through the point (4, -1) and has a
slope of -2?
Answer:
y = - 2x + 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )
7 = c
y = - 2x + 7 ← equation of line
You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers union) and mail a questionnaire to 2,500 teachers chosen at random from this list. In all 1,347 teachers return the questionnaire. In this situation, the sample is: a. the 1,347 teachers who mailed back the questionnaire b. the 2,500 teachers to whom you mailed the questionnaire. call members of the National Education Association. d. all American school teachers. e. all American school students.
You want to know the opinions of American school teachers about establishing a national test for high school graduation then correct option is D) all American school teachers.
In statistics, A population is a very large set of individuals or values that belong to a specified group established by researcher.
A sample is a subset of population that represents the entire population in research.
Given : We want to know the opinions of American school teachers about establishing a national test for high school graduation.
Clearly , by the above definition
Population = all American school teachers.
You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list.
sample = 2500 teachers chosen at random from this list.
Hence, the intended population is all American school teachers.
Thus , the correct answer is D) all American school teachers.
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B is the set of integers greater than or equal to -3 and less than or equal to 0
Integers higher than or equal to -3 and less than or equal to 0 make up the set of numbers (-3 , -2 , -1, 0)
Explain about the set of integers?The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.
The formal definition of the set Z of integers is as follows: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Unknown or unidentified integers are denoted in mathematical equations by lowercase, italicised letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.
The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0.
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What is the result when -3x - 4 is subtracted from -4x - 3?
What is the reference angle for the given angle measure drawn in standard position?
The reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6What is a radian?The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics
Given are the angles as shown in the figure.
We can write the reference angles as -
{ 1 } -- 34π/3 → -34 x π/3 → π/3
- 34π/3 → π/3
{ 2 } -- 5π/12 → -5x π/12 → π/12
- 5π/12 → π/12
{ 3 } -17π/6 → 17 x π/6 → π/6
17π/6 → π/6
Therefore, the reference angles are given as -
- 34π/3 → π/3- 5π/12 → π/12 17π/6 → π/6To solve more questions on reference angles, visit the link below -
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how many total atoms of each element are present in the following formulas?
3 CaCl₂
Tap in the fields to enter the answers directly OR
tap on the Number Pad icon to use our built-in Number Pad.
To ascertain an element's molar mass, use the periodic table. Calculate the quantity of moles by dividing the supplied mass in grammes by the molar mass.
How many types of atoms are in an element?One type of atom makes up each individual element. Protons, neutrons, and electrons, three additional subatomic particles, make up atoms. Chemical reactions allow elements to interact with one another to create molecules.The number of atoms can be calculated by multiplying the number of moles by Avogadro's number. An atom's atomic number is equal to the quantity of protons in its nucleus or the quantity of electrons in an electrically neutral atom.CaCl2 contains 3 atoms. We can determine the number of atoms in a compound by counting the subscripts after each ingredient. Counting moles is the initial step in calculating the number of atoms.To learn more about element's refer to:
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Cual es la propiedad de 8x0=0?
The following shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and area of the shaded part. Give your answer as a completely simplified exact value in terms of pi. (no approximations) FIRST PERSON TO ANSWER GETS 100 POINTS
Answer:
Perimeter = 8π cm
Area = (32π - 64) cm²
Step-by-step explanation:
ABCD is a square.
Therefore:
AB = BC = CD = DA = 8 cmArea = 8 × 8 = 64 cm²PerimeterThe perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.
The arcs AC are quarter circles of a circle with radius 8 cm.
Therefore the perimeter of the shaded area is:
[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]
AreaTo find the area of the shaded area, subtract the two unshaded areas from the area of the square.
As the two unshaded areas are congruent we only need to find the area of one unshaded area.
The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).
[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]
Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:
[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]
Classify these events. Selecting a king from a deck of cards, replacing it and selecting a queen from the same deck. These events would be considered:
Group of answer choices
A) Subjective
B) Empirical
C) Independent
D) Dependent
Picking a king from a deck of cards, swapping it out for a queen, then continuing. These occurrences would constitute Dependent events.
'What is dependent probability?'
A dependent variable is precisely what it sounds like, just like an independent variable. It is something on which other elements depend.
A test score, for instance, may be a dependent variable because it could vary based on a number of variables, including how much you studied, how much sleep you got the night before the test, and even how hungry you were. Typically, when attempting to establish a connection between two variables, the goal is to determine what causes the dependant variable to vary in the manner that it does.
Many people struggle to recall which variable is the independent variable and which variable is the dependent variable.
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Suppose y = c1ekx + c2e-kx where k > 0 is a constant, and c1 and c2 are arbitrary constants. Find the following. Enter c1 as c1 and c2 as c2
The c1 and c2 are arbitrary constants.
What is the arbitrary constant?
y=mx+c is the general equation of a straight line in two dimensions, where m and c are arbitrary constants that represent the gradient of the line and the y-intercept. And ∫2x dx=x 2+c where c is an arbitrary constant whose value can be determined by a boundary condition.
y = c1ekx + c2e-kx is a general solution to the homogeneous linear differential equation y' + ky = 0. This means that any specific solution to this equation can be obtained by plugging in appropriate values for c1 and c2.
The general solution y = c1ekx + c2e-kx is a linear combination of ekx and e-kx.
The differential equation y' + ky = 0 is a first-order, linear differential equation.
The general solution y = c1ekx + c2e-kx is valid for all values of x.
The general solution y = c1ekx + c2e-kx is a sum of two linearly independent solutions to the differential equation.
The general solution y = c1ekx + c2e-kx is a particular solution if c1 and c2 are determined by initial or boundary conditions.
The general solution y = c1ekx + c2e-kx is a general solution if c1 and c2 are arbitrary constants.
The general solution y = c1ekx + c2e-kx is a unique solution if c1 and c2 are determined by initial or boundary conditions, otherwise, it is not unique.
The general solution y = c1ekx + c2e-kx is a solution to the homogeneous differential equation y' + ky = 0, it does not contain any particular solution for the non-homogeneous differential equation.
Hence, The c1 and c2 are arbitrary constants.
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find the fixed point of the function f. [a fixed point of a function f is a real number c such that f(c)
The fixed point of the function f(x) = x^2 + 1 is c = 0.
f(x) = x^2 + 1
c = 0
To find the fixed point of the function f, we can set the equation f(x) = x^2 + 1 equal to x, since the fixed point is when f(x) is equal to x.
Therefore, we can solve for x by setting x^2 + 1 = x. Re-arranging the equation, we get x^2 - x + 1 = 0.
Using the quadratic formula, x = (-(-1) ± √(1 - 4(1)(1))/(2(1))
Simplifying this expression, x = (-1 ± √3)/2.
Since we are looking for a real number, we can eliminate the negative solution and set x = (1 + √3)/2.
Therefore, the fixed point of the function f is c = 0.
The fixed point of the function f(x) = x^2 + 1 is c = 0.
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Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?The function is decreasing on the interval (0, [infinity]).The function is decreasing on the interval (–[infinity], 0).The function is increasing on the interval (0, [infinity]).The function is increasing on the interval (–[infinity], 0).
The function is decreasing on the interval (0, [infinity])
The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.
The derivative of h(x) is -2/sqrt(x).
For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.
For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.
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4.A) A straight line L1 whose equation is 3y-2x-2 meets the x-axis at R. Determine the co-ordinates of R byAsecond line l2 is perpendicular to LI at R Find the equation of L2 in the form y=mx+c A Third line l3 passes through (-4,1) and is parallel to LI Find, i) the equation of L3 in the form y=mx+c the co-ordinates of points at which l3 intersects l2.
Answer:
69
Step-by-step explanation:
use the method of mathematical Induction to Prove that 4+9+14+19+_ _ + (5n-1) = n/₂ (3+5n) for all natural numbers n
Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
To prove mathematical induction?Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).
First, establish that P1 is accurate when n equals 1.
LHS= 4
RHS
= 1/2(5 + 3)
= 1/2(8)
= 4
= LHS
Is P1 true.
2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)
3) Establish Pn+1 as true in the induction stage.
Replace (n+1) on both sides of n to obtain Pn+1.
Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=
Establish the RHS and LHS's parity.
LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]
Bold expression in (2) should be replaced with the value of Pn:
.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.
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In a class there are 42 students. the numbers of girls is 2times the numbers of boys. how many boys and girls are there in the class
Answer: 14 boys & 28 girls
Step-by-step explanation:
the number of girls= 2x
the number of boys= x
now create an algebraic equation:
x + 2x = 42
3x = 42
x = 14 (boys)
multiply 14 by 2 as the number of girls is two times the number of boys.
14 x 2 = 28 girls
For which of the following functions is the chain rule an appropriate method to find the derivative with respect to x ?y=sin(3x2)y=extanxy=18x4−2x
The chain rule tells us where to search the derivative of a composite function.
d/dx[f(g(x))] =f'[f[g(x)g'(x).
A function is composite if you can write it as f(g(x)) In other words, it is a function within a function, or a function of a function.
Following steps should be followed to find chain rule:
1: Recognize the chain rule: The function needs to be a composite function, which implies one function is nested over the other one.
2: Know the inner function and the outer function respectively.
3: Determine the derivative of the outer function, dropping the inner function
4: Obtain the derivative of the inner function Step
5: Multiply the outcomes from step 4 and step 5 respectively.
6: Simplify the obtained chain rule derivative.
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