The matrix A with eigenvector v has eigen value equal to -3.
A is the matrix
[tex]A = \left[\begin{array}{ccc}1&2&-2\\-2&5&-2\\-6&6&-3\end{array}\right][/tex]
v is the vector.
[tex]v = \left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
λ is the corresponding eigenvalue
v is an eigenvector of A calculate the corresponding eigenvalue,
Av = λv
Substituting the values of matrix A and eigenvector v , we have,
Calculate left hand side we have,
Av
=
[tex]\left[\begin{array}{ccc}1&2&-2\\-2&5&-2\\-6&6&-3\end{array}\right]. \left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-3\\-3\\-9\end{array}\right][/tex]
Now, calculate the right hand side value we have,
λv
= λ[tex]\left[\begin{array}{ccc}1\\1\\3\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}\lambda\\\lambda\\3\lambda\end{array}\right][/tex]
Now, Equate both the sides to get the eigen value ,
λ = -3
Therefore, the eigen value of the matrix A for the eigenvector v is equal to -3.
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The above question is incomplete , the complete question is:
Is [tex]v = \begin{bmatrix}1 \ 3\end{bmatrix}[/tex] an eigen vector of [tex]A = \begin{bmatrix}-1 & 1 \ 6 & 0 \end{bmatrix}\\[/tex] . If so, find the eigenvalue. Hint: use the definition of an eigenvalue problem Ax = λx.
QUESTION 3
A pan of brownies is cut into eight equal rows. Two thirds of one of those rows is what fraction of the whole pan.
Answer:
1/12
Step-by-step explanation:
Each row would be 1/8 of the whole pan. Now multiply 1/8 by 2/3.
Multiply the numerators: 1*2=2
Multiply the denominators: 8*3=24
Your answer: 2/24 or 1/12 simplified (dividing both top and bottom by 2)
Hope this helps. :)
Answer:
[tex]\frac{1}{11}[/tex]
Step-by-step explanation:
[tex]\frac{2}{22}[/tex] = [tex]\frac{1}{11}[/tex]
I drew a pan when I divided into 8 rows. Then I divided that up inot 2/3. In the first row that is divided into 3 parts, I want one of those 2 parts. The total parts are 22. 2/22
Under certain conditions, sound can travel 768 miles per hour. Under these conditions, Alan hears thunder 45 seconds after seeing lightening. His friend, Ryan hears thunder after seeing the same lightening in 30 seconds. What is the longest and the shortest possible distance that Alan and his friend are apart.
The shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles
What is distance?Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it has magnitude but no direction. Distance is usually measured in units such as meters, kilometers, miles, or feet, depending on the system of measurement used.
What is sound?Sound is a type of physical energy that is produced by vibrating objects and travels through a medium, such as air, water, or solids, as a series of pressure waves. When an object vibrates, it creates a disturbance in the surrounding medium that causes molecules to move back and forth, creating areas of high and low pressure that propagate outward from the source of the sound.
In the given question,
Let d be the distance between Alan and Ryan in miles. Then, the time it takes for sound to travel this distance is given by d/768. Therefore, we have:
d/768 = 45 - 30 = 15
Solving for d, we get:
d = 15 x 768 = 11520
So the distance between Alan and Ryan is 11520 miles.
If we take the lower bound of 750 miles per hour, we can calculate the minimum distance between Alan and Ryan as follows:
d/750 = 15
d = 15 x 750 = 11250
Therefore, the minimum distance between Alan and Ryan is 11250 miles.
If we take the upper bound of 800 miles per hour, we can calculate the maximum distance between Alan and Ryan as follows:
d/800 = 15
d = 15 x 800 = 12000
Therefore, the maximum distance between Alan and Ryan is 12000 miles.
Therefore, the shortest possible distance between Alan and Ryan is 11,250 miles, and the longest possible distance is 12,000 miles.
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Solve and then answer the question below.
*MUST SHOW WORK*
Half a number plus eight is fourteen minus a number. How many solutions does this equation have?
To answer the question, this equation has only one solution, which is x = 4.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It usually consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=).
The expressions on both sides can contain variables, constants, and mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), exponentiation (^), and others. The goal of an equation is to find the values of the variables that make both sides equal.
by the question.
Let's start by setting up the equation:
[tex]1/2x + 8 = 14 - x[/tex]
where x is the number, we're trying to find.
Now let's simplify the equation by combining like terms:
[tex]3/2x + 8 = 14[/tex]
Subtracting 8 from both sides:
[tex]3/2x = 6[/tex]
Multiplying both sides by 2/3:
[tex]x = 4[/tex]
So, the solution to the equation is x = 4.
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how do you use TAN in equations and what is it?
Answer:
TAN is a mathematical function in trigonometry that stands for tangent. It is used to calculate the tangent of an angle in a right triangle, which is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In equations, you can use TAN to find the value of the tangent of an angle. For example, if you have an angle of 30 degrees in a right triangle and you want to find the value of the tangent of that angle, you can use the TAN function in your calculator or programming language.
The syntax of the TAN function is usually "tan(x)", where x is the angle in radians. If your calculator or programming language uses degrees instead of radians, you may need to convert the angle to radians first using the conversion formula: radians = degrees * (pi/180).
For example, to find the value of the tangent of 30 degrees, you can use the TAN function as follows:
In degrees mode: TAN(30) = 0.57735027
In radians mode: TAN(30*pi/180) = 0.57735027
TAN can be used in various trigonometric equations and identities to solve for unknown sides or angles of a right triangle.
Step-by-step explanation:
Will give Brainlest!!!
A car dealership offers a convertible that can be purchased in one of four colors: red, black, white, or silver. The number of cars purchased in each color is listed below.
red: 400
black: 325
white: 475
silver: 300
Based on the information shown in the list, what is the probability that the next car purchased will be silver? Please put your answer in the form of a percentage.
In this case, we are given a car dealership that offers a convertible that can be purchased in one of four colors: red, black, white, or silver. It is asked in the problem to give the probability for the next car purchased will be silver. since there are 300 silver colors, then the probability is 300/1500 or 1/5 in lowest terms. this is equal to 0.20.
Work out the recipricol of 0.5
Answer:
the answer is 2
Step-by-step explanation:
this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
180
Step-by-step explanation:
Form an equation
27x+17=180
Solve it for x
x = 6.0recurring
the perimeter is 180
Let me know if it helps
The equation y = -4/7x - 5 has a slope of
a ramp 27ft long rises to a platform. the bottom of the platform is 16ft from the foot of the ramp. find , the angle of elevation of the ramp. round your answer to the nearest tenth of a degree.
Angle of elevation of the ramp with a height of 27ft and a platform of 16ft is approximately 59.35°.
The ramp is 27ft long and rises to a platform, the bottom of the platform is 16ft from the foot of the ramp.
We need to find the angle of elevation of the ramp.
The angle of elevation of the ramp is the angle made by the ramp with the horizontal.
Let ABC be the ramp and D be the platform, as shown below: Let AB = 16ft and BC = 27ft.
We need to find the angle ABD.
Consider right-angled ΔABC In right-angled ΔABC,
we have:
tan⁻¹ (BC / AB)
θ = tan⁻¹ (27 / 16)
θ ≈ 59.35°
Hence, the angle of elevation of the ramp is approximately 59.35°.
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PLS HELP MEEEEEEE ASAP
Answer:
[tex]{ \sf{a = { \blue{ \boxed{{53 \: \: \: \: \: \: \: \: }}}}} \: cm}[/tex]
Step-by-step explanation:
[tex] { \mathfrak{formular}}\dashrightarrow{ \rm{4 \times side \: length}}[/tex]
Each side has length of a?
[tex]{ \tt{perimeter = a + a + a + a}} \\ \dashrightarrow{ \tt{ \: 212 = 4a}} \\ \\ \dashrightarrow{ \tt{4a = 212}} \: \\ \\ \dashrightarrow{ \tt{a = \frac{212}{4} }} \: \: \\ \\ { \tt{a = 53 \: cm}}[/tex]
The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:f(x) = 10(1.3)xWhich of the following graphs best represents the function? (1 point)a Graph of f of x equals 1.3 multiplied by 10 to the power of xb Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinityc Graph of f of x equals 10 multiplied by 1.3 to the power of xd Graph of f of x equals 1.3 to the power of x
The graph of an exponential function with an initial value of 10 and a base of 1.3z. Therefore option D is correct.
The function f(x) is an exponential function with a base of 1.3 and an initial value of 10. The graph of an exponential function with a base greater than 1 increases rapidly as x increases. Therefore, option a can be eliminated.
Option b is not a graph of an exponential function, as the function is not continuous and does not approach any asymptote.
Option c shows an exponential function with an initial value of 10 and a base of 1.3/10, which is less than 1. This means that the function would decrease over time, which is not consistent with the problem statement.
Option d shows an exponential function with an initial value of 10 and a base of 1.3, which is consistent with the problem statement. Therefore, option d is the correct answer.
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There are 25 pupils in a class who take part in a drinking milk initiative. Pupils have a 210
millilitre glass each. During the break each pupil drinks a full glass of milk. Milk comes in 1000
millilitre bottles. How many bottles of milk are needed?
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
Each student in a class of 25 drinks a full 210 millilitre glass of milk, hence the amount of milk consumed overall during the break is:
25 students times 210 millilitres each equals 5250 millilitres.
Milk comes in 1000 millilitre bottles, thus to determine how many bottles are needed, divide the entire amount eaten by the volume of milk in each bottle.
5.25 bottles are equal to 5250 millilitres divided by 1000 millilitres.
We must round up to the nearest whole number because we are unable to have a fraction of a bottle. This results in:
6 bottles in 5.25 bottles
In order for each of the 25 students in the class to get a full glass of milk during the break, six bottles of milk are required.
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the two sides of a right triangle opposite the non-right angles are called
The two sides of a right triangle opposite the non-right angles are called as adjacent and opposite angle or Legs.
A triangle is a three-sided regular polygon in which the total of any two sides is always larger than the sum of the third side.
A right-angled triangle is one with one of its internal angles equal to 90 degrees, or any angle is a right angle. As a result, this triangle is also known as the right triangle or the 90-degree triangle. In trigonometry, the correct triangle is very significant.
A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees. The sides that include the right angle are perpendicular and form the triangle's base. The third side is known as the hypotenuse, and it is the longest of the three sides.
The three sides of the right triangle are connected. Pythagoras' theorem explains this relationship. This theorem states that in a right triangle,
Perpendicular² + Base² = Hypotenuse²
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biconditional of that of two angles are supplementary,then the sum of their measures is 180
Answer:
just a Condit
Step-by-step explanation:
hfjgygdhydv htfhdfjyfdg hyfjkg
Answer:
If two angles are supplementary, then the sum of their measures is 180°.
Identify the type of sequence 56,49,42,35,28,21
It is Arithmetic Sequence. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence.
For the given sequence
d= 49-56 = -7
d= 42-49 = -7
Thus, there is -7 as a common difference between the terms.
The distance between succeeding terms in an arithmetic series is always the same. It is often referred to as an arithmetic series or arithmetic progression. The following statement can be used to represent an arithmetic sequence: a, (a + d), (a + 2 d), (a + 3 d),..., where a is the first term and d is the constant difference between values.
To determine the sum of an arithmetic sequence, it is generally simple to add or subtract all the terms in a short series together. An individual can quickly determine the sum of an arithmetic series for a particular number of terms by using the generic formula for the nth term of an arithmetic sequence.
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If an object is dropped from the top of a building, its position in feet above the ground is given by s(t)=−8t^2+288, where t is the time in seconds since it was dropped. What is the velocity when it hits the ground? a) Increasing 96 feet per second b)decreasing 16 feet per second c) 0 feet per second d)decreasing 96 feet per second
The velocity when the object hits the ground is 4.025 ft/s. The answer is: C) 0 feet per second.
If an object is dropped from the top of a building, its position in feet above the ground is given by s(t)=−8t^2+288, where t is the time in seconds since it was dropped. Given that an object is dropped from the top of a building,
then its initial velocity, u = 0 (since it was dropped and not thrown). We want to find the velocity when the object hits the ground, i.e., the time it takes the object to reach the ground. We know that the position of the object when it reaches the ground is s(t) = 0.
Therefore:−8t^2+288 = 0Solving for t, we get:−8t^2 = −288t^2 = 36t = sqrt(36) = ±6 sSince time cannot be negative, t = 6 s. Then the final velocity at impact, v, can be calculated as follows:v = u + at + s/v = 0 + (-32.2)(6) + (-8(6)² + 288)/v = -193.2 + (-288 + 288)/v = -193.2 + 0/v = -193.2/v = -193.2/-48v = 4.025 (rounded to three decimal places)
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Anita borrowed ₹6000 from a bank at 15% interest rate per annum. Find the interest and
amount to be paid at the end of 3 years.
Answer: The interest and amount to be paid at the end of 3 years is Rs.8700
Step-by-step explanation:
let P ,R, T be the Principle amount , Rate of interest and Time
Given that ,P= 6000rs
R= 15%
T=3 years
Interest= PRT÷ 100=6000rs×15r×3t÷100
=2700rs
value to be paid after 3 years = 6000rs+2700rs= 8700rs
the combined score on this test ranges from 400 to 1600. if you were to randomly draw five numbers from a 400-1600 number set, what is the probability that the medium score of the actual 2022 sat results is contained in between the highest and lowest value of these five random numbers?
The combined score on the 2022 SAT test ranges from 400 to 1600. If you were to randomly draw five numbers from a 400-1600 number set, the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers is approximately 0.004%
How do we find the probability?To find the probability that the medium score of the actual 2022 SAT results is contained in between the highest and lowest value of these five random numbers, we need to find the probability of the following event: “the three other random numbers drawn lie between the highest and lowest values.
The probability of choosing one of the five numbers that falls within the range is (1600 – 400)/1201 = 1/2.25.
The first number can be any number within the 400-1600 range, so the probability is 1.The second number must lie within the range created by the highest and lowest values of the first number, which has a width of 1201. Thus, the probability is 1201/3201.
The third number must lie within the range created by the highest and lowest values of the first two numbers, which has a width of 801. Thus, the probability is 801/2401.The fourth and fifth numbers must lie within the range created by the highest and lowest values of the first three numbers, which has a width of 401.
Thus, the probability is 401/1601.Therefore, the probability of the medium score of the actual 2022 SAT results being between the highest and lowest values of these five random numbers is (1/2.25) * (1201/3201) * (801/2401) * (401/1601) * 1 = 0.000038 or approximately 0.004%.
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The sales of books at a local book fair are shown in the histogram.
A histogram titled Book Sales with the x-axis labeled Number of Books. The x-axis has intervals of 0 to 1, 2 to 3, 4 to 5, 6 to 7, 8 to 9 and 10 to 11. The y-axis is labeled Frequency and starts at 0 with tick marks every two units up to 10. There is a shaded bar above 1 to 3 that stops at 3, above 2 to 3 that stops at 4, above 5 to 6 that stops at 8, above 6 to 7 that stops at 2, above 8 to 9 that stops at 4 and above 10 to 11 that stops at 8.
Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 11. This might be because the book fair offers fair prices, so most costumers bought books.
The data is skewed, with a maximum range of 14. This might be because many of the customers wanted to stock up before the winter.
The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
The data is symmetric with a maximum range of 10. This might mean that most customers bought less than 3 books because that is all that they could carry.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter."
What is a histogram?A histogram is a type of graph used in statistics to represent the distribution of a set of continuous data. It consists of a set of adjacent bars, where the area of each bar represents the frequency or relative frequency of observations within a specific interval or "bin" of the data.
The x-axis of a histogram shows the range of values for the variable being measured, divided into intervals or bins. The y-axis shows the frequency or relative frequency of observations within each interval or bin. Histograms are commonly used to show the shape, center, and spread of a distribution of data, as well as any potential outliers or gaps in the data.
In the given question, the histogram shows a skewed distribution, where the majority of book sales occurred in the lower intervals (1-3, 2-3, and 5-6) and the frequency decreases as the number of books sold increases. The maximum range of the data is 14 (from the interval 10-11 to the interval 2-3), which suggests a wide spread of book sales across different intervals.
"The data is skewed, with a maximum range of 14. This could be due to the fact that many customers wanted to stock up before the winter." comes the closest to describing the spread and distribution of the data shown in the histogram.
The other options do not accurately describe the shape or spread of the data shown in the histogram.
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Answer:
C: The data is bimodal, with a maximum range of 11. This might occur if there is a sale, if you buy 4, or 10 books, you get one free.
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!!
The system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
What is system of inequalities?A group of two or more linear inequalities are grouped together and graphed on a coordinate plane to discover the solution that concurrently solves all of the inequalities. Each inequality forms a half-plane on the coordinate plane, and the location where all the half-planes overlap is where the system is solved. Each point inside the feasible area meets all of the system's inequalities. This region is known as the feasible region. To identify the optimum solution given a set of constraints, systems of linear inequalities are frequently utilised in optimization issues.
Let us suppose the number of boards of Mahagony sold = x.
Let us suppose the number of black walnut boards sold = y.
According to the given problem the equation can be set as follows:
x ≤ 260 (the company has 260 boards of mahogany available)
y ≤ 320 (the company has 320 boards of black walnut available)
x + y ≤ 360 (the company expects to sell at most 360 boards of wood)
Hence, the system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
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(1) Bought a Box of 100 Phone X
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Find the surface area of the box shown.
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Therefore , the solution of the given problem of surface area comes out to be the box's surface size is 304 in².
What precisely is a surface area?Its total size can be determined by figuring out how much room would be required to completely cover the outside. When choosing comparable substance with a rectangular shape, the surroundings are taken into account. Something's total dimensions are determined by its surface area. The volume of water that a cuboid can contain depends on the number of edges that are present in the region between its four trapezoidal angles.
Here,
Six faces make up the box: the top, bottom, two sides, and both extremities. Given that both the top and lower faces are rectangles with 10 by 8-inch measurements, the area of each face is:
=> 80 in²= 10 in * 8 in
The region of each side face is thus:
=> 10 in * 4 in = 40 in²
=> 8 in * 4 in = 32 in²
As a result, the box's surface area equals the total of the areas of its six faces:
=> Surface area = 2(80 in²) + 2(40 in²) + 2(32 in²)
=> Surface area = 160 in² + 80 in² + 64 in²
=> Surface area = 304 in²
Consequently, the box's surface size is 304 in².
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what is the average time gap between the first cyclists time and each of the remaining cyclists' times (second through fifth) in the 1995 volta a catalunya cycle race if we know the result?
The average time gap between the first cyclist's time and each of the remaining cyclists' times (second through fifth) in the 1995 Volta a Catalunya cycle race is approximately 6 minutes and 7 seconds.
To calculate this, we need to subtract the time of the first cyclist from each of the remaining cyclists' times (second through fifth).The time for the first cyclist was 41:38:33.
The times for the remaining cyclists were as follows:
We can calculate the difference for each cyclist by subtracting the first cyclist's time from their own time:
Adding up all of the times and dividing by four, we get an average of 00:06:07.
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Given a square with area a, you can use the formula P = 4a² to find the
perimeter P of the square. Find the perimeter of a square that has an area of 64 m².
The perimeter of the square is 256 m.
What ia area?Area is a measure of the amount of two-dimensional space enclosed by a closed figure or shape. It is usually measured in square units, such as square meters, square feet, or square centimeters.
What is a Square?A square is a regular quadrilateral with four equal sides and four right angles. It is a special case of a rectangle and a rhombus, and its properties are a combination of both.
In the given question,
We can start by using the formula for the area of a square, which is:
a = s²
where a is the area and s is the length of one side of the square.
If the area of the square is 64 m², then we have:
64 = s²
Solving for s, we get:
s = √64 = 8 m
Now, we can use the formula for the perimeter of a square in terms of its area:
P = 4a²
Substituting a = 64, we get:
P = 4(64) = 256 m
Therefore, the perimeter of the square is 256 m.
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Question 8 (4 points)
For a meat raffle, 100 tickets were sold.
The following were prizes:
number of winners
1
4
15
prize
grand prize - $1000 cash
$250 meat package
$50 meat package
What is the probability of winning the grand prize? 1/20
What is the expected value for someone buying a single ticket for $10.00 ? $
For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?
Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.
What is the difference between real and integer?Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.
What's a real number?A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.
by applying the binomial theorem:
[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]
where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]
The first few terms of this expansion are:
[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:
[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Equating coefficients of [tex]x^3[/tex] on both sides, we get:
[tex]c = n(n-1)(n-2)(a^3/6)[/tex]
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A sample of automobiles traversing a certain stretch of highway is selected. Each automobile travels at a roughly constant rate of speed, though speed does vary from auto to auto. Let x = speed and y = time needed to traverse this segment of highway. Would the sample correlation coefficient be closest to 0.9,0.3,-3,or -0.9? Explain.
The right answer is -0.9, but I do not know the reason.
The sample correlation coefficient would be closest to -0.9.
Here's why:
Correlation Coefficient: The correlation coefficient is a statistical measure of the degree of correlation (linear relationship) between two variables. Pearson’s correlation coefficient is the most widely used correlation coefficient to assess the correlation between variables.
Pearson’s correlation coefficient (r) ranges from -1 to 1. A value of -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation. There is a negative correlation between speed and time. As the speed of the car increases, the time needed to traverse the segment decreases. So, the sample correlation coefficient would be negative.
Since the sample size is large enough, the sample correlation coefficient should be close to the population correlation coefficient. The population correlation coefficient between speed and time should be close to -1, which implies that the sample correlation coefficient should be close to -1.
Therefore, the sample correlation coefficient would be closest to -0.9.
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we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?
Probability of D2 being sunny = 0.78.
On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.
Therefore, we need to find the chances that D2 is sunny.
There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.
Now, Let us find the probability of D2 being sunny.
We have the following possible cases for D2.
D1 = Sunny; D2 = Sunny
D1 = Sunny; D2 = Rainy
D1 = Rainy; D2 = Sunny
D1 = Rainy; D2 = Rainy
The probability of D1 being sunny is 0.9.
When a sunny day follows a sunny day, the probability is 0.8.
When a sunny day follows a rainy day, the probability is 0.6.
Therefore, the probability of D2 being sunny is given by the formula:
Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.
Therefore, the probability that D2 is sunny are 0.78 or 78%.
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A bank statement is shown. Fill in the gaps to complete the sentence below. This bank statement shows a profit / loss of £ Description Sales - Monday Staff wages Sales - Tuesday Supplies - office equipment Sales - Wednesday Rent for office space Customer refund Money in £315.00 £265.00 £190.00 Money out £210.00 £30.00 £450.00 £100.00
The bank statement that is shown in the question shows a loss of £285.00 and calculated by subtracting the total expenses (money out) from the total revenue (money in).
Define profit or loss?Profit or loss is a measure of the financial performance of a business, organization, or individual over a given period of time.
Profit refers to the positive difference between the revenue earned by a business or individual and the expenses incurred during a given period.
A loss occurs when the expenses incurred exceed the revenue earned during a given period.
To calculate the profit or loss, you need to subtract the total expenses (money out) from the total revenue (money in).
In this case, the total revenue is £315.00 + £265.00 + £190.00 = £770.00, and the total expenses are £210.00 + £30.00 + £450.00 + £100.00 = £790.00.
So, the calculation would be:
Total revenue - total expenses = profit/loss
£770.00 - £790.00 = -£20.00
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Mrs. Perez's class donated 99 different products for the food drive. One-ninth of it was vegetables,2/3 pasta,
and 2/9 was soup. How much of each product did they donate?
Simplifying Mrs. Perez's class donated 11 units of vegetables, 66 units of pasta, and 22 units of soup.
What does the term "simplify expression" mean?The process of solving a math problem is simply known as simplifying an expression. An expression is simplified when it is written in the most straightforward way feasible
vegetables = (1/9) x 99
Simplifying this expression, we get:
vegetables = 11
So the class donated 11 units of vegetables.
Next, we can figure out how much of the donation was pasta. We know that 2/3 of the donation was pasta, so we can set up the equation:
pasta = (2/3) x 99
Simplifying 66 units homemade pasta, 22 units of soup, and 11 units of veggies were all provided by Mrs. Perez's students.
Which expression should I simplify?
A math difficulty is simply solved by simplifying the expression. When you simplify a phrase, your goal is essentially to make it as simple as you can. There shouldn't be any more multiplication, dividing, adding, or removing to be done at the conclusion.
veggies = 1/9 times 99
When we condense this statement, we get:
eleven vegetables
Hence, the class gave away 11 units of produce.We can then determine what proportion of the contribution was pasta. Given that we know that pasta made up 2/3 of the donation, we can construct the following equation:
spaghetti equals (2/3) x 99
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VERY IMPORTANT DBA !!!
Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.
What is a linear equation?
A linear equation is an algebraic equation that represents a straight line on a graph. In general, a linear equation takes the form:
y = mx + b
A linear relationship between two variables, x and y, is one in which the change in y is directly proportional to the change in x. This means that for any change in x, there is a corresponding change in y that can be expressed as a constant multiple of x.
For example, if we have a linear relationship y = mx + b, where m is the slope of the line and b is the y-intercept, then if we increase x by 1 unit, y will increase by m units. This relationship holds true for all values of x and y along the line.
A proportional relationship, on the other hand, is a special case of a linear relationship in which the ratio of y to x is always the same constant. This means that if we increase x by 1 unit, y will increase by a constant multiple of x. In other words, the relationship between x and y is one of scaling, where the size of y is always a fixed multiple of the size of x.
Therefore, Table C represents a linear relationship that is also proportional. This is because the ratio of the output (y) to the input (x) is always constant, which is a characteristic of proportional relationships.
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