if matrix a is symmetric show that any two eigenvectors of a correspond to different eigenvalues are orthogonal

The statement 2( g = f + a) and 5(c = f) are true where as statement 3(a = d), 4(d = g - c), and 6(a = -b) are false.

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Answer:

In probability and statistics, the law of big numbers holds that as a sample size increases, its mean gets closer to the average of the entire population. This is because as the sample size increases, the sample becomes more representative of the population.

According to the law of large numbers, a large entity that is expanding quickly cannot continue doing so indefinitely. Often used as instances of this phenomenon are the largest blue chips, with market values in the hundreds of billions.

Two distinct subjects can be covered by the law of huge numbers. First, there are many topics to which the law of large numbers can be applied in statistical analysis. In order to acquire the necessary amount of data, it may not be practical to survey every member of a given population, but every additional data point has the potential to raise the probability that the result is an accurate representation of the mean.

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Answer:

DCBA

Step-by-step explanation:

It's just reverse look closely and you'll notice

By applying the formula of cuboid volume, the volume of the box can be expressed as 225x - 60x² + 4x³.

Cuboid is a 3-D shape formed by three pairs of rectangles (6 sides), 12 edges, and 8 vertices.

The volume of a cuboid can be calculated as follows:

Volume = length * width * height

Initially, we have a 15 x 15-inch piece of metal, then we cut out the four corners so that the sides can be folded up to make a box.

Now we have a shape as the attached image, where x represents the length of the sides of the squares that are to be cut out.

Thus, after the cutting, the length of the new side is 15 - 2x.

This value also represents the length and width of the box, whilst the height is x.

Now we can calculate the volume of the box:

Volume = length * width * height

             = (15 - 2x) * (15 - 2x) * x

             = (225 - 60x + 4x²) * x

             = 225x - 60x² + 4x³

Thus, the volume of the box can be expressed as 225x - 60x² + 4x³.

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The exact value of sin(x + y) is (1 - 2√6) /6. The 2nd option is the answer.

We have sin(x) = -1/2 and cos(y) = -1/3

x is an angle in quadrant III, and y is an angle in quadrant II

For x:

Using trigonometric ratio

sin(x) = -1/2 (sin = opposite/hypotenuse)

adjacent = √(2²-(-1)²) = √3

cos(x) = (-√3)/2  (cos = adjacent/hypotenuse)

Note: adjacent in quadrant III is negative

For y:

Using trigonometric ratio

cos(y) = -1/3  (cos = adjacent/hypotenuse)

opposite = √(3²-(-1)²) = √8 = 2√2

sin(y) = (2√2)/3  (sin = opposite/hypotenuse)

Using trigonometric identity:

sin (x + y) = sin (x)·cos(y) + cos (x)·sin (y)

sin (x + y) = -1/2·(-1/3)  +  [(-√3)/2]·[(2√2)/3]

sin (x + y) = 1/6 - (√6)/3

sin (x + y) = (1 - 2√6) /6

Thus, the exact value of sin(x + y) is  (1 - 2√6) /6

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A function is what happens even if [tex]$f(-x)=f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] and A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex] .

Parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}, \frac{\pi}{2} < y < \pi$[/tex] : Even .

Defining parity

A function is what happens even if. [tex]$f(-x)=f(x)$[/tex] [tex]for all $x \in \mathbb{R}$[/tex]                      A function is what happens odd if [tex]$f(-x)=-f(x)$[/tex] for all [tex]$x \in \mathbb{R}$[/tex]

[tex]$$\begin{aligned}& f(-y): \quad \sqrt{y^2}+\sqrt{\tan ^2(y)} \\& -f(y): \quad-\sqrt{\tan ^2(y)}-\sqrt{y^2}\end{aligned}$$[/tex]

Check parity of [tex]$\sqrt{\tan ^2(y)}+\sqrt{y^2}$[/tex]

Equal or equivalentness, as a trait or state. Women have battled for equal pay to males in the workplace, or the equivalent of a commodity's price in one currency to that in another.

An integer's evenness or oddness is defined by its parity. In light of the fact that both 6 and 14 are even, it can be claimed that their parities are the same, but 7 and 12 have the opposite parity (since 7 is odd and 12 is even). the state of equality, particularly the state of equal pay or status Prison guards are want pay parity with the police. Women still lack balance in many occupations, especially at the top levels.

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A counterexample to the statement given in this problem is:

Three colinear points.

The statement for this problem is given as follows:

You can connect any three points to form a triangle.

This statement is false, as for example, three points on a line do not form a function.

The counterexample is the statement that proves that a conjecture(another statement) is false, hence the first option is the correct option in the context of this problem.

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The net surface area of rectangular prism is 242.2 meters square.

A rectangular prism is a three-dimensional shape with two top and bottom faces and four lateral faces. A rectangular prism seems to be a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism seems to be a cuboid, and a cuboid and a rectangular prism both have the same cross-section.

This rectangular prism's surface area = l x b

We have provided

4 rectangular areas

A₁ = 4.3m x 10m

= 43 m²

2 rectangular areas

A₂ = 6.75m x 5.2m

= 35.1 m²

As a result, the rectangular prism's surface area is:

S.A. = 4A₁ + 2A₂

S.A. = 4(43) + 2(35.1)

= 172+ 70.2

= 242.2 meter square

As a result, the net surface area of the rectangular prism is 242.2 meters square.

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The Venn diagram that represents the description on Events A and B would be the A. First Diagram.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other.

This means that Events A and B cannot happen at the same time and therefore cannot share circles on the Venn diagram.

Events B and C are non - mutually exclusive however and so will share a circle on the Venn Diagram as shown below.

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Answer: D

last one

Step-by-step explanation: just did the test

Since it is possible to drive a fraction of a mile, so it will be appropriate to use fractions; however, it is not possible to drive a negative number of miles, so only positive rational numbers are appropriate.

A rational number is said to be positive if its numerator and denominator are both positive.

Now, we are told that lian's truck uses 0.05 gallon of gas for every mile driven. Thus;

Rate of consumption of gas = 0.05 gallons per mile

The function for number of gallons is;

y = -0.05x + 25

where;

x is number of miles

y is number of gallons

We can use a fraction for the number of miles because it is possible but then the number of miles must be positive rational numbers because number of miles cannot be negative.

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the smallest possible answer in the class is 30.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Mr. Abraham’s is able to divide the learners in his Mathematics class into equal groups of 2, 5 or 6 members without leaving any learners out.

You just need to find the smallest number that can be divided by 2    or  5    or   6    evenly

  The Least Common Multiple

there are various ways to do this  

start with 5    

multiples of 5   are    5   10  15   20  25  30   35    etc.    

see any number in there that is also divisible by 2   and  6

Therefore, 30 is the smallest possible answer in the class.

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Complete question:

Mr. Abraham’s is able to divide the learners in his Mathematics class into equal groups of 2, 5 or 6 members without leaving any learners out. What is the smallest possible number of learners in the class?

Answer:

Start: 400

After 1 Year: 7020

Step-by-step explanation:

You will have a good b-day tmrw

          HAPPY EARLY BIRTHDAY!!!!

So, b) and e) are subspaces of R3, and a), c), and d) are not.

a) {(x,y,z) ∈R3 : x = 0} is not a subspace of R3, because it doesn't contain the zero vector (0,0,0) which is a requirement for a subspace. It's also not closed under scalar multiplication.

b) {(x,y,z) ∈R3: x + y = 0} is a subspace of R3, because it's closed under scalar multiplication and addition and it contains the zero vector (0,0,0).

c) {(x,y,z) ∈R3 : xz = 0} is not a subspace of R3, because it's not closed under scalar multiplication and it's not closed under addition

d) {(x,y,z) ∈ R3: y ≥0} is not a subspace of R3, because it's not closed under addition, it doesn't contain the zero vector (0,0,0) and it's not closed under scalar multiplication.

e) {(x,y,z) ∈ R3: x = y = z} is a subspace of R3 because it satisfies all the properties of a subspace, it is closed under addition, scalar multiplication, it contains the zero vector (0,0,0) and the negative of any vector in the set is also in the set. This set contains all the vectors that are multiples of (1,1,1) which forms a subspace.

So, b) and e) are subspaces of R3, and a), c), and d) are not.

Complete Question: For each of the following subsets of R3 determine whether it is a vector subspace of R3 or not. Justify your answer.                                                                                                                                                      

a) {(x,y,z) ∈R3 : x = 0}

b) {(x,y,z) ∈R3: x + y = 0}

c) {(x,y,z) ∈R3 : xz = 0}

d) {(x,y,z) ∈ R3: y ≥0}

e) {(x,y,z) ∈ R3: x = y = z}

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a) The number of microstates associated with tossing a coin N times and having it come up H times heads and T times tails is given by the binomial coefficient "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!)

b) For a series of 1000 tosses, with 50% heads and 50% tails, there are a total of "1000 choose 500" microstates. This is approximately 2.07*10²⁵ microstates.

c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable.

a) The number of microstates associated with a coin flip can be determined using combinatorics. The coin flip can have two possible outcomes: heads or tails. To calculate the number of microstates for N coin flips with H heads and T tails, we use the binomial coefficient formula "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!) where ! denotes factorial. This formula gives the number of ways to choose H heads out of N coin flips.

b) To calculate the total number of microstates for a series of 1000 tosses with 50% heads and 50% tails, we use the binomial coefficient formula "1000 choose 500". This is equivalent to (1000!/(500!500!)) which is approximately 2.0710²⁵ microstates.

c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable. We can calculate this using the binomial probability mass function which is ( n choose k ) * p^k * (1-p)^(n-k) where n is the number of trials, k is the number of successful outcomes, p is the probability of success in one trial, 1-p is the probability of failure in one trial.

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The expression when distributed is 3 + 2k

From the question, we have the following parameters that can be used in our computation:

1/5(15 + 10k)

The distribution property states that

a(b + c) = ab + ac

using the above as a guide, we have the following:

1/5(15 + 10k) = 1/5 * 15 + 1/5 * 10k

Evaluate the products

1/5(15 + 10k) = 3 + 2k

Hence, the equivalent expression is 3 + 2k

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well, we know that π is 180°, so what's 11π/6?

[tex]\begin{array}{ccll} radians&degrees\\ \cline{1-2} \pi &180\\\\ \frac{11\pi }{6}&x \end{array}\implies \cfrac{\pi }{ ~~ \frac{11\pi }{6} ~~ }~~ = ~~\cfrac{180}{x}\implies \cfrac{ ~~ \frac{\pi}{1} ~~ }{\frac{11\pi }{6}}~~ = ~~\cfrac{180}{x} \\\\\\ \cfrac{6\pi }{11\pi }=\cfrac{180}{x}\implies \cfrac{6 }{11 }=\cfrac{180}{x}\implies 6x=1980\implies x=\cfrac{1980}{6}\implies x=330[/tex]

The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.

Given information:

The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.

The director tested the hypotheses H.

p=0.08

[tex]\alpha =\\[/tex]0.05

p-value of of the test is found to be 0.03 which is smaller than the significance level of [tex]\alpha =0.05\\[/tex]

Now, for smaller value of p-value, the null hypothesis is ignored.

Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.

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The correct conclusion should be that the null hypothesis is rejected because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.

Given information:

The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect.

The director tested the hypotheses H.

p=0.08

α =0.05

p-value of of the test is found to be 0.03 which is smaller than the significance level of α =0.05

Now, for smaller value of p-value, the null hypothesis is ignored.

Therefore, the correct conclusion should be that the null hypothesis is reject because of smaller p-value, and the true proportion of stitching defect is not equal to 0.08.

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The increasing and decreasing function is discussed above.

Given is the function f(x).

Increasing and decreasing functions are functions in calculus for which the value of f(x) increases and decreases respectively with the increase in the value of x. We can write -

Therefore, the increasing and decreasing function is discussed above.

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Answer:

56

Step-by-step explanation:

The base area will be 4 times the side length

56 units

The equation of the line that passes through (-3,1) and is parallel to y=4-3x is y = -3x -8.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

An equation y = 4 - 3x

The slope of a line that is parallel to y = 4 - 3x is,

= -3

The equation of the line that passes through (-3,1) and is parallel to y=4-3x,

y - 1 = -3(x + 3)

y - 1 = -3x -9

y = -3x -8

Therefore, y = -3x -8 is the required equation.

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Answer:

Its either .5 or 5

Step-by-step explanation:

im not sure which one though lol

:)

a. Without finding the confidence intervals, the larger margin of error will be the statistics class.

b. The confidence interval is (50.5%, 55.5%)

c. The group that concludes that the outcome is "too close to call is the statistics class.

.

It should be noted that the Without finding the confidence intervals, the larger margin of error will be the statistics class. This is because of the smaller sample size.

The group that concludes that the outcome is "too close to call is the statistics class. This is because the intervals that are obtained contains 50%.

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The required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Benita buys 2 shirts for the same price s the sales tax rate is 6.5%

1 way, paid the cost of 2 shirts jointly
The total cost of the two shirts becomes,
Total cost = 2[ s + 0.065s]
Total cost = 2.13s

2nd way paid the cost of two shirts individually,
total cost = s + 0.065s + s + 0.065s
               = 2.13s

Thus, the required total cost of the two shirts after 6.5% of the tax is given as 2.13s.

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Answer: We can use a system of equations to solve this problem. Let x be the number of oranges sold and y be the number of apples sold. Then we know that:

x + y = 15 (the total number of fruits sold)

1x + 2y = 25 (the total cost of the fruits sold)

We can use the first equation to solve for one variable in terms of the other.

For example, we can solve for x:

x = 15 - y

Now we can substitute this expression into the second equation:

1(15 - y) + 2y = 25

15 - y + 2y = 25

3y = 10

y = 10/3 = 3.333

We can round it to 3 apples sold

So we have 3 apples and 12 oranges sold.

This can be represented in a graph with a point (12,3)

Alternatively, we can solve for y:

y = 15 - x

Now we can substitute this expression into the second equation:

1x + 2(15 - x) = 25

1x + 30 - 2x = 25

-x = -5

x = 5

So we have 5 oranges and 10 apples sold.

This can be represented in a graph with a point (5,10)

Both solutions represent the same values, the number of oranges and apples sold, but represented in a different way.

Step-by-step explanation:

The measure of angle Y is given as follows:

m < Y = 90º.

The sum of the measures of the internal angles of a triangle is of 180º.

For the larger triangle, the measures are given as follows:

Hence the measures of angles x and z are given as follows:

x + z + 50 = 180º

2x = 130

x = 130/2

x = z = 65º.

Then for the smaller triangle, the measures are:

Meaning that the measure of angle y is given as follows:

y + 25 + 65 = 180

y + 90 = 180

y = 90º.

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The formula in cell B3 using the VLOOKUP function to find the meaning for the medical abbreviation listed in cell A3, using the "abbreviation" lookup table, would be: =VLOOKUP(A3, "abbreviation", 2, FALSE).

A3 is the cell that contains the medical abbreviation we want to find the meaning for.

"abbreviation" is the name of the lookup table that contains the item names and meanings.

2 is the column number of the lookup table where the meanings are located.

FALSE is used to require an exact match for the abbreviation in cell A3, so that the correct meaning is returned.

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The height of the tree is 29 feet.

A measure of an angle formed which an object is viewed above the horizontal plane is termed angle of elevation.

Let the distance from the top of the tree to the student's eyes be represented by x. Thus, applying the required trigonometric function;

Tan θ = opposite/ adjacent

Tan 50 = x/ 20

x = 20*Tan 50

  = 23.8351

x = 24 ft

So that;

the height of the tree = 24 + 5

                                    = 29 feet

Therefore, the height of the tree is 29 feet.

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The correct arrangement regarding the angles of the triangle is;

m∠Y < m∠Z < m∠X

In triangle XYZ, the lengths of sides are;

XY = m + 8

YZ = 2m + 3

ZX = m - 3

If m ≥ 6, then;

m + 8 ≥ 14

2m + 3 ≥ 15

m - 3 ≥ 3

Thus;

m - 3 ≤ m + 8 ≤ 2m + 3

The greatest angle is opposite to the greatest side, the smallest angle is opposite to the smallest side, so;

the greatest side is  YZ = 2m + 3- the greatest angle is ∠X

the smallest side is ZX = m - 3 - the smallest angle is ∠Y

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