find a basis for the nullspace of the matrix. (if there is no basis, enter none in any single cell.) a

In this sample, the events "bride" and "groom"  are not mutually exclusive.

In logic and probability theory, mutually exclusive events are events that do not take place at the same time.  This means that any such two or more events are not going to happen together but will take place at different times. For example - when a die is rolled, we might get any of the six numbers but they don't appear at the same time together.

In the given problem we see that the randomly selected person can either be the groom's friend or the bride's friend or they can be a friend of both of them. This means that both events can take place together at the same time. And, hence, these are not mutually exclusive events.

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Answer: x=6

Step-by-step explanation: The absolute value | x | of a real number is a positive value of x even if the value of x had a sign(negative sign, etc.).

Students that ran faster than Amy are Chris and Ethan.

Speed is the ratio between distance and time. The formula for speed

v = d ÷ t

Amy's speed

Brian's speed

Chris's speed

Ethan's speed

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Answer:

x=-1

Step-by-step explanation:

3x^2+6x=-3

factor:

3x(x+2)=-3

Here, its obvious what x has to be: -1, just solve to confirm:

(3*-1)(-1+2)=-3

(-3)(1)=-3

-3=-3

Hope this helps.

The angles for the triangle are 42°, 68° and 70° and x=21.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

As sum of all angles of a triangle is 180°

2x+3x+5+4x-14=180

x=21

hence,

         The angles for the triangle are 42°, 68° and 70° and x=21.

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Right question:-

Angles in the question are 2x°,(3x+5)° and (4x-14)° of a triangle.

Three standard deviations contain a portion of the data equal to 88.9%.

According to Chebyshev's theorem, you can use the equation to roughly estimate the fraction of the data that lies within k standard deviations of the mean given a normal distribution.

Portion of data[tex]$=\left(1-1 / k^2\right)$[/tex]

The answer is, per Chebyshev's theorem, the range of of prices in which [tex]$88.9 \%$[/tex] of data lies is [tex]$[\$ 3.62, \$ 4.28]$[/tex].

The equation for Chebyshev's theorem is:

Portion of data [tex]$=\left(1-1 / k^2\right)$[/tex]

Where:

- k is the number of standard deviations a value is from the mean.

In this case the portion of data interest is [tex]$88.9 \%$[/tex]

Solve the equation for k

[tex]& 0.889=\left(1-1 / k^2\right. \\[/tex]

[tex]& -0.111=-1 / k^2 \\[/tex]

[tex]& k^2=1 / 0.111 \\[/tex]

[tex]& k^2=9.0 \\[/tex]

[tex]& k=3.0[/tex]

Three standard deviations contain a portion of the data equal to[tex]$88.9 \%$[/tex].

That is 3 times [tex]$\$ 0.11=\$ 0.33$[/tex]

Range is [tex]$\$ 3.95 \pm \$ .33$[/tex].

The complete question is,

Suppose that prices of a gallon of milk at various stores in one town have a mean of $3.95 with a standard deviation of $0.11. Using Chebyshev's Theorem, state the range in which at least 88.9% of the data will reside.

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The value of x makes that makes the parallelogram a rectangle is D. 5

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with opposite sides that are parallel and equal is known as a parallelogram. The interior opposite angles of it are equal. Additionally, the angles on the same side of the transversal are complementary to one another or add up to 180 degrees.

This will be:

2x + 4 = 14

Collect the like terms

2x = 14 - 4.

2x = 10

Divide

x = 10 / 2

x = 5

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B) In a right triangle where a=1 and b=1, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 1^2 + 1^2 = 1+1 =2, so c = √2

C) In a right triangle where a=5 and b=6, the hypotenuse can be found using the Pythagorean theorem which states that c^2 = a^2 + b^2, where c is the length of the hypotenuse. In this case, c^2 = 5^2 + 6^2 = 25+36 =61, so c = √61

Less than 2 units separate the median from the lower quartile for customers making purchases. The correct option is E.

Quartile deviation: The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q-1. The median or second quartile is also referred to as Q-2. Third quartile: Also referred to as the higher quartile or Q-3.

Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q-3) and lower quartile (Q-1) can be used to depict quartile deviation as the letters Q-D. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.

The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.

Therefore, the correct answer is option E.

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The value of 1st number is 4 + 4/√3 and value of 2nd number is 4 - 4/√3

let the 2 number be a,b

given a+b=8 -- (i)

let the difference of the number is x

so let a-b =x

a-b = x ---(ii)

adding equation (i) and equation (ii) we get

2a = 8 +x

=> a = (8+x)/2

so a = 4+x/2

subtract (ii) from (i) we get:

2b = 8-x

=> b = (8-x)/2

so b = 4-x/2

now the product of both number and their difference is given as a*b*x

=> (4+x/2)*(4-x/2) *x

=> (16 - x²/4)*x

=> 16x - x³/4

let the above value be A

so A = 16x - x³/4

in order to find maximum value of A we have to made dA/dx = 0

=> d(16x - x³/4)dx

=>  16 - 3x²/4

so 16 -  3x²/4 =0

=> 3x²/4 = 16

=> 3x² = 64

=> x² = 64/3

so x = 8/√3

now we got value of x

so a = 4+ x/2

=> 4 + 8/2√3

=> 4 + 4/√3

so value of a =  4 + 4/√3

value of b = 4 - 4/√3

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Answer:

“Song of myself ” is written by Walt Whitman in 1855

Answer:

The Song of Myself is written by Walt Whitman in 1855

Step-by-step explanation:

The credit term 3/15, n/45 states that the buyer will receive a 3% discount if the payment is made within 15 days. Otherwise, full payment is expected within 45 days from the invoice date.

This term can be expressed as a formula and calculation as follows:

Discount = 3% of Invoice Total

Payment due within 15 days = Invoice Total - Discount

Payment due within 45 days = Invoice Total

For example, if the invoice total is $500, then the buyer will receive a 3% discount (Discount = 3% x $500 = $15) if the payment is made within 15 days. The payment due within 15 days is then equal to the invoice total minus the discount ($500 -$15 = $485). On the other hand, if the payment is not made within 15 days, the buyer is expected to pay the full invoice total within 45 days ($500).

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Answer:

transformed function, g (x) =1/7x+5

Step-by-step explanation:

The Ordinary integral of the Line integral [tex]\int _c {(y-z)} \, ds[/tex] where C is the helix ⟨7cos t, 7sin t, t⟩ is [tex]\int\limits^0 _{-2\pi} \sqrt{50}{(7sin\ t -t)} \, dt[/tex] and its value in the range -2π ≤ t ≤ 0 is 10√2 π²

We have x = 7cos t, y = sin t and z = t.

We also need ds =[tex]\sqrt{(\frac{dx}{dt})^{2} +(\frac{dy}{dt})^{2} +(\frac{dy}{dt})^{2} }dt[/tex]

     ds  = [tex]\sqrt{(-7sin\ t)^{2} +(7cost\ t)^{2} +(1)^{2} }dt[/tex]

           = [tex]\sqrt{49sin^{2}t +49cos^{2}t+1 }dt[/tex]

           = [tex]\sqrt{49(sin^{2}t +cos^{2}t)+1 }dt[/tex]

     ds  = [tex]\sqrt{50}dt[/tex]

Now,  [tex]\int _c {(y-z)} \, ds[/tex] =  [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

Evaluating the integral [tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]

[tex]\int\limits^0 _{-2\pi} {(7sin\ t -t)}\sqrt{50} \, dt[/tex]   =  [tex]\sqrt{50}\ {[-7cos\ t -\frac{t^{2} }{2} ]}\limits^0 _{-2\pi}[/tex]

                                     =  [tex]\sqrt{50}\ {[-7+7+2\pi ^{2}]}[/tex]

                                     =  [tex]10\sqrt{2}\pi ^{2}}[/tex]

The question is incomplete, the complete question is

" Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.[tex]\int _c {(y-z)} \, ds[/tex] ; C is the helix ⟨7cos t, 7sin t, t⟩, for -2π ≤ t ≤ 0 "

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In order to get another number, a number must be raised to a certain power, which is known as a logarithm.

calculation is attached below :

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6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.

6! = 720

6! is short for 6 factorial and is calculated by multiplying all the integers from 1 to 6. So the answer is 720 ways.

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

So the answer is 720 ways.

There are 720 ways in which a multiple-choice question on an online quiz with six answer choices can be displayed. This is calculated by multiplying all the integers from 1 to 6, which is referred to as 6 factorial, or 6!. 6! is calculated by multiplying 6 x 5 x 4 x 3 x 2 x 1, which equals 720. This means that there are 720 possible combinations of answer order that can be shown to each student when they take the quiz. With such a wide variety of possible answers, students can focus on the content of the question rather than on the order of the answers, which can help to reduce bias and ensure the validity of the quiz.

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The cosecant of angle U is csc(U) = 1 / sin(U) = √55 / 4

To find the cosecant of angle U in triangle UTV, we need to find the sine of angle U. To do this, we can use the sides of the triangle that are opposite and adjacent to angle U. In a right triangle, the sine of an angle is equal to the opposite side divided by the hypotenuse.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]VT^2 + UT^2 = UV^2[/tex]

4^2 + (√39)^2 = UV^2

16 + 39 = UV^2

55 = UV^2

UV = √55

So, the length of the hypotenuse is √55. To find the sine of angle U, we can use the ratio of the opposite side (UT) to the hypotenuse:

sin(U) = UT / UV = 4 / √55

The cosecant of angle U is then:

csc(U) = 1 / sin(U) = √55 / 4.

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b = (2,-1,6) is a linear combination of a1 = (1,-2,0), a2 = (0,1,2) and a3 = (5,-6,8) with weights (1,3,1) respectively.

To determine if b is a linear combination of a1, a2, and a3, we can set up a system of equations using the coefficients of the linear combination and the variables a1, a2, and a3. The equation for a linear combination of the form b = k1a1 + k2a2 + k3a3, where k1, k2 and k3 are the coefficients, can be written as:

b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8)

So,

x = k1 + 5k3

y = -2k1 + k2 - 6k3

z = 2k2 + 8k3

We know the values of x,y,z from b = (2,-1,6)

So, we can set up the following system of equations:

x = k1 + 5k3 = 2

y = -2k1 + k2 - 6k3 = -1

z = 2k2 + 8k3 = 6

We can solve the system of equations using methods such as substitution or elimination to find the values of k1, k2, and k3.

k1 = 1, k2 = 3, k3 = 1

Therefore, we can express b as a linear combination of a1, a2, and a3 with the weights k1, k2, and k3 which are (1, 3, 1) respectively.

b = 1a1 + 3a2 + 1 × a3

This means that b is a linear combination of a1, a2, and a3 with weights (1, 3, 1) respectively.

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The question is -

Determine if b is a linear combination of a1, a2, and a3.

a1=(1,-2,0)

a2=(0,1,2)

a3=(5,-6,8)

b=(2,-1,6)

If Brick San Antonio playing a game of counters Rick has some counters Selma. the number of count as Tony has = 1: P work out the value of paid is 1.5.

Let x represent the number of counter brick

Let 2x counter represent  Selma

Let 2x -6 counter  represent Tony

Hence,

x+2x+2x -6 =54

5x -6 =54

5x =60

x =60/5

x =12

So Brick has 12

Tony has 2×12 -6

= 24 -6

=18

Thus

12:18 = 1: 18/12

=1:1.5

Hence,

P =1.5

Therefore the number of count as Tony has = 1: P work out the value of paid is 1.5.

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Answer:

-1/2

Step-by-step explanation:

first u would label ur x and ys 2,6 would be x1, y1 then u would put 8,4 would be x2 and y2 . You would put 4-6 as y2 - y1  and 8-2 as x2 - x1 to get -2 divided by 4 to get your -1/2

The original dimension of the metal is width = 21 and length = 41 before cutting off the squares.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry.

Let us suppose the width of the rectangular metal = w.

Then the length of the rectangular metal is = 20 + w

Given that squares of 4in are cut from the four corners, then the new width and length will be:

width = w - 8

length = 20 + w - 8

The height of the rectangular metal when the flaps are folded are 4 in.

The volume of the rectangular prism is:

V = (l)(w)(h)

Substituting the value of V = 1716, width = w - 8, length = 20 + w - 8, and h = 4 we have:

1716 = (w - 8)(20 + w - 8)(4)

1716 = 80w + 4w^2 - 32w - 640 - 32w + 256

1716 = 4w^2 + 16 w - 384

4w^2 + 16w -384 - 1716 = 0

4w^2 + 16w - 2100 = 0

w^2 + 4w - 525 = 0

w^2 + 25w - 21w - 525 = 0

w(w + 25) - 21 (w + 25) = 0

(w - 21) (w + 25) = 0

w = 21

w = -25

The dimensions of the box cannot be negative hence, the width is 21.

length = 20 + 21

length = 41

The original dimensions of the metal is width = 21 and length = 41 before cutting off the squares.

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The equation as a single logarithm is log(4x)^3)/(4y)^2

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) \times log_b(c) = \log_a(c)[/tex]

Log with base e = 2.71828... is written as

[tex]\ln(x)[/tex]

Log with base 10 is written as

[tex]\log(x)[/tex]

Given;

Equation=3log4x-2log4y

=log(4x)^3-log(4y)^2

=log(4x)^3)/(4y)^2

Therefore, the answer of logarithm will be log(4x)^3)/(4y)^2

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The required correct way of division has been shown, as per the long division.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
The questions seem to be incomplete, so we assume the number 729 that Allie divides it by the number 9.
According to the question,
Long division,

9 ] 729  [8 1
   - 72
---------------
       0 9
        - 9
---------------
          0

Thus, the required correct way of division has been shown, as per the long division.

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The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.

Given data :

calculate a 95% two-sided confidence interval on the mean for women and men separately :

A) The confidence interval for women: [1711.70] <u< [1894.10]

Women = [tex]\frac{1674+ 1622 + 1637 + 1838 + 1964 + 1836 + 1728 +1913 + 1885 + 1932}{10}[/tex] = 1802.9

B) B) The confidence interval for men: [2096.50] <u< [2513.80]  

Men =   [tex]\frac{1852 + 2403 + 2383 + 2336 + 2597 + 2581 + 2169 + 2120}{8}[/tex] =  2305.125

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The matrix expression for this model is given by

T=

[ 1-a, a, 0; 0, 1-B, B; 0, 0, 1]

When a = 0.10 and B = 0.05, the matrix expression becomes:

T=

[ 0.90, 0.10, 0; 0, 0.95, 0.05; 0, 0, 1]

This matrix expression describes the transition probabilities of the virus over time. Specifically, it describes the probability of a person who has never been infected (S) becoming infected (I) in the next day (a = 0.10), the probability of a person who is infected (I) in the current day  in the next day (B = 0.05), and the probability of a person who has recovered (R) staying recovered in the next day (1). Thus, this matrix expression models the progression of a contagious virus through a population over time.

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$50 is the constant charge used for each minute.

We must put up two variables in order to fix this issue. In this instance

F = constant Fee

R = rate used per minute.

So the cost for the month of January is calculated like this:

F+250R= 70

And the cost for February is calculated like this:

F+275R= 72

So no we have a system of equations we can solve simultaneously. This can be solved using different methods, elimination, substitution, graphically, or by using matrices. I will solve this by substitution.

So let's solve the first equation for R:

[tex]R = \frac{70-F}{250}[/tex]

And let's substitute this first equation into the second equation:

[tex]F+275(\frac{70-F}{250})= 72[/tex]

And now we can solve this for F:

[tex]F+275(\frac{70-F}{250})= 72\\F+11(\frac{70-F}{10})= 72\\F+(\frac{770-11F}{10})= 72.....eq(1)\\[/tex]

We can multiply both sides by 10 so we get:

[tex]10*F+10(\frac{770-11F}{10})= 10*72\\\\10F+770-11F= 720\\\\770-720 = 11F - 10F\\50 = F[/tex]

Therefore, $50 is the constant charge used for each minute.

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The domain of the given set of functions is (Alex, Alesia, Bob,  Yolanda, Maria , Elvis)

The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A-> B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The domain of the given set of functions is (Alex, Alesia, Bob,  Yolanda, Maria , Elvis)

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The sample space for rolling a fair eight-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8}.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.

Given an eight-sided die,

to find the sample space,

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.

when eight sides die is tossed there will be 8 sample spaces that are,

1, 2, 3, 4, 5, 6, 7, 8,

so S = {1, 2, 3, 4, 5, 6, 7, 8}

Hence option D is correct.

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The value of the equation is A = 11,025

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 105²

On simplifying the equation , we get

A = ( 100 + 5 )²

The equation is of the form ( a + b )² = a² + 2ab + b²

On further simplification , we get

A = ( 100 )² + 2 ( 100 ) ( 5 ) + ( 5 )²

A = 10000 + 1000 + 25

A = 11,025

Hence , the equation is A = ( 100 + 5 )² = 11,025

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