Use the Gram-Schmidt process to obtain an orthogonal basis of Col(K): 1 -1 3 1 0 -1 -2 1 K= -3 -1 3 1 -2 1 3 -2 -3 0 -1 -1 2 6 3 2 -1 2 -1 0 1 0 ܝ

\( \fbox{(2,5)}\)

Hello, substitute all the given coordinates & see if RHS match with LHS

given equation,

y = 4x-3

First coordinate,

(x,y) = (2,5)

5= 4×2-3

5=5

Hence, first solution satisfies the given equation,

let's solve for rest other cordinates,

second coordinate,

(x,y) = (5,5)

5= 4×5-3

5 ≠ 17

does not satisfy,

third coordinate,

(x,y) = (4,5)

5= 4×4-3

5 ≠ 13

does not satisfy,

fourth coordinate,

(x,y) = (4,5)

5 = 4×3-3

5 ≠ 9

does not satisfy.

Hence the correct answer is (2,5)

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the matrix \(\( (BA^{\top})^{\top} \)\)is given by:

\(\[ \left[\begin{array}{cc} 2 & -1 & 2 \\ 2 & -1 & 2 \end{array}\right] \]\)

To compute the matrix \( (BA^{\top})^{\top} \), we need to perform the following steps:

1. Compute the transpose of matrix \(\( A \)\) by interchanging its rows and columns.

2. Multiply matrix \(\( B \)\)by the transpose of matrix\(\( A \).\)

3. Compute the transpose of the resulting matrix.

Let's perform these steps using the given matrices:

Matrix \( A \):

\(\[ A = \left[\begin{array}{lll} 0 & 1 & -1 \\ 0 & 1 & -1 \end{array}\right] \]\)

Transpose of matrix \(\( A \):\[ A^{\top} = \left[\begin{array}{ll} 0 & 0 \\ 1 & 1 \\ -1 & -1 \end{array}\right] \]\)

Matrix\(\( B \):\[ B = \left[\begin{array}{cc} 1 & 2 \\ -1 & 0 \\ 3 & 1 \end{array}\right] \]\)

Multiplying matrix \( B \) by the transpose of matrix\(\( A \):\)

\(\[ BA^{\top} = \left[\begin{array}{cc} 1 & 2 \\ -1 & 0 \\ 3 & 1 \end{array}\right] \left[\begin{array}{ll} 0 & 0 \\ 1 & 1 \\ -1 & -1 \end{array}\right] = \left[\begin{array}{cc} 2 & 2 \\ -1 & -1 \\ 2 & 2 \end{array}\right] \]\)

Taking the transpose of the resulting matrix:

\(\[ (BA^{\top})^{\top} = \left[\begin{array}{cc} 2 & -1 & 2 \\ 2 & -1 & 2 \end{array}\right] \]\)

Therefore, the matrix \(\( (BA^{\top})^{\top} \)\)is given by:

\(\[ \left[\begin{array}{cc} 2 & -1 & 2 \\ 2 & -1 & 2 \end{array}\right] \]\)

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Answer:

x= -1/3

x = -7

Step-by-step explanation:

9x^2 +66x+21 = 0​

a=9 b=66 c=21

quadratic formula

x=(-b +/- square root of (b^2 – 4ac))/(2a)

x = (-66 +/- square root of (66^2 -4*9*21))/(2*9)

x = (-66 +/- square root of (4356 -756))/(18)

x = (-66 +/- square root of (3600))/(18)

x = (-66 +/- 60)/18

split the fraction

(-66 +/- 60)/18 = -6/18 and -126/18 because of the +/-

x = -6/18  x = -126/18

x = -1/3   x = -7

\(~~~~~~9x^2+66x+21 = 0\\\\\implies 3(3x^2+22x+7)=0\\\\\implies 3x^2+22x+7=0\\\\\implies 3x^2 +21x +x +7=0\\\\\implies 3x(x+7) +(x+7)=0\\\\\implies (x+7)(3x+1)=0\\\\\implies x = -7~~ \text{or}~~ x =-\dfrac 13\)

Answer:

12a - 18

Step-by-step explanation:

6 x 2 = 12 (then add the "a" = 12a

6 x 3 = 18

put the minus in the middle then get

12a- 18

(a) Variance of Z = 1600, Standard deviation of Z = 40

(b) Variance of Z = 2304, Standard deviation of Z = 48

(c) Variance of Z = 80, Standard deviation of Z ≈ 8.94

(d) Variance of Z = 80, Standard deviation of Z ≈ 8.94

(e) Variance of Z = 320, Standard deviation of Z ≈ 17.89

To find the variance and standard deviation of the random variable Z in each case, use the properties of variance and standard deviation, as well as the given information about X and Y.

Given:

X has a mean of 30 and a standard deviation of 4.

Y has a mean of 50 and a standard deviation of 8.

The correlation between X and Y is zero.

calculate the variance and standard deviation for each case:

(a) Z = 35 + 10X

The mean of Z can be calculated as:

Mean(Z) = 35 + 10 * Mean(X) = 35 + 10 * 30 = 335

The variance of Z can be calculated as:

\(Var(Z) = (10^2) * Var(X) = 100 * (4^2) = 1600\)

The standard deviation of Z is the square root of the variance:

\(SD(Z) = \sqrt(Var(Z)) = \sqrt(1600) = 40\)

(b) Z = 12X - 5

Mean(Z) = 12 * Mean(X) - 5 = 12 * 30 - 5 = 355

\(Var(Z) = (12^2) * Var(X) = 144 * (4^2) = 2304\)

\(SD(Z) = \sqrt(Var(Z)) = \sqrt(2304) = 48\)

(c) Z = X + Y

Mean(Z) = Mean(X) + Mean(Y) = 30 + 50 = 80

\(Var(Z) = Var(X) + Var(Y) = (4^2) + (8^2) = 16 + 64 = 80\)

\(SD(Z) = \sqrt(Var(Z)) = \sqrt(80) ≈ 8.94\)

(d) Z = X - Y

Mean(Z) = Mean(X) - Mean(Y) = 30 - 50 = -20

\(Var(Z) = Var(X) + Var(Y) = (4^2) + (8^2) = 16 + 64 = 80\)

\(SD(Z) = \sqrt(Var(Z)) = \sqrt(80) ≈ 8.94\)

(e) Z = -2X + 2Y

Mean(Z) = -2 * Mean(X) + 2 * Mean(Y) = -2 * 30 + 2 * 50 = 40

\(Var(Z) = (-2^2) * Var(X) + (2^2) * Var(Y) = 4 * (4^2) + 4 * (8^2) = 64 + 256 = 320\)

\(SD(Z) = \sqrt(Var(Z)) = \sqrt(320) ≈ 17.89\)

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Answer:

y=x+2.5

Step-by-step explanation:

The arrow is in -7 on the number line since 3 + (-10) = -7.

A number line is a pictorial representation of numbers on a straight line.

It is a horizontal line that has equally spread number increments.

We have,

3 + (-10)

This can be written as:

= 3 - 10

= -7

We can draw a number line to represent graphically:

                         <↓-------(subtracting 10)-------------->

< ---------(-9)-(-8)-(-7)-(-6)-(-5)-(-4)-(-3)-(-2)-(-1)-0-1-2-3-4-5-6-7-8------------->

Thus the equation can be represented graphically with an arrow in -7 on the number line since 3 + (-10) = -7.

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===================================================

Explanation:

It costs $91.50 for the first 200 copies.

Roger needs 200 more copies to get to 400 total.

He's charged $42 per 100 copies at this point, so he is charged 42*2 = 84 extra dollars to do those extra 200 copies.

Before tax, his total is 91.50+84 = 175.50 dollars.

The sales tax will increase the bill by 6%

To increase by 6%, we use the multiplier 1.06

1.06*175.50 = 186.03

Or you can follow the steps shown in the next section.

-----------------

6% of 175.50 = 0.06*175.50 = 10.53

The sales tax is $10.53

175.50 + 10.53 = 186.03

-----------------

Whichever method you use, you should end up with an after-tax cost of $186.03

After taxes, Roger is required to pay a total of $186.03 in fees.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

Given, Roger's local print shop charges $91.50 for the first 200 copies and $42 for every 100 additional copies.

Charges for 200 copies = 91.50

remaining copies = 400- 200

Charges for the remaining 200 copies = 2 * 42 = 84

Total charges for 400 copies = 91.50 + 84

Total charges for 400 copies = 175.5$

Total charges for 400 copies after 6% tax = 175.5*(1.06)

Total charges for 400 copies after 6% tax = 186.03

therefore, Roger has to pay a Total charge of $186.03 after taxes.

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Answer:

\(\frac{9\pm\sqrt{61}}{2}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-(-9)\pm\sqrt{(-9)^2-4(1)(5)}}{2(1)}=\frac{9\pm\sqrt{81-20}}{2}\\\\=\frac{9\pm\sqrt{61}}{2}\)

The diagonal measurement as √5625 ft, which is approximately 75 feet, the correct answer is B. 75 ft 0 in.

The diagonal measurement of the rectangular slab on grade can be found using the Pythagorean theorem. The diagonal is the hypotenuse of a right triangle formed by the length and width of the slab.

To calculate the diagonal measurement, we can apply the Pythagorean theorem:

Diagonal² = Length² + Width²

Substituting the given values, we have:

Diagonal² = (60 ft 0 in.)² + (45 ft 0 in.)²

Calculating this expression, we find:

Diagonal² = 3600 ft² + 2025 ft²

Diagonal² = 5625 ft²

Taking the square root of both sides, we obtain:

Diagonal = √5625 ft

Diagonal ≈ 75 ft

Therefore, the diagonal measurement of the rectangular slab on grade is approximately 75 feet.

To find the diagonal measurement of the rectangular slab on grade, we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (length and width).

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This year a grocery store is paying the manager a salary of $48,680 per year. The percent change in the manager's salary from last year to this year is approximately 7.41%.

To find the percent change in the manager's salary, we can use the percent change formula:

Percent Change = ((New Value - Old Value) / Old Value) * 100

Given that last year's salary was $45,310 and this year's salary is $48,680, we can substitute these values into the formula:

Percent Change = (($48,680 - $45,310) / $45,310) * 100

Calculating this expression, we get:

Percent Change = ($3,370 / $45,310) * 100 ≈ 0.0741 * 100 ≈ 7.41%

Therefore, the percent change in the manager's salary from last year to this year is approximately 7.41%. This indicates an increase in salary.

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Aiden's balance after 15 years will be approximately $1,130.86.

The formula accrued amount in a compounded interest is expressed as;

\(A = P( 1 + \frac{r}{n})^{nt}\)

Where A is accrued amount, P is the principal, r is the interest rate and t is time.

Given that:

Principal P = $675

Compounded annually n = 1

Time t = 15 years

Interest rate r = 3.5%

Accrued amount A =?

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035

Plug the given values into the above formula and solve for accrued amount A:

\(A = P( 1 + \frac{r}{n})^{nt}\\\\A = 675( 1 + \frac{0.035}{1})^{1*15}\\\\ A = 675( 1 + 0.035})^{15}\\\\A = 675( 1.035})^{15}\\\\A = \$ 1,130.86\)

Therefore, the accrued amount is $1,130.86.

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Step-by-step explanation:

3 more than twice n = 3+2n

3 more than twice n is atmost 50,

=> 3+2n <= 50 {(3+2n) is less than or equal to 50}

Answer:

3 + 2n ≤ 50

Step-by-step explanation:

"at most 50" means 50 or less.

Hope this helps.

Answer:

$16.40 tip

Step-by-step explanation:

82 * .20 = 16.40

Archimedes drained the water in his tub by removing 62.5 liters of water per minute. After 888 minutes, the tub was completely drained. The relationship between the amount of water left in the tub and time can be graphed to show a linear decrease over time.

Archimedes drained his tub at a constant rate of 62.5 liters of water per minute. This means that after every minute, the amount of water left in the tub decreased by 62.5 liters. After 888 minutes, the tub was completely drained. This relationship between the amount of water left in the tub and time can be graphed to show a linear decrease over time. The slope of the graph represents the rate at which the water was drained from the tub.

The graph will start at the initial volume of water in the tub and will decrease linearly over time until it reaches zero after 888 minutes. The rate of change can be calculated by taking the change in the amount of water over a given time interval, which will always be 62.5 liters per minute in this case.

This linear relationship can be described by the equation y = mx + b, where y is the amount of water left in the tub, x is the time, m is the slope (which is -62.5 in this case), and b is the initial amount of water in the tub.

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This problem involves graphing a negative linear relationship between the time and the remaining water in the tub. The graph starts with the tub full (0,55350) and ends with the tub empty (888,0).

This is a problem about linear relationships. To graph this relationship, you want to use time (in minutes) as the x-axis and the amount of water left in the tub (in liters) as the y-axis.

Essentially, this graph represents a negative linear relationship between the amount of water left in the tub and the time since the water started draining.

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Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer:

{-12,12}

Step-by-step explanation:

-|-x| = -12 multiply both sides by -1

|-x| = 12 apply rule for solving absolute value equations

-x = 12 and -x = -12 solve

x = -12 and x =12

Answer:

x = -56

Step-by-step explanation:

x/7 = -8

Multiply each side by 7

x/7 *7 = -8*7

x = -56

To find the values of sin D, sin E, cos D, and cos E, we need additional information such as the measures of angles D and E or the lengths of the sides of the triangle.

However, based on the information you provided (9, 12, 15), we can make some assumptions.

If we assume that the triangle is a right triangle, with side lengths of 9, 12, and 15, we can use the Pythagorean theorem to find the missing side lengths. The side lengths satisfy the Pythagorean theorem: 9^2 + 12^2 = 15^2.

Using these assumptions, we can calculate the values of sin D, sin E, cos D, and cos E. Since angle D is opposite side 9 and angle E is opposite side 12, we have:

sin D = 9/15 = 3/5

sin E = 12/15 = 4/5

cos D = 12/15 = 4/5

cos E = 9/15 = 3/5

Please note that these values are based on the assumption of a right triangle with side lengths of 9, 12, and 15.

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Complete question: Find Sin D, Sin E, Cos D, And Cos E. Write Each Answer As A Fraction In Simplest Form. 9 12 15 E Sin D = Sin E= Cos D= Cos E.

Answer:

2

Step-by-step explanation:

The required answer is the all of the given points (A, B, C, and D) are on the unit circle.

The unit circle is a circle with a radius of 1 unit centered at the origin of a coordinate plane. Points on the unit circle can be represented by their coordinates (x, y), where x is the cosine of the angle and y is the sine of the angle.

To determine which of the following points is on the unit circle, we need to check if the coordinates satisfy the equation x^2 + y^2 = 1. If the coordinates satisfy this equation, then the point is on the unit circle.

consider the points given and check if they are on the unit circle:

- Point A: (1, 0)
- Point B: (0, -1)
- Point C: (-√2/2, √2/2)
- Point D: (0, 1)

Checking each point:

- Point A: (1, 0)
   - 1^2 + 0^2 = 1 + 0 = 1
   - The coordinates satisfy the equation, so point A is on the unit circle.

- Point B: (0, -1)
   - 0^2 + (-1)^2 = 0 + 1 = 1
   - The coordinates satisfy the equation, so point B is on the unit circle.

- Point C: (-√2/2, √2/2)
   - (-√2/2)^2 + (√2/2)^2 = 2/4 + 2/4 = 4/4 = 1
   - The coordinates satisfy the equation, so point C is on the unit circle.

- Point D: (0, 1)
   - 0^2 + 1^2 = 0 + 1 = 1
   - The coordinates satisfy the equation, so point D is on the unit circle.

In conclusion, all of the given points (A, B, C, and D) are on the unit circle because their coordinates satisfy the equation x^2 + y^2 = 1.

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The fitted model log( ) = 1.6 - 0.2c is equivalent to the models y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\)), y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\)), and y = 1.6 - 0.22.

The fitted model log( ) = 1.6 - 0.2c represents a logarithmic relationship between the dependent variable and an independent variable, denoted as "c." To identify equivalent models, we need to examine the given options.

Option 1: y = 21.6 - 0.25(1+\(e^(1.6-0.2c)\))

This model is equivalent to the fitted model log( ) = 1.6 - 0.2c because the right side of the equation contains the term 1+\(e^(1.6-0.2c)\), which corresponds to the exponential function e^(1.6-0.2c). The coefficient -0.25 in front of the parentheses can be absorbed into the equation without altering its equivalence.

Option 2: y = 1.6 - 0.22/(1+\(e^(1.6+0.2)\))

This model is also equivalent to the fitted model because it contains the term 1+e^(1.6+0.2) in the denominator. The coefficient -0.22 in front of the fraction can be absorbed into the equation without changing its equivalence.

Option 3: y = 1.6 - 0.22

This model is a simplified version of the fitted model. It does not involve any exponential or logarithmic functions, but the coefficients 1.6 and -0.22 remain the same as in the original equation.

Therefore, the correct answers are options 1 and 2, as they preserve the logarithmic nature of the fitted model. Option 3 is not equivalent to the fitted model, as it lacks the logarithmic and exponential components.

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The value of y is :

y = ln(2/(eˣ + 1))

Given equation is :

(e-2x+y +e-2x) dx - eydy = 0

To solve the separable equation, we need to separate the variables in the differential equation.

The given differential equation can be written as,

(e-2x+y +e-2x) dx - eydy = 0

Let's divide by ey and write it as,

(\(e^{-y}\) (e⁻²ˣ+y +e⁻²ˣ )) dx - dy = 0

(\(e^{-y}\) (e⁻²ˣ+y +e⁻²ˣ )) dx = dy

Taking the integral of both sides of the equation we get:

∫(\(e^{-y}\)  (e⁻²ˣ+y +e⁻²ˣ )) dx = ∫ dy

On the left side we can write,

\(e^{-y}\)  ∫(e⁻²ˣ+y +e⁻²ˣ ) dx= y + C

After solving this differential equation, the value of y is y = ln(2/(eˣ + 1)).

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Answer:

Hola losiento no se ablar inglés

Answer:

3

Step-by-step explanation:

-4c - 2 = 10 - 8c

-4c + 8c = 10 + 2

4c = 12

c = 12/4

c = 3

Using the binomial distribution, you would expected to draw a face card 8 times.

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

For this problem, the parameters are given as follows:

Then the expected value is found as follows:

E(X) = np = 35 x 12/52 = 420/52 = 8.

Thus, you would expected to draw a face card 8 times.

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The vector X in \(R^{2}\) whose coordinates with respect to the basis B are [6, -1] is X = [4, -35]

An ordered basis B in \(R^{2}\) is a pair of linearly independent vectors that can be used to uniquely represent any vector in the 2-dimensional space.

In this case, the ordered basis B consists of the vectors [1, -6] and [2, -1].
A vector X in \(R^{2}\) can be written as a linear combination of the basis vectors. To find the vector X whose coordinates with respect to basis B are [6, -1], we can represent it as follows:
X = 6 × [1, -6] + (-1) × [2, -1]
Now, we just need to perform the linear combination:
X = 6 × [1, -6] + (-1) × [2, -1]
X = [6 × 1, 6 × (-6)] + [(-1) × 2, (-1) × (-1)]
X = [6, -36] + [-2, 1]
Next, add the corresponding components of the two resulting vectors:
X = [(6 + -2), (-36 + 1)]
X = [4, -35]

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Solution

For this case we can see that < XQL and < MQR are opposed by the vertex so then are equal

And if we set up equal the measures given we got:

-12x+133= 3x+79

Now we can solve for x. We can add 12x in both sides of the equation and we got:

133= 15x+79

Now we can subtract both sides of the equation 79 and we got:

54= 15x

And finally we got:

x= 54/15= 3.6º

Now we can find the angle < MQR replacing the value of x like this: