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To find a vector with a magnitude of 14 in the same direction as (2, 6, -3), the vector (4, 12, -6) has a magnitude of 14 and is in the same direction as (2, 6, -3).

we need to scale the original vector while preserving its direction. By normalizing the vector, we can determine its unit vector and then multiply it by the desired magnitude to obtain the final vector. magnitude = √(x² + y² + z²), where x, y, and z are the components of the vector. In this case, the magnitude of the vector (2, 6, -3) is √(2² + 6² + (-3)²) = √(4 + 36 + 9) = √49 = 7.

To obtain a vector with a magnitude of 14, we need to scale the original vector by a factor of 14/7. This ensures that the new vector has the desired magnitude while maintaining the same direction. Scaling a vector involves multiplying each of its components by the scaling factor. Therefore, we can calculate the new vector as follows: New vector = (2, 6, -3) * (14/7) = (2 * 14/7, 6 * 14/7, -3 * 14/7) = (4, 12, -6).

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The determinant of the matrix formed by the given vectors is -4, indicating that the vectors are linearly independent in R⁴.

To evaluate the determinant of the given set of vectors V₁ = [5, 4, 0, 4] and V₂ = [3, 2, 2, 2] using the expanded matrix form, we can write:

| 5 3 |

| 4 2 |

| 0 2 |

| 4 2 |

Expanding the determinant along the first row, we can calculate it as follows:

det = 5 * det(| 2 2 |) - 3 * det(| 4 2 |)

| 4 2 | | 0 2 |

We can evaluate each determinant separately:

det(| 2 2 |) = (2 * 2) - (2 * 0) = 4 - 0 = 4

det(| 4 2 |) = (4 * 2) - (2 * 0) = 8 - 0 = 8

Substituting these determinants back into the expanded expression:

det = 5 * 4 - 3 * 8

= 20 - 24

= -4

Therefore, the determinant of the given matrix is -4.

Based on the determinant being nonzero (-4 ≠ 0), we can conclude that the vectors V₁ = [5, 4, 0, 4] and V₂ = [3, 2, 2, 2] are linearly independent in R⁴.

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Complete question :

A builder has an 6-acre plot divided into 1/4 -acre home sites. How many 1/4 -acre home sites are there?

Answer:

24 home sites

Step-by-step explanation:

Given :

Total size of land = 6 - acre

Size of each home site = 1/4 acre

Number of home sites obtainable from the 6-acre land :

Total size of land ÷ size of each home site ;

6 ÷ 1/4

6 * 4/1

= 24

Hence, 24 home sites are on the plot of land.

There are 32 purple marbles in the bag.

All bags of marbles from Esteban's Marble Company have 7 green marbles for every 4 purple marbles.

To find out the number of purple marbles, let's represent the ratio of the number of green marbles to purple marbles as 7:4.

Since the ratio of green marbles to purple marbles is constant for all bags of marbles, we can create the following equation:

x/4 = 56/7 where x is the number of purple marbles in the bag.

To solve for x, we can cross-multiply:7x = 224

Dividing by 7 on both sides,

x = 32

Hence, the number of purple marbles in the bag is 32.

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After considering the given data  and performing a series of serious calculations we conclude that the evaluated slope of the given line is 2, under the condition that the given line equation [tex]y = 2x - 8.[/tex]

Here we have to apply the principles of coordinate geometry, to evaluate the dedicated slope engaged to a line.
The  given equation [tex]y = 2x - 8[/tex]is present in the slope-intercept form,
[tex]y = mx + b,[/tex]
Here as we can see that
the slope is m  and b is the y-intercept.
Hence, the slope of the given line is 2 and the y-intercept is -8, this can be seen in the diagram given below.
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Answer:

x = –1 AND (-1,2)

Step-by-step explanation:

The axis of symmetry is x = –1

and the vertex is (-1,2)

i know this because the graph is on -1, 2

and I also took the quiz hope it helps ;)

The vertex of the function is (-1, 2).

The axis of symmetry of the function is -1.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x + 1)² + 2

f(x) = x² + 2x + 1 + 2

f(x) = x² + 2x + 3

Now it is in the form of ax² + bx + c

a = 1

b = 2

c = 3

The coordinate of the Vertex of the function is (-b/2a, f(x)) = (x, y)

-b/2a = -2/2 = -1

f(x) = (-1)² + 2 x (-1) + 3 = 1 - 2 + 3 = 4 - 2 = 2

Vertex = (-1, 2)

The axis of symmetry is the x-coordinate of the vertex.

= -1.

Thus,

Vertex is (-1, 2).

The axis of symmetry is -1.

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Answer: 5/2

Step-by-step explanation:

If 1 house key weighs 1/2 ounce,

Then do 5×1/2 which is 5/2

or [tex]\frac{1key}{5key} \frac{1/2ounce}{?}[/tex]

With this cross multiply and get 1x=5/2

giving a total of 5/2 again when divided by 1.

Answer:

2 + 3 2+ 4 = 5 − 9 2 +2 5 2 − 5 4 − 5 0 − 2 8 1 = 0

Step-by-step explanation:

There really isn't an easier way to put that, sorry :/

Hope this helped, and please mark as brainliest <3

True. The graphical interpretation involves calculating the slope of the line connecting two points on the graph of the function, with the distance between the points denoted as h, where h is greater than zero.

The 3-point central difference formula is a numerical approximation technique used to estimate the derivative of a function at a specific point. In this formula, the slope of the line joining two points on the graph of the function is used to approximate the derivative.

To apply the 3-point central difference formula, three points on the graph are considered: (x-h, f(x-h)), (x, f(x)), and (x+h, f(x+h)), where h is a positive value. These three points create two lines: one connecting (x-h, f(x-h)) and (x, f(x)), and the other connecting (x, f(x)) and (x+h, f(x+h)).

The slope of the line joining the points (x-h, f(x-h)) and (x+h, f(x+h)) is then calculated, which represents the approximation of the derivative at x using the 3-point central difference formula. The distance between the two x-coordinates, h, is taken to be greater than zero to ensure that the points are not too close together, allowing for a more accurate estimation of the derivative.

Therefore, the statement is true, as the graphical interpretation of the 3-point central difference formula involves calculating the slope of the line joining the points with a positive value of h.

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Step-by-step explanation:

I really want to help you but there's no question.

Answer:

Yes. it is 5. bc u need to trust me

Answer:

1/4

Step-by-step explanation:

P(red,red) = 4/8 x 4/8 = 1/2 x 1/2 = 1/4

Answer: 7 1/2 cubic yards

Step-by-step explanation: sorry if this is wrong lol

Answer:

After t =  1.67 seconds, the rocket will have reached a height of 250 centimeters.

Step-by-step explanation:

Given

[tex]h = -90t^2 + 300t[/tex] --- correct expression

Required: When does height = 250 cm

To do this, we have:

[tex]h = 250[/tex]

This gives:

[tex]250 = -90t^2 + 300t[/tex]

Rewrite as:

[tex]90t^2 - 300t + 250 = 0[/tex]

Divide through by 10

[tex]9t^2 - 30t + 25 = 0[/tex]

Expand

[tex]9t^2 - 15t - 15t + 25 = 0[/tex]

Factorize:

[tex]3t(3t - 5) -5(3t - 5) = 0[/tex]

[tex](3t - 5)(3t - 5) = 0[/tex]

This gives:

[tex]3t - 5 = 0[/tex]

Solve for 3t

[tex]3t = 5[/tex]

Solve for t

[tex]t = \frac{5}{3}[/tex]

[tex]t = 1.67s[/tex]

Answer:

1 inch

Step-by-step explanation:

hshuehevdjdbevejdj

where's the circle? :v

I think it is 8.6.. but I am not 100% sure

Step-by-step explanation:

Answer:

weight of a water=0.5

spherical ball is filled With water=0.95.

so dear for

22\7*0.5*0.95=1.49

Answer:d

Step-by-step explanation: there are 6 candys and only one is butterfinger therefore it would be 1/6

Answer:

answer should be 1/36

option (b)

good day mate

explanation : the sample space is 36 and butterfinger comes only once to both of them.

Answer:

b. $342

Step-by-step explanation:

Base = Length * width

Base Area = 12 * 5

B = 180 square inches.

Perimeter of the prism will be :

P = 2 (length) + 2 (15)

P = 2 * 12 + 30

P = 54 inches

Height of the jewelry container will be :

X = Ph + 2B

X = 54 * 6 + 2 * 180

X = 684 square inches.

Total cost for paint of jewelry box is :

X * cost per inch

Total cost = 682 * $0.50

Total Cost = $342.

Answer:

If every bar is scored into 4 parts, then Simon has 5*4 parts in total = 20 parts.

To split them between 4 people, each person gets 20/4 parts - 5 parts in total. The way to realize this the easiest would be to give each person a single bar, and then split the last bar into 4 parts and give each person one of them.

Answer:

-246

Step-by-step explanation:

Add all the numbers together and divide by the amount of numbers added to find the mean. -246 is the only right answer.

Answer:

14

Step-by-step explanation:

To get the mean, you have to add all the numbers together, and then divide them by how many numbers there are. Here, i'll show you.

There are 6 numbers, including [tex]Y[/tex], which we need to find out.

The Equation:  [tex]\frac{4+6+9+Y+16+19}{6} = 13[/tex]

To find [tex]Y\\[/tex], we can do the inverse, and multiply [tex]13[/tex] by [tex]6[/tex].

(The 6 on the left side of the equation is then cancelled out)

For this final equation to be true, [tex]Y[/tex] would have to equal [tex]14[/tex].

Hope the rest of your math goes well :)

Answer:

Step-by-step explanation:

That'd be 617,501.  This is greater than 617,500.

Answer:

m= 5/2

Step-by-step explanation:

Points: (0, 2) and (4, 12)

Slope:

m=(y2-y1)/(x2-x1)

m=(12-2)/(4-0)

m=10/4

m= 5/2

Answer:

2.5

Step-by-step explanation:

Hello There!

We can easily calculate the slope using the slope formula

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

all we need to do is pick to ordered pairs from the table and plug in the x and y values of the selected pairs

The ordered pairs selected can vary but i chose the points (0,2) and (4,12)

now we plug in the values into the formula

(remember y values on top and x values down below)

[tex]m=\frac{12-2}{4-0} \\12-2=10\\4-0=4\\\frac{10}{4}=2.5[/tex]

so we can conclude that the slope of the function is 2.5

K = 1/4, fY(y) = (8 - Y)/9

Random variables X and Y have a joint probability density function f(x,y) = K(2x+y) where 0<=x<=1, 0<=y<=2 and f(x,y) = 0 elsewhere. Also, Y = 2^(-X) + 3. Let's determine the value of K.

Determination of K

The probability density function f(x,y) must satisfy the following condition:

i.e., the integral of f(x,y) over the entire range of (x,y) should be equal to 1.

f(x,y) = 0 elsewhere implies that f(x,y) = 0 for x<0 and x>1 and y<0 and y>2. Hence, the range of integration should be [0,1] for x and [0,2] for y.

The integral of f(x,y) over the entire range of (x,y) can be expressed as follows:

[tex]∫∫K(2x+y)dydx = 1[/tex]

On integrating with respect to y first, we get:

[tex]∫(2x+y)dy = [2xy + (1/2)y^2][/tex]evaluated from 0 to 2

= 4x + 2

On integrating with respect to x, we get:

[2x^2 + 2x] evaluated from 0 to 1

= 4

On equating the integral value with 1, we get:

[tex]4K = 1K = 1/4[/tex]

Determination of probability density function of Y

We have [tex]Y = 2^(-X) + 3[/tex]. Therefore, for a given value of Y, the range of X can be determined as follows:

[tex]2^(-X) = Y - 3= > X = -log2(Y-3)[/tex]

Hence, the probability density function of Y can be obtained as follows:

[tex]fY(y) = ∫f(x,y)dxfY(y) = ∫f(x,2^(-X) + 3)dx[/tex]

From the given expression, we can observe that f(x,y) = 0 elsewhere implies that f(x,2^(-X) + 3) = 0 for x<0 and x>1 and y<3 and y>2. Also, the range of integration for x can be determined as follows:

For y<=3, X>=-log2(y-3). For y=2, the minimum value of X can be obtained by taking the limit as y tends to 2 from the right. The minimum value of X is therefore equal to [tex]-∞[/tex]. Therefore, the range of integration for x is [tex][-∞,1].[/tex]

fY(y) =[tex]∫f(x,2^(-X) + 3)dx = ∫(1/4)(2x + 2^(-X) + 3)dx[/tex]

fY(y) = (1/4)(x^2 - 2^(-X)x + 3x) evaluated from [tex]x=-∞ to x=1[/tex]

fY(y) = [tex](1/4)(1 - 2^(log2(Y-3)) + 3)[/tex]= (8 - Y)/9

Let's draw the probability density function of Y. The probability density function of Y is as follows:

fY(y) = (8 - Y)/9

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with 09) Let x, y be random variables joint probability density function f(x,y) = K (2x+ +y) of as 4 of y=2 443 Find K and (Hind : draw P CY<SX ) a picture )

Answer:

FV= 11.369 gr

Step-by-step explanation:

Giving the following information:

Growth rate (g)= 25% per day

Number of periods (n)= 14 days

Present Value (PV)= 0.5 gr

To calculate the Future Value(FV) in grams, we need to use the following formula:

FV= PV*(1+i)^n

FV= 0.5*(1.25^14)

FV= 11.369 gr

Answer:

108

Step-by-step explanation:

Answer:

108 hope this helps! :)

Answer:

32%

Step-by-step explanation:

[tex]\frac{1088}{3400}[/tex]=[tex]\frac{x}{100}[/tex]

(1088)(100)=(3400)(x)

108800=3400x

x=32

32%

The percent of the budget spent on housing is 31.76%.

What is percentage?

Percentage is a mathematical term which means number or ratio expressed in terms of fractions of 100. it can be calculated by dividing given value to the whole value and multiplied by 100. we represent it through ' %'.

Given that, The riddle family income is 3400 per month.

They spend 1088 per month on housing.

We know the formula for percentage which is;

Percentage = (given value/whole value)*100,

Percentage =  (1080/3400)*100

Percentage = 31.76

Hence, The percentage is 31.76%.

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The value of z in the solution set is approximately -8.33 for the determinant of the matrix of coefficients is −3, Option E is the correct answer.

To solve the system of equations, we can use the method of determinants. The value of z can be determined by finding the determinant of the matrix of coefficients.

The given system of equations can be represented as:

| 1 3 1 | | x | | -2 |

| 2 5 1 | × | y | = | -5 |

| 1 2 3 | | z | | 0 |

The determinant of the matrix of coefficients is -3, which is non-zero. This means that the system of equations has a unique solution.

To find the value of z, we need to calculate the determinant of the matrix obtained by replacing the z-column with the constants column:

| 1 3 -2 |

| 2 5 -5 |

| 1 2 0 |

Using the rule of determinants for a 3x3 matrix, we can calculate the determinant:

Det = (1 × (50 - -52)) - (3 × (20 - -51)) + (-2 × (2 × -5 - 51))

= (1(0 + 10)) - (3 × (0 + 5)) + (-2 × (-10 - 5))

= (110) - (35) + (-2 × -15)

= 10 - 15 + 30

= 25

Since the determinant is non-zero, the system has a unique solution. To find the value of z, we divide the determinant of the matrix obtained by replacing the z-column with the constants column by the determinant of the matrix of coefficients:

z = Detz / Det

= 25 / -3

= -8.33

Therefore, the value of z in the solution set is approximately -8.33.

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The question is -

Given the system of equations x + 3y + z = -2

                                                   2x + 5y + z = -5

                                                   x+ 2y + 3z = 0

The determinant of the matrix of coefficients is -3. The value of z in the solution set is:

(a) z=−2/3

(b) z=5/3

(c) z=4/3

(d) z=−2

(e) None of the above

Answer: 12

Step-by-step explanation: Use the quadratic equation to solve the equation.

a = 1

b = -8

c = 12

Answer:

x=6 is the answer

Step-by-step explanation:

x squared -8 x +12=0

6 squared=36

36-8x +12=0

x= 6 so 8*6 =48

36-48+12=0

36-48= -12

-12+12=0

hope this helps