can someone please help me with problem, thank u.

It is true that the eigenvectors of the covariance matrix are equal to the principal components. Concretely, the first principal component (i.e. the largest eigenvector and associated largest eigenvalue) gives you the direction of the maximum variability in your data

The covariance matrix's eigenvectors are identical to its major components, which is a well-known fact. In more concrete terms, the direction of the most variability in your data is provided by the first principal component, which is represented by the largest eigenvector and related largest eigenvalue. After that, each primary component provides you decreasingly variable output. The fact that each primary component is orthogonal to the others is also important to note.

The above picture was taken from the Principal Component Analysis article on Wikipedia, which I previously referred to. This is a scatter plot of samples having a bivariate Gaussian distribution with a center at (1,3), a standard deviation of 3 roughly in the (0.878, 0.478) direction, and a standard deviation of 1 roughly in the orthogonal direction. The first principal component is the one with a standard deviation of 3, and the second is the orthogonal component. The shown vectors are the eigenvectors of the covariance matrix scaled by the relevant eigenvalue's square root and moved to place their tails at the mean.

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Answer:

Step-by-step explanation:

105 min

60 min in a hour and then 3/4 of a hour is 45 min.

Total: 105 minutes

For the given triangle, its greatest possible perimeter is 45 cm.

The term perimeter has to do with the distance round on object. In this case we do have a triangle and the triangle has three sides. The perimeter of the triangle would be the distance round the triangle.

From the statements we have;

Third side = 15

second side = x

first side = 3x

Then;

x + 15 > 3x

15 > 3x - x

15> 2x

x < 7.5

Thus;

For the first side; 3 * 7.5 = 22.5

For the second side = 7.5

Third side = 15

Greatest possible perimeter of the triangle = 22.5 + 7.5  + 15

= 45 cm

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Answer:

1.209  <  1.29  <  1.9  <  3.76

Step-by-step explanation:

The number of nickels is 25

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The total number of nickels and quarters = 63

Total value = $10.75

20 nickels = 1 dollar

4 quarters = 1 dollar

Now,

1 nickel = $0.05

1 quarter = $0.25

Let the number of nickels = x

Let the number of quarters = y

We can make equations as,

0.05x + 0.25y = 10.75 _____(1)

x + y = 63 ______(2)

From (2) we get,

x = 63 - y

Putting in (1) we get,

0.05 (63 - y) + 0.25y = 10.75

3.15 - 0.05y + 0.25y = 10.75

3.15 + 0.20y = 10.75

0.20y = 10.75 - 3.15

0.20y = 7.6

y = 7.6/0.20

y = 38

Now,

x = 63 - y = 63 - 38 = 25

Thus,

The number of nickels is 25

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Answer:

64000

Step-by-step explanation:

When you are rounder you must look at the last number to determine if you are rounding up or down.

Point A, C and F lies on the given line y = [tex](\frac{1}{4} )^{x}[/tex] .

Given in question,

y = [tex](\frac{1}{4} )^{x}[/tex]

y = [tex]4^{-x}[/tex]

Points A(-2,16),  B(2,8),  C(-1,4), D(0,4), E(1,4), F(0,1) and G(-2,0)

We will points in the equation.

For point A(-2,16)

[tex]16 = 4^{-(-2)}[/tex]

    [tex]= 4^{2}[/tex]

    [tex]16=16[/tex]       True

For point B(2,8)

[tex]8= 4^{-2}[/tex]

  [tex]=\frac{1}{4^{2} }[/tex]

  [tex]=\frac{1}{16}[/tex]

[tex]8=\frac{1}{16}[/tex]            False

For point C(-1,4)

[tex]4=4^{-(-1)}[/tex]

  [tex]=4^{1}[/tex]

[tex]4=4[/tex]             True

For point D(0,4)

[tex]4=4^{-0}[/tex]

[tex]4= 1[/tex]            False

For point E(1,4)

[tex]4=4^{-1}[/tex]

[tex]4=\frac{1}{4}[/tex]           False

For point F(0,1)

[tex]1=4^{-0}[/tex]

[tex]1=1[/tex]            True

For point G(-2,0)

[tex]0=4^{-(-2)}[/tex]

  [tex]= 4^{2}[/tex]

[tex]0=16[/tex]          False

Hence, only point A,C and F satisfies the equation.

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Answer:

(0,-22)

Step-by-step explanation:

Plug in 0 for x and solve for y

Answer:

I'll try my best B r u h ....

Step-by-step explanation:

Bowling:

15+5x  where x is the number of people

Skating:

20+3x

We have 50 dollars so the amount must be less than or equal to 50

Bowling

15+5x≤50

Subtract 15 from each side

15-15+5x≤50-15

5x ≤35

Divide each side by 5

5x/5 ≤35/5

x ≤7

She can have 7 or less people

Skating

We have 50 dollars so the amount must be less than or equal to 50

20+3x  ≤50

Subtract 20 from each side

20-20+3x  ≤50-20

3x  ≤30

Divide each side by 3

3x/3 ≤30/3

x ≤10

She can have up to 10 people

She can invite more people skating

Hope this helped.

Answer:  2/3+ 1/6

Step-by-step explanation: 2/3= 4/6   4/6 + 1/6 = 5/6

Answer:

B

Step-by-step explanation:

[tex]x-y=-4 \\ \\ x-f(x)=-4 \\ \\ f(x)-x=4 \\ \\ f(x)=x+4[/tex]

Answers:

V = 30 cubic cm

D = 4 grams per cubic cm

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

Explanation:

The volume of a rectangular solid (aka block or brick) is equal to its length times width times height

V = length*width*height

V = 5*2*3

V = 10*3

V = 30 cubic cm

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

You haven't mentioned it, but the "D" probably refers to the density. This is a measure how much stuff occupies a certain volume of space. The higher the density, the more stuff in that space. Think of it like cramming more packing peanuts in a box.

To find the density, we divide the mass over the volume

density = mass/volume

density = (120 grams)/(30 cubic cm)

density = 4 grams per cubic cm

In each cubic centimeter of space, there are 4 grams of mass.

Answer:

16.53

Step-by-step explanation:

Start by finding the length of the line in the center. I will call this line a. Using the Pythagorean Theorem with 12.3 as the hypotenuse:

[tex]c^2=a^2+b^2\\a=\sqrt{c^2-b^2} \\a=\sqrt{12.3^2-5.4^2} \\a=\sqrt{122.13} \\a=11.05[/tex]

Now that this line is known, x can be found. Once again using the Pythagorean Theorem:

[tex]x^2=a^2+b^2\\x=\sqrt{a^2+b^2} \\x=\sqrt{12.3^2+11.05^2} \\x=\sqrt{273.39} \\x=16.53[/tex]

The function f (x) has steeper slope.

So, The Paige is correct.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The input output pairs of f (x) are (- 6, 5/2) and (- 1, 17/2)

And, The input output pairs of g (x) are (2, 13/3) and (6, - 1)

Now,

Find the slope for f (x) as;

m₁ = (17/2 - 5/2) / (- 1 - (-6))

m₁ = (15/2) / 5

m₁ = 15/10

m₁ = 3/2

And, Slope for g (x) is;

m₂ = (- 1 - 13/3) / (6 - 2)

m₂ = (- 16/3) / 4

m₂ = - 16 / 12

m₂ = - 4 / 3

Thus, The function f (x) has steeper slope.

So, The Paige is correct.

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Answer:

No

Step-by-step explanation:

parallel is when 2 lines never touch and move in the same direction and these touch and move in different directions

Hopes this helps please mark brainliest

Answer:

10 + 5i

Step-by-step explanation:

[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]

The indoor temperature ranges between 68.5 and 76.5 degrees Fahrenheit.

Given data;

According to the equation |x - 72. 5| = 4, the home's heating system is configured to maintain the minimum and maximum temperatures (in degrees Fahrenheit).

To find the minimum and maximum temperatures in the house,

We know that modulus is used to make a negative value into a positive;

|x - 72. 5| = 4

|A| = -A < x < A

|x - 72. 5| = 4

⇒ x - 72.5 = -4  x - 72.5 = +4

   x = 72.5 - 4    x = 4 + 72.5

   x = 68.5         x = 76.5

Hence, the minimum and maximum temperatures in the house are 68.5 and 76.5 Fahrenheit.

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Answer:

90 m

Step-by-step explanation:

because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects

Answer:

Yolanda bought 48 yards of ribbon, and spent 7.68 cents on it.

Step-by-step explanation:

First Step: Find out how much Yolanda spent

20.00 -12.32 = 7.68

Second Step: Divide Total Cost by Price of one Yard

7.68/0.16 = 48

Third Step: Double Check

48 x 0.16 = 7.68

I hope my answer helped you, good luck on your homework!

Answer:

Step-by-step explanation:

18 Vans. That will hold 162 Students if 9 student per Van

19 Vans since we need 163.

Answer: 19 Vans, and All but one will be full the one that isn't full holds one Student.

Answer:

Step-by-step explanation:

Given isosceles triangle DOG with DO≅GO, DO = (n²+1), GO = (4n-2) and DG = (2n -3), you want the value of n and the lengths of the sides.

The expressions for the congruent sides will have the same value, so ...

  DG -GO = 0

  (n² +1) -(4n -2) = 0

  n² -4n +3 = 0 . . . . . . . . simplify

  (n -3)(n -1) = 0 . . . . . . factor

  n = 1 or 3 . . . . . . . . values of n that make the factors zero

The length of leg DG is ...

  2n -3 = 2{1, 3} -3 = {2, 6} -3 = {-1, 3}

Side DG cannot be negative, so the "solution" n = 1 is extraneous.

  GO = 4n -2 = 4(3) -2 = 10

The number is 3, the leg lengths are DO = OG = 10, and the base length is DG = 3.

The first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

According to the question,

We have the following expression:

f(n) = n³-1

Now, in order to find the first four values of the given expression, we will change the values of n from 0 to 3.

So, putting the value of n as 0, we have:

f(0) = 0³-1

0-1 = -1

Now, putting the value of n as 1, we have:

1³-1

1-1

0

Now, putting the value of n as 2, we have:

2³-1

8-1

7

Now, putting the value of n as 3, we have:

3³-1

27-1

26

Hence, the first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

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The simplest form of the given expression is -19x + 10.

The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.

Given that

(-10x+2) + (-9x+8)

We have to simplify the given expression

= -10x + 2 - 9x + 8

= (-10x - 9x) + (2 + 8)

= -19x + 10

Therefore the simplest form of the given expression is -19x + 10

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Andre used 2983 gallons of liquid all through this month.

Given;

Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.

To get the measurement that is closest to the number of liters Andre used during this month;

The total gallons of water used in a month = 785 gallons

The quantity of water in a single gallon = 3.8 liters

Therefore, the number of liters Andre used during this month;

U = total gallons of water used in a month * quantity of water in a single gallon

U = 785 * 3.8

U = 2983

Hence, the number of liters Andre used during this month is 2983 gallons.

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The needed sample size Smaller if the margin of error .

Given,

In the question:

This question in the form of: Fill in the blanks.

So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.

Hence, The answer is smaller the margin of error.

Let's Know:

What is Confidence level?

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

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Answer:

y = - x

Step-by-step explanation:

-y = -x is the same as y=x and to get an equation that is perpendicular to another one you just have to find the reciprocal (opposite) number of the SLOPE. The reciprocal of 1 is -1, therefore the perpendicular equation to -y=-x is y=-1