A 100kg bag of granulated sugar is to
be put into smaller polythene (nylon)
bags each containing 250g. How
many polythene bags will needed?

If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Answer:

  94.3

Step-by-step explanation:

You want to know how to fill in the proportion associated with the question, "What is 115% of 82?"

The diagram is intended to help you match parts of the question to parts of the proportion. The attachment shows the intended relation.

The solution is found by multiplying both sides by 82:

  (x/82)·82 = (115/100)·82

  x = 94.3

The question can also be written as a statement:

  "what" is 115% of 82

When written as an equation, "is" means "equals", and "of" means "times":

  what = 115% × 82

Of course, you can use any variable name of your choosing in place of "what". In your diagram, that is "x". And, you know how to write a percentage as a fraction or decimal, so this becomes ...

  x = 115/100 × 82 = 1.15 × 82

All that remains is to evaluate this expression.

  x = 1.15 × 82 = 94.3

So, the answer to the question is ...

  94.3 is 115% of 82.

Answer:

D is your answer

Step-by-step explanation:

Just did it and it was right : )

Also for anyone else who needs the other answers they are as follows:

1. D. \(6x^4\)  then  C. \(3x^4\)

2. B. \(-30x^2 \sqrt{2x}\)  then  C. \(4x^4^3 \sqrt{2x^2}\)

3. D. \(2x\sqrt{10x} - 2x \sqrt{5}\)

4. B. \(32x^2 \sqrt[3]{2x} -8x^3\)

5. A. \(-22\)  then  C. \(4x^4 \sqrt{5} +2x^2 \sqrt{3x} + 4x^3 \sqrt{30} +6x \sqrt{2x}\)

6. B. \(x^\frac{2}{12}* y^\frac{9}{12}\)  then  C. \(\sqrt[12]{x^2*y^9}\)

NC Math 2 -22092x0

Multiplying Radicals

Assignment

Due March 11

Multiplying radicals with like indices.

The solution of the given equation will be 2√5x(√2-1).

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

The expression will be solved as below:-

= √5x ( √8x² - 2√x)

= √5x ( 2√2x - 2√x)

= √5x(√2-1)(2√x)

= 2√5x(√2-1).

Therefore the solution of the given equation will be 2√5x(√2-1).

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Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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The the length of each side of the triangle are: 5 units, 8.7 units and 10 units respective

A triangle is a polygon with three sides, three angles, three vertices and sum of angles equal to 180 degrees

From the triangle, Using the trigonometric ratio of sine

Sin C = opposite/Hypothenuse

Sin30 = 5/H

Making h the subject of the relation we have

h= 5/sin30

h=5/0.5

Therefore the value of h=10 units

To find the third side use Pythagoras theorem

10² = 5²+p²

100-25 = p²

75 = p²

Taking the square of both sides

p=√75

p=8.7 units

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Answer: \(x=4\sqrt{2}\)

Step-by-step explanation:

Using the properties of a 45-45-90 triangle, the hypotenuse is \(\sqrt{2}\) times the length of a leg.

Therefore, \(x=4\sqrt{2}\).

Answer:

\(173 \div 2 = 86.5 \\ \)

Step-by-step explanation:

Each of the two employees earn $86.50

im pretty sure its 0.19 because the sqyare root of 49 is 7. the square root of 1250 is 35.35

7/35.35=0.19

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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The amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

Recall the compounding formula:

A = P * \(e^{rt}\)

Where:

A = Final amount in the account

P = Initial principal (deposit)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (as a decimal)

t = Time in years

Given:

Initial principal (P) = $16,000

Annual interest rate (r) = 2%  = 0.02

time (t) = 4 years.

Substitute these values into the formula, we get:

A = $16,000 * \(e^{0.02 * 4}\)

Using a calculator, we can calculate:

A = $16,000 * \(e^{0.08}\)

A = $16,000 * 1.0833

A = $17,332.8

Therefore, the amount in the account after 4 years, rounded to the nearest cent, will be approximately $17,332.8.

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Answer:

100/12.4= about 8.06 seconds

Step-by-step explanation:

Simplify:

(3) + (-4) =

Note: the numbers are with different signs

I mean the first one is (+) and the second is (-)

In this case make the operation of subtraction and put the sign of the largest number

So, (3) + (-4) = -1

The answer is option B. -1

Answer: -4/3 < x< 1/2

Step-by-step explanation: inequality form

Answer:

   Y = 2.843+ 0.037 X

Step-by-step explanation:

Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are

∑Y = na +b ∑X

∑XY = a∑X + b∑X²

We now calculate ∑X, ∑Y , ∑X², and ∑XY

X                Y                XY              X²

5                  4                 20            25

7                  3              21                49

6                  2                 12            36

2                  5                 10             4

1                    1                1                 1          

21                 15                 64           115  

Thus the normal equation becomes

                                                 5a + 21b =15

                                                21a +115b = 64

Solving these two equations simultaneously we get

                                                105 a + 441b = 315

                                                105a + 575b = 320

                                                            134b= 5

b= 0.037 , a= 2.843

Hence the equation for the required straight line is

                    Y = 2.843+ 0.037 X

Answer:

The answer is "Option 2".

Step-by-step explanation:

Please find the complete question in the attached file.

When there is a mean value k in a set of data. Otherwise, we will assert with certainty that at least one of the values is k. They can't say anything at all about the maximum or even the minimum using knowledge only. Nevertheless, we know that certain numbers cannot be over and that all numbers cannot be below than mean. Mean also no value throughout the data set must be equal.

The actual distance represented by 23.7 cm on the map is 355.5 km.

To find the ratio of the amount of money Mabaso has to the amount of money Thabo has and the amount of money Ally has, we can divide each amount by the smallest amount (which is R35) to simplify the ratio.

Mabaso has R140, Thabo has R70, and Ally has R35.

The ratio of Mabaso's money to Thabo's money is:

R140 ÷ R35 = 4

The ratio of Mabaso's money to Ally's money is:

R140 ÷ R35 = 4

Therefore, the ratio of the amount of money Mabaso has to the amount of money Thabo has and to the amount of money Ally has is 4:1:1.

To calculate the percentage discount of a steel table, we need to find the difference between the original price and the discounted price, and then divide it by the original price. Finally, we multiply the result by 100 to get the percentage.

Original price: R750

Discounted price: R600

Discount: R750 - R600 = R150

Percentage discount: (R150 ÷ R750) × 100 = 20%

So, the table has a 20% discount on Black Friday.

To convert 125 grams to kilograms, we divide the amount in grams by 1,000 (since there are 1,000 grams in a kilogram).

125 g ÷ 1,000 = 0.125 kg

Therefore, 125 grams is equal to 0.125 kilograms.

If a green grocer packs 12 apples in a plastic bag and has 285 apples, we divide the total number of apples by the number of apples per bag to determine the number of bags needed.

Number of bags needed: 285 apples ÷ 12 apples/bag = 23.75 bags

Since we can't have a fraction of a bag, we round up to the nearest whole number. Therefore, the green grocer would need 24 bags.

If the scale of a map is 1,500,000 and the measurement on the map is 23.7 cm, we can use the scale to determine the actual distance.

1 cm on the map represents 1,500,000 cm in reality.

23.7 cm on the map represents x cm in reality.

x = 23.7 cm × 1,500,000 cm = 35,550,000 cm

To convert cm to km, we divide by 100,000 (since there are 100,000 cm in a kilometer).

35,550,000 cm ÷ 100,000 = 355.5 km

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Answer:

$500-$50x

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you make $54,000 a year living in the region of California, USA, you will be taxed $9,450. Your average tax rate is 9.01% and your marginal tax rate is 22%. This marginal tax rate means that your immediate additional income will be taxed at this rate.

The domain of a function is the set of all values of x that satisfies the function. On the graph, it is between the minimum value of x on the left and the maximum value of x on the right.

Looking at the graph, it extends infinitely to the left. It moves towards x = 7 but never touches it. This means that there is a vertical asymptote at x = 7. It extends towards infinity on the right. Thus, the domain is

Domain = (-∞, 7) U (7,∞)

The range is the set of all values of y that satisfy the function. It extends from negative infinity at the bottom to y = 0 but never touches it. It extends from this point towards positive infinity at the top. Thus,

Range = (-∞, 0) U (0,∞)

Answer:

She will make 40 hops in 50 seconds

Explanation:

According to the given data we have the following:

Luna made 24 hops in 30 seconds

Hops will she make in 50 seconds?

In order to calculate the amount of Hops will she make in 50 seconds we would need to calculate the following:

Luna made 24 hops in 30 seconds, hence the hopes per second will be equal:

hopes per second=24/30=4/5

Therefore, the rate per second will be 4/5

So, amount of Hops will she make in 50 seconds=rate per second*50 seconds

amount of Hops will she make in 50 seconds=4/5*50

amount of Hops will she make in 50 seconds=40 hops

Therefore, she will make 40 hops in 50 seconds

Answer:

40 hops

Step-by-step explanation:

24/30=x/50

1200/30=x

40=x

Answer:

matrix multiplication is possible in this matrix

Step-by-step explanation:

\( ( \frac{1}{ - 1} ) \times (0 \: \: 4)\)

Answer:

D

really sorry if wrong

but I am positive that is the answer

Answer:

14

Step-by-step explanation:

Just Add 4+3+2+5=14 ans easy :D

Answer:

I dont know what the answer is exactly

The answer is 16

Explanation:16/4=4

4+5=9

9*3=27

Answer:

x=16

Step-by-step explanation:

We'll say that x represents the number.

3(\(\frac{x}{4}\)+5)=27      given equation

\(\frac{3x}{4}\)+15=27        distributive property

3x/4=12         subtract

3x=48             multiply

x=16               divide

Answer:

I would believe it is the final answer by the way it's put! hope this helps :)

The correct inequality is 43x + 72 ≤ 1,128.

Given,

Jasmine wants to use her savings of $1,128 to buy video games and movies.

The total price of the movies she bought was $72.

The video games cost $43 each.

We need to choose the inequality that would be used to solve the maximum number of video games Jasmine can buy with her savings.

We have,

< - less than

> - greater than

≤ - less than and equal

≥ - greater than and equal

Find the total cost of the movies.

= $72

Find the cost of each video game.

= $43

Find the savings Jasmine has.

= $1,128

The amount Jasmine can use to buy movies and video games is $1,228.

So, we can use less than or equal to $1,228 to buy movies and video games.

i.e ≤ $1,128

We have,

Cost of movie = $72

Cost of each video game = $43

We can write the inequality as:

$72 + $43x ≤ $1,128

Where x is the number of video games.

Thus the correct inequality is 43x + 72 ≤ 1,128.

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After answering the presented question, we can conclude that We use a logarithm calculator to determine that t is approximately 6.6 years. As a result, the town's doubling time is around 6.6 years.

The logarithm is a power's reciprocal in mathematics. Accordingly, the exponent by which b must be raised to obtain a number x equals the logarithm of that number in base b. For instance, since 1000 = 103, its base-10 logarithm is 3, or log10 = 3. As an illustration, the base 10 logarithm of 10 is 2, while the square of 10 is 100. Log 100 = 2. To answer a question like, For example, how many times must a base of 10 be multiplied by itself to achieve 1,000, a logarithm (or log) is the mathematical term utilized. The solution is 3 (1,000 = 10 10 10).

To calculate the doubling time, we must first determine how long it takes for the population to double, or when the population is twice its initial size.

After one year, the population will be P * 1.10 (because it grows at a 10% annual rate). P * 1.10 * 1.10 = P * 1.102 after two years. In general, the population will be P * 1.10t after t years.

We need to find t so that P * 1.10t = 2P. (since the population has doubled). When we divide both sides by P, we get:

\(1.10^t = 2\\log(2)/log t (1.10)\)

We use a calculator to determine that t is approximately 6.6 years. As a result, the town's doubling time is around 6.6 years.

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Rested numbers in group is 33 out of 76.

A percentage is expressed as a number or ratio that can be expressed as fraction of 100. It is denoted by % symbol.

Total numbers in a group = 76.

44% of them were rested.

That is 44% of 76.

To find how many are rested we have to find the value in numbers.

Convert 44% of 76 to numbers.

For this, it can be written as

\(\frac{44}{100} *76\) = 33.44

Therefore 44% of 76  ≅ 33 numbers.(approximately)

Hence, rested numbers in group is 33.

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