10 The mass of a cube of side 2 cm is given as 100 g. The side is accurate
to the nearest millimetre and the mass accurate to the nearest gram.
Calculate the maximum and minimum possible values for the density of
the material (density = mass = volume).​

Using Algebraic equation, Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

Let's review all the information given for solving this question:

Rate per hour of Job A = US$ 6.20

Rate per hour of Job B = US$ 6.50

Earnings received by Kathy during the week = US$ 140.60

Total time worked by Kathy during the week = 22hours

Hours at job A = x

Hours at job B = 22 -x

In order to find how many hours Katy worked at each job: This is the Algebraic equation that we'll use:

6.20x + 6.50 (22 - x) = 140.60

6.20x + 143- 6.50x = 140.60

-0.3x = 140.60 - 143

-0.3x = - 2.4

    x = -(2.4)/-(0.3)

x = 14.3/0.3 = 8 (Dividing by 0.3 at both sides)

Kathy worked 8 hours at job A.

Hours at job B = 22 - x. Put x = 11 we get

Hours at job B = 22 -11

= 11

Hence, using Algebraic equation Kathy worked 22 hours at job A and 12 hours at job B, the week she made US $ 140.60.

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(i) The number of different divisions possible when 15 children divide themselves into teams of 5 each (Team A, B, and C) is 756.

(ii) If the teams are not distinguishable, the number of different divisions possible is 756 divided by 3!, which equals 126.

(i) To determine the number of different divisions when 15 children divide themselves into three teams of 5 each, we can calculate the number of combinations.

Since the order of the teams does not matter, we use the combination formula.

The formula is nCr = n! / (r! * (n - r)!), where n is the total number of children and r is the number of children per team.

Plugging in the values, we have 15C5 * 10C5 = (15! / (5! * 10!)) * (10! / (5! * 5!)) = 756.

(ii) If the teams are not distinguishable, we need to account for the fact that the order of the teams doesn't matter.

Each division would be counted multiple times if we considered the teams distinguishable. Since there are 3! (3 factorial) ways to arrange the teams, we divide the previous result by 3!, which gives us 756 / 3! = 126.

This accounts for the different arrangements of the same teams and gives us the number of distinct divisions.

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Answer:

54 seats

Step-by-step explanation:

To make it easier, I'll put it like this.

Row    |    Seats

 1        |      24

 2       |      30

 3       |      36

 4       |      42

 5       |      48

 6       |      54

(Add 6, because each row has 6 more seats than the row in front of it.)

So, the 6th row has 54 seats.

Hope this helped !

Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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Answer:

6.15*104

Step-by-step explanation:

The resulting divide-and-conquer algorithm for matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions is efficient for multiplying two 3 × 3 matrices.

To analyze the divide-and-conquer algorithm for matrix multiplication, let's set up and solve the recurrence relations based on the given conditions.

Let's assume we have two 3 × 3 matrices A and B, and we want to compute their product C = A × B.

According to the given information, we can perform the matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions.

In a divide-and-conquer algorithm, we can split the matrices into smaller submatrices to simplify the multiplication process. Let's assume we divide the matrices into 2 × 2 submatrices:

A = [A11 A12]

   [A21 A22]

B = [B11 B12]

   [B21 B22]

C = [C11 C12]

   [C21 C22]

The recurrence relation for this algorithm can be expressed as follows:

C11 = A11 × B11 + A12 × B21

C12 = A11 × B12 + A12 × B22

C21 = A21 × B11 + A22 × B21

C22 = A21 × B12 + A22 × B22

Since each entry of matrix C requires a scalar multiplication and there are four entries in total, we have a total of 4 scalar multiplications.

To solve the recurrence relation, we can express the number of scalar multiplications as a function of the subproblem size. In this case, the subproblem size reduces to 2 × 2 matrices, and the number of scalar multiplications can be considered constant.

Therefore, the resulting divide-and-conquer algorithm for matrix multiplication using 25 scalar multiplications and a constant number of scalar additions and subtractions is efficient for multiplying two 3 × 3 matrices.

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Answer:

1) -2

2) 8/7

Step-by-step explanation:

1) 10x+8=3(x-2)

  10x+8=3x-6

  10x-3x=-6-8

  7x=-14

  x=-2

2) 10x+8=3x

   10x-3x=8

   7x=8

   x=8/7

Hope it helps

chamber of commerce’s claim at the 0.02 level of significance, z = -1.75

What is z test?

If the data is distributed normally, a z test can be used to determine whether the means of two populations differ from one another. The z test statistic's value must be determined, together with the null hypothesis and alternative hypothesis setups, for this reason. On the z critical value, the decision criterion is based. The distribution graph is divided into acceptance and rejection zones during hypothesis testing by the z critical value. The null hypothesis can be rejected if the test statistic lies inside the rejection region; otherwise, it cannot.

a recent survey reported that small businesses spend 24 hours a week marketing their business.

these businesses are spending less than 24 hours a week on marketing. the chamber conducts a survey of 58 small businesses within their state and finds that the average amount of time spent on marketing is 22.7 hours a week.

assuming that the population standard deviation is 6.1 hours.

Given n = 93, u =24, x' = 23, α=5.5

z = x'- u / α(/√n) = (23-24/5.5/√5) = -1.75

Hence, chamber of commerce’s claim at the 0.02 level of significance, z = -1.75

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Answer:

it is 7.5 rate

Step-by-step explanation:

I used a calculator to get the answer and it is correct.

Table A and Table C is a function. Table B and Table D is not a function.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

We know that a relation is a function if it is one-to-one or many-to-one.

But a relation is not a function if it is many.

Table A; It is a function and it is a many-to-one function.

Table B; It is not a function as input 1 leads to two different outputs 1, - 1.

Table C; It is a function and it is a one-to-many function.

Table D; It is not a function as one input leads to 3 different outputs.

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Answer:

218

Step-by-step explanation:  

ATQ,

22%of total books = 48

Let the total no. of books in library be x.

22/100x=48

x=4800/22

X=218(approximately)

Answer:

∞

Step-by-step explanation:

I don’t know just think it out. That is the explaination

The wrong conclusions that can be drawn from the circle graph are:

The Country section has the smallest area.

The Classical section is not included in the Circle Graph.

A circle graph is a graph that displays information in a circle. The circle is divided into slices which represent a numerical proportion. The sum of angles in a pie chart is 360 degrees

In the circle graph, the country section has a percentage of 10% while the classical section has a percentage of 2%.

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Answer:

the answer is D  

Step-by-step explanation:

look at the table there are 5 music genres but there's only 4 on the circle graph.

Average rate of change of the function F (x ) = 9/ -2 (x)-7. Average rate is -3, 9

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function. A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

Divide the change in y-values by the change in x-values to determine the average rate of change. In order to determine changes in measurable parameters like average speed or average velocity, finding the average rate of change is extremely helpful.

f (x ) = -2

f (x) = 9/ -2 (-2)-7

      = 9 / 4 - 7

      =9 / -3

      = -3

f (x ) = -4

f (x) = 9/ -2 (4)-7

      = 9 / 8 - 7

      =9 / 1

      = 9

Average rate is -3, 9

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Answer:

1. 250x12= 3000. So she earned $3000 in that 12 weeks, if you include the 500 then it would be 3500 dollars if not then it would be 3000 dollars.

2. Divide 75 and 12 and you get 6.25 if you want to estimate. Then the answer would be, all of the fields will be harvested in just 6 days.

3. Divide 54 and 3 and you get 18. 18 weeks if they frame the sanem number each week.

4. If you divide 8,000 and 450 you get 17.7777777778. If you want to estimate then the it would be 18. So it would take about 18 days to fill up the 8,000 gallons of water.

5. This graph is y=20x

6. Don't really know, if the 0 is 360 then 10 and 300 are pretty easy because 10=30. so 0, 10, 20 is 360, 300,240 likes the graph and I would think you can solve this

Answer:

First of all he goes throughout the whole WORLD so UK would take an average of 30 an hour. Santa would travel an approx. of 650 mph per second

Step-by-step explanation:

78 miles per household, a total trip of 75-1/2 million miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding and etc. This means that Santa's sleigh is moving at 650 miles per second, 3,000 times the speed of sound.

100th digit of the pi is 7

Pi (represented by the Greek letter π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. It is approximately equal to 3.14159,

The decimal representation of pi (π) is an infinite non-repeating sequence of digits, so there is no simple formula or algorithm to determine the value of its digits. However, you can use a computer program or online tool to calculate the digits of pi to a certain number of decimal places.

Assuming you are looking for the 100th decimal digit of pi, it is 7. This means that if you write out the first 100 digits of pi, the 100th digit is 7.

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Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

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Answer:

n ÷ 20.7 = 9

Step-by-step explanation:

Let n be the unknown number

Quotient is division and is means equals.

n ÷ 20.7 = 9

Answer:

6 granite, 3 marble, 14 sandstone, 1 slate

ratio of sandstone to marble

how many sandstone does she have .....14

how many marble does she have......3

so the ratio would be 14:3

Answer:

C. 14:3

Step-by-step explanation:

Dana has 14 pieces of sandstone.

Dana has 3 pieces of marble.

The ratio of pieces of sandstone to pieces of marble is 14:3.

The ratio cannot be simplified further.

Answer: 63.28

Step-by-step explanation:

To increase a number by a certain percentage, you can multiply the number by (1 + the percentage as a decimal). In this case, you would multiply 56 by 1.13 to find the result.

56 * 1.13 = 63.28

So, if you increase 56 by 13%, the result is 63.28. The decimal representation of this number is 0.6328.

the answer should be 63.28 if its wrong then i don't know what it is.

Answer:

ans of an 1 is option b

Step-by-step explanation:

because x and y both are +ve

False. Each triangle in the STL file is defined by the vertices, but not necessarily by the inward pointing surface normal vector. The surface normal vector is often calculated based on the vertex positions.

False. The STL file is a mesh representation of the CAD model, and it does not contain all the information needed to fully reconstruct the original CAD model. It lacks information such as parametric features, assembly relationships, and design intent, making it difficult to recreate the exact original model.

The option "Increasing the heat exchange area for a heat exchanger" is NOT an advantage of using a lattice structure. Lattice structures are known for their lightweight properties, material-saving benefits, and simplified design and manufacturing processes.

However, increasing the heat exchange area for a heat exchanger is not typically associated with lattice structures. Heat exchangers usually rely on other design considerations, such as fin arrays or extended surfaces, to enhance heat transfer efficiency, rather than lattice structures.

Therefore, increasing heat exchange area is not a direct advantage of lattice structures.

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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(a) Ω is unitary as Ω†Ω = I, where Ω† is the conjugate transpose of Ω and I is the identity matrix.

(b) The eigenvalues of Ω are e^(iθ) and e^(-iθ), with corresponding eigenvectors [1, e^(-iθ)] and [e^(iθ), 1].

(a) To show that Ω is unitary, we need to verify that Ω†Ω = I, where Ω† denotes the conjugate transpose of Ω and I is the identity matrix.

Calculating Ω†, we have:

Ω† = ( cosθ sinθ​−sinθ cosθ​)

Now, let's compute the product Ω†Ω:

Ω†Ω = ( cosθ sinθ​−sinθ cosθ​)( cosθ−sinθ​sinθ cosθ​)

     = (cos^2θ + sin^2θ  cosθsinθ - sinθcosθ  -sinθcosθ + cosθsinθ  sin^2θ + cos^2θ)

     = (1  0  0  1)

     = I

Since Ω†Ω = I, we have shown that Ω is unitary.

(b) To find the eigenvalues and corresponding eigenvectors, we solve the characteristic equation:

|Ω - λI| = 0

where λ is the eigenvalue and I is the identity matrix.

Ω - λI = ( cosθ−λ −sinθ​sinθ cosθ−λ)

Setting the determinant of Ω - λI equal to zero, we get:

( cosθ - λ)(cosθ - λ) - (-sinθ)(sinθ) = 0

(cos^2θ - 2λcosθ + λ^2) + sin^2θ = 0

2λcosθ - λ^2 - 1 = 0

Solving this quadratic equation, we find two eigenvalues:

λ = e^(iθ) and λ = e^(-iθ)

To find the corresponding eigenvectors, we substitute each eigenvalue into the equation (Ω - λI)v = 0 and solve for v.

For λ = e^(iθ):

(cosθ - e^(iθ))v1 - sinθv2 = 0

sinθv1 + (cosθ - e^(iθ))v2 = 0

Solving these equations, we find the eigenvector v1 = [1, e^(-iθ)] and v2 = [e^(iθ), 1].

For λ = e^(-iθ):

(cosθ - e^(-iθ))v1 - sinθv2 = 0

sinθv1 + (cosθ - e^(-iθ))v2 = 0

Solving these equations, we find the eigenvector v1 = [1, -e^(iθ)] and v2 = [-e^(-iθ), 1].

(c) Constructing the unitary matrix U using the eigenvectors, we have:

U = [v1, v2] = [[1, e^(-iθ)], [e^(iθ), 1]]

To verify that U†ΩU is a diagonal matrix, we calculate:

U†ΩU = [[1, -e^(iθ)], [e^(-iθ), 1]] * [[cosθ, -sinθ], [sinθ, cosθ]] * [[1, e^(-iθ)], [e^(iθ), 1]]

     = [[e^(iθ)cosθ + e^(-iθ)sinθ, -e^(iθ)sinθ + e^(-iθ)cosθ], [e^(-iθ)cosθ + e^(iθ)sinθ, -e^(-iθ)sinθ + e^(iθ)cosθ]]

     = [[e

^(iθ)cosθ + e^(-iθ)sinθ, 0], [0, e^(-iθ)cosθ + e^(iθ)sinθ]]

     = [[e^(iθ)cosθ, 0], [0, e^(-iθ)cosθ]]

The resulting matrix is indeed a diagonal matrix with the eigenvalues on the diagonal, as expected.

Therefore, U†ΩU = [[e^(iθ)cosθ, 0], [0, e^(-iθ)cosθ]], confirming the diagonalization of Ω.

Note: The choice of phase factor for the eigenvectors may vary, as long as they satisfy the eigenvector equations.

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Answer:

x=-3 im pretty sure

Step-by-step explanation:

so if y=4 and 4 is something plus 7, 7+-3=4 so im abut 98% its -3

Given information:

Raoul collects sports cards.

He has six baseball cards, three football cards, four hockey cards, and three basketball cards.

Raoul has a total of 6 + 3 + 4 + 3 = 16 sports cards.

The number of hockey cards he has is 4.

Therefore, the fraction of his sports cards that are hockey cards is:

4/16

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

1/4.

So, 1/4 of Raoul's sports cards are hockey cards.

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Answer:

Hi there!

The domain is:

20<=x<=40

Step-by-step explanation:

This states that:

x>=20

x<=40

Which fits the problem!

Hope this helps

For a given function f(x) we define the domain as the set of possible values of x that we can use in the function.

Here we will find that the domain is D: [20h, 40h]

We know that Ally wins $18 per hour, and she has two restrictions:

She cant' work more than 40 hours.

She needs to work at least 20 hours.

Then her weekly salary can be written as:

s(x) = $18*x

Where x is the number of hours that she works each week.

With the above restrictions we have:

20h ≤ x ≤ 40h

Then the domain is:

D: [20h, 40h]

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