Work out the value of X.

Answer:x+x+1=13

2x+1=13

2x=13−1

2x=12

x=

2

12

​

x=6

x+1=6+1=7

Step-by-step explanation:yes

Answer:

C   D  and E

Step-by-step explanation:

Answer:

The smallest number that Aleena could be thinking of is 2.75.

In an ideal crystal lattice, two general points r and r' are related by a lattice vector if their difference vector Δr can be expressed as a linear combination of the lattice translation vectors a₁, a₂, and a₃ with integer coefficients. This condition ensures that the lattice symmetry and periodicity are preserved between the two points.

In an ideal crystal lattice, the condition between two general points r and r' that must hold for lattice vectors is that the difference vector Δr = r' - r should be a linear combination of the lattice translation vectors a₁, a₂, and a₃ with integer coefficients.

Mathematically, this condition can be expressed as:

Δr = r' - r = u₁a₁ + u₂a₂ + u₃a₃

where u₁, u₂, and u₃ are arbitrary integers.

The reason for this condition is rooted in the concept of translational symmetry in crystal lattices. In an ideal crystal lattice, the arrangement of atoms, ions, or molecules is characterized by a repeating pattern that extends infinitely in space.

The lattice translation vectors a₁, a₂, and a₃ define the periodicity and symmetry of the lattice, representing the fundamental translation operations that generate the lattice points.

By expressing the difference vector Δr as a linear combination of the lattice translation vectors, we ensure that r' and r are related by a lattice vector. In other words, if we apply the lattice translation operation represented by Δr to r, it should bring us to another lattice point r' within the crystal lattice.

If the condition is not satisfied, it means that Δr cannot be expressed as a linear combination of the lattice translation vectors. In such cases, r' and r are not related by a lattice vector, indicating that r' does not belong to the same crystal lattice as r.

In summary, the condition for lattice vectors between two general points r and r' in an ideal crystal lattice is that the difference vector Δr should be expressible as a linear combination of the lattice translation vectors a₁, a₂, and a₃ with integer coefficients. This condition ensures that r' and r are related by a lattice vector and maintains the translational symmetry inherent in crystal lattices.

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Complete Question:

2. The general point r in an ideal crystal lattice is defined by the relation: r = u₁a₁ + u₂a₂ + u₃a₃ where a₁, a₂, and a₃ are the lattice translation vectors, and u₁, u₂ and u₃ are arbitrary integers. What is the condition between two general points r and r’ which has to hold for lattice vectors? Explain why.

Answer:

4min:1min

Step-by-step explanation:

60:15

divide by 5

12:3

divide by 3

4:1

Answer:

670.21 inches^3

Step-by-step explanation:

To find the volume of the spheres, all you need to know is the formula for the volume of a sphere, which you've included in your problem. From the problem, you also know that r = 2. From here, you calculate the volume of 1 of the spheres, which turns out to be:

V = 33.51032

Since there are 20 spheres in this box, you multiple the volume of a single sphere by 20 to get the total volume occupied by the spheres.

V = 20 * 33.51032

V = 670.2064

If you round to 2 decimal places, this becomes 670.21.

Answer:

18.5

Step-by-step explanation:

The length of fringe Sharon needs to purchase is: 16 feet

If Sharon gets a new bedsheet of 1.25 feet longer, she will need a new length of fringe of: 18.5 feet

Recall:

Perimeter of a rectangular = 2(length + width)

Given the following:

The length of fringe Sharon will need to purchase = perimeter of Sharon's rectangular bedspread

Perimeter = 2(3 + 5) = 16 feet

For a new bedspread that is 1.25 feet longer, she would get the following length of fringe:

Length = 3 + 1.25 = 4.25 feet

Width = 5 feet

New Perimeter = 2(4.25 + 5) = 18.5 feet

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Answer:

x=14

Step-by-step explanation:

Let's solve your equation step-by-step.

1/4x−5=3/4x−12

Answer:

x = 14

Step-by-step explanation:

Method : isolating the x

Subtract 1/4x from both sides to get -5 = 2/4x - 12. Then, add 12 to both sides, 7 = 2/4x, which is also 7 = 1/2x. Solve to get x = 14.

Answer:

option c is the correct one

Answer:

200

Step-by-step explanation:

55 / 5x = 20

5x=1100

x=200

1) In this question, we can start setting our table:

2) Now let's find the regression line by finding the slope and the linear coefficient, according to these formulas below:

So

Therefore we can write the regression line as:

3) Now let's find the correlation coefficient through another formula:

The relation "r" on the set of all integers, where x = y^2, is not reflexive.

A relation is reflexive if every element in the set is related to itself. In this case, for the relation x = y^2 to be reflexive, every integer "x" should be related to itself, meaning that x = x^2. However, this is not true for all integers.

For example, if we consider x = 2, it is not equal to 2^2 = 4. Similarly, if we consider x = -3, it is not equal to (-3)^2 = 9.

Since there are integers that do not satisfy the condition x = x^2, the relation x = y^2 is not reflexive on the set of all integers.

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Answer:

A Mid-Segment

Step-by-step explanation:

A triangle mid-segment is a line segment whose endpoints are the midpoints of a triangle.

Hope I helped!

No, C is not a subspace of R². A subset is a subspace if and only if it contains the zero vector of the space.

To verify if C is a subspace of R², we need to check if it satisfies the three conditions of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector.

Closure under addition:

Let's consider two points in C, [x₁, y₁] and [x₂, y₂], such that x₁² + y₁² ≤ 1 and x₂² + y₂² ≤ 1.

However, the sum of these two points, [x₁ + x₂, y₁ + y₂], does not satisfy the condition (x₁ + x₂)² + (y₁ + y₂)² ≤ 1 in general. Therefore, C does not satisfy closure under addition.

Since C fails to satisfy one of the conditions for a subspace, it is not a subspace of R².

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Answer:

We have a problem here, Houston.

Step-by-step explanation:

Is "(x+5)2=36" supposed to be (x+5)^2=36 ?

If so,

x = ± 11

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

If it is indeed (x+5)2=36

then:

2x + 10 = 36

2x = 26

x = 13

None of the answer options fir either of these two interpretations of the equation provided.  Please check the equation.

Answer:

-11 and 1

Step-by-step explanation:

did the test

Answer: 118 degrees

Step-by-step explanation:

By the exterior angle theorem.

3x + 12 + 2x + 16 = 6x + 10

5x + 28 = 6x + 10

x = 18

So measure of angle 3 = 6(18) + 10 = 118 degrees

Answer:

B.

Step-by-step explanation:

First Equation. (x - 1)² = 8

1. (x - 1) = √8

2. x - 1 + 1 = 2√3 + 1

3. x = 2√3 + 1

3.

Second Equation. x² - 1 = 8

1. x² - 1 + 1 = 8 + 1

2. x² = 9

3. x = ±3

Answer:

Its B.

Step-by-step explanation:

I just got it correct on edge :)

The researcher needs a sample size of at least 10 to assure with 90% confidence that the sample mean will not differ from the population mean by more than 2 units.

To find the sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 2 units, we can use the formula:

n = (Z * σ / E)²

where:
n = sample size
Z = Z-score corresponding to the desired confidence level (in this case, 90% confidence corresponds to a Z-score of approximately 1.645)
σ = standard deviation of the population (given as the square root of the variance, so σ = √14)
E = maximum allowable error or margin of error (given as 2 units)

Plugging in the values:

n = (1.645 * √14 / 2)²

Simplifying:

n = (1.645 * 3.74 / 2)²
n = (6.1393 / 2)²
n = 3.06965²
n ≈ 9.42

Therefore, the sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 2 units is approximately 9.42.

The researcher should gather a sample of at least 10 adults to estimate the mean score achieved by all adults on the test with 90% confidence that the sample mean will not differ from the population mean by more than 2 units.

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The required probability is 3/4.

We have to compute the probability

P(Female |Junior) because we have to find the probability of the female student and the given condition is that the student is junior.

Determine the total number of juniors.

Juniors=2+6=8

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Since the number of females who are junior is 6, determine the required probability.

P(Female|Junior)=6/8=3/4

Therefore, the required probability is 3/4.

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Premise 1: Hard water can damage home appliances. Premise 2: A water softening system can prevent hard water. Conclusion: Therefore, a water softening system can prevent damage to home appliances.

The argument consists of two premises and a conclusion. Premise 1 states that hard water can cause damage to home appliances. Premise 2 states that a water softening system can prevent hard water. The conclusion drawn from these premises is that a water-softening system can prevent damage to home appliances.

In standard form, the argument is presented by listing the premises first, followed by the conclusion. This format helps to clearly identify the statements being made and their logical relationship. By representing the argument in this way, it becomes easier to analyze the structure and validity of the reasoning presented.

Therefore, the standard form representation of the argument is:

Premise 1: Hard water can damage home appliances.

Premise 2: A water softening system can prevent hard water.

Conclusion: Therefore, a water softening system can prevent damage to home appliances.

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Answer:

109

Step-by-step explanation:

Answer:

109 degrees

Step-by-step explanation:

A triangle has a total of 180 degrees in angles

Substituting the unknown as x, it will lead to the following:

23+48+x=180

71+x=180

x=109

Hope this helped!

Explanation:

We are asked to get the slope of the graph

To do so, we have to make use of the relationship:

From the graph given

We have the following points:

So we can obtain the slope as follow

Thus, the slope

Answer:

5x - 8y = -48

Step-by-step explanation:

Move 5/8x to the y side to get (-5/8)x + y = 6. Multiply both sides by -8 to get 5x - 8y = -48.

The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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Answer: 6

Step-by-step explanation:

The area of the sector of the circle is A = 119.2415 units²

Given data ,

The formula for Area of a sector is given as;

A = θ/360 x πr²

where

θ is the central angle of the sector

r is radius

A = ( 279 / 360 ) x ( 3.14 ) ( 7 )²

A = ( 0.775 ) x ( 153.86 )

On simplifying the equation , we get

A = 119.2415 units²

Hence , the area of sector is A = 119.2415 units²

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Answer:

$0.33 per inch

Step-by-step explanation:

Divide cost by inch to get cost per inch.

These are the corresponding snapshots of memory after each set of statements have been executed.The value of x becomes 2 and the value of z becomes 2.

To answer this question, we need to understand how memory works in a computer. Whenever we declare a variable, it is assigned a memory location, and whenever we assign a value to it, that value is stored in that memory location. The corresponding snapshot of memory is the state of memory after each set of statements has been executed.
So, let's look at the given statements and their corresponding snapshots of memory:
1. int x1; x1 = 3+4
In this statement, we are declaring a variable x1 of type integer and assigning it the value 3+4, which is 7. Therefore, the corresponding snapshot of memory would look like this:
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
2. int x(1), z(5); x = __z = __z = z/++x;
In this statement, we are declaring two variables x and z of type integer and assigning the value 1 to x and 5 to z. Then, we are dividing z by the pre-incremented value of x and assigning the result to both x and z.
The pre-increment operator increases the value of x by 1 before it is used in the division. Therefore, the value of x becomes 2 and the value of z becomes 2.
So, the corresponding snapshot of memory would look like this:
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
| x        | 1004           | 2     |
| z        | 1008           | 2     |
In summary, the corresponding snapshots of memory after executing the given set of statements are:
1. x1 = 7
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
2. x = 2, z = 2
| Variable | Memory Location | Value |
|----------|----------------|-------|
| x1       | 1000           | 7     |
| x        | 1004           | 2     |
| z        | 1008           | 2     |
Therefore, these are the corresponding snapshots of memory after each set of statements have been executed.

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