when the two countries did not specialize, the total production of chinos was 23 million pairs per day, and the total production of pistachios was 68

Step-by-step explanation:

The translation of triangle P by the vector (2, 3) results in the triangle being moved 2 units to the right and 3 units up. The new coordinates of the triangle are (6, 7), (4, 6), and (3, 5).

The stem-and-leaf plot is finished as follows:

4| 1 3 7.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

To complete the stem-and-leaf plot, we must obtain the measures above 40 from the table, which are given as follows:

41, 43 and 47.

Considering the format of the plot, the plot is completed as follows:

4| 1 3 7.

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People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.

Recurrent episodes of binge eating are the hallmark of a specific type of eating disorder called binge eating disorder. Food addiction and compulsive overeating are both symptoms of this eating disorder. Uncontrollable and quick eating without feeling hungry, as well as negative emotions, depressive symptoms, and guilt over the eating, are prominent symptoms of this illness.

given

People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.

Pica is a kind of pagophagia. It entails consuming ice, snow, or ice water excessively.

Individuals who have pica are not forced to consume ice due to a physical condition like anaemia.

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The median of 20 is the most accurate to use since the data is skewed.

Option C is the correct answer.

A histogram is a representation of the distribution of data with intervals.

We have,

The data given shows a histogram that is skewed to the right.

Now,

Since the data is skewed.

The median is a better measure of the center of data than the mean.

Now,

Arrange the data in order:

10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55

Median = middle value.

Median = 20

Thus,

The median of 20 is the most accurate to use since the data is skewed.

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Answer:

your question is a bit confusing...

Step-by-step explanation:

Answer:

5025π m³

Step-by-step explanation:

the figure consists of two figures;

a cone and phere

volume of a cone=1/3πr²h

volume of hemisphere=2/3πr³

1/3×π×15×15×37=2775π

2/3×π×15×15×15=2250π

sum up the volumes

2775π+2250π

=5025π m³

Answer: We can solve the system of equations using the substitution method.

First, we'll isolate "y" in one of the equations and substitute it into the other equation:

Y = x - 11

7x + 7y = -21

Substituting the first equation into the second equation:

7x + 7(x - 11) = -21

7x + 7x - 77 = -21

14x = 56

x = 4

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y:

Y = x - 11

Y = 4 - 11

Y = -7

The solution to the system of equations is (x, y) = (4, -7).

Step-by-step explanation:

The value of x and y in the equation is 4 and -7 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Using substitution method to solve the system,

y = x-11 equation 1

7x+7y = -21 equation 2

substitute x-11 for y in equation 2

7x + 7( x-11) = -21

7x + 7x -77 = -21

14x = -21+77

14x = 56

divide both sides by 14

x = 56/14

x = 4

substitute 4 for x in equation 1

y = 4-11

y = -7

therefore the value of x and y is 4 and -7 respectively

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Solution of equation x² - 6x = 11 are,  x = 7.47 and x = - 1.47

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ x² - 6x = 11

Now, Solve the equation by completing the square as,

⇒ x² - 6x = 11

Add 9 both side, we get;

⇒ x² - 6x + 9 = 11 + 9

⇒ (x - 3)² = 20

⇒ x - 3 = √20

⇒ x - 3 = ± 4.47

This gives two solutions,

⇒ x - 3 = 4.47

⇒ x = 4.47 + 3

⇒ x = 7.47

⇒ x - 3 = - 4.47

⇒ x = - 4.47 + 3

⇒ x = - 1.47

Thus, Solution of equation x² - 6x = 11 are,

⇒ x = 7.47 and x = - 1.47

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Answer:

[tex]x+\sqrt{2}[/tex]

Step-by-step explanation:

The conjugate of [tex]x-\sqrt{2}[/tex] would simply be [tex]x+\sqrt{2}[/tex]. All you have to do is simply change the sign to its opposite.

The correct answer is option b.The approximate value of pool in that area is $20.000c.

A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.

Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.

Value of home with a swimming pool in the area = $250,000

Value of home without a swimming pool in the same area = $230,000.

The approximate value of pool in the area = 250000 - 230000 = 20000.

Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.

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37.96 is the average atomic mass of the element in the data table .

What does average mean?

The average is calculated by dividing the total number of values by the total number of values. It can also be described as mean. The mean in statistics is the average value across the specified sample or data set.

                                      Mean, median, and mode are the three primary categories of average. Each of these methods operates a little bit differently and frequently yields values that diverge a little bit from the norm. The most popular type of average is the mean.

the average atomic mass = 35.97 + 37.96 + 39.96/3

                                          = 113.89/3

                                           =  37.96

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Answer:

39.96

Step-by-step explanation: I think

Based on the data, the total number of people would be 350. So the missing value in the table would be 54.

To find the missing value of people in the graph we must do the following procedure. We must add the number of people who are already registered in the graph in the frequency column.

Additionally, we must establish a total number of people, for example 350. In this case we must subtract the result of the people registered in the graph from the total number of people:

350 - 295 = 54.

Then we can establish that the remaining number of people (54) corresponds to the frequency table.

Note: This question is incomplete. The complete information is here:

Total number of people: 350

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A phase change occurs when the kinetic energy decrease enough so that the attraction between molecules pulls them together.

A substance with weaker molecular attraction will freeze at a lower temperature because it requires more energy to be taken out before the attraction pulls the molecules together.

A substance with stronger molecular attraction will evaporate at a higher temperature because it requires less energy to be added to overcome attraction between the molecules.

In Science, a phase change refers to the change in the state of matter of a given chemical compound or substance. Additionally, some examples of a phase change include the following;

Generally speaking, a change in the state (phase) of matter that results in the release of energy is known as an exothermic reaction and they include:

In conclusion, sublimation, melting, and evaporation are other processes that are associated with a change in the state (phase) of matter.

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The ratio of circular chips to square chips is 1:4.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

A box contains 16 square chips, 12 triangular chips, and 4 circular chips.

The ratio of circular chips to square chips,

= Circular chips / square chips

= 4 / 16

= 1/4

= 1: 4

Therefore, the ratio is 1:4.

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The side length x of the triangle rounded to the nearest tenth is 31.3.

The figure in the image is a right triangle.

To determine the value of x, use trigonometric ratio.

Tangent = Opposite / Adjacent

tan( 38° ) = x / 40

Solve for x

x = tan( 38° ) × 40

x = 0.781285 × 40

x = 31.3

Therefore, the value of x is 31.3.

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Let V be an inner product space, S and S0 be subsets of V, and W be a finite-dimensional subspace of V. To prove the other side,

1 ) Suppose (e1,…,en) is basis for W. Suppose x∈(W⊥)⊥. Consider the projection w of x onto W, specifically:

w=⟨x,e1⟩e1+…+⟨x,en⟩en∈W.

Then, x−w is perpendicular to each ei, since

⟨x−w,ei⟩=⟨x,ei⟩−∑j=1n⟨⟨x,ej⟩ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩⟨ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩δij=⟨x,ei⟩−⟨x,ei⟩=0.

Since the linear map ⟨⋅,x−w⟩ is constantly 0 on the basis of W, it is constantly zero on all of W, hence x−w∈W⊥.

But then, since x∈(W⊥)⊥, we have ⟨x−w,x⟩=0, and since ⟨x−w,w⟩=0,

∥x−w∥2=⟨x,x−w⟩−⟨w,x−w⟩=0,

i.e. x=w∈W, completing the proof.

2 ) Suppose that w∈(W⊥)⊥

then ⟨w,x⟩=0

for all x∈W⊥

If w∉W, then w=v+v′ where v∈W and v′∈W⊥∖{0}.

Then.

0=⟨w,x⟩=⟨v,x⟩+⟨v′,x⟩=⟨v′,x⟩

for all x∈W⊥.

However, v′∈W⊥ and ⟨v′,v′⟩≠0 so it is a contradiction.

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The given quantity as a single logarithm are as follows:

1. 20.8In(4x)

2. 3cos(3Inx)Inx

3. 4cos'zln'z

Function ve process of state of instruction that text input papa mississippi start x and output function ladki company it's a programming language allow me the code to create the complex command with simple instruction for example function in the used to it to numbers together a generator and i'm number from san also be combined to create more public sequence are instruction.

Express the given quantity as a single logarithm: In(a + b) + In(a - b) - 4Inx = In[(a+b)(a-b)] - 4Inx

Differentiate the function f(x) = 5.2In(4x) - 52: f'(x) = 20.8In(4x)

Differentiate the function f(t) = sin(3Inx): f'(t) = 3cos(3Inx)Inx

Differentiate the function f(x) = ln(4sin'z): f'(x) = 4cos'zln'z

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Computing the surplus producers receive when a $30 per unit price floor is imposed on the market is option C.$25.

To calculate the surplus producers receive, we need to find the difference between the price they receive at a given quantity and the price they would have received in the absence of the price floor.

When a price floor of $30 per unit is imposed on the market, the quantity supplied and demanded at this price are:

QX = (50 - 30)/4 = 5 units (demand)

QX = (30 - 10)/2 = 10 units (supply)

So, the surplus received by the producers is the difference between the price floor and the price they would have received in the absence of the price floor:

Surplus = 30 - (10 + 2 * 10) = 30 - 30 = $0.

However, the surplus for consumers is the difference between the price they would have paid in the absence of the price floor and the price floor:

Surplus = (50 - 4 * 5) - 30 = 25 - 30 = -$5.

So, the total surplus received by producers and consumers combined is $0 + (-$5) = -$5, which means that the price floor imposes a dead weight loss on the market.

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Answer: To determine the length of the paths connecting the entrance to the opposite entrance, we first need to find the midpoint of each side of the park. Then, we will use the distance formula to calculate the distance between each pair of midpoints.

Let's begin by finding the midpoint of each side of the park.

JK: (-3 + 3, 1 + 3) / 2 = (0, 2)

KL: (3 + 5, 3 - 1) / 2 = (4, 2)

LM: (5 - 1, -1 - -3) / 2 = (2, -2)

MJ: (-1 + -3, -3 + 1) / 2 = (-2, -1)

Next, we'll use the distance formula to calculate the distance between each pair of midpoints.

JK: sqrt((4 - 0)^2 + (2 - 2)^2) = sqrt(16 + 0) = 4

KL: sqrt((2 - 4)^2 + (-2 - 2)^2) = sqrt(16 + 16) = 4 sqrt(2)

LM: sqrt((-2 - 2)^2 + (-1 + 2)^2) = sqrt(16 + 9) = sqrt(25) = 5

MJ: sqrt((-2 - 0)^2 + (-1 - 2)^2) = sqrt(4 + 9) = sqrt(13)

The total length of the paths is 4 + 4 sqrt(2) + 5 + sqrt(13), which when rounded to the nearest whole number is 14.

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The column on an accounting worksheet that may not balance at the end of an accounting period is the Adjustments column.

The Adjustments column on an accounting worksheet includes all the adjusting entries that are needed to update the accounts before the financial statements are prepared. These adjustments can include accruals, deferrals, depreciation, and other adjustments that need to be made to the accounts to accurately reflect the financial position of the company.

Since the Adjustments column is used to record these adjusting entries, it is possible that this column may not balance at the end of the accounting period, as the adjustments may not perfectly offset each other. However, this is not a problem, as the purpose of the worksheet is to help prepare the financial statements, not to balance each individual column.

Therefore, the correct answer is option D, the Adjustments column.

Answer:

C. The Income Statement

Step-by-step explanation:

The Income Statement column on an accounting worksheet may not balance at the end of an accounting period.

An accounting worksheet is a tool used by accountants to help organize and summarize financial information and to prepare financial statements. The worksheet is typically a multi-column form that includes columns for the unadjusted trial balance, adjustments, adjusted trial balance, income statement, and balance sheet.

The Adjustments column is used to record adjusting entries and to update the account balances to reflect accruals, deferrals, and other accounting adjustments. The Adjusted Trial Balance column is the result of the adjustments made in the Adjustments column and should include all the account balances that will be used to prepare the financial statements.

Mr. Garcia's homeroom had a more consistent collection of canned goods.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

The two daily food drives:

Mr. Garcia:

The mean number of canned goods collected = 18.75.

The median number of canned goods collected = 18.

The range of data for Mr. Garcia's homeroom = 11.

The IQR (interquartile range) of data = 4.25.

Ms. Vicario's homerooms:

The range of data = greater than 11.

The IQR of data = greater than 4.25.

The number of canned goods collected = more variable than the number of canned goods collected by Mr. Garcia's homeroom.

Based on these observations.

We can conclude that,

Mr. Garcia's homeroom had a more consistent collection of canned goods. i.e

Smaller range and IQR.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

i.e

Wider range and IQR

Thus,

Mr. Garcia's homeroom had a more consistent collection of canned goods.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

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Answer:

uajajjahajajaaajjsjaja

The time shown is 15:40, which indicates that it is 20 minutes to 4 o'clock in the afternoon.

The time displayed is 15:40, which is consistent with a 24-hour clock. It indicates that there are now 20 minutes left until 6:00.

The time 15:40 is in the afternoon because the afternoon begins at 12:00 and lasts until 18:00.

The 24-hour clock format avoids any doubt regarding AM (morning) or PM (afternoon/evening), it is vital to highlight.

As a result, 15:40 specifies that it is in the afternoon and that there are still 20 minutes until 4 o'clock.

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The solution of the  the linear equation is y = 3/(x - 9xlnx)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

xy' + y = 3xy², y(1) = -3

This is Bernoulli  equation: y' + (1/x)y = 3y²;

Let u = y^(1 - 2) = 1/y is new function.

Then u' = - y'/y

or

y' = -u'/u²;

y = 1/u.

Substitute all this in our ODE:  - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.

we get linear, 1st order not homogenies ODE:

integrated factor:

μ = e∫(-1/x)dx = e-lnx = 1/x²

u'·1/x - 1/x2 = -3/x;

(u/x)' = - 3/x; u/x

       = ∫(-3/x)dx;

 u/x = -3lnx + C;

u = - 3xlnx + Cx;

y =1/u = 1/(- 3xlnx + Cx)

To get C ,use initial conditions:

y(1) = 3;

3 = 1/(-3·1·ln1 + C);

C = 1/3;

y = 3/(x - 9xlnx)

The solution of the  the linear equation is y = 3/(x - 9xlnx)

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The solution of the  the linear equation is y = 3/(x - 9xlnx)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

xy' + y = 3xy², y(1) = -3

This is Bernoulli  equation: y' + (1/x)y = 3y²;

Let u = y¹⁻² = 1/y is new function.

Then u' = - y'/y

or

y' = -u'/u²;

y = 1/u.

Substitute all this in our ODE:  - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.

we get linear, 1st order not homogenies ODE:

integrated factor:

μ = e∫(-1/x)dx = e-lnx = 1/x²

u'·1/x - 1/x2 = -3/x;

(u/x)' = - 3/x; u/x

      = ∫(-3/x)dx;

u/x = -3lnx + C;

u = - 3xlnx + Cx;

y =1/u = 1/(- 3xlnx + Cx)

To get C ,use initial conditions:

y(1) = 3;

3 = 1/(-3·1·ln1 + C);

C = 1/3;

y = 3/(x - 9xlnx)

The solution of the  the linear equation is y = 3/(x - 9xlnx)

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The solution of the system of equations is equal to (3, 4).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by  ordered pair (3, 4).

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In this matrix question where percentages are listed, answers to all these questions are written below.

In the matrix given in the image, we can calculate following things:

a. S32 is a value that represents the percentage of sick students in the third grade of the elementary school. From data we can say it is 10%

b. P22 is a value that represents the number of middle school students in the second grade. From data we can say there are 795 such boys.

c. To find[tex][s] * [p][/tex] we need to multiply the percentage of students in each category by the corresponding population in each grade level.

      [tex]\left[\begin{array}{ccc}1190.75&1311.75\\1194&1366.25\\1233&1405.5\end{array}\right][/tex]

Columns: Girls, Boys

Rows: Susceptible, Sick, Infected

d. [tex][[s] * [p]]21[/tex] represents the number of sick students in the second grade of the elementary school.

It represents that 1194 girls are sick.

e. To find the number of sick girls, we need to multiply the number of girls in each grade level by the corresponding percentage of sick students.

1194

f. To find the number of infected boys, we need to multiply the number of boys in each grade level by the corresponding percentage of infected students.

1406

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Complete Question: Image is uploaded for it.

a. Describe what S32 value is and what it will represent

b. Describe what P22 value is and what it will represent

c. Find [tex][s] * [p][/tex]

d. Describe what[tex][[s] * [p]]21[/tex] value is and what it will represent

e. How many sick girls are present?

f. Number of boys infected?

Answer:

x = 24, y = 12

Step-by-step explanation:

We can use the law of sines to solve for x

The law of sines says the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides (and angles)

In this triangle

the side with length 12√3 is opposite 60°

the side with length x is opposite 90°

Using the law of sines,

[tex]\dfrac{12\sqrt{3}}{\sin60}=\dfrac{x}{\sin 90}\\[/tex]

sin 60 = [tex]\dfrac{\sqrt{3}}{2}[/tex]

sin 90 = 1

[tex]\rightarrow \dfrac{12\sqrt{3}}{\dfrac{\sqrt{3}}{2}}=\dfrac{x}{1}\\\\\\x = 12\sqrt{3} \div \dfrac{\sqrt{3}}{2}}\\\\\textrm{When dividing fractions, flip the divisor and multiply}\\\\\rightarrow 12\sqrt{3} \times \dfrac{2}{\sqrt{3}}\\\\\textrm{$\sqrt{3}$ cancels out from numerator and denominator}:\\\\\\\rightarrow x = 12 \times 2 = \boxed{24}\\\\\\[/tex]

To solve for y we can again use the law of sines
[tex]\dfrac{y}{\sin 30} = \dfrac{x}{\sin 90}\\\\\textrm{again, as before $\sin 90$ is 1}\\\\\rightarrow \dfrac{y}{\sin 30} = x\\\\\rightarrow x = \dfrac{y}{\sin 30}\\\\\rightarrow y = x \sin 30\\\\\sin30 = \dfrac{1}{2}[/tex]

So y = x/2 = 24/ 2 = 12

ans:
x = 24, y = 12

Note
Another way to solve this question is to first recognize the triangle as a 30-60-90 right triangle

In a triangle of this kind, if the longest side side is a, the shortest side is a/2, and the third side is √3/2a

We could have solved this in this manner also

Here longest side = x, shortest side is y

The other side is 12√3 = x √3/2

So x = 12√3 ÷ √3/2 = 24 (as in the first method)

y = x/2 = 12

This approach is ok too, I find it less intuitive and we have to remember the ratios

The effective annual rate (EAR) is the actual rate of interest that is earned or paid over a given period of time, taking into account the compounding of interest. For example, a stated rate of 7.80% with 4 compounding periods per year would result in an EAR of 15.30%.

The effective annual rate (EAR) is a measure of the actual rate of interest that is earned or paid over a given period of time. It takes into account the effect of compounding, which is the process of earning interest on both the principal and the accumulated interest. This means that the rate of return can increase over time. The EAR is calculated by taking the stated rate of interest, which is the rate of interest stated by the lender, and multiplying it by the number of compounding periods per year. For example, if the stated rate is 7.80% and the compounding periods per year are 4, then the EAR would be 15.30%. Similarly, if the stated rate is 12.40% and the compounding periods per year are 365, then the EAR would be 11.40%. If the compounding period is infinite, then the EAR will be the same as the stated rate, in this case 12.40%. Therefore, the EAR is the actual rate of return that is earned or paid over a given period of time.

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Answer: qt=0.6

Step-by-step explanation:

3.5=

60%=0.6

qt=0.6

Answer: Option D, "C-E-G-A-Bb-A-G-E" is not an example of a boogie-woogie bass line. Boogie-woogie is a genre of blues music that is characterized by a repetitive bass pattern that usually consists of 8th notes. The bass line is usually made up of the root note, fifth note, and octave of a chord, and it is played in a swung or shuffle rhythm. The most common boogie-woogie bass line consists of the notes of a I-IV-V chord progression in a 12-bar blues structure. Option D deviates from this typical pattern and therefore would not be considered a boogie-woogie bass line.

Step-by-step explanation:

The function operation f( x + h ) in the function f(x) = x² / (x + 3 ) is ( x + h )² / (x + h + 3 ).

A function is simply a relationship that maps one input to one output.

Given that;

To determine f( x + h ),  replace all the occurrence of x with (x + h) in the function and simplify.

f(x) = x² / (x + 3 )

f(x + h) = ( x + h )² / (( x + h ) + 3 )

f(x + h) = ( x + h )² / (x + h + 3 )

Therefore, the operation f(x + h) equals ( x + h )² / (x + h + 3 ).

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The shortest distance between the two skew lines is equal to 11√38 / 38 units.

According to linear algebra, lines are defined by vectorial equations of the form:

(x, y, z) = P(x, y, z) + t · T(x, y, z)

Where:

And the shortest distance between two skew lines is determined by the following expression:

[tex]d = \frac {|[P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)]|}{|T_{1} (x, y, z) \times T_{2} (x, y, z)|}[/tex]

First, determine the points contained in each line:

P₁(x, y, z) = (3, 2, 1)

P₂(x, y, z) = (2, 4, - 1)

Second, find each vector slope:

T₁(x, y, z) = (2, 1, 0) - (3, 2, 1)

T₁(x, y, z) = (- 1, - 1, - 1)

T₂(x, y, z) = (3, 0, - 2) - (2, 4, - 1)

T₂(x, y, z) = (1, - 4, - 1)

Third, determine the vector subtraction:

P₂(x, y, z) - P₁(x, y, z) = (2, 4, - 1) - (3, 2, 1)

P₂(x, y, z) - P₁(x, y, z) = (- 1, 2, - 2)

Fourth, determine the cross product:

T₁(x, y, z) × T₂(x, y, z) = (- 1, - 1, - 1) × (1, - 4, - 1)

T₁(x, y, z) × T₂(x, y, z) = (- 3, - 2, 5)

Fifth, use the dot product:

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = (- 1, 2, - 2) \,\bullet\,(- 3, - 2, 5)[/tex]

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = 3 - 4 - 10[/tex]

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = - 11[/tex]

Sixth, calculate the norm of the cross product:

|T₁(x, y, z) × T₂(x, y, z)| = √[(- 3)² + (- 2)² + 5²]

|T₁(x, y, z) × T₂(x, y, z)| = √38

Finally, determine the shortest distance between the two skew lines:

d = |- 11| / √38

d = 11 / √38

d = 11√38 / 38

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