What happens if the opportunity costs of production are constant?

Option (a) is correct. There'll be No Solution to the given system of linear equations.

According to the solutions of linear equations, we know the following things,
1. If two intersecting lines are at one common point, the system has only one solution.
2. If two coincidental lines mean both equations give the same line, that means the system has infinitely many solutions.
3. If the lines are parallel to each other, the system will have no solution.

We can see lines are parallel but we can also find whether the given lines are parallel or not by simply finding their slope m.

For Line 1, we have the following data
[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,2)$[/tex]

[tex]$\left(\mathrm{x}_2, \mathrm{y}_2\right)=(3,1)$[/tex]

For slope m of the line 1,
slope m₁ = [tex]\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{3-0}=-\frac{1}{3}[/tex]

For Line 2, we have the following data

[tex]$\left(\mathrm{x}_1, \mathrm{y}_1\right)=(0,-1)$[/tex]

[tex]- $\left(x_2, y_2\right)=(3,-2)$[/tex]

For slope m of line 2,
slope m₂[tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-(-1)}{3-0-x_1}=-\frac{1}{3}$[/tex]

As the slope of both lines is equal, so lines are parallel to each other, and hence, if lines are parallel so there'll be no solution to the system.
Hence, option (a) is correct.

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Your question was incomplete, the most probably question you asked was:

How many solutions does the system of linear equations represented in the graph have? Coordinate plane with one line that passes through the points (0, 2) and (3, 1) and another line that passes through the points (0, -1) and (3, -2).
(a) No solution
(b) One solution at (−1, 0)
(c) One solution at (0, −1)
(d) Infinitely many solutions

Answer:

It looks like you're trying to solve a problem involving geometry and algebra. To solve this problem, you need to use the information given in the statements to find the value of x and then use that value to find the lengths of the sides of the trapezoid.

Starting with the first statement, we have:

WH = 10x + 2.6

NH = 11x - 7.4

Next, we can use the information about Y being the midpoint of WT to find the value of WT:

WT = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2

Using the information about R being the midpoint of HN, we can find the value of HN:

HN = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2

Finally, using the information about TN, we can find the value of TN:

TN = 23x - 3.9

With these values, we can now find the lengths of the sides of the trapezoid. The length of the top side (WH) is 10x + 2.6, the length of the bottom side (TN) is 23x - 3.9, the length of the left side (NH) is 11x - 7.4, and the length of the right side (WT) is 36x - 8.2.

Note: To fully solve the problem, you will need to use the given equations to find the value of x.

To find the value of x, we need to equate the midpoint formula with the given expressions.

The midpoint formula is (x1 + x2)/2 = x and (y1 + y2)/2 = y.

We can use this formula to find the value of x.

For example, for the midpoint R:

x = (WT + NH)/2

x = (8x + 5.2 + 11x - 7.4)/2

x = (19x - 2.2)/2

x = 9.5x - 1.1

And for the midpoint Y:

y = (WH + TN)/2

y = (10x + 2.6 + 23x - 3.9)/2

y = (33x - 1.65)/2

y = 16.5x - 0.825

Now we have two equations:

9.5x - 1.1 = 16.5x - 0.825

7x = 0.725

x = 0.725/7

x = 0.104285714

So the value of x is approximately 0.104285714.

Answer:

Step-by-step explanation:0.1

Answer:

y= x/2 - 3 : linear

y= 6/x -2 : nonlinear

3x + y = 12: linear

y = x: linear

The length of the side x in the triangle is 82.1 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sun of angle in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows

Hence,

tan 75 degrees = opposite / adjacent

opposite side = x

adjacent side = 22 units

Therefore,

tan 75° = x / 22

cross multiply

x = 22 tan 75

x = 22 × 3.73205080757

x = 82.1

Therefore,

x = 82.1

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The factor is the variable that the experimenter will use to judge its impact on the response variable.

A dependent variable is one that is altered as a result of the modification of an independent variable. The outcome you're trying to measure "depends" on your independent variable. Response variables in statistics are another name for dependent variables (they respond to a change in another variable).

The coefficient of a variable term is that word's numerical factor.

The variable being measured or tested in an experiment is known as the dependent variable.

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There are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

In this scenario, we have 6 people to seat at 2 round tables, meaning each table must have at least 3 people.

We can start by finding the number of ways to seat 6 people at one table, then divide that by 2 to account for the two tables.

For one round table, there are 6! (6 factorial) ways to seat 6 people. This is because, for the first seat, there are 6 options. For the second seat, there are 5 options remaining; for the third seat, there are 4 options, and so on.

However, this number counts the same arrangement of people multiple times, as the arrangement can start with any person. So, to correct this, we divide 6! by 6, which gives us 720/6 = 120 ways to seat 6 people at one round table.

Now, since we have two tables, each table must have 120/2 = 60 arrangements. This means there are 60 x 60 = 3600 ways to seat 6 people at two round tables.

In conclusion, there are 3600 ways to seat 6 people at two round tables, with at least one person at each table.

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The ratio of the area of a regular hexagon to the area of the smaller hexagon that uses its midpoints as vertices is 4:1. The common factor in this expression is 4

The closed polygonal shape of a regular hexagon has six equal sides and six equal angles. Any regular polygon has equal sides and angles on all sides. Regular pentagons, for instance, have 5 equal sides, and regular octagons have 8 equal sides. When these requirements are not met, polygons might resemble many other asymmetrical shapes. A regular hexagon is formed when six equilateral triangles are placed side by side. The regular hexagon's area then increases to six times that of the same triangle. In this post, let's learn about its features, the formula for area, and the perimeter.

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Answer:

Factor 4 out of 12+4x 4(3+x)

Step-by-step explanation:

Answer:

1183

Step-by-step explanation:

75th term of Arithmetic sequence is 1183 Given: -1, 15, 31,... is Arithmetic series To find: The 75th term of the arithmetic sequence -1, 15, 31

The spatial scale at which the data was collected is the distance from the shore of Lake Erie.

We can see that the data shows a gradual decline in snowfall totals with increasing distance from the shore of Lake Erie. The decline starts at around 425 cm at 0 km and decreases to 375 cm by 30 km. It then decreases more quickly over the next 20 km before declining relatively consistently out to 100 km, where the snowfall is 150 cm.

The graph shows the declining snowfall totals with increasing distance from the shore of Lake Erie, starting from 0 km and ending at 100 km. The data points are measured in increments of 10 km, with the total snowfall measured in cm.

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The number 5.634x10 to the 2nd power can be expressed as 563.4. The numbers between which 563.4 falls are 560 and 567.

The following pairs of equations have its second equation valid

7 + 5x= 3 - 2x and 7 + 7x = 3

1/(x - 5) = 10 and 1 = 10(x - 5)

The invalid equations are;

3(x - 4) = 15 and x - 4 = 15

x^2 = 6x and x = 6

1. 7 + 5x= 3 - 2x and 7 + 7x = 3

Add 2x to both sides

7 + 5x + 2x = 3

7 + 7x = 3

Valid

2. 3(x - 4) = 15 and x - 4 = 15

3x - 12 = 15

Invalid

3. x^2 = 6x and x = 6

find the square root of both sides

√x² = √6x

x = √6x

Invalid

4. 1/(x - 5) = 10 and 1 = 10(x - 5)

cross product

1 × 1 = 10(x - 5)

1 = 10(x - 5)

Valid

Therefore, 7 + 5x= 3 - 2x and 7 + 7x = 3;

1/(x - 5) = 10 and 1 = 10(x - 5) are the valid equations.

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The correct response is 503 acres. Around 503 acres with more than 190 bushels of maize per acre is what we would anticipate.

Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.

Let X serve as the random variable representing the yield of corn. The issue reveals that the formula for the random variable X's distribution is as follows:

[tex]X[/tex]≅Nμ=185.2, σ=23.5

A sample of n=1200 acres is taken by a quality control inspector. The sample size is reflected by that.

The likelihood that the random variable X contains more than 190 bushels of maize per acre is also something we wish to calculate. Consequently, we seek to discover:

[tex]P(X > 190)[/tex]

Additionally, we may use the z score this calculation produces:

z=X-μ/σ

If we substitute the provided values, we get:

[tex]z=190-185.2/0.2042[/tex]

We desire the possibility that:

[tex]P(z > 0.2042)=1-P(z < 0.2042)=1-0.5809=0.4191[/tex]

And to determine how many, it would be necessary to assume that each acre would produce more than 190 bushels of maize. The faction obtained can be multiplied by the sample size.

[tex]r=1200*0.4191=502.92=503[/tex]acres

A 503acre crop with more than 190 bushels of maize per acre is what we would anticipate.

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The difference 120.45-116.9 is 3.55.

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The two decimal numbers,

120.45 and 116.9.

Applying subtraction operation,

the difference 120.45-116.9.

By adding on strategy,

116.9 is 3.55 left to the number 120.45 on the number line.

That means,

116.9 + 3.55 = 120.45.

Therefore, the difference is 3.55.

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Based on the data of increase in ice cream sales as the weather gets warmer the data is

A statistical measure known as correlation expresses how linearly connected two variables are (meaning they change together at a constant rate). It is frequently used to describe straightforward relationships without explicitly stating cause and effect.

In this case, the data shows a relationship between the weather (one variable) getting warmer and an increase in ice cream sales (another variable). However, just because two variables are correlated does not necessarily mean that one causes the other.

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According to the solving triangle proportion proves that cos ∠d = cos ∠a is

3/3.61 = 6/7.22

A triangle seems to be a three-sided polygon with three vertices. The angles of both the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees.

According to the given information:

Right angled triangles BAC and BDE are comparable to one another.

This is due to the fact that when a shape is dilated, then new shape would resemble the previous shape but be smaller. Both shapes' angles are the same if they both stay the same.

Scale factor = 2

BE = 3, BD = 2, DE = 3.61

Each of the corresponding sides of ∆BDE will be multiplied to get each of the corresponding sides of ∆ABC.

BC = 2×BE = 2×3 = 6

AB = 2×DE = 2×3.61 = 7.22

See second diagram

sin ∠D = opposite/hypotenuse = BE/DE

BE/DE = 3/3.61

sin ∠A = BC/AC

BC/AC =  6/7.22

Therefore sin ∠D = sin ∠A

3/3.61 = 6/7.22 (C)

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Answer:3/3.61 = 6/7.22

Step-by-step explanation:

got it right on the test

si por qué si y si por qué obvio si

The 96 % confidence interval for the cans, given the diameter and standard deviation, is (50.45, 53.55).

The 96% confidence interval for the mean diameter of soda cans manufactured by the company can be calculated using the following formula:

= Mean ± (critical value x standard deviation / square root of sample size)

The critical value for a 96 % confidence interval is 2. 33 so the lower bound of the interval is:

= 52 - ( 2.33 x 2. 3 / √12 )

= 50. 45

The upper bound of the interval is:

= 52 + ( 2.33 x 2. 3 / √12 )

= 53. 55

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Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do note that to solve this question, there are multiple ways (using Pythagoras' Theorem), this is only one of the ways.

A woman you know has five children among which all five  are boys. probability for a woman that she will have all five boy as a five children is  0.5.

The probability or the outcome  in which a women with five children have all the girls and none of them as boys is :-

0.5x0.5=0.25.

So for the  first child there is a a 50% chance that is will be of a male. And same for the  second child being male there will be equal probability that it can be boy so it  also will have a probability .

So the probability of having five females is  0.55=0.03125

Except the above define value all the other outcome or choices means that the women have a least one son in the five children  and the total probability of an event is 1.

.The theoretical probability is mainly reasoning bases which is behind probability. For example, if a coin is tossed then the theoretical probability or the outcome of getting a head will be ½.

Probability provides information about the happening of   something which might happen and might not depending upon the outcome demand happen. Meteorologists, also take the help of probability to predict whether the rain may happen or not for instance In epidemiology, also probability theory is used to understand  about various risk related to life an to demonstrate various relation .

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A vertical asymptote basically means of a graph on a  vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

In a graph a vertical asymptote  is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a. And similarly the horizontal asymptote in a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.

At x = a in a graph  where  a is a zero for a factor in the denominator the removable discontinuity occur that is common with a factor in the numerator.

Factor the numerator and denominator.

It is set it equal to zero and solve if any factors are common to both the numerator and denominator.

This is removable discontinuity type location.

In mathematics a graph is defined as a diagrametical or a pictorial representation  that helps to represents data or values in an organized manner. The points that are shown on the graph are use to mark of represent the various value or relation between two value .

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The total amount spent by Mrs. Rivera is given by the equation A = $ 2.25

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount spent by Mrs. Rivera be represented as A

Now , the equation will be

The cost of one pound of banana = $ 0.45

The total amount of bananas = 5 pounds

So , the total amount of money for 5 pounds = 5 x cost of one pound of banana

Substituting the values in the equation , we get

The total amount of money for 5 pounds of banana A = 5 x 0.45

The total amount of money for 5 pounds of banana A = $ 2.25

Hence , the total amount is $ 2.25

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Answer:

7

Step-by-step explanation:

3^2 = 9

18-9=9

63÷ 9=7

Answer:

7

Step-by-step explanatio

63 ÷ (18-9)

63÷9= 7

The interest you can get from this account after two years is $382.49.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

Given:

P= $3000

R= 6%
T= 2 years

A = P[tex]e^{rt[/tex]

A = 3,000.00[tex](2.71828)^{(0.06)(2)[/tex]

A = $3,382.49

and, A = P + I

I (interest) = $3,382.49- $3000

I =  $382.49.

Hence, the interest is $382.49.

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If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),

all the possible values of x and y are those values that  satisfy the equation 3x - 2y = 16.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:

If line r through (1, 1) and (5, 7) is parallel to line s through (4, -2) and (x, y),

then their slopes are equal.

(7 -1)/(5 - 1) = (y + 2)/(x-4)

3/2 = (y + 2)/(x-4)

3x - 12 = 2y + 4

3x - 2y = 16.

Therefore,  all the values that satisfy the equation 3x - 2y = 16.

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The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32, etc.

Given here: The numbers containing fractions and decimal numbers.

To get a clarity on the magnitude of the numbers, let's convert every fraction to decimal numbers

Thus 7¹⁹/₂₅=7.76

31/4=7.75

Hence, The order of the numbers from least to greatest is as follows:

7, 31/4,7¹⁹/₂₅,7.765,8.44

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The population of the green sea turtle on the island in 2012 is 68 turtle

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics.

To find the exponential decrease in a population which obtain it by using the formula;

P(t) = P(o) e^-kt

P(o) = 750

k = 0.2

t = 12

P (t) = 750 e ^ -0.2 ×12

p(t) = 750 e^ -2.4

p(t) = 750 × 0.09

p(t) = 68( approximately) turtle

Therefore in 2021 the population of turtle on the island is 68

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The length and width of a rectangle are 36cm and 4.5cm

Finding the Width:

The formula to find the perimeter of the rectangle is:

P=2(l+w),

where P is the perimeter, l be the length, and w be the width.

Now substitute the given values to solve for w, since we need to find the width.

The given information is:

the length of a rectangle is six inches more than eight times the width so the equation becomes:

L=8w+6

P=120

w=8w

now plug the values in the above formula:

P=2(l+w),

120=2(8w+6)+8w

120=16w+12+8w

120=24w+12

24w=108

w=4.5

To find the length just substitute in the L.

L=8(4.5)+6

L=30+6

L=36

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As a result, Company B is more likely to make you an offer of $33,000 or more than Company A.

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

Here,

To determine which company you are more likely to receive an offer of $33,000 or more, we need to look at the standard deviations of each company's starting salary. Company B has a standard deviation of $5000, which is 5 times greater than Company A's standard deviation of $1000. This means that the salaries offered by Company B are spread out over a larger range, with a higher chance of extreme values.

We can calculate the z-score for an offer of $33,000 from each company using the formula:

z = (x - μ) / σ

For Company A:

z = ($33,000 - $31,000) / $1000 = 2

For Company B:

z = ($33,000 - $31,000) / $5000 = 0.4

A z-score of 2 for Company A indicates that an offer of $33,000 is 2 standard deviations above the mean, which is relatively rare. On the other hand, a z-score of 0.4 for Company B indicates that an offer of $33,000 is only 0.4 standard deviations above the mean, which is much more likely.

Therefore, you are more likely to receive an offer of $33,000 or more from Company B than Company A.

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