use the definition of a limit to fill in the blanks and prove the statement below. lim x → 2 1 2 x + 2 = 3

The work (or energy expended) by a one newton (N) force applied across a one meter distance is equivalent to one joule (m).

The SI unit of energy, the joule (symbol J), measures the ability to do work or produce heat. One newton is equal to a force that accelerates a mass of one kilograms (kg) by one meter per second (s) per second. As a result, one joule is equal to one newton meter.

In SI Unit

1 Joule = 1 kgm^2/s^2

In CGS units:

1 Joule = 1 kgm^2/s^2

As we know that 1 kg = 1000 g and 1 m = 100 cm. Now

1 Joule = 1(1000 g) × (100cm)^2/(1s)^2    

Now solving

1 Joule = 1000 × 10^4 gcm^2/s^2

1 Joule = 10^7 gcm^2/s^2

As we know that 1 gcm^2/s^2 = 1 erg. So

1 Joule = 10^7 erg

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The ratio of [PAB]/[QAB]. is 1/3

From the question, we have the following parameters that can be used in our computation:

The triangle

Also, we have

PQ/QR = 1/3

This means that;

The line segments divide PAB to 1/3

So, we have

PAB = 1

QAB = 1 - 1/3 = 2/3

When represented as quotient, we have

[PAB]/[QAB] = 3/2

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Answer:

3.5

Step-by-step explanation:

1 x 2 = 2

2 x 6 = 12

3 x 4 = 12

4 x 1 = 4

5 x 2 = 10

6 x 5 = 30

1+1+2+2+2+2+2+2+3+3+3+3+4+5+5+6+6+6+6+6 = 70

70 / 20 = 3.5

The probability of a fair coin landing heads up is 0.5

The probability of a fair coin landing heads up is 0.5 and the probability of it landing tails up is also 0.5.

Theoretically, this means that if a fair coin is flipped an infinite number of times, half of the flips will result in heads and half of the flips will result in tails.

In the case of an unfair coin, the probability of landing heads up and the probability of landing tails up will not be equal.

The exact probabilities will depend on the weight of the coin, but one side will have a greater probability of landing face up.

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Recruiting participants for research can be done through various methods such as:

1. Online advertisements

2. Flyer distributions in public places

3. Collaboration with organizations or schools

4. Referral from previous participants

5. Direct mailing to potential participants

6. Social media promotion.

It is important to consider ethical guidelines and informed consent procedures when recruiting participants for research.

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The total number of vertices a full 5-ary tree with 100 internal vertices have is 501.

A tree with m or less offspring at each node is known as an m-ary tree. When m = 2, a binary tree is the particular case, and a ternary tree, which has m = 3 and a maximum of three offspring, is another special case.

A m-ary tree with just a root node has a height of 0, as the height h of an m-ary tree does not include the root node. The maximum depth D of any tree node determines the height of the tree.

In computer science, a collection of nodes often represented hierarchically in the following way is referred to as a "m-ary tree." At the root node, the tree is initiated. A list of pointers to each node's child nodes is kept by each node in the tree. There are less than or as many child nodes as m.

It is given the m-ary tree as 5-ary tree (m)

And the number of Intervals = 100(i)

We can calculate the number of vertices by using

n = m*i + 1 = 100*5 + 1 = 501

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The probability is P(z < -1.76) = 0.0040

Voter turnout is a helpful statistic that indicates how engaged voters were in a particular election. Generally, this is understood as the percentage of voters who vote in a given election and is calculated by dividing the number of votes by the number of voters.

People's participation in the election is measured by voter turnout figures. Turnout indicates the per cent of eligible voters who actually cast their vote. 1. In India, the poor, illiterate and underprivileged people vote in larger proportion as compared to the rich and privileged sections.

In statistics, a population proportion refers to the fraction of individuals in a population with a certain characteristic.

The sample proportion is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty. Viewed as a random variable it will be written ˆP. It has a mean μˆP and a standard deviation σˆP. Here are formulas for their values.

z = (phat - p)/sqrt(p*(1-p)/n

where phat = sample proportion

p = population proportion

n = sample size

here phat = 0.489, p = 0.533 and n=400

z = (0.489 - 0.533)/sqrt(0.533*0.467/400)

z = -1.76

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The probability is P(z < -1.76) = 0.0040 in a random sample of 400 voters, less than 48.9% say they will vote for the incumbent.

A useful metric that reveals how involved people were in a specific election is voter turnout. Calculated by dividing the total number of votes by the total number of voters, this is typically viewed as the percentage of voters who participate in a particular election.

Voter turnout numbers are used to gauge voter involvement in elections. The turnout rate represents the proportion of eligible voters who actually cast a ballot. 1. Compared to the wealthy and privileged parts, more impoverished, ignorant, and underprivileged individuals vote in India.

The percentage of people who share a particular attribute within a population is referred to as a population proportion in statistics.

The formula is:

[tex]Z=\frac{(P_{hat}-P) }{\sqrt{\frac{P*(1-P)}{n} } }[/tex]

Where

[tex]P_{hat}[/tex] = sample proportion

P = population proportion

n = sample size

Here [tex]P_{hat}[/tex] = 0.489, p = 0.533 and n=400

[tex]Z=\frac{(0.489-0.533)}{\sqrt{\frac{(0.533*0.467)}{400} } }[/tex]

[tex]Z=-1.76[/tex]

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The second term of the geometric sequence is 1260

The sum of the first 6 terms of a geometric sequence is 7812. This means that the formula for the sum of the first n terms of a geometric sequence, Sn = a(1-r^n)/(1-r), can be used to solve for the first term, a. 7812 = a(1-5^6)/(1-5). Solving for a, the first term is equal to 252.

The common ratio is 5, meaning that each term of the sequence is 5 times the previous term. Therefore, the second term is equal to 252 * 5, or 1260. This can also be seen by looking at the sequence, 252, 1260, 6300, 31500, 157500, 787500.

To conclude, the second term of the geometric sequence is 1260. This was calculated by taking the first term and multiplying it by the common ratio, 5.

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So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.

Relative error can be calculated using the following formula:

Relative error = (|measured value - actual value|) / actual value

In this case, the actual value is 3 inches, and the measured value is 2.98 inches. So, we can calculate the relative error as follows:

Relative error = (|2.98 - 3|) / 3 = (0.02) / 3 = 0.0067

To find the relative error to the nearest thousandth, we round the result to three decimal places:

Relative error = 0.007

So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.

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So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.

The relative error can be calculated using the following formula:

Relative error = (measured value - actual value|) / actual value

In this case, the actual value is 3 inches, and the measured value is 2.98 inches. So, we can calculate the relative error as follows:

Relative error = (|2.98 - 3|) / 3 = (0.02) / 3 = 0.0067

To find the relative error to the nearest thousandth, we round the result to three decimal places:

Relative error = 0.007

So Eric's relative error to the nearest thousandth is 0.007 or 0.7%.

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The day that she run faster is given as follows:

Thursday.

She ran 0.3 miles per hour faster on Thursday than on Wednesday.

Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:

v = d/t.

Considering the time in hours, each hour = 60 minutes, the velocity on Wednesday is given as follows:

v = 6/(50/60)

v = 7.2 miles per hour.

The velocity on Thursday is given as follows:

v = 4/(32/60)

v = 7.5 miles per hour. -> faster, as 7.5 > 7.2.

The difference is of:

7.5 - 7.2 = 0.3 miles per hour.

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None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.

[ ] The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and 0.

[ ] The operation of vector addition is not commutative.

[ ] The magnitude of a vector cv is c times the magnitude of v, where c is any scalar.

None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.

None of the choices is correct. The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and the origin (not just 0). The operation of vector addition is not commutative, meaning that the order of addition matters. The magnitude of a vector cv is c times the magnitude of v, where c is any scalar and v is a vector. A column vector in R^2 is a matrix with two columns and one row (1x2 matrix).

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Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

What is the section formula in coordinate geometry?

When the line segment is divided internally in the ratio m:n, we use this formula.  That is when point C lies somewhere between points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)

Given here,  point B on AC such that the ratio of AB to AC is 5:6

Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,

p= (mx₂+nx₁)/(m+n)

q= (my₂+ny₁)/(m+n)

Here. m=5 and n=6

p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11

Hence, the Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

I hope this helps <3

Answer: 0 students did not study Art, Music, or Dance.

Step-by-step explanation:

The values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.

A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.

To make the function continuous at x = -3, the value of f(-3) must be equal for both the first and second parts of the definition. That is, 3 * -3 + 4 = -3 * -3 + a * -3 + b. Solving for a and b gives us:

a = -3

b = 19

To make the function differentiable at x = -3, the limits of the first and second parts of the definition must be equal, and their derivatives must also be equal.

The limit from the left of f(-3) is:

[tex]\lim_{x \to \ -3}[/tex]f(x) = 3 * -3 + 4 = 5

The limit from the right of f(-3) is:

[tex]\lim_{x \to \ -3}[/tex] + f(x) = -3 × -3 + a × -3 + b = -3 × -3  + 19 = 19

So the function is continuous at x = -3. To check for differentiability, we find the derivative of the first part:

f'(x) = 3

And the derivative of the second part:

f'(x) = -6x + a

The derivative of the two parts must be equal at x = -3, so we have:

3 = -6 × -3 + a

3 = 18 - a

a = -15

This value of a is different from the value we found in the first step, so the function is not differentiable at x = -3. To make it differentiable, we must choose the value of a that makes the function continuous, which is a = -3.

So the values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.

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The class that has more students, given the percentage of students in both classes is Emily's homeroom tab .

To find the class with the higher number of students, you need to find the total number of students in these classes.

The number of students in Emily's homeroom class is:

= Number of students / Percentage of students

= 15 / 75 %

= 20 students

Students in Santiago's homeroom class is :

= 12 / ( 2 / 3 )

= 12 x 3 / 2

= 18 students

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The answer we have states that the typical retail cost of Yen's car is $21,210.

The price that the automaker, or manufacturer, advises that the seller ask for the vehicle is known as the Mfg Suggested Retail Price (MSRP). It is not necessary for it to be the price you really pay. Many buyers haggle to get the automobile for less than the MSRP.

We must add the numbers she added and minus the sums she reduced to obtain the vehicle's average retail price.

$17,600 + $1,700 + $475 + $800 + $225 + $125 + $325 + $3,125 + $450 = $24,825

And let's subtract $3,615 as from manual transmission's cost, and brings us back amount approximately $21,210.

Hence, Yen's car has an average retail price of $21,210.

Therefore, the average retail price of Yen's vehicle is $21,210 .

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The scalar and vector projection of a vector onto another vector is found using dot product.

The scalar projection of a vector A onto a non-zero vector B is given by:

scalar projection = (A . B) / ||B||

where (A . B) is the dot product of vectors A and B and ||B|| is the magnitude of vector B.

The vector projection of A onto B is given by:

vector projection = (scalar projection) * (unit vector in the direction of B)

The unit vector in the direction of B is given by B/||B||. A unit vector has a magnitude of 1.

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Pattern in mathematic help individual better undertand the world and predict what come next because patterns follow a predictable rule and that rule allows us to predict what will come next.

What is Predictable Rule?

A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.

Reasons:

Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.

Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.

Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.

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Patterns in mathematic help individual better understand the world and predict what comes next because patterns follow a predictable rule and that rule allows us to predict what will come next.

What is the Predictable Rule?

A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.

Reasons:

Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.

Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.

Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.

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The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.

The normal curve is a symmetrical bell-shaped distribution with the mean, median, and mode all equal to 100. If we take 15 as the standard deviation, then 68% of the scores will lie between 85 (100-15) and 115 (100+15). We can calculate this using the z-score formula: z=(x-μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.

In this case, the z-score for the lower limit (85) is (85-100)/15=-1. The z-score for the upper limit (115) is (115-100)/15=1. We can then use the z-score table to determine that the area between -1 and 1 is 68%. Therefore, 68% of the scores are between 85 and 115.

To determine the percentage of test-takers who earned at least a 100, we can use the same z-score formula. The z-score for x=100 is (100-100)/15=0. We can then use the z-score table to determine that the area above 0 is 60%. Therefore, 60% of test-takers earned at least a 100.

Therefore, the first two choices are true. The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.

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Data to predict the count of each bird that will be in the sanctuary during this year's visit is red-tailed hawks, Turkish vultures, northern goshawks and bald eagles.

What does predict mean in math?

In general, prediction is the process of determining the magnitude of statistical variates at some future point of time.

12 + 2 + 4 + 7 = 25 (The total number of birds observed in the last year)

Turkish vultures = 175 × 12 / 25 = 84

bald eagles = 175 × 2 / 25 = 14

northern goshawks = 175 × 4 / 25 = 28

red-tailed hawks = 175 × 7/ 25 = 49

So,

49 ↔ red-tailed hawks

84 ↔ Turkish vultures

28 ↔ northern goshawks

14  ↔ bald eagles

Hence, data to predict the count of each bird that will be in the sanctuary during this year's visit is red-tailed hawks, Turkish vultures, northern goshawks and bald eagles.

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To predict the count of each bird that will be in the sanctuary during this year's visit, we need to assume that the proportion of each bird species in the sanctuary remains the same as it was last year when Jeff visited.

Last year, Jeff saw a total of 12 Turkish vultures + 2 bald eagles + 4 northern goshawks + 7 red-tailed hawks = 25 birds.

So, the proportion of each bird species in the sanctuary last year was:

Turkish vultures: 12/25 = 48%

Bald eagles: 2/25 = 8%

Northern goshawks: 4/25 = 16%

Red-tailed hawks: 7/25 = 28%

Using these proportions, we can predict the count of each bird species in the sanctuary this year:

Turkish vultures: 48% of 175 birds = 84 birds

Bald eagles: 8% of 175 birds = 14 birds

Northern goshawks: 16% of 175 birds = 28 birds

Red-tailed hawks: 28% of 175 birds = 49 birds

These are the predicted counts of each bird species in the sanctuary during this year's visit.

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The height of each candle at 11:00 PM will be 3.5 inches.

This is because each candle starts at 8 inches tall and decreases by 3/4 of an inch per hour as it burns

To find out the height of each candle at 11:00 PM, we need to calculate the total change in height of each candle over the 6 hours it was burning.

Each hour, the height of each candle changes by -3/4 inch. So over 6 hours, the height of each candle changes by:

Since each candle started at 8 inches, the height of each candle at 11:00 PM will be:

This question is incomplete and should be provided as:

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The system of equations 2x + 5y = 1 and 3x - 4y = 2 has one solution.

A pair of equations system can be categorized as follows:

The system has no solution if the y-intercepts are varied but the slopes are the same.

The system has a single solution if the slopes are different.

The system has an endless number of solutions if the slopes and y-intercepts match.

The given system of equations are:

2x + 5y = 1

3x - 4y = 2

Write the equations in the standard form:

5y = -2x + 1

4y = 3x - 2

Here, the slope of equation 1 is -2 and the slope of equation 2 is 3.

We know that if the slope is different the system of equations has one solution.

Hence, the system of equations 2x + 5y = 1 and 3x - 4y = 2 has one solution.

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The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches has height of triangular base as 9√2 inches.

We are given that.

Length of equilateral triangle = a =18 inches

Base is an equilateral triangle.

height of the triangular base of the pyramid

h= a.cosθ

Each angle of equilateral triangle is equivalent to 60 degree

θ = 60/2

θ = 30 degree

Substitute the values,

Height of triangular base of the pyramid,

h=18.cos30

h = 18x √3/2 in

Using the value of

Cos30 = √3/2

Height of triangular base of the pyramid, h= 9√3 inches

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therefore, the function [tex]f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})}-7/12[/tex] whose tangent slope is given.

In Geometry, the tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.

We have the slope of the function as-

[tex]=\sqrt{\frac{1+\sqrt(x)}{8 \sqrt{x}}[/tex]

passes through the point (9,3/4).

Now, from the Fundamental Theorem of Calculus, we can integrate f′(x)

to get f(x). And then using the point that they gave us we can solve for the constant of integration. Do you know how to proceed from here? Do you know how to integrate that?

[tex]f'(x)=\sqrt{1+\sqrt{x}}/8 \sqrt{x}\\\\x=u^2\\\\2uf'(u^2)=\frac{\sqrt{1+u}}{{4}}}\\\\f(u^2)=\frac{1}{6}(1+u)\sqrt{1+u}+c\\\\f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})+c[/tex]

the tangent passes through the (9,3/4)

[tex]\frac{3}{4}=\frac{1}{6}(1+3)(\sqrt{1+3})+c\\\\3/4=8/6+c\\3/4-4/3=c\\\\c=-7/12[/tex]

therefore, the function [tex]f(x)=\frac{1}{6}(1+\sqrt{x})(\sqrt{1+\sqrt{x})}-7/12[/tex]

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The point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.

The confluence point of the elevations in a triangle is known as the orthocenter. The intersection of three or more lines, rays, segments, or planes is referred to as a point of concurrency.

This point will be equidistant from the sides of a triangle, as the central axis’s junction point is the center point of the triangle’s inscribed circle.

A point that is equally spaced from a triangle's sides contains all three of its angle bisectors simultaneously.

Therefore, the point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.

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The two sides of an inequality are not the same so inequality can never be true.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that the inequality is 2(3x - 1) +4> 6x + 2. The inequality will be solved as below;-

2(3x - 1) +4> 6x + 2

6x - 2 + 4 > 6x + 2

6x + 2 > 6x + 2

The two sides are equal so inequality can never be true.

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A congruent rectangle is a rectangle that has the same size and shape as another rectangle. In other words, two rectangles are congruent if they have the same length and width.

Since the rectangle is 4 inches by 7 inches, one of the dimensions represents the length and the other represents the width. The length and the width can be interchanged to form a different rectangle with the same area.

Since the rectangle is congruent to the 4-inch by 7-inch rectangle, the length and width of the rectangle are either 4 inches or 7 inches. Therefore, the length of segment JM can be either 4 inches or 7 inches.

So, there are two possible values for the length of segment JM: 4 inches and 7 inches.

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[tex]\frac{9}{20}[/tex] Quarts of lemonade concentrate are needed to make the lemonade for 24 people.

Given data :

For 40 people = 3 / 4 quart lemon + 6 and 2/3 quarts of water

For 24 people = ?

Multiply proportion the given :

[tex]\frac{3}{4}[/tex] x [tex]\frac{24}{40}[/tex] = [tex]\frac{9}{20}[/tex] Quarts

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Utilize only nematode-free plants that you buy from reputable nurseries to keep nematodes out of your garden.

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The best time to begin protecting a seedling crop from infection by nematodes is  at the time of ordering the seedlings.

Use only nematode-free plants that you buy from reputable nurseries to keep nematodes out of your garden. Move plants and soil away from nematode-infested areas of the garden to stop the spread of the parasite. Avoid letting irrigation water from plants that are infected run off since nematodes can also spread through this method.

Larvae go through four molts as they develop, with the third stage, the filariform larva, often being the infective stage.

Crop rotation is a cultural method of nematode management that has good potential. Even some cover crops generate compounds that are poisonous to worms. Finding a crop rotation that can starve out all of the nematodes in your soil, though, might be challenging if you have a variety of them there.

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Value of a and b make the solution of the equation x=-2 is a=1, b=1.

Given the equation: a(3-x)=-2x+b

If the solution of the equation = -2

Then to find the values of a and b, we substitute = -2 into the equation.

a(3-x) = -2x+b

a(3-(-2)) = -2(-2)+b

5a=4+b

= 5a-b=4

If we make the substitution a=1, b=1 into the abov 5(1)-1= 4 is true.

Therefore: a=1, b=1

The coefficients are located in front of the variables. For example, there are 2 pencils and 4 markers, if written in the equation is:

Pencil = x , marker = y

So the equation is 2x + 5y. So, because x and y are variables, the numbers 2 and 5 are coefficients.

Your question is incomplete but most probably your full question was:

Consider the equation a(3-x)=-2x+b

What value of a and b make the solution of the equation x=-2?

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https://brainly.com/question/30303182.

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