a group of seven people are attending the movies together. (a) two of the seven insist on sitting side-by-side. in how many ways can the seven be seated together in a row?

The lateral area of the cylinder is 24π square units.

To find the lateral area of the cylinder, we need to use the formula:

Lateral Area = Circumference of circular base × Height.

First, we will find the circumference of the circular base using the area given.
1. We know the area of the circular base is 36π square units.

The formula for the area of a circle is A = πr²,

where A is the area and r is the radius.
2. We are given A = 36π,

so 36π = πr².
3. Divide both sides by π to isolate r²:

36 = r².
4. Take the square root of both sides to find the radius:

r = 6 units.
5. Now that we have the radius, we can find the circumference of the circular base using the formula C = 2πr,

where C is the circumference.
6. Substitute r = 6 into the formula:

C = 2π(6) = 12π.
7. The circumference of the circular base is 12π units.
8. The height of the cylinder is given as 2 units.
9. Finally, we can find the lateral area using the formula Lateral Area = Circumference × Height.
10. Substitute C = 12π and H = 2 into the formula:

Lateral Area = 12π × 2 = 24π.

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The probability that a randomly selected point within the square falls in the red shaded area is approximately 0.2146 or about 21.46%.

To find the probability that a randomly selected point within the square falls in the red shaded area, we need to compare the area of the red shaded region to the area of the entire square.

Let the side length of the square be 2 units, and let the center of the circle be at the center of the square. Then, the radius of the circle is also 1 unit.

The area of the square is [tex](side length)^2[/tex] = [tex]2^2[/tex] = 4 square units.

The area of the circle is π[tex](radius)^2[/tex] = π[tex](1)^2[/tex] = π square units.

The red shaded area is the difference between the area of the square and the area of the circle, which is 4 - π square units.

Therefore, the probability that a randomly selected point within the square falls in the red shaded area is:

(red shaded area) / (area of the square) = (4 - π) / 4 ≈ 0.2146

So the probability is approximately 0.2146 or about 21.46%.

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The values of the sides are;

11. SR = 25

12. RU = 25

13. SU = 35.4

14. Perimeter = 100 units

15. Area = 625 square units

It is important to note that a square have 4 equal sides and 4 equal angles.

From the information given, we have that;

Line SR = line RU

But we have that;

SR = 2k + 7

RU = 3k - 2

Equate the sides, we have;

2k + 7 = 3k - 2

collect the like terms

2k - 3k = - 2 - 7

subtract the terms

-k = - 9

k = 9

Then, SR =2(9) + 7 = 25

RU = 3(9) - 2 = 25

The line SU is the hypotenuse side

Using the Pythagorean theorem

SU² = 25² + 25²

SU² = 625 + 625

SU = √1250

SU = 35. 4

15. The perimeter of a square is expressed as;

Perimeter = 4a

Perimeter = 4(25)

Perimeter = 100 units

16. The area of a square is expressed as;

Area = a²

Area = 25²

Area = 625 square units

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the altitude of the airplane would decrease by 1628 feet over a period of 37 seconds.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

To find the change in altitude, we need to multiply the rate of decrease by the time period:

change in altitude = rate of decrease × time period

So, in this case:

change in altitude = 44 feet/second × 37 seconds

change in altitude = 1628 feet

Therefore, the altitude of the airplane would decrease by 1628 feet over a period of 37 seconds.

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The equation that describes the relationship between the time a zebra runs at a speed and the distance it covers is y = 2/3(x).

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Assuming that the relationship between the time a zebra runs at a speed and the distance it covers is a linear one, we can use the formula for the equation of a straight line:

y = mx + b

where y is the distance covered, x is the time the zebra runs at a speed, m is the slope (i.e., the speed of the zebra), and b is the y-intercept (i.e., the distance covered when the zebra is not running).

From the table two points can be formed as (x, y) that are, (3, 2) and (6, 4)

Using these two points, we can find the slope of the line:

m = (y₂ - y₁)/(x₂ - x₁)

 = (4 - 2)/(6 - 3)

 = 2/3

Now as we have the slope m we can use it in point slope form, i.e.

y - y₁ = m(x - x₁)

Using the point (3, 2),

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

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

y  = 2/3(x) - 2 + 2

y  = 2/3(x)

Hence, the equation that describes the relationship between the time a zebra runs at maximum speed and the distance it covers is:

y  = 2/3(x)

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Complete question:

The relationship between the amount of time a zebra run at maximum speed in the distance it covers is shown.

Write an equation to describe this relationship.

[tex]\begin{array}{cccccccccc} &\frac{-1}{4}\left( -\frac{1}{2} \right)&\frac{1}{8}\left( -\frac{1}{2} \right)&\frac{-1}{16}\left( -\frac{1}{2} \right)&\frac{1}{32}\left( -\frac{1}{2} \right)\\ -\cfrac{1}{4}&\cfrac{1}{8}&-\cfrac{1}{16}&\cfrac{1}{32}&-\cfrac{1}{64}... \end{array}\hspace{5em}\stackrel{\textit{common ratio}}{r=-\frac{1}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\qquad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ r=-\frac{1}{2}\\ a_1=-\frac{1}{4} \end{cases}\implies \sum_{n=1}^{n=4}~-\frac{1}{4}\left( -\frac{1}{2} \right)^{n-1}[/tex]

Triangle ABC's sides are not equal in length, hence it's not an equilateral triangle.

It has three equal sides. The three angles are equal. Every edge of an equilateral is 60 degrees since the total of the inner angles equals 180 degrees. It has three regular sides and is a polygon. A vertex's height and median are represented by a single line.

A triangular with equally length sides is known as an equilateral in geometry. The three angles opposing the three equal sides are equal in size because the three are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle.

Using the distance formula, we can find the lengths of the three sides:

[tex]AB = \sqrt{((5 - 4)^2 + (5 - (-2))^2)} = \sqrt{(2^2 + 7^2)} = \sqrt{(53)}[/tex]

[tex]BC = \sqrt{((-1 - 5)^2 + (3 - 5)^2) } = \sqrt{((-6)^2 + (-2)^2)} = \sqrt{(40)}[/tex]

[tex]CA = \sqrt{((4 - (-1))^2 + (-2 - 3)^2)} = \sqrt{(5^2 + 5^2)} = \sqrt{(50)}[/tex]

Since AB, BC, and CA have different lengths, the triangle is not equilateral.

Therefore, the answer is: Triangle [tex]ABC[/tex] is not an equilateral triangle because its sides have different lengths.

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Since AB and AC have the same length, but BC has a different length, Therefore,  ΔABC is not an equilateral triangle.

Equilateral triangles are those with three sides that are all the same length.

In other words, all three sides of an equilateral triangle are of the same length, and all three angles within the triangle are also equal to 60 degrees.

Equilateral triangles are a type of regular polygon, which means that they have congruent sides and congruent angles.

Triangle ABC is not an equilateral triangle because its side lengths are not all equal.The lengths of the sides can be determined using the distance formula:

AB = √((5-4)² + (5-(-2))²) = √(1 + 49) = √(50)

BC = √((5-(-1))² + (5-3)²) = √(36 + 4) = √(40)

AC = √((4-(-1))² + (-2-3)²) = √(25 + 25) = √(50)

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The probability that the baseball player has exactly 1 hit in his next 7 at-bats is 0.2908, rounded to 4 decimal places.

It is a statistic that measures the performance of baseball players. It is the ratio of the number of hits to the number of at-bats.

Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1.

Static means the precise value of something, without approximation or estimation.

It is a process of approximating a number to a specific number of decimal places.

A baseball player has a batting average of 0.365. The probability that he has exactly 1 hit in his next 7 at-bats is to be found.

Step 1: Calculate the probability of getting a hit in one at-bat. The probability of getting a hit in one at-bat is equal to the batting average of the player.

P(hit) = 0.365

Step 2: Calculate the probability of not getting a hit in one at-bat. The probability of not getting a hit in one at-bat is equal to the difference between 1 and the batting average.

P(not hit) = 1 - 0.365 = 0.635

Step 3: Calculate the probability of getting exactly 1 hit in 7 at-bats. The probability of getting exactly 1 hit in 7 at-bats can be calculated using the binomial probability formula:

P(1 hit in 7 at-bats) = 0.2908 (rounded to 4 decimal places)

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Answer: I would say 21 feet.

Step-by-step explanation:

Bernard is 12 feet ahead of Austin

So add 12 feet to get to Austin first

Then add the 9 feet that is apart from Austin and Bernard

12+9 = 21

21 feet would be the answer

Hope this helps ! ^^

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Answer:

Either A or c

Step-by-step explanation:

Solving the probability and permutations, we get (a) 20,160. (b) Larry, Moe, Curly, and Shemp can be arranged in the four front seats in 24 ways, and the ILB block can be arranged with the remaining students in 720 ways, and (c) 1/280.

(a) The number of possible seating arrangements can be calculated using the formula for permutations of n objects taken r at a time: P(n,r) = n!/(n-r)!. In this case, there are 8 students and 8 desks, so there are 8! possible seating arrangements.

To find the number of days before a seating arrangement is repeated, we need to subtract 1 from this number (since the first day is a unique arrangement) and divide by 2 (since there are two possible ways to arrange the students in any given seating arrangement, by simply rotating the arrangement). So the number of days before a seating arrangement is repeated is (8! - 1)/2 = 20,160.

(b) Larry, Moe, Curly, and Shemp must occupy the four front seats, so we need to choose four of the remaining four desks for the other students to sit at. This can be done in 4!/(4-4)! = 4! = 24 ways.

(c) We can treat the block of three students (ILB) as a single object, and then arrange the five remaining objects (M, O, A, X, and the ILB block) in a row. The ILB block can be arranged in 3! = 6 ways, and the other five objects can be arranged in 5! = 120 ways.

So the total number of potential seating arrangements in which ILB remains together is 6 x 120 = 720.

(d) The probability that Larry, Moe, Curly, and Shemp are sitting in the front seats is the number of possible seating arrangements in which they occupy the four front seats (24, from part b) divided by the total number of possible seating arrangements ([tex]8![/tex], from part a). So the probability is 24/8! = 1/280.

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How can a telephone survey of 1000 randomly selected US adults provide evidence that more than 1 in 4 US adults believe in ghosts?The survey results provide evidence that more than one in four US adults believe in ghosts. The telephone survey was conducted on a random sample of 1000 US adults. The survey found that 31 percent of US adults believed in ghosts.

To determine whether more than one in four US adults believe in ghosts, the null and alternative hypotheses will be tested.The null hypothesis in this scenario is that less than or equal to 25% of US adults believe in ghosts. The alternative hypothesis is that more than 25% of US adults believe in ghosts.Therefore, the level of significance (α) will be determined.

The α level is typically set to 0.05. This means that the likelihood of making a type I error is 5%. Then, the z-score will be calculated as follows:z = (0.31 - 0.25) / sqrt[(0.25 x 0.75) / 1000]z = 2.83The obtained z-score will be compared to the critical z-value using a z-distribution table. The critical z-value is 1.96. Since the obtained z-score is greater than the critical z-value, the null hypothesis will be rejected. Therefore, there is evidence to suggest that more than one in four US adults believe in ghosts.

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The probability that a person who purchased the game did not see the advertisement is:0.659.

what is  probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probability is used in many areas, including statistics, mathematics, science, finance, and gambling.

In the given question,

To solve this problem, we will use Bayes' theorem, which allows us to update our beliefs about the probability of an event based on new information.

Let A be the event that a person has seen the advertisement, and B be the event that a person has purchased the game. We want to find the probability of A given B, i.e., the probability that a person who has purchased the game has also seen the advertisement.

We know that P(A) = 0.24 (24% of the market has seen the advertisement), P(B|A) = 0.42 (42% of those who see the ad have purchased the game), and P(~A|~B) = 0.93 (93% of those who have not seen the advertisement have not purchased the game).

We can use the complement rule to find P(B|~A), the probability of purchasing the game given that the person has not seen the advertisement:

P(B|~A) = 1 - P(~B|~A) = 1 - 0.93 = 0.07

Now we can use Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B) = P(B|A) * P(A) + P(B|~A) * P(~A)

Plugging in the values, we get:

P(B) = 0.42 * 0.24 + 0.07 * (1 - 0.24) = 0.2956

P(A|B) = 0.42 * 0.24 / 0.2956 = 0.3408

Therefore, the probability that a person who purchased the game did not see the advertisement is:

1 - P(A|B) = 1 - 0.3408 = 0.659

Rounded to the nearest thousandth, the answer is 0.659.

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Answer:

1.5 m

Step-by-step explanation:

Volume = base * height

12 = 8 * h

12/8 = h

1.5 = h

The sides of the parallelogram are thus congruent. Hence, the parallelogram is similar.

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another. We will see that they will superimpose, or be positioned entirely on top of, one another. This demonstrates the congruence of the two circles. The circles below may be put perfectly over one another and have the same radius, hence they are considered to be congruent.

For the parallelogram ESPR and ECTF, the scale factor is:

Scale factor = 9/3 = 3

The sides of the parallelogram are thus congruent. Hence, the parallelogram is similar.

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The surface area of the rectangular prism with a length of 4 units, a width of 3 units, and a height of 5 units is 94 square units.

To find the surface area of a rectangular prism, you need to add up the area of all six faces. The formula for the surface area of a rectangular prism is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism.

So, to find the surface area of a rectangular prism, you simply need to plug in the values for l, w, and h into this formula and solve.

For example, if the length of the rectangular prism is 4 units, the width is 3 units, and the height is 5 units, the surface area would be:

Surface Area = 2(4)(3) + 2(4)(5) + 2(3)(5)
Surface Area = 24 + 40 + 30
Surface Area = 94 square units

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Required corresponding sides are side AB corresponds to side A'B', side BC corresponds to side B'C', side AC corresponds to side A'C'

What is corresponding side?

In geometry, when two figures are similar, their corresponding sides are the sides that are in the same position and have the same relative orientation in each figure.

For example, consider two triangles ABC and DEF, where angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. If the length of AB is proportional to the length of DE, BC is proportional to EF, and AC is proportional to DF, then side AB corresponds to side DE, side BC corresponds to side EF, and side AC corresponds to side DF.

To list all the corresponding sides of two triangles ABC and A'B'C', we need to identify which side of triangle ABC corresponds to which side of triangle A'B'C'. Corresponding sides are those that are in the same position relative to each triangle.

We can identify the corresponding sides by comparing the positions of the vertices. For example, the side opposite vertex A in triangle ABC corresponds to the side opposite vertex A' in triangle A'B'C'. Similarly, the side opposite vertex B in triangle ABC corresponds to the side opposite vertex B' in triangle A'B'C', and so on.

Therefore, the corresponding sides are side AB corresponds to side A'B', side BC corresponds to side B'C', side AC corresponds to side A'C'.

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The point (1, 5) is a solution of the first equation, and is not a solution of the second one (and thus the system)

Here we want to see if the point (1, 5) is a solution of some given equations.

The first equation is:

d + s = 6

let's assume that the notation for the point is (d, s), then we can replace these values in the equation above to get:

1 + 5 = 6

6 = 6

So yes, the point is a solution here.

For the next equation we have:

10d + 28s = 78

Replacing the values:

10*1 + 5*28 = 78

150 = 78

So no, here is not a solution.

And the point is a solution of the system only if it is a solution of both of the equations, then the point is not a solution of the system,

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Answer:

534×10³

5340×10²

53400×10

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis C. is rejected

A one-tailed hypothesis test refers to a statistical test in which the alternative hypothesis is either greater than or less than the null hypothesis, but not both. Since the problem states that it is a one-tailed hypothesis test (upper tail), the alternative hypothesis, H1, will be a greater than or > sign. Hypothesis testing is the method of determining whether or not an assertion about a population parameter is consistent with sample data. A hypothesis test is conducted to assist in deciding between two competing hypotheses. One hypothesis is the null hypothesis (H0), which is a statement of the population parameter that is being tested.

In a hypothesis test, the null hypothesis is rejected if the test statistic falls in the rejection region. The test statistic, which measures the distance between a sample estimate and the null hypothesis, is used to assess whether or not the null hypothesis should be rejected. Reject the null hypothesis if the p-value is less than or equal to α. Since the p-value of 0.034 is less than the level of significance, α, of 0.05, the null hypothesis will be rejected, according to the question above. Therefore, option C is correct.

The Question was Incomplete, Find the full content below :

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. could be rejected or not rejected depending on the sample size.

b. could be rejected or not rejected depending on the sample mean.

c. is rejected.

d. is not rejected.

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Answer:

Step-by-step explanation:

Surface area of a cylinder = 2πr(r + h)

radiius = 1/2 diameter so the radius is 1/2 of 2 = 1

Surface are = 2(22/7)(1 )[(1 + 1.25)]

                     44/7 (2.25) = 99/7

This is for ONE muffin - mulitply by 6 to find out how much paper for

6 muffins,

6 × 99/7 = 594/7 = 84 6/7 in²

Answer:

Either plane XYS or plane Q

Step-by-step explanation:

They are the only points lying on the plane in general.

The tree's height changes 2.5ft bases per time.

The rate of change function is defined as the rate at which one volume changes relative to another volume. In simple terms, the rate of change is the quantum of change in one item divided by the corresponding quantum of change in another.

We can find the rate of change in the tree's height by calculating the slope of the line that represents the direct function relating the tree's height to the number of times since it was planted.

To do this, we can use the slope formula

Slope = ( change in height)/( change in time)

Let's choose the points

( 1,4.5) and( 4, 12)

Change in height = 12-4.5 = 7.5

Change of time = 4- 1 = 3

Slope = (7.5/ 3) = 2.5

So, the tree's height changes 2.5 bases per time.

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Alemu's net income after deducting income tax is 9,470 birrs per month, assuming he lives in Ethiopia and the income tax rates for the current tax year apply.

We must take into account the income tax rates in Alemu's nation for the current tax year in order to determine how much income tax he must pay. We cannot provide an exact response since we are unsure about Alemu's country of residence. The income tax rates in Ethiopia, where the first 6,000 birr of income are tax-free and the remaining amount is subject to progressive taxes, range from 10% to 30%, can be used as an example, though.

Alemu's monthly taxable income, assuming he resides in Ethiopia, would be 4,000 birrs (between 10,000 and 6,000). He must pay the following amount of income tax:

180 birr (10% of the first 1,800 birr)

15% of the following 1,800 birrs is 270 birrs.

80 birrs are 20% of the remaining 400 birrs.

Alemu would therefore pay 530 birrs in total income tax each month.

Alemu's net income would be 9,470 birrs after income tax. This is the sum of cash he would have on hand to cover personal costs, savings, investments, and any other debts. It is crucial to remember that the net income amount may change depending on a number of variables, including deductions for social security, health insurance, or any other needed legal payments.

In conclusion, assuming Alemu lives in Ethiopia and the income tax rates for the current tax year are applicable, Alemu's net income after income tax is 9,470 birrs each month.

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Answer:

Area of the rectangle - 144 in^2

Area of the circle - 28,26 in^2

Total shaded area - 115,74 in^2

Step-by-step explanation:

[tex]a(rectangle) = 18 \times 8 = 144 \: {in}^{2} [/tex]

[tex]a(circle) = \pi \times {r}^{2} = {3}^{2} \times \pi = 9\pi = 9 \times 3.14 = 28.26 \: {in}^{2} [/tex]

[tex]a(shaded) = a(rectangle) - a(circle)[/tex]

[tex]a(shaded) = 144 -28.26 = 115.74 \: {in}^{2} [/tex]

Answer:

Step-by-step explanation:

17f+1i

6f+5f+4f=15f

11i+4i+10i=25i     ---------> 2f+1i

1feet=12inch

Answer:

( 2q + 1 ) ( q + 3 )

Step-by-step explanation:

➟ 2q^2+7q+3

➟ ( 2q + 1 ) ( q + 3 )

The median of the samples can give an idea of the central tendency of the data and can help in making an inference about the population.

In this case, since the percent of students that bike to school varies from 20% to 50% in the samples, the median of the samples can provide an estimate of the median percent of students who bike to school in the population.

By analyzing the median of the samples, it may be possible to make an inference about the central tendency of the population, which could inform decisions about encouraging or improving biking to school.

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--The given question is incomplete, the complete question is given

"  a group of friends wants to know how many students bike to school. Survey Results In the samples, the percent of students that bike to school varies from 20% to 50% 19 20 21 22 14 15 16 17 18 Number of Students that Bike to School How can the median of the samples help you make an inference about the population? "--

The child should be given 8.75 mL of the medicine. option B

To determine the correct dosage, we first need to find out how much paracetamol the child needs based on their weight and then convert that amount to the appropriate volume of the medicine.

Calculate the required amount of paracetamol based on the child's weight:

Child's weight: 14 kg

Dosage: 15 mg per 2 kg of body weight

Required_paracetamol = (Child's weight / Dosage per kg) * Dosage

Required_paracetamol = (14 kg / 2 kg) * 15 mg

Required_paracetamol = 7 * 15 mg

Required_paracetamol = 105 mg

The child needs 105 mg of paracetamol.

Convert the required paracetamol amount to the appropriate volume of the medicine:

Medicine concentration: 120 mg of paracetamol per 10 mL

Required_volume = (Required_paracetamol / Medicine concentration) * 10 mL

Required_volume = (105 mg / 120 mg) * 10 mL

Required_volume = 0.875 * 10 mL

Required_volume = 8.75 mL

The child should be given 8.75 mL of the medicine.

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