If the volume of the smaller cylinder is 24 in3, what is the volume of the larger cylinder?
A.
48 in3
B.
96 in3
C.
72 in3
D.
120 in3

The surface area of the prism is [tex]169cm^{2}[/tex]

A measurement of an object's whole space is, in fact, its surface area. The total area around a three-dimensional form makes up its surface area.

The whole surface area of a three-dimensional shape is referred to as "surface area". By summing the areas from each face, it is possible to determine the surface area of a cuboid with six rectangular faces.

Alternatively, you may use the following formula to name this box's dimensions:

The surface area is made up of [tex]2lh, 2lw, 2hw[/tex]. (SA). The amount of space occupied by the surface of a three-dimensional shape is measured in terms of surface area.

Given

[tex]S_{1} = 7 cm, S_{2} = 7 cm, S_{3} = 9 cm[/tex]

[tex]base = 9 cm, h = 6 cm, l = 5 cm[/tex]

[tex]area = ( perimeter * length) + 2* base area\\[/tex]

[tex]perimeter= S_{1} +S_{2} +S_{3}[/tex]

[tex]P = 7 cm +7 cm+9 cm\\= 23 cm[/tex]

∴[tex]area= (Perimeter* l) +bh[/tex]

[tex]A = (23*5) +( 9*6)\\= 115 cm + 54cm\\= 169 cm^{2}[/tex]

Therefore the surface area of the prism is [tex]169cm^{2}[/tex]

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Answer: a. x ≤7 b. x<6

Step-by-step explanation:

a. 6x-3≤4x+11

6x-4x≤11+3

2x≤14

x≤7

b. x<-x+12

x+x<12

2x<12

x<6

Answer:

Step-by-step explanation:

The correct explicit rule is f(n) = 50 + 30n

An explicit rule is a mathematical formula that directly gives the n-th term of a sequence or the value of a function for a given input, without the need to find other terms first. It can be expressed using variables, constants, and operations such as addition, subtraction, multiplication, and division.

To determine who is correct, we need to first understand the meaning of the variables in the explicit rules.

Let n be the number of days the car is rented for.

Let f(n) be the cost of renting the car for n days.

The deposit is a one-time charge and is not dependent on the number of days rented. Therefore, the constant term in the explicit rule should be 50.

Now, for each day rented, the cost is $30. This means that the cost for n days should be 30n.

So the correct explicit rule is:

f(n) = 50 + 30n

Therefore, Kevin is correct with the explicit rule f(n) = 50 + 30(n-1). This is because we subtract 1 from n since the deposit is charged only once at the beginning and is not included in the daily rate.

Suzanne's explicit rule, f(n) = 80 + 30(n-1), adds an extra $30 to the cost of renting the car, which is not correct.

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The x and y intercepts are some of the features of the graph and their values are -7 and 6 respectively.

The graph of the function f(x) = 2log₂ (x + 8) has the following features:

Domain: The domain of the function is all real numbers greater than -8, because the argument of the logarithmic function must be positive.

Vertical asymptote: The graph has a vertical asymptote at x = -8, because the logarithmic function is not defined for x = -8.

X-Intercept: The function has an x-intercept at (-7, 0), which can be found by setting f(x) = 0 and solving for x.

Y-Intercept: The function has a y-intercept at (0, 2log₂ 8), which is 6.

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The area of the shaded region in this shape that has a rectangle and a circle within is 27.73 square cm.

The area of the rectangle can be found using the formula:

Area rectangle = length × width

Area rectangle = 8 cm × 7 cm = 56 square cm

The area of the circle can be found using the formula:

Area circle = π × radius^2

Given the radius is 3 cm, we have:

Area circle = π × (3 cm)^2 = 9π square cm  =  28.27 square cm

Now, to find the area of the shaded region (which is the rectangle minus the circle):

Area shaded = Area rectangle - Area circle

Area shaded = 56 square cm - 28.27 square cm = 27.73 square cm

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An equation to represent the mass of nickel-63, in milligrams, as a function of 9.8 [tex]e^{(-.00001899 d)}[/tex]  .

What's a linear equation in  calculation?

A linear equation is an algebraic equation of the form y =  mxb. involving only a constant and a first- order( linear) term, where m is the  pitch and b is the y- intercept. sometimes, the below is called a" linear equation of two variables," where y and x are the variables.

The equation for half life is

n = no  [tex]e^{ (-kt)}[/tex]

Where no is the initial amount of a substance , k is the constant of decay and t is the time

no = 9.8

1/2 of that amount is 4.9 so n = 4.9 and t = 100 years

4.9 = 9.8 [tex]e^{ (-k 100)}[/tex]

Divide each side by 9.8

1/2 = [tex]e^{-100k}[/tex]

Take the natural log of each side

ln(1/2) = ln([tex]e^{(-100k)}[/tex]

ln(1/2) = -100k

Divide each side by -100

-ln(.5)/100 = k

Our equation in years is

n = 9.8  [tex]e^{(ln.5)/100 t)}[/tex]

Approximating ln(.5)/100 =-.006931472

n = 9.8 [tex]e^{(-.006931472 t) }[/tex] when t is in years

Now changing to days

100 years = 100*365 days/year

36500 days

Substituting this in for t

4.9 = 9.8 [tex]e^{(-k 36500)}[/tex]

Take the natural log of each side

ln(1/2) = ln([tex]e^{(-36500k))}[/tex]

ln(1/2) = -36500k

Divide each side by -100

-ln(.5)/36500 = k

Our equation in years is

n = 9.8  [tex]e^{(ln.5)/36500 d)}[/tex]

Approximating ln(.5)/365=-.00001899

n = 9.8 [tex]e^{(-.00001899 d)}[/tex]  when d is in days

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Answer:

The answer to your problem is, A semicircle is half of a circle

What is Semicircle?

If a circle is cut into half along the diameter, that half-circle is called a semicircle. The two halves are of equal measure. A semicircle can also be referred to as a half-disk and it represents a circular paper plate folded into halves. There is one line of symmetry in the semicircle that is considered as the reflection symmetry. Since the semicircle is the half of a circle which is 360°, hence the arc of the semicircle always measures 180°.

Or if you have no time imagine

You have an entire pizza you tell you other friend “ Lets half the pizza “ You do that next you can tell your friend that this is a semicircle and we both have semicircles your friend might not know but know they know . .

Interesting story I know but that is our answer.

Thus the answer to your problem is, A semicircle is half of a circle

Answer:

le demi-cerclec'est une figure plate délimitée par un diamètre de la circonférence et l'un des deux arcs de cercle plats déterminés par ledit diamètre. De cette façon, un demi-cercle est bordé par un demi-circonférence, qui se compose d'un arc de cercle plat et d'un segment droit qui joint les extrémités de l'arc de cercle plat.

Step-by-step explanation:

Answer:

[tex] {( - 7)}^{2} - 4(6)( - 1) = 49 + 24 = 73[/tex]

Josephine did not distribute the -1 correctly. -4(6)(-1) = 24.

Here are the correct solutions:

x = (7 + √73) / 12

x = (7/12) + (1/12)√73

The given expression 14 - 0.6t  is representing the amount of fuel that has been remaining after "t" days of use.

14 - 0.6t is an algebraic expression. The car had 14 gallons of fuel at first and after each day of use, the car used 0.6 gallons which means that the amount of fuel that is remaining in the car at the end of the day is continuously decreasing by 0.6 per day. So, after "t" days of use, the car must have 0.6×t gallons of fuel, and the amount of fuel that remains in the car will be 14 - 0.6t.

When the warning light comes on, the remaining fuel is 1.5 gallons or less. So we can set the expression 14 - 0.6t to 1.5 and solve for t to find the number of days it takes for the warning light to come on:

14 - 0.6t = 1.5

0.6t = 12.5

t = 20.83

Therefore, it takes approximately 20.83 days of use for the warning light to come on.

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To simplify this expression, we can follow the order of operations:

1. Simplify the expression inside the parentheses first:

(3x2^y - 2 - 7x2^(y-2))

2. Combine like terms:

3x2^y - 7x2^(y-2) - 2

3. Rewrite the denominator with a common base of 2:

5x2^(y-2)

4. Divide the numerator by the denominator:

(3x2^y - 7x2^(y-2) - 2) ÷ (5x2^(y-2))

5. Simplify by dividing each term in the numerator by 5x2^(y-2):

(3x2^y)/(5x2^(y-2)) - (7x2^(y-2))/(5x2^(y-2)) - (2/(5x2^(y-2)))

6. Simplify the exponents:

(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)

So the final simplified expression is:

(3/5)x^(y-2) - (7/5) - (2/5)x^(-2)

The number such that twice a number is fourteen is 7

If we let the number be "x", we can write the given information as an equation:

2x = 14

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides by 2:

2x/2 = 14/2

x = 7

Therefore, the number is 7.

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Answer: The length, breadth, and height of the rectangular prism are:

Length = 3x + y cm

Breadth = 2x + 2y cm

Height = 3y cm

The volume of the rectangular prism is given by the formula:

Volume = Length x Breadth x Height

Substituting the values, we get:

Volume = (3x + y) x (2x + 2y) x (3y)

Simplifying the expression, we get:

Volume = 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3

Therefore, the volume of the rectangular prism is 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3 cubic cm.

Step-by-step explanation:

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.835, 0.866), option B.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Confidence intervals are used by statisticians and other analysts to comprehend the statistical significance of their estimates, conclusions, or forecasts. One cannot reasonably assert that a result from data produced by testing or experimentation is to be ascribed if a confidence interval involves the value of zero.

Confidence interval for Population Proportion is given as below:

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Where, p is the sample proportion, Z is critical value, and n is sample size.

We are given

x = number of items/observations of interest = 3010

n = sample size = 3539

Best Point Estimate = p = x/n

= 3010/ 3539

= 0.850522747

Confidence level = 99%

Critical Z value = 2.5758

(We can find this z-value by using R, excel, z-table, Ti-83/84 calculator, software, etc.)

[Excel command: =NORMSINV(1 - (1 - 0.99)/2)]

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Confidence Interval = [tex]0.850522747 \pm 2.5758 \sqrt{\frac{0.850522747(1-0.850522747)}{3539} }[/tex]

Confidence Interval = 0.850522747 ± 2.5758 x 0.0060

Confidence Interval = 0.850522747 ± 0.015

Lower limit = 0.850522747 - 0.015 = 0.835

Upper limit = 0.850522747 + 0.015 = 0.866

Confidence interval = (0.835, 0.866)

B. (0.835, 0.866).

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Complete question:

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Select one answer 10 points Suppose we take a poll (random sample) of 3539 students classified as Juniors and find that 3010 of them believe that they will find a job immediately after graduation What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation A. (0.839, 0.862) B.O(0.835, 0.866) C. (0.845, 0.857) D.O(0.841, 0.86)

Answer:

x = -30

y = 18

Step-by-step explanation:

-2,4x - 3y is equal to both 18 and y

Since there are two equal signs, we have a double equation (we can write each equation seperately and put them in a system):

{y = -2,4x - 3y,

{-2,4x - 3y = 18;

.

We move 3y to the left, so we change the sign to the opposite:

{4y = -2,4x, / : 4 (put y and 3y together)

{-2,4x - 3y = 18;

.

y = -0,6x,

-2,4x - 3y = 18;

Replace y in the 2nd equation with its value from the 1st equation:

-2,4x - 3 × (-0,6x) = 18

-2,4x + 1,8x = 18

-0,6x = 18 / : (-0,6)

x = -30

y = -0,6 × (-30) = 18

there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

How to find the volume ?

To find the volume of the remaining wood, first find the volume of the cube-shaped block. To find the volume of a cube use V = s³ where s is the side of the cube. In this case, s = 8 inches, so V = 8³ = 512 cubic inches.

Then, find the volume of the hole using the side lengths of the hole and the same depth as the cube, which is 8 inches. The hole has side lengths of 5 inches, so its volume is V = 5² * 8 = 200 cubic inches.  

To find how much wood is left after cutting out the hole, subtract the volume of the hole from the volume of the cube:

512 - 200 = 312 cubic inches

Therefore, there are 312 cubic inches of wood left after cutting out a square hole with side lengths of 5 inches from a cube-shaped block with side lengths of 8 inches.

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Answer:

the scale factor is 2

Step-by-step explanation:

Take each x and y value and multiply it by 2 and you get the coordinates for the image.

Helping in the name of Jesus.

The scale factor is 2. Point B goes from (3,3) to (6,6). 6/3 is 2. Similar triangles have the same shape and the three angles' measurements are likewise the same.

Their sides are the only thing that differs. The scale factor, which is what is referred to here as this, is the ratio of one triangle's sides to those of another triangle. To calculate the scale factor for the smaller triangle to the bigger triangle, divide one of the sides in the bigger triangle by its corresponding side in the smaller triangle. In the example, the scale factor would be 2 if you divided 40 by 20.

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Answer:

All of the above.

Step-by-step explanation:

It is 2 and 3 because they are next to each other and when added together equal to 180 degrees.

It is 5 and 8 for the same reason and so on for the rest.

Answer:

All of the above

Step-by-step explanation:

Supplementary means two angles that add up to 180 degrees.

now, since all of the angles are beside each other, it's automatic that they add up to 180 degrees.

I'm guessing you are learning about transversals and rules on lines.

I did this ixl as well and I understand why you're confused

based on my guessing on what you are learning in school, 4 and 5 would also be supplementary because they are consecutive interior angles

I don't know if you learned this term but that's the best I can explain it.

Answer: wassup, so basically the price just increases by like 20% because of how many more people are coming thats the best way i can say to help u understand it. hope I helped a bit

Therefore, the cost of the meal was $15.

Describe the dollar sign.

The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol ), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred is cifro.

The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).

Let’s call the cost of the meal x.

Karen gave the waiter a tip of three dollars which is 1/5 of the total cost of the meal.

This can be written as:

3 = (1/5) * x

Multiplying both sides by 5 gives:

15 = x

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The median in this situation is the average of the two middle values, which are 48 and 76: (48 + 76) / 2 = 62

When a dataset is sorted in order of magnitude, the median, a statistical measure of central tendency, reflects the middle value of the dataset. The values must first be arranged from lowest to highest in order to determine the median (or largest to smallest). The median is the middle value when the dataset has an odd number of values. The median is indeed the average of the two middle values when the dataset does have an even number of values.

given

We must first determine the values of the first and third quartiles in order to determine the interquartile range (IQR) of a data set.

The median of the lower half of the data set makes up the first quartile (Q1), and the median of the higher half, the third quartile (Q3).

For this data set's Q1 and Q3, you can:

Sort the information from smallest to largest:

23 33 45 48 76 78 94 94

Determine the data set's overall median.

The median in this situation is the average of the two middle values, which are 48 and 76: (48 + 76) / 2 = 62 .

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79 hours will it take for one person to harvest the entire strawberry patch.

The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.

Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.

The strawberry patch's measurements must first be changed from decameters (dam) to meters.

1 decameter (dam) = 10 meter

Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.

The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.

The strawberry patch's area is therefore:

Area of strawberry patch = length × width = 17 m × 14 m = 238 m²

We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:

= a number of hours needed to harvest the complete patch.

The total harvesting time is  = 79.33 hours nearly equal to 79

Therefore, it would take one person 79 hours to gather the complete strawberry patch.

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The probability that the part can be assembled in 7 minutes or less is 0.2592.

To solve the problem, we need to use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the random variable X (in this case, the time required to assemble the part) is less than or equal to a certain value x.

The CDF of the exponential distribution is given by:

F(x) = [tex]1 - e^{(-λx)}[/tex]

where λ is the rate parameter of the exponential distribution, which is equal to 1/mean. In this case, the mean is 14 minutes, so λ = 1/14.

To find the probability that the part can be assembled in 7 minutes or less, we plug x = 7 and λ = 1/14 into the CDF formula: F(7) = [tex]1 - e^{(-(1/14)*7)} \approx 0.2592[/tex]

So, there is a chance of about 25.92% (rounded to four decimal places) that the part can be assembled in 7 minutes or less.

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Answer:

x ≥ 5

Step-by-step explanation:

Let's represent the number of action figures in a complete set by the variable "x".

Carlos has 5 complete sets plus 4 individual figures, which is a total of:

5x + 4

Josh has 3 complete sets plus 14 individual figures, which is a total of:

3x + 14

The problem states that Carlos has at least as many action figures as Josh, so we can set up the inequality:

5x + 4 ≥ 3x + 14

Simplifying this inequality, we can subtract 3x from both sides:

2x + 4 ≥ 14

Then, we can subtract 4 from both sides:

2x ≥ 10

Finally, we divide both sides by 2:

x ≥ 5

Therefore, the inequality that represents how many action figures can be in a complete set is:

x ≥ 5

The exact dimensions of the rectangular prism are:

Width = [tex]((\sqrt{282} + \sqrt{1975})/3)/2[/tex]

Height = [tex](141 - (\sqrt{282} + \sqrt{1975})/3) / 2[/tex]

(I may have formatted my response incorrectly. If so, please let me know. I will update my response accordingly.)

The rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

To find the dimensions of the rectangular prism with a fixed surface area of 282 square units and maximum volume, we need to use the fact that the volume of a rectangular prism is given by V = lwh and the surface area is given by SA = 2lw + 2lh + 2wh. Since we want to maximize the volume, we can use the surface area formula to solve for one of the dimensions in terms of the other two, and then substitute into the volume formula to obtain a function of two variables.

We can then take the derivative of this function and set it equal to zero to find the maximum volume. Solving this equation, we obtain l = w = 9 and h = 14, which gives the desired dimensions.

Therefore, the rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

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Step-by-step explanation:

These are the steps to this Question...

Answer: Dog show 1 was a dog show for smaller dogs while dog show 2 was a dog show for larger dogs.

Step-by-step explanation:

To find out how much Diana paid, we need to first calculate the total cost of the pizza, the chicken wings, the salad, the drinks, and the tip, and then divide that total by 2, since Diana is paying for half.

The total cost of the pizza, chicken wings, salad, and drinks is:

$13.02 (pizza) + $12.99 (chicken wings) + $6.25 (salad) + $3.25 (Diana's drink) + $3.25 (Carrie's drink) = $38.76

Adding the tip of $10.00 to this total gives:

$38.76 + $10.00 = $48.76

Half of this total is:

$48.76 / 2 = $24.38

Therefore, Diana paid $24.38 for her food, half the cost of the pizza, and half the tip.

Diana paid $19.65, which includes $9.02 for her share of the pizza, $5.00 for her share of the tip, $12.99 for chicken wings and $3.25 for a drink. Below is the working on the sketchpad.What is shown on the sketchpad?It is shown on the sketchpad below how Diana paid for her lunch at the restaurant.

The items that she paid for are indicated in the table below the sketchpad.What is the calculation for the amount Diana paid for lunch?Diana's share of the pizza is half of $13.02, which is $6.51. Adding $6.51 to the cost of the chicken wings and a drink gives a total of $22.75 for the cost of the lunch.

After adding the tip to the total cost of the lunch, we have $32.75 ($22.75 + $10.00 tip). To find the amount Diana paid, we need to find half of the total cost of the lunch and half of the tip.The following calculation shows the amount Diana paid:Her share of the cost of the lunch was $11.37 (($6.51 + $12.99 + $3.25)/2).Her share of the tip was $5.00/2, which is $2.50.The amount Diana paid for her food, plus her share of the cost of the pizza and tip is therefore $13.87 ($11.37 + $2.50).

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Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

A graph is a visual representation of data that is used to show the relationship between two or more variables. Graphs are commonly used in mathematics, science, engineering, and other fields to help visualize and analyze data.

There are many different types of graphs, each with its own unique features and applications. Some of the most common types of graphs include:

Line graphs: Line graphs are used to show the trend or change in a variable over time. They consist of a set of data points that are connected by straight lines.

Bar graphs: Bar graphs are used to compare data across different categories or groups. They consist of rectangular bars that are proportional in height to the values they represent.

Pie charts: Pie charts are used to show the proportion or percentage of each category within a larger whole. They consist of a circle that is divided into sections, with each section representing a different category.

If Leroy set the price at $3.99, then based on the given chart, Demand will be 1,500 units whereas Supply will be 500 units. Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

Therefore, Correct answer is Option (b), The demand will exceed the supply.

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The complete question is:

Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller.

A scientific experiment known as a randomised controlled trial (RCT) includes randomly allocating participants or subjects to various groups, often a treatment group and a control group. The intervention or therapy under test is administered to the treatment group while being withheld from the control group. Researchers can isolate the impact of the intervention on the desired outcome and reduce the impacts of confounding variables by randomly allocating individuals to these groups. To evaluate the effectiveness of therapies and treatments, RCTs are often employed in the medical, psychological, and other domains.

In the given experiment, the fertiliser appeared to be helpful in boosting plant development for this specific type of seedling since the plants that got it grew noticeably taller than the ones that did not.

Hence, option 4 is correct.

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