A machine can fill 24 jars in 30 seconds. How many jars can the machine fill in 4 minutes?

For the logistic equation of

white-tailed deer population, [tex]A = \frac{ 180}{1 + 8e^{-0.35t}}[/tex],

a) Total 36 deer expected in the herd after 2 years.

b) The carries capacity is equals to 180.

c) Total 4 years for the herd to grow to 60 deer.

The logistic equation is one of the foremost models of population growth which has both continuous as well as discrete versions. The continuous logistic equation has the following form,

[tex]f(t) = \frac{ L}{1+ ae^{−bt}}[/tex]

where, L = maximum possible value of the curve, called the carrying capacity.

a= related to the midpoint of the curve

b = related to the steepness of the curve or the growth rate of the population. We have, the deer population with respect to time is modeled by the logistic equation,

[tex]A = \frac{ 180}{1 + 8e^{-0.35t}}[/tex]

a) when t = 2 year, we have to calculate the value of A. So, [tex]A = \frac{ 180}{1+ 8e^{−0.35× 2}}[/tex]

[tex]A = \frac{ 180}{1+ 8e^{−0.70}}[/tex]

= 36.20 ~ 36

b) The maximum possible value of deers is equals to 180.

c) now, we determine the number of years, when A = 60 deers

so, [tex]60 = \frac{ 180}{1+ 8e^{−0.35t}}[/tex]

[tex]\frac{ 180}{60} = 1 + 8e^{−0.35t}[/tex]

[tex]8e^{−0.35t} = 2[/tex]

[tex]e^{−0.35t} = 0.25[/tex]

Taking natural logarithm both sides

=> - 0.35 t = ln( 0.25)

=> t = 3.960 ~ 4

Hence, required value is 4 years.

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Complete question:

a herd of 18 white-tailed deer is introduced to a coastal island where there had been no deer before. their population is predicted to increase according to A=180/(1+8e−0.35t), where where a is the number of deer expected in the herd after t years. (a) determine the number of deer, rounded to a whole number, after 2 years: (b) determine the carrying capacity, rounded to a whole number: (c) determine the number of years, rounded to a whole number, for the herd to grow to 60 deer?

18 shirts can be stitched using 40m of cloth, and 130cm of cloth will remain.

To stitch one shirt, 2m 15cm (or 215cm) of cloth is needed.

Therefore, the number of shirts that can be stitched using 40m (or 4000cm) of cloth can be found by dividing the total cloth by the cloth required to stitch one shirt:

Number of shirts = 4000cm / 215cm per shirt

Number of shirts = 18.60 (rounded to two decimal places)

Since we can't stitch a part of a shirt, we can only stitch 18 shirts using 40m of cloth.

To find the amount of cloth that will remain after stitching 18 shirts, we can multiply the cloth required to stitch one shirt by the number of shirts stitched, and then subtract this amount from the total cloth available:

Cloth used for 18 shirts = 18 shirts x 215cm per shirt

Cloth used for 18 shirts = 3870cm

Cloth remaining = 4000cm - 3870cm

Cloth remaining = 130cm

Therefore, 18 shirts can be stitched using 40m of cloth, and 130cm of cloth will remain.

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The Fundamental Theorem of Calculus states that if a function f is continuous on the closed interval [a,b] and F is the antiderivative of f on [a,b], then the definite integral of f from a to b is equal to F(b) - F(a).

For the first question, we can use the Fundamental Theorem of Calculus and the Chain Rule to find the derivative:

ddx∫x−1(3t5−t)30dt = (3x5-x)/30

For the second question, we can use Part 2 of the Fundamental Theorem of Calculus:

d/da ∫a^3 (7t^2 + 6) dt = 7a^6 + 6a^3

Then, we can use the Chain Rule to find the derivative of the function with respect to t:

d/dt (7a^6 + 6a^3) = 42a^5(da/dt) + 18a^2(da/dt)

Since the problem gives us da/dt = 20, we can substitute to find:

d/dt (7a^6 + 6a^3) = 8400a^5 + 3600a^2

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The fractions of the total current carried by R1, R2, and R3 are 1/60, 1/24, and 1/18, respectively.

To determine the fraction of the total current carried by resistors R1, R2, and R3, we need to add their individual currents and calculate the ratio to the total current.

Given resistors:

R1: 1/5

R2: 1/2

R3: 2/3

Total current = 12A

To calculate the fraction of total current carried by each resistor, we can add the individual currents and divide by the total current:

Fraction of total current carried by R1:

(1/5) / 12 = 1/60

Fraction of total current carried by R2:

(1/2) / 12 = 1/24

Fraction of total current carried by R3:

(2/3) / 12 = 1/18

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The variance of Y = e^X, where X be a continuous random variable, is :

(C) 1300.

The variance of Y can be found using the formula Var[Y] = E[Y^2] - (E[Y])^2.

First, we need to find E[Y]. We have Y = e^X, and X follows a uniform distribution in the interval [0,5]. The probability density function (PDF) of X is f(x) = 1/5 for 0 <= x <= 5, and 0 otherwise.

Using the transformation method, we can find the PDF of Y as follows:

g(y) = f(x) / |dy/dx|, where y = e^x

dy/dx = e^x, so |dy/dx| = e^x (since e^x is always positive)

g(y) = (1/5) / e^x = (1/5y) for 0 <= y <= e^5, and 0 otherwise.

Now we can find E[Y]:

E[Y] = ∫(0 to e^5) y g(y) dy = ∫(0 to e^5) (y/5y) dy = (1/5) ∫(0 to e^5) 1 dy = (1/5) e^5

Next, we need to find E[Y^2]:

E[Y^2] = ∫(0 to e^5) y^2 g(y) dy = ∫(0 to e^5) (y^2/5y) dy = (1/5) ∫(0 to e^5) y dy = (1/10) e^10

Therefore, Var[Y] = E[Y^2] - (E[Y])^2 = (1/10) e^10 - [(1/5) e^5]^2 = 1300.

Hence, the answer is (C) 1300.

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The best description of the spread and distribution of the data is

The data is bimodal with an approximate range of 6.

This might mean that most students owned a pet that was either 2 or 7 years old.

Option C is the correct answer.

We have,

Based on the given information,

The line plot shows the age of pets owned by a group of students.

The dots are above certain ages, indicating the frequency of pets owned by students that are of that age.

Since there are two dots above 1, 5, and 6 and four dots above 2 and 7, it can be inferred that these ages have the highest frequency of pets owned.

Therefore, the data is bimodal.

The approximate range of 6 means that the difference between the maximum and minimum values is approximately 6.

Thus,

The best description of the spread and distribution of the data is

The data is bimodal with an approximate range of 6.

This might mean that most students owned a pet that was either 2 or 7 years old.

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The area of the entire rectangle as an expression is x² + 8x + 12

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

The figure

To express the area of the entire rectangle as an expression, we calculate the area of the individual rectangles in the bigger rectangle

using the above as a guide, we have the following:

Area 1 = x * x = x²

Area 2 = x * 2 = 2x

Area 3 = 6 * x = 6x

Area 4 = 6 * 2 = 12

So, we have

Total area = x² + 2x + 6x + 12

Evaluate

Total area = x² + 8x + 12

Hence, the total area is x² + 8x + 12

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The given connected planar graph has 15 edges and 8 faces.

To find the number of edges in a connected planar graph with the given degrees of vertices, we can use the formula known as Euler's formula. Euler's formula states that for a connected planar graph, the number of vertices (V), edges (E), and faces (F) are related by the equation V-E+F=2.

Using the given information, we can calculate the total number of vertices as 9. The sum of the degrees of these vertices is 30, which means the total number of edges can be calculated as (30/2) = 15.

To find the number of faces, we can use another formula: F = E - V + 2. Substituting the values we know, we get F = 15 - 9 + 2 = 8. Therefore, the given connected planar graph has 15 edges and 8 faces.

It's worth noting that the degrees of the vertices play an important role in determining the structure of a planar graph. In particular, the fact that all the vertices in this graph have low degree means that it is likely to have a simple and straightforward structure. By contrast, if the degrees were all high, the graph would be more complex and harder to visualize.

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Kellen will pay approximately $11.07 in interest over 6 months if she continues to pay $100 per month.

To calculate the interest Kellen will pay in 6 months, we first need to calculate her monthly interest fee, that's 4.9% APR divided by using 12 months:

monthly interest fee = 4.9% / 12 = 0.4083%

We also want to calculate the full amount of time Kellen will take to pay off her debt, which is 6 months. we will then use this records to calculate the closing stability on her credit score card after 6 months of paying $100 in step with month:

overall payments = 6 x $100 = $600

remaining stability = $5,877 - $600 = $5,277

Next, we want to calculate the each day periodic charge, that's the monthly interest rate divided with the aid of the variety of days in a billing cycle (35 days):

daily periodic rate = 0.4083% / 35 = 0.0117%

Finally, we are able to use the method for finance charge to calculate the quantity of interest Kellen pays in 6 months:

Finance charge = closing balance x daily periodic rate x number of days in 6 months

Finance charge = $5,277 x 0.0117% x 180

Finance charge = $11.07

Therefore, Kellen will pay approximately $11.07 in interest over 6 months if she continues to pay $100 per month.

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1) The period of function is, 2.5

And, The amplitude of the function is, 3

2) The period of function is, 2

And, The amplitude of the function is, 2

3) The period of function is, 2.5

And, The amplitude of the function is, 5

We have to given that;

Graphs are shown in figure.

Now,

1) The period of function is,

⇒ 3 - (- 2) / 2

⇒ 5 /2

⇒ 2.5

And, The amplitude of the function is,

⇒ 3

2) The period of function is,

⇒ 2 - (- 2) / 2

⇒ 4 /2

⇒ 2

And, The amplitude of the function is,

⇒ 2

3) The period of function is,

⇒ 3 - (- 2) / 2

⇒ 5 /2

⇒ 2.5

And, The amplitude of the function is,

⇒ 5

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The relationship between the confidence interval and the margin of error is that the margin of error determines the width of the confidence interval.

The margin of error is a measure of the uncertainty associated with a sample statistic, such as the mean or proportion. It represents the maximum amount by which the sample statistic may differ from the true population parameter, with a certain degree of confidence. The confidence interval, on the other hand, is a range of values that is likely to contain the true population parameter, with a certain degree of confidence. The width of the confidence interval is determined by the margin of error.

Therefore, none of the options given in the question is correct. The width of the confidence interval is typically calculated by multiplying the margin of error by a factor that depends on the desired level of confidence. For example, a 95% confidence interval is typically calculated by multiplying the margin of error by 1.96, which corresponds to a confidence level of 95%. In summary, the margin of error determines the width of the confidence interval, but the relationship between the two is not as simple as any of the options given in the question.

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1. The given equation is [tex]27x^8y^5/9x^4y^5[/tex]

Upon simplification it becomes [tex]3[x^8x^{-4}][y^5y^{-5}][/tex]

Final equation will be [tex]3x^4[/tex]

2. The given equation is [tex]8x^8y^3/8x^4y^7[/tex]

Upon simplification it becomes [tex][x^8x^{-4}][y^3y^{-7}][/tex]

Final equation will be [tex]x^4/y^4[/tex]

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The measure of angle KLM is 46°. Therefore, option B is the correct answer.

Given that, LK bisects ∠JLM. If m∠JLK = (13x - 6)° and m∠KLM = (11x + 2)°.

Since, LK bisects ∠JLM

m∠JLK=m∠KLM

(13x - 6)°=(11x + 2)°

13x-11x=2+6

2x=8

x=4

Substitute x=4 in m∠KLM = (11x + 2)°, we get

m∠KLM = 46°

Therefore, option B is the correct answer.

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3x-1 of the following must be odd .The correct  option (d) .

The properties of odd and even integers. An integer is even if it is divisible by 2, and odd if it is not divisible by 2.

Let's simplify the given equation: x = 50y + 69
We can rewrite this as: x = (49y + 50y) + 19

Notice that 49y + 50y is an even integer (since it is the sum of two even integers) and adding 19 to an even integer will result in an odd integer. Therefore, x is always odd.

Now, let's look at each option:

a. xy = (50y + 69)y = 50y^2 + 69y
This could be either even or odd, depending on the value of y.

b. x + y = (50y + 69) + y = 51y + 69
This could be either even or odd, depending on the value of y.

c. x + 2y = (50y + 69) + 2y = 50y + 2y + 69 = 52y + 69
This could be either even or odd, depending on the value of y.

d. 3x - 1 = 3(50y + 69) - 1 = 150y + 206
This must be odd, because an odd integer (3) multiplied by an odd integer (x) and then subtracting an odd integer (1) will always result in an odd integer.

e. 3x + 1 = 3(50y + 69) + 1 = 150y + 208
This could be either even or odd, depending on the value of y.

Therefore, the only option that must be odd is (d) 3x - 1.

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The vertex form of h(x) is h(x) = -1/2(x - 2)² + 18.

The standard form of h(x) is h(x) = -1/2(x)² + 2x + 16.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex, we can determine the value of a as follows:

f(x) = a(x - h)² + k

16 = a(0 - 2)² + 18

16 - 18 = 4a

-2 = 4a

a = -1/2

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = -1/2(x - 2)² + 18

For the standard form, we have:

h(x) = -1/2(x - 2)² + 18

h(x) = -1/2(x - 2)(x - 2) + 18

h(x) = -1/2[(x² - 4x + 4) + 18]

h(x) = -1/2(x)² + 2x + 16

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The equation for the drop factor is:

d = 1000

We can solve the given equation for d as follows:

Y = (v/t) * d

Multiplying both sides by t/v, we get:

(Y * v) / t = d

Substituting the given values, we get:

d = (50 * 1200) / 60

= 1000

Therefore, the equation for the drop factor is:

d = 1000

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Consider the equation that gives the flow rate of medicine administered intravenously, where

Y is the flow rate in milliliters per minute,

⚫v represents volume in milliliters,

⚫t represents time in minutes, and

d represents the drop factor.

Y = v/t * d

Enter an equation for which the solution is the drop factor of the medicine when the volume is 1200 milliliter flow rate is 50 milliliters per minute, and the time is 60 minutes.

The Greek letter alpha (α) represents the probability that is the level of significance in statistical hypothesis testing and helps control the risk of making Type I errors.

The Greek letter alpha (α) represents the level of significance in statistical hypothesis testing. It is a predetermined threshold that determines the probability of rejecting the null hypothesis when it is true. In other words, it measures the willingness of a researcher to make a Type I error, which is the incorrect rejection of a true null hypothesis.

The level of significance (α) is typically set before conducting the hypothesis test and is commonly chosen at 0.05 (5%) or 0.01 (1%). It represents the maximum probability that a researcher is willing to accept for making a Type I error.

When performing hypothesis tests, the p-value (probability value) is compared to the level of significance (α) to determine whether the null hypothesis should be rejected or not. If the p-value is smaller than the level of significance, the null hypothesis is rejected in favor of the alternative hypothesis.

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To be classified as rain, water droplets that fall from a cloud must have a minimum diameter of 0.5 millimeters.

To be classified as rain, water droplets that fall from a cloud must have a minimum diameter of 0.5 millimeters (0.02 inches).

In geometry, the diameter of a circle is the part of a straight line that goes through the center and ends in the circle. It can also be defined as the longest chord of a circle. These two concepts also apply to the diameter of a sphere.

In modern usage, the length d of a diameter is also called a diameter. In this sense, we speak of diameter rather than diameter (referring to the line segment itself), because all diameters of a circle or sphere have the same length, which is twice the radius r.

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The total cost of ordering 3 bacon egg & cheese sandwiches with delivery from Dunkin Donuts during the sale is $11.25.

As, the cost of one bacon egg & cheese sandwich is $2.75, and there is a delivery fee of $3.00.

So, Total cost = (Cost per sandwich x Number of sandwiches) + Delivery fee

Total cost = ($2.75 x 3) + $3.00

Total cost = $8.25 + $3.00

Total cost = $11.25

Therefore, the total cost of ordering 3 bacon egg & cheese sandwiches with delivery from Dunkin Donuts during the sale is $11.25.

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Exactly 84 days will pass until Ross and Annie do their chores on the same day again.

We need to find the least common multiple (LCM) of 12 and 21 to determine the number of days until Ross and Annie do their chores on the same day.

One way to find the LCM is to list the multiples of each number until we find the smallest multiple that they have in common. For 12, the multiples are:

12, 24, 36, 48, 60, 72, ...

For 21, the multiples are:

21, 42, 63, 84, ...

The smallest multiple that they have in common is 84, so Ross will mow the lawn and Annie will bathe the dog on the same day every 84 days.

Therefore, 84 days will pass until Ross and Annie do their chores on the same day again.

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Answer:

2/5

Step-by-step explanation:

This is true simply because 5-3 =2, so 2 out of 5 students don't make honor role.

Explanation of vector addition, subtraction, and scalar multiplication is shown below.

We have to given that;

To explain vector addition, subtraction, and scalar multiplication.

Now, We know that;

Vector Addition:

To add two vectors in component form, add the first components together and the second components together.

Example,

⇒ ⟨a, b⟩+⟨c, d⟩=⟨a + c, b + d⟩

Vector subtraction;

The subtraction of vectors is the same as adding the reverse or inverse of one vector to another vector. T

Scalar Multiplication:

To multiply a vector in component form by a scalar, multiply each component by the scalar.

Example,

⇒ c⟨a , b⟩ = ⟨ca, cb⟩

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Rounding this amount to the nearest whole number, Kathy can contribute a maximum of $16,560 to her SEP IRA for 2018.

The maximum amount Kathy can contribute to a Simplified Employee Pension (SEP) IRA for 2018 is based on her net self-employment income. To calculate this, we subtract her expenses from her revenues:

Net self-employment income = Revenues - Expenses

= $138,000 - $55,200

= $82,800

The maximum contribution limit for a SEP IRA is 20% of the net self-employment income. Therefore, Kathy can contribute:

Maximum contribution = 20% of Net self-employment income

= 20% of $82,800

= $16,560

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The measure of central angle of the circle is x = 130°

Given data ,

Let the measure of the major arc of the circle is = 295°

So , the measure of the minor arc = 65°

Now , Central Angle = 2 x Angle in other segment

On simplifying , we get

Central angle x = 2 ( 65 )

x = 130°

Hence , the measure of x of circle is 130°

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The change that would increase the range of the ball shown in the original figure is (a) Increase v0 above 30 m/s.


The range of a projectile (the horizontal distance it travels) can be affected by its initial velocity (v0) and launch angle (θ). The formula for the range is:

Range = (v0² * sin(2θ)) / g

Where g is the acceleration due to gravity (approximately 9.81 m/s²).

(a) Increasing the initial velocity (v0) would directly increase the range, as the range is directly proportional to the square of the initial velocity.

(b) Reducing the initial velocity (v0) would decrease the range, as the range is directly proportional to the square of the initial velocity.

(c) Reducing θ from 60 degrees to 45 degrees could increase the range, but it would depend on the initial velocity. The optimal angle for maximum range is 45 degrees, assuming there is no air resistance.

(d) Reducing θ from 60 degrees to less than 30 degrees would decrease the range, as the projectile would be launched at a less optimal angle.

(e) Increasing θ from 60 degrees up toward 90 degrees would decrease the range, as the projectile would be launched more vertically and have less horizontal distance to cover.


To increase the range of the ball shown in the original figure, the best option would be (a) Increase v0 above 30 m/s, as increasing the initial velocity directly affects the range in a positive manner.

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The solution of the equation based on the information given is x = 0.

Combine the like terms on both sides of the equation.

X + 3 - 3 = 2x + 3 => X = 2x + 3 - 3

Simplify the expression on the right side by combining the like terms.

X = 2x

Subtract "2x" from both sides of the equation to isolate the variable "x" on one side.

X - 2x = 0

Simplify the expression on the left side by combining the like terms.

-x = 0

x = 0

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X +3–3= 2x +3

The angle between the ski run and the horizontal when x = 10 m is approximately 14.04°.


1. First, we need to find the slope of the curve y = 0.01x^2 - 0.4x + 4 at x = 10 m. To do this, we'll take the derivative of y with respect to x:
dy/dx = 0.02x - 0.4

2. Now, plug in x = 10 m into the derivative equation to find the slope at that point:
dy/dx = 0.02(10) - 0.4 = 0.2 - 0.4 = -0.2

3. The slope is the tangent of the angle between the ski run and the horizontal. To find the angle, we'll take the arctangent of the slope:
Angle = arctan(-0.2) ≈ -11.31°

4. Since we want the angle between the ski run and the horizontal, we'll take the absolute value of the angle:
|Angle| = |-11.31°| ≈ 11.31°


The angle between the ski run and the horizontal when x = 10 m is approximately 11.31°.

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The value of the angles in the lines is as follows:

m∠x = 155°

m∠y = 146°

When lines intersect, angle relationships are formed such as vertically opposite angles, adjacent angles, etc.

Therefore, let's find the x and y in the line intersection as follows:

m∠a = 34 degree

m∠b = 59 degree

m∠y = 180 - 34(sum of angles on a straight line)

m∠y = 146 degrees

Therefore,

m∠x = 180 - (180 - (180 - 59) - 34)

m∠x = 180 - (180 - 121 - 34)

m∠x = 180 - 25

m∠x = 155 degrees.

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The volume of the figure is 71487 ft³.

We have,

The figure has two shapes.

The volume of a cone is 1/3 x πr²h

The volume of a semisphere is 1/2 x 4/3 x πr³

Now,

Cone:

Radius = 39 ft

Height = 42 ft

Volume.

= 1/3 x π x 39² x 42

= 31941 π ft³

Semisphere:

Radius = 39 ft

Volume.

= 1/2 x 4/3 x π x 39³

= 39546 π ft³

Now,

The volume of the figure.

= 31941 + 39546

= 71487 ft³

Thus,

The volume of the figure is 71487 ft³.

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In a stratified sample of 50 students, approximately 10 Year 7 students are picked.

We have,

The total number of students in the population.

= 135 (Year 7) + 150 (Year 8) + 120 (Year 9) + 154 (Year 10) + 132 (Year 11)

= 691

The proportion of Year 7 students in the population.

= 135/691

= 0.1957

To calculate how many Year 7 students are picked in a sample of 50 students, we multiply the sample size by the proportion of Year 7 students in the population.

= 50 × 0.1957

= 9.785

Rounding to the nearest whole number.

= 10

Therefore,

In a stratified sample of 50 students, approximately 10 Year 7 students are picked.

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