Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 2.5 to create triangle A′B′C′. Determine the vertex of point B′.

B′(7.5, −2)
B′(3, −5)
B′(−7.5, −2)
B′(7.5, −5)

By Stoke's theorem, the flux of the vector field F across surface S is equal to the line integral of F over the boundary curve C: Flux = ∮C (F ⋅ dr) = 20

To find the flux of the vector field F = 3i + 2j + 4k across the surface S using Stoke's theorem, we first need to find the curl of F: Curl(F) = (∂Fz/∂y - ∂Fy/∂z)i - (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k Since Fz = 4, Fy = 2, and Fx = 3, all their partial derivatives are constants: Curl(F) = (0)i - (0)j + (0)k = 0

Now, let's find the line integral over the boundary curve C: ∮C (F ⋅ dr) = ∫₀^4 3dx + ∫₀^2 2dy + ∫₀^1 4dz We can integrate each part separately: ∫₀^4 3dx = 3(4) - 3(0) = 12 ∫₀^2 2dy = 2(2) - 2(0) = 4 ∫₀^1 4dz = 4(1) - 4(0) = 4

Now, add up the results: ∮C (F ⋅ dr) = 12 + 4 + 4 = 20

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-12x will be the value of the linear portion in this quadratic equation. Thus, option A is correct.

A linear portion will establish a condition that the value should have the power of the variable as 1. j

In the given equation 7[tex]x^{2}[/tex] - 12x + 16 = 0 which is a trinomial equation:

7[tex]x^{2}[/tex] will have a power of 2

- 12x have a power of 1

16 has a power of o.

The condition of the linear equation states that the value of power should be equal to one. Therefore, option A is correct.

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The question is incomplete, Complete question probably will be  is:

Select the term that describes the linear portion in this quadratic equation.

7[tex]x^{2}[/tex] - 12x + 16 = 0

a. -12x

b. 7x2

c. 16

The function f(x) is concave downward on the interval (-∞, -1).

a. To determine the interval on which the function f(x) = x³+ 3x² - 9x + 14 is increasing, we need to find the values of x for which the derivative of f(x), denoted as f'(x), is positive.

Taking the derivative of f(x) with respect to x, we get:

f'(x) = 3x² + 6x - 9.

Setting f'(x) > 0, we have:

3x² + 6x - 9 > 0.

Factoring the left-hand side of the inequality, we get:

3(x² + 2x - 3) > 0.

Now, solving for x, we have:

x²+ 2x - 3 > 0.

To find the values of x that satisfy this inequality, we can factor the quadratic expression on the left-hand side:

(x + 3)(x - 1) > 0.

From this expression, we can see that the inequality is satisfied when x < -3 or x > 1. Therefore, the function f(x) is increasing on the intervals (-∞, -3) and (1, ∞), and including the endpoints, the interval on which f(x) is increasing is [-∞, -3] U [1, ∞].

b. To determine the interval on which the function f(x) is concave downward, we need to find the values of x for which the second derivative of f(x), denoted as f''(x), is negative.

Taking the second derivative of f(x) with respect to x, we get:

f''(x) = 6x + 6.

Setting f''(x) < 0, we have:

6x + 6 < 0.

Solving for x, we get:

x < -1.

Therefore, the function f(x) is concave downward on the interval (-∞, -1), including the endpoint, the interval on which f(x) is concave downward is [-∞, -1].

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The probability that Anna picks out two red sweets and eat them is equal to (x² - x)/870 in terms of x.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 30

number of red sweets = x

number of blue sweets = 30 - x

probability of Anna picks out 2 red sweets = x/30 × (x -1)/29

probability of Anna picks out 2 red sweets = (x² - x)/870

Therefore, the probability that Anna picks out two red sweets and eat them is equal to (x² - x)/870 in terms of x.

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∫ g(x) dx = A∫ g(x) dx + B = 1∫ g(x) dx - 33.6. We can simplify this to ∫ g(x) dx = ∫ g(x) dx - 33.6.

Using the given information, we can set up a system of two equations in two unknowns, let's say A and B:

10A = 10

47A + B = 13.4

Solving for A in the first equation, we get A = 1. Now we can substitute that into the second equation to solve for B:

47(1) + B = 13.4

B = -33.6

Therefore, we have found that ∫ g(x) dx = A∫ g(x) dx + B = 1∫ g(x) dx - 33.6. We can simplify this to ∫ g(x) dx = ∫ g(x) dx - 33.6.

This may seem contradictory, but it simply means that there is no unique solution for the integral of g(x), given the information we have. It is possible that we made an error in our calculations, but if not, we would need additional information about g(x) to determine its integral with certainty.

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The standard deviation of wait time is 13.8564.

The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 25 minutes and 73 minutes. We have to find the standard deviation of the wait time.

The square root of the variance of a random variable, sample, statistical population, data collection, or probability distribution is its standard deviation.

The standard deviation in statistics is a measure of the degree of variation or dispersion in a set of values.

A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.

S² = (73 - 25)²/12

S² = (48)²/12

S² = 192

S = √192

S = 13.8564

Hence, The standard deviation of wait time is 13.8564.

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complete question:

the length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 25 minutes and 73 minutes. what is the standard deviation of wait time? group of answer choices

The problem asks for the number of different samples of size 2 that can be selected from a population of size 10. To solve this problem, we can use the formula for the number of combinations of n objects taken r at a time, which is given by nCr = n!/(r!(n-r)!), where n is the size of the population and r is the size of the sample.

In this case, we have n=10 and r=2, so the number of different samples of size 2 that can be selected from a population of size 10 is given by 10C2 = 10!/(2!(10-2)!) = 45. Therefore, there are 45 different samples of size 2 that can be selected from a population of size 10.

Another way to think about this problem is to consider that when selecting a sample of size 2 from a population of size 10, we can choose the first element from any of the 10 objects in the population, and then choose the second element from the remaining 9 objects in the population (since we can't choose the same object twice).

Therefore, the total number of different samples of size 2 that can be selected is 10 x 9 = 90. However, since the order in which we choose the elements of the sample doesn't matter, we need to divide by 2 (the number of ways to arrange 2 elements), giving us a total of 45 different samples of size 2.

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Complete question:

How many different samples of size 2 can be selected from a population of size 10?

The interval and radius of convergence for the power series  is (-1/2, 3/2) and the radius of convergence is not inclusive of its boundary.

The interval of convergence for a power series is the range of values of x for which the series converges. It can be found using various tests, such as the ratio test, root test, or alternating series test.

Based on the ratio test, the radius of convergence for the power series is:

r = lim(k→∞) |a_{k+1}/a_k|

= lim(k→∞) |(k+2)/(2(k+1))|

= 1/2

Since the ratio test guarantees convergence for |x - c| < r, where c is the center of the power series, we know that the interval of convergence is:

(-1/2, 3/2)

Note that 1 is included in the interval because the power series converges at x = 1 (as the terms all become 0), and the radius of convergence is not inclusive of its boundary.

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(a) The average value of f(x) = 3x - 2 over the interval [2,4] is 1.

(b) The average value of f(x) = 2x^2 - 2x + 2 over the interval [1,2] is 5/3.

To find the average value of a function f(x) over an interval [a,b], we use the formula:

Average value of f(x) over [a,b] = (1/(b-a)) * Integral(a to b) of f(x) dx

(a) For f(x) = 3x - 2 over the interval [2, 4], we have:

Average value of f(x) over [2,4] = (1/(4-2)) * Integral(2 to 4) of (3x-2) dx

= (1/2) * [(3/2)x^2 - 2x] from 2 to 4

= (1/2) * [(3/2)*(4^2) - 2(4) - (3/2)*(2^2) + 2(2)]

= (1/2) * [12 - 8 - 6 + 4]

= 1

Therefore, the average value of f(x) = 3x - 2 over the interval [2,4] is 1.

(b) For f(x) = 2x^2 - 2x + 2 over the interval [1,2], we have:

Average value of f(x) over [1,2] = (1/(2-1)) * Integral(1 to 2) of (2x^2 - 2x + 2) dx

= (1) * [(2/3)x^3 - x^2 + 2x] from 1 to 2

= (2/3)*(2^3 - 1^3) - (2^2 - 1^2) + 2(2-1)

= (2/3)*7 - 3 + 2

= 5/3

Therefore, the average value of f(x) = 2x^2 - 2x + 2 over the interval [1,2] is 5/3.

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To calculate the number of pizza combinations available at the shop, we need to multiply the number of options for each category. 16 toppings x 3 crusts x 2 cheese options = 96 possible pizza combinations. Therefore, there are 96 different pizza options available at the shop.

To calculate the total number of pizza combinations available at the shop, you'll want to use the multiplication principle. This states that you can find the total number of possible combinations by multiplying the number of options for each variable.
In this case, you have:
- 16 different toppings
- 3 types of crust
- 2 different cheese options
To calculate the total number of combinations, simply multiply these values together:
16 toppings * 3 crusts * 2 cheeses = 96 possible pizza combinations
So, there are 96 different pizza combinations available at the shop.

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An advantage of stem-and-leaf plots compared to most frequency distributions is that provide more information about the distribution of the data.

Stem-and-leaf plots offer several advantages over most frequency distributions.

One advantage is that stem-and-leaf plots provide a more detailed representation of the data than frequency distributions.

They allow you to see the individual data values and their magnitudes, which can provide more information about the distribution, such as the spread, central tendency, and outliers.

Additionally, stem-and-leaf plots can be easier to read and interpret than frequency distributions, especially for small data sets.

They can reveal patterns and trends in the data that might not be apparent in a frequency distribution.

Finally, stem-and-leaf plots can be used to compare different data sets or to identify similarities or differences within a single data set.

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Using the expression 220 - a, The correct answer is 200 bpm, 189 bpm & 172 bpm. We can calculate the maximum heart rate for the given ages as follows:

For a person who is 20 years old:

Maximum heart rate = 220 - 20 = 200 bpm

Answer: 200 bpm

For a person who is 31 years old, the equation for calculating the heart rate

Maximum heart rate = 220 - 31 = 189 bpm

Answer: 189 bpm

For a person who is 48 years old:

Maximum heart rate = 220 - 48 = 172 bpm

Answer: 172 bpm

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The amount of money that Gina will earn after working 40 hours is given as follows:

C. $250.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

From the table, the constant is given as follows:

k = 93.75/15 = 125/20 = 6.25.

Hence the equation is:

y = 6.25x.

Then the amount earned working 40 hours is given as follows:

y = 6.25 x 40

y = $250.

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1) The height of the arrow after two seconds is 27.8 meters

2) The time it takes for the arrow to hit the ground after it is fired is approximately 3.27 seconds.

3) The time when the arrow is 10 meters in the air is approximately 0.63 seconds.

1) To find the height of the arrow after 2 seconds, we need to substitute t = 2 in the equation:

h(2) = -9.8(2)² + 32(2) + 3

h(2) = -39.2 + 64 + 3

h(2) = 27.8

2) To find the time it takes for the arrow to hit the ground, we need to find the value of t when h(t) = 0. This is because when the arrow hits the ground, its height is zero. So we can set h(t) = 0 and solve for t:

-9.8t² + 32t + 3 = 0

Using the quadratic formula, we get:

t = (-32 + √(32² - 4(-9.8)(3))) ÷ (2(-9.8))

t = (-32 +√(1280.4)) ÷ (-19.6)

t = 3.27

3) To find the time when the arrow is 10 meters in the air, we need to solve the equation h(t) = 10 for t:

-9.8t² + 32t + 3 = 10

-9.8t² + 32t - 7 = 0

Using the quadratic formula, we get:

t = (-32 +√(32² - 4(-9.8)(-7))) ÷ (2(-9.8))

t = (-32 + √(1033.6)) ÷ (-19.6)

t = 0.63

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The complete question is:

An archer shoots an arrow up into the air the height h(t) in meters of the arrow after t seconds is modeled by h(t) = -9.8t^2 + 32t + 3

1) What is the height of the air after two seconds?

2) How long will it take for the air to hit the ground after it is fired?

3) At what time will the arrow be 10 m in the air?

Answer:

im pretty sure the answer is 7

The given statement "– = If g(x) = x5, then lim lim g(x) – g(2) = 80. X - 2 x - 2" is False because the limit does not exist.

We have:

g(x) = [tex]x^5[/tex]

g(2) = [tex]2^5[/tex] = 32

We want to evaluate:

lim lim (g(x) - g(2))

x → 2 x - 2

Using algebra, we can rewrite the expression as:

lim lim [tex](x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)[/tex]

x → 2 x - 2

We can see that the denominator approaches 0 as x approaches 2, while the numerator approaches a nonzero value. Therefore, the limit does not exist, and the statement is false.

Note that we can also use L'Hôpital's rule to evaluate the limit, which gives the same result:

lim lim (g(x) - g(2))

x → 2 x - 2

= lim lim ([tex]5x^4[/tex])

x → 2 1

= 80

However, this is incorrect, since L'Hôpital's rule can only be used if both the numerator and denominator approach 0 or infinity. In this case, only the denominator approaches 0, while the numerator approaches a nonzero value.

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To eliminate the parameter and find the Cartesian equation of the curve, we first need to know the parametric equations for x and y.

For example, let's say the parametric equations are:

x = 1 + t
y = √t

To eliminate the parameter t, we can solve for t in one of the equations and substitute that into the other equation. Solving for t in the x equation:

t = x - 1

Now, substitute this into the y equation:

y = √(x - 1)

This is the Cartesian equation of the curve: y = √(x - 1). To sketch the curve, start at the point (1, 0) and trace it in the direction of increasing x as the parameter t increases. The curve will be an upward-opening square root function, beginning at (1, 0) and extending towards the right.

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The surface area of the regular pyramid is 178.3 mm² if the area of the base is 43.3 mm².

The surface area of a regular pyramid can be calculated using the following formula

Surface Area = Base Area + (1/2) x Perimeter of Base x Slant Height

Base area = 43.3 mm²

Perimeter of base = 10 + 10 + 10 = 30 mm

Slant height = 9 mm

Substitute the values in the formula, we get the surface area

= 43.3 + 1/2 x 30 x 9

= 43.3 + 15 x 9

= 43.3 + 135

= 178.3 mm²

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

"Use the net to find the surface area of the regular pyramid."

The formula for the number of cells after t days, given that 200 cells are present at t = 0 is [tex]N(t) = 40(3^t - 1) + 200\;ln(3)[/tex], whereas the number of cells present after 11 days is approximately 7,085,864.

The given differential equation [tex]N'(t) = Ae^{kt}[/tex] describes the rate of increase in the number of diseased cells N(t) at time t, where A is the rate of increase at time 0 and k is a constant. The solution to this differential equation is  [tex]N(t) = (A/k) \times e^{kt} + C,[/tex] where C is an arbitrary constant that can be determined from an initial condition.

a. Using the given information, A = 40 and N'(5) = 120. Substituting these values into the equation [tex]N'(t) = Ae^{kt}[/tex], we get:

[tex]120 = 40e^{(5k)}[/tex]

Solving for k, we have:

k = ln(3)

Substituting A = 40 and k = ln(3) into the equation for N(t), and using the initial condition N(0) = 200, we get:

[tex]N(t) = (40/ln(3)) \times e^{(ln(3)t)} + 200[/tex]

Simplifying this expression, we obtain:

[tex]N(t) = 40(3^t - 1) + 200ln(3)[/tex]

b. To find the number of cells present after 11 days, we substitute t = 11 into the expression for N(t) that we obtained in part a:

[tex]N(11) = 40(3^{11} - 1) + 200ln(3)[/tex]

Simplifying this expression, we get:

[tex]N(11) = 40(177146) + 200ln(3) \approx 7,085,864[/tex]

Therefore, the number of cells present after 11 days is approximately 7,085,864.

In summary, the given differential equation [tex]N'(t) = Ae^{kt}[/tex] describes the rate of increase in the number of diseased cells N(t) at time t, and the solution to this equation is [tex]N(t) = (A/k) \times e^{kt} + C,[/tex]  where C is an arbitrary constant that can be determined from an initial condition.

We used this equation to find a formula for the number of cells after t days, given A, k, and an initial condition, and used it to find the number of cells present after 11 days.

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The bearing of L from N is 343°.

We have,

The bearing of M from L is 103⁰.

So, bearing from L to N opposite side

= 180 - (103 + 60)

= 180 - 163

= 17

Then, the bearing of L from N

= 360 - 17

= 343°

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The variance in the dependent variable can be explained by the variance in the independent variable 66.67%.

To find the variance in the dependent variable that can be explained by the variance in the independent variable, we need to first calculate the coefficient of determination (R-squared).

The R-squared value is a statistical measure that determines the proportion of the variation in the dependent variable that can be explained by the independent variable.
R-squared is calculated as the ratio of the explained variation (SSR) to the total variation (SST).

Therefore, we can calculate the R-squared as follows:
R-squared = SSR/SST = 24/36 = 0.67
This means that 67% of the variation in the dependent variable can be explained by the variation in the independent variable.
To find the variance in the dependent variable that can be explained by the variance in the independent variable, we need to multiply the R-squared value by the total variance in the dependent variable (SST).

Therefore, we can calculate the variance explained by the independent variable as follows:
Variance explained = R-squared * SST = 0.67 * 36 = 24.12
Therefore,

The variance in the dependent variable that can be explained by the variance in the independent variable is 24.12.

This means that the independent variable can explain 24.12 units of variation in the dependent variable, while the remaining 11.88 units of variation are due to other factors not accounted for by the independent variable.

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One day, the store sells a total of 260 fruits. If apples are 45% of the total number of fruits sold, 117 apples were sold.

To find the number of apples sold, we need to first determine what 45% of 260 is.

We can do this by multiplying 260 by 0.45 (or dividing 260 by 100 and then multiplying by 45). This gives us:

260 x 0.45 = 117

So, 117 apples were sold.

To understand how we got this answer, it's helpful to understand what percentages are. A percentage is a way of expressing a fraction or portion of a whole as a fraction of 100. For example, 45% is the same as 45/100 or 0.45.

To find the number of apples sold, we used this percentage to determine what fraction of the total number of fruits sold were apples. We did this by multiplying the total number of fruits sold by the percentage (expressed as a decimal). This gave us the number of apples sold.

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An equation that could be used as a line of best fit to approximate the data in the scatterplot is y = 0.601x + 21.757.

In order to determine an equation for the line of best fit that models the data points contained in the graph (scatter plot), we would have to use a graphing calculator (Microsoft Excel).

Based on the scatter plot (see attachment) which models the relationship between the x-values and y-values, an equation for the line of best fit is given by:

y = 0.601x + 21.757

In conclusion, we can reasonably infer and logically deduce that the scatter plot most likely indicates a linear relationship between the x-values and y-values.

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To minimize z subject to the given equation, we need to carry out Phase 1 of the Simplex Method. In Phase 1, we introduce artificial variables to convert the inequality constraints into equations.

First, we rewrite the given equation in standard form as follows:

X1 + 3x2 + 5x3 - 2xy + 7x7 = 20

Next, we introduce artificial variables u1, u2, u3, and u4 for the four inequality constraints:

X1 + x2 + 2x3 + u1 = 0
-x2 + 2x3 + u2 = 0
-x1 - x3 + u3 = -1
x7 + u4 = 2

We then form the initial tableau:

   BV  X1  x2  x3  x7  u1  u2  u3  u4  b
    u1   1   1   2   0   1   0   0   0   0
    u2   0  -1   2   0   0   1   0   0   0
    u3  -1   0  -1   0   0   0   1   0   1
    u4   0   0   0   1   0   0   0   1   2
     z   0   0   0   0   0   0   0   0   0

We choose u1, u2, u3, and u4 as the basic variables since they correspond to the artificial variables in the constraints. The objective function z is zero in the initial tableau since it does not include the artificial variables.

We then use the Simplex Method to find the optimal solution for the initial tableau. After a few iterations, we obtain the following optimal tableau:

   BV  X1  x2  x3  x7  u1  u2  u3  u4  b
    x2   0   1   2   0   1   0   0  -1   0
    u2   0   0   4   0   1   1   0  -1   0
    u3   0   0   1   0   1  -1   1  -1   1
    u4   0   0   0   1   1  -2   2  -2   2
     z   0   0   0   0   4   1   1   1   4

The optimal solution is x1 = 0, x2 = 0, x3 = 0, x7 = 2, with a minimum value of z = 4. We can then use this solution to carry out Phase 2 and obtain the optimal solution for the original problem.

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The equation that best represents the graph is given as follows:

A. y = 200x.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

For the graph in this problem, when x increases by 1, y increases by 200, hence the constant is given as follows:

k = 200.

Then the equation is:

y = 200x.

The graph is given by the image presented at the end of the answer.

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The point estimate of the proportion of women who trust recommendations made on Pinterest is 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is 0.60

A 95% confidence interval estimate of the difference between the proportion of women and men who trust recommendations made on Pinterest is (0.809, 0.2791).

The point estimate of the proportion of women who trust recommendations made on Pinterest is:

= 117 / 150

= 0.78.

The point estimate of the proportion of men who trust recommendations made on Pinterest is:

= 102 / 170

= 0.60

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No, the use of the binomial distribution may not be appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten.

The binomial distribution assumes that the trials are independent, there are only two possible outcomes (success or failure), and the probability of success remains constant throughout the trials. In the case of consuming alcoholic beverages, the assumption of independence may not hold, as one person's decision to consume alcohol may influence another person's decision. Additionally, the probability of consuming alcohol may not remain constant throughout the sample, as some people may have stronger tendencies or preferences for drinking than others.

A more appropriate distribution for this scenario may be the hypergeometric distribution, which takes into account the finite population size (i.e. the total number of 18-20 year olds from which the sample is drawn) and the varying probabilities of success (i.e. the varying number of individuals in the population who consume alcohol).

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The other point where the tangent line is horizontal is (-5, 17).

To find where the tangent line is horizontal, we need to find the value of t that corresponds to that point on the curve.

First, we can find the derivative of y with respect to x using the chain rule:

dy/dx = dy/dt / dx/dt = (-30 sin(t)) / (5(cos(t) - sin(t))) = -6 tan(t)

Now we need to find the value of t that makes the derivative equal to zero, which is where the tangent line is horizontal:

-6 tan(t) = 0

tan(t) = 0

t = 0, π

So we need to find the corresponding values of x and y for t = 0 and t = π.

When t = 0, we have:

x = 5(sin(0) + cos(0)) = 5

y = 47 - 15cos²(0) - 30sin(0) = 32

So one point where the tangent line is horizontal is (5, 32).

When t = π, we have:

x = 5(sin(π) + cos(π)) = -5

y = 47 - 15cos²(π) - 30sin(π) = 17

So the other point where the tangent line is horizontal is (-5, 17).

To learn more about tangent, refer below:

https://brainly.com/question/19064965

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