Drew wanted to determine whether there is a relationship between the quality of sneakers worn by volleyball players and their average number of points scored per game. Based on a random sample of 20 players, he found r = .21. He claimed that this provides evidence that better quality sneakers are related to better performance. How would you evaluate this claim?

Answer: a

Step-by-step explanation:a

The sample space can be represented as S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

The sample space for rolling a fair 10-sided die represents all possible outcomes when rolling the die.

In this case, each outcome corresponds to a number that can appear on the face of the die.

Since the die has 10 sides, the numbers 1 to 10 are the possible outcomes.

Therefore, the sample space for rolling a fair 10-sided die can be listed as {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Each element in the sample space represents a distinct possibility and covers all the potential results of rolling the die.

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The angles of △ABC are approximately equal to :

A ≈ 36.9°

B ≈ 53.1°

C ≈ 90.0°

To find the angles of △ABC given the side lengths a = 15, b = 20, and c = 25, you can use the Law of Cosines.

1. For angle A, use the formula: cos(A) = (b² + c² - a²) / (2bc)
cos(A) = (20² + 25² - 15²) / (2 * 20 * 25)
A ≈ 36.9° (rounded to the nearest tenth)

2. For angle B, use the formula: cos(B) = (a² + c² - b²) / (2ac)
cos(B) = (15² + 25² - 20²) / (2 * 15 * 25)
B ≈ 53.1° (rounded to the nearest tenth)

3. For angle C, use the formula: cos(C) = (a² + b² - c²) / (2ab)
cos(C) = (15² + 20² - 25²) / (2 * 15 * 20)
C ≈ 90.0° (rounded to the nearest tenth)

So, the angles of △ABC are approximately A ≈ 36.9°, B ≈ 53.1°, and C ≈ 90.0°.

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The vector function r(t) representing the curve of intersection is r(t) = <5cos(t), 5sin(t), 25sin(t)cos(t)>.

To find the vector function r(t) that represents the curve of intersection of the given surfaces. We have the cylinder x^2 + y^2 = 25 and the surface z = xy.

1. Parameterize the cylinder:
Let x = 5cos(t) and y = 5sin(t), as this will satisfy x^2 + y^2 = 25.
Then, substitute these values into the equation for the surface z = xy:
z = (5cos(t))(5sin(t)) = 25sin(t)cos(t)

2. Write the vector function r(t):
Now that we have x, y, and z in terms of t, we can write the vector function r(t) as follows:
r(t) =  = <5cos(t), 5sin(t), 25sin(t)cos(t)>

So the vector function r(t) representing the curve of intersection is r(t) = <5cos(t), 5sin(t), 25sin(t)cos(t)>.

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A person with compromised pinch strength can exert a force of only 6.0 N on either side of a pinched object, such as a book. To understand the impact of this limited strength on the person's ability to hold objects, we need to analyze the forces acting on the object.

Step 1: Identify the forces acting on the object.
In this case, we have the force exerted by the fingers (6.0 N) and the force due to gravity acting on the object (weight).

Step 2: Calculate the weight of the object.
Weight = Mass x Gravity
Let's assume the book's mass is 0.5 kg, and gravity is approximately 9.81 m/s^2.
Weight = 0.5 kg x 9.81 m/s^2 = 4.905 N

Step 3: Determine if the pinch strength is sufficient.
If the force exerted by the fingers (6.0 N) is greater than or equal to the weight of the object (4.905 N), the person can hold the object securely. In this case, 6.0 N > 4.905 N, which means the person with compromised pinch strength can hold the book without dropping it.

In conclusion, despite having limited pinch strength, this person can still hold objects that weigh less than or equal to the force they can exert (6.0 N). However, they may struggle to hold heavier objects or perform tasks requiring a strong grip.

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Multiplying ampere (amp) by ohm gives units of volt (V).

Therefore, the answer will be in volts (V). This is because ohm is the unit of electrical resistance, ampere is the unit of electrical current, and volt is the unit of electrical potential difference, which is calculated as the product of current and resistance according to Ohm's law: V = I × R.

Ohm is the unit of electrical resistance, which measures how much a material opposes the flow of electric current. One ohm (1 Ω) of resistance is defined as the amount of resistance that allows one ampere (1 A) of current to flow when a potential difference of one volt (1 V) is applied across it.

Ampere is the unit of electrical current, which measures the rate at which electric charge flows through a material. One ampere (1 A) of current is defined as the flow of one coulomb of electric charge per second.

Volt is the unit of electrical potential difference, which measures the amount of energy required to move a unit of electric charge from one point to another. One volt (1 V) of potential difference is defined as the amount of energy required to move one coulomb of electric charge across a circuit element that has one ohm of resistance.

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Answer:

  D.  -3 must be a root

Step-by-step explanation:

You want to know what it means that dividing 2x² +9x +9 by x+3 leaves a remainder of zero.

The remainder theorem tells you that dividing f(x) = (2x² +9x +9) by (x +3) has a remainder equal to f(-3). When that remainder is zero, it tells you that ...

  f(-3) = 0   ⇒   -3 is a root of the polynomial (2x² +9x +9), choice D.

__

Additional comment

It also tells you that 2x+3 = 0 will give you the other root: x = -3/2.

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The relation r2 on {a, b, c, d} is r2 = {(a,c),(a,d),(b,a),(b,c),(b,d),(c,c),(d,a),(d,c)}.

To find r2, we need to compute the composition of r with itself.

r2 = r ∘ r

To do this, we need to take each element in r and find all possible pairs that can be formed by combining the first element of the pair with the second element of another pair. Then we need to remove any duplicates from the resulting set.

Starting with r = {(a,b),(a,d),(b,c),(c,c),(d,a)}, we can form the following pairs:

(a,b) ∘ (a,d) = (b,d)

(a,b) ∘ (b,c) = (a,c)

(a,b) ∘ (d,a) = (b,a)

(a,d) ∘ (b,c) = (a,c)

(a,d) ∘ (c,c) = (a,c)

(a,d) ∘ (d,a) = (b,a)

(b,c) ∘ (c,c) = (b,c)

(b,c) ∘ (d,a) = (b,a)

(c,c) ∘ (c,c) = (c,c)

(d,a) ∘ (c,c) = (d,c)

(d,a) ∘ (d,a) = (a,a)

Removing duplicates, we get:

r2 = {(a,c),(a,d),(b,a),(b,c),(b,d),(c,c),(d,a),(d,c)}

Therefore, the relation r2 on {a, b, c, d} is r2 = {(a,c),(a,d),(b,a),(b,c),(b,d),(c,c),(d,a),(d,c)}.

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Answer:

manufacturing is the right answer

Therefore, the slope of the line passing through the points (2, 1) and (8, 9) is 4/3. Answer choice A is correct.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, we have:

x1 = 2, y1 = 1

x2 = 8, y2 = 9

slope = (9 - 1) / (8 - 2) = 8 / 6 = 4 / 3

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The terminal-point P(x, y) on the unit circle for "t = 7π/6' is (-√3/2 , -1/2), and the labelled graph of "y = 3+cos(x)" is shown below.

We have to find the terminal-point for t = 7π/6.,

The angle is given to be 7π/6, which means in degree it's measure is 210 degrees, and since the circle is unit circle ,So, radius = 1

The value of x and y, for terminal-point can be calculated as:

x = r × cos(θ)  = 1 × cos(210°) = -√3/2,

y = r × sin(θ) = 1 × sin(210°) = -1/2,

So, the required terminal point will be = (-√3/2 , -1/2).

To sketch graph of function "y = 3+cos x",

We substitute the values, and plot them,

For x = -2π, we get y = 4, the point is (-2π, 4);

For x = -π, we get y = 2, the point is (-π, 2);

For x = 0, we get y = 4, the point is (0, 4);

For x = π, we get y = 2, the point is (π, 2);

For x = 2π, we get y = 4, the point is (2π, 4);

Therefore, the graph of these points is sketched below.

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The given question is incomplete, the complete question is

Find the terminal point P(x, y) on the unit circle determined by the given value of t. (Remember to show work to justify your answer.) t = 7π/6.

Sketch the graph of y = 3+cos x. Remember to label your axes carefully (with numbers) and to show the five points accurately.

a. True. A square matrix with orthonormal columns is invertible because its columns are linearly independent.

Therefore, the determinant of the matrix is nonzero and the matrix is invertible.

b. True. Let be an matrix with orthonormal columns. Then the product is the identity matrix because the dot product of any two distinct columns of is zero.

c. True. Suppose that is an orthogonal set in that is linearly dependent. Then there exist coefficients , not all zero, such that . Let be the smallest index for which .

However, since is orthogonal, we have , which contradicts the assumption that is linearly dependent. Therefore, every orthogonal set in is linearly independent.

d. False. Consider the set in , where . Then, , but this set is not orthonormal because the second vector has norm 2.

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b. no

Explanation:

The z-score measures how many standard deviations a given value is away from the mean. It helps us understand how unusual or typical a value is within a distribution.

In this case, we are given that the mean life span of the tires is 38,000 miles, with a standard deviation of 2,100 miles. This information allows us to calculate the z-scores for specific life spans.

To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.

Let's calculate the z-scores for the given life spans:

For the life span of 35,000 miles: z = (35,000 - 38,000) / 2,100 = -0.43

For the life span of 37,000 miles: z = (37,000 - 38,000) / 2,100 = 0.43

For the life span of 32,000 miles: z = (32,000 - 38,000) / 2,100 = -1.7

Now, to determine if these life spans are unusual, we typically use a cutoff of z-score greater than 2 or less than -2. If a z-score falls beyond these values, it suggests that the corresponding value is significantly different from the mean.

In this case, none of the calculated z-scores (-0.43, 0.43, and -1.7) fall beyond the cutoffs of 2 or -2.

Since all the z-scores fall within the range of -2 to +2, we can conclude that none of the life spans of the tires would be considered unusual based on the given z-scores.

Therefore, the answer is b. no, as none of the life spans of the tires are considered unusual based on the provided z-scores.

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You are testing H0:μ=100 against Ha:μ<100 with degrees of freedom of 24. The t statistic is 2.25.

The P-value for the statistic falls between 0.01 and 0.025.

We are testing H0:μ=100 against Ha:μ<100 with degrees of freedom of 24 and the t statistic is 2.25. To find the P-value for this t statistic, follow these steps:

1. Look up the t distribution table or use a t-distribution calculator with the given degrees of freedom (24) and the t statistic (2.25).
2. Since this is a one-tailed test (Ha:μ<100), look for the corresponding one-tailed probability.

The P-value for the t statistic of 2.25 with 24 degrees of freedom falls between 0.01 and 0.025. This is because, at 24 degrees of freedom, a t statistic of 2.25 corresponds to an area in the right tail of the distribution, and we need to find the complementary area to calculate the one-tailed P-value for a left-tailed test.

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The group describes 16% of the population of Algebra 2 quiz scores is scores above 82

Given data ,

On a Algebra 2 quiz are normally distributed with a mean of 79 and a standard deviation of 3

Now , the group that describes 16% of the population of Algebra 2 quiz scores, we need to find the z-scores that correspond to the values that mark off the lowest and highest 16% of the distribution.

Using a standard normal distribution table, we can find that the z-score corresponding to the 16th percentile is approximately -1.00, and the z-score corresponding to the 84th percentile is approximately +1.00.

Now we can use the formula for standardizing a normal variable to find the corresponding values in the original distribution:

z = (x - mu) / sigma

For the 16th percentile:

-1.00 = (x - 79) / 3

x - 79 = -3

x = 76

So the lowest 16% of Algebra 2 quiz scores are below 76.

For the 84th percentile:

1.00 = (x - 79) / 3

x - 79 = 3

x = 82

Hence , the highest 16% of Algebra 2 quiz scores are above 82

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The 95% confidence interval for the proportion of cell phone users who prefer texting is 53% to 59%.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the survey found that 56% of the respondents prefer to use cell phones for texting, and a 95% confidence interval for the estimate of all cell phone users who prefer to use cell phones for texting has a margin of error of 3%.

This means that if we were to conduct the same survey multiple times and calculate a confidence interval for each survey, we would expect 95% of those intervals to contain the true population proportion of cell phone users who prefer texting. Additionally, the margin of error of 3% means that the estimate of 56% could be off by as much as 3%, either higher or lower. Therefore, we can say with 95% confidence that the true proportion of cell phone users who prefer texting is between 53% and 59%.

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To plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

To determine what sample volume should yield a countable plate, we need to calculate the appropriate dilution factor.

The sample has a density of 7.9 x 10^9 CFU/mL, and we want to plate 1 mL of a 10^-8 original dilution, which means we need to dilute the sample by a factor of 10^8 to obtain a countable plate.

We can calculate the required dilution factor using the following formula:

Dilution factor = (Volume of sample plated) / (Total volume of diluted sample)

To dilute the sample by a factor of 10^8, we can calculate the total volume of diluted sample as follows:

Total volume of diluted sample = (Volume of sample plated) x (Dilution factor)

Substituting the values, we get:

10^8 = 1 mL / (Total volume of diluted sample)

Total volume of diluted sample = 1 mL / 10^8

Total volume of diluted sample = 0.00000001 mL

Therefore, to obtain a countable plate, we need to plate 1 mL of a sample that has been diluted in 0.00000001 mL of diluent, or a dilution factor of 10^8.

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The cartesian equation for the curve given by r = 9 tan(θ) sec(θ) is:

y = x(sec(x))^2, where x = θ - π/2.

The given polar equation can be simplified using the trigonometric identity for tangent and secant:

r = 9 tan(θ) sec(θ)

r = 9 sin(θ) / cos(θ) * 1 / cos(θ)

r = 9 sin(θ) / cos^2(θ)

Converting to cartesian coordinates using r^2 = x^2 + y^2 and x = r cos(θ), y = r sin(θ), we get:

(x^2 + y^2) = 81 y / x^2

Multiplying both sides by x^2, we get:

x^2 + y^2 = 81y / x^2 * x^2

x^2y^2 + x^4 - 81y = 0

Substituting x = θ - π/2, we get:

(y / (θ - π/2))^2 + (y / (θ - π/2))^4 - 81y = 0

Simplifying this expression gives us the cartesian equation for the curve:

y = x(sec(x))^2, where x = θ - π/2.

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Step-by-step explanation:

32,538÷10⁴=

32,538÷10⁴=10⁴=10000

32,538÷10⁴=10⁴=1000032.538÷10000

32,538÷10⁴=10⁴=1000032.538÷100000.0032538

Using the left-rectangle approximation with five rectangles, we estimate that the total cost of producing 100 bar stools is approximately $1814.16.

Using the left-rectangle approximation with five rectangles, we can estimate the total cost of producing 100 bar stools as follows:

First, we need to find the width of each rectangle, which is the width of the interval [0, 100] divided by the number of rectangles, which is 5:

Width of each rectangle = (100 - 0)/5 = 20

Next, we need to evaluate the marginal cost function at the left endpoint of each rectangle and multiply it by the width of the rectangle. We then add up these products to get an estimate of the total cost:

Total cost ≈ MC(0) * 20 + MC(20) * 20 + MC(40) * 20 + MC(60) * 20 + MC(80) * 20

Plugging in the values from the given marginal cost function, we get:

Total cost ≈ (20 - 0.5√0) * 20 + (20 - 0.5√20) * 20 + (20 - 0.5√40) * 20 + (20 - 0.5√60) * 20 + (20 - 0.5√80) * 20

Simplifying this expression, we get:

Total cost ≈ $1814.16

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Answer:

E3-11 The Polishing Department of Major Company has the following production and manufacturing cost data for September . Materials are entered at the beginning of the process . 100 % complete

The equation of the line passing through the points (3, -6) and (5, -5) can be expressed in either general form or slope-intercept form. the equation of the line can be written as y = (1/2)x - 15/2 in slope-intercept form or 2x - 4y = 30 in general form.

To find the equation, we first calculate the slope (m) using the formula (y₂ - y₁) / (x₂ - x₁). Using the coordinates (3, -6) and (5, -5), the slope is found to be 1/2. Next, we substitute the slope and one point's coordinates into the slope-intercept form, y = mx + b, to determine the y-intercept (b).

Solving the equation -6 = (1/2)(3) + b, we find b = -15/2. Thus, the equation of the line can be written as y = (1/2)x - 15/2 in slope-intercept form or 2x - 4y = 30 in general form.

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the median value in the series is 3.

To find the median value in a series of numbers, we arrange them in ascending order and determine the middle value.

The given series of numbers is: 1, 2, 3, 4, 10.

Arranging them in ascending order: 1, 2, 3, 4, 10.

The middle value is 3.

what is numbers?

Numbers are mathematical symbols or representations used to quantify or express quantities, measurements, or values. They are fundamental to mathematics and serve various purposes, such as counting, measuring, calculating, and representing relationships between quantities. Numbers can be classified into different types, including natural numbers (1, 2, 3...), integers (..., -2, -1, 0, 1, 2, ...), rational numbers (fractions), irrational numbers (such as π), and real numbers (including all rational and irrational numbers). Numbers are used in a wide range of fields, including science, engineering, economics, and everyday life.

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The probability that a 2 is observed on the first trial or at least two trials are required to observe a 2 is 7/36.

Let's break down the possible outcomes of the experiment to find P(A or B):

A: 2 is observed on the first trial (probability of A = 1/6).

B: 2 is not observed on the first trial, but is observed on the second, third, fourth, etc. trial (probability of B = 5/6 * 1/6 + 5/6 * 5/6 * 1/6 + 5/6 * 5/6 * 5/6 * 1/6 + ...)

We can write the probability of B as a geometric series:

B = 5/6 * 1/6 + 5/6 * 5/6 * 1/6 + 5/6 * 5/6 * 5/6 * 1/6 + ...

B = (5/6 * 1/6) * (1 + 5/6 + (5/6)^2 + (5/6)^3 + ...)

B = (5/36) * (1 / (1 - 5/6)) (using the formula for an infinite geometric series)

B = 5/36

Therefore, P(A or B) = P(A) + P(B) - P(A and B) = 1/6 + 5/36 - 0 (since A and B are mutually exclusive events).

P(A or B) = 7/36

So the probability that a 2 is observed on the first trial or at least two trials are required to observe a 2 is 7/36.

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A combination lock has 3 settings, where any digit from to can be selected for each setting, and any digit may be repeated. Total 1000 different numeric combination codes can be set on this lock.

There are a total of 10 digits to choose from (0 to 9), and each of the three settings can have any of these digits repeated, so there are 10 options for each setting.

Therefore, the total number of different numeric combination codes that can be set on this lock is calculated as:

10 x 10 x 10 = 1,000

So, there are 1,000 different numeric combination codes that can be set on this lock. This means that there are a total of 1,000 possible ways to select the settings on this combination lock, with each setting being a digit between 0 and 9.

It is important to note that the order in which the digits are selected does not matter, as the lock will only recognize the specific combination of digits, not the order in which they were entered.

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Answer:

80, 160

Step-by-step explanation:

this is a geometric sequence

formula = ar^(n-1)

where a is the first term and r is the ratio/multiple

r = 10/5 = 20/10 = 40/20 = 2

we know first term is 5. put this into formula

ar^(n-1) = (5)(2)^(n-1) = 5(2)^(1-1) = 5(2)^0 = 5(1) = 5.

second term is 10

confirm this with formula.

ar^(n-1) = 5(2)^(2-1) = 5(2)^1 = 5(2) = 10

so to find next two terms (the fifth and sixth terms):

ar^(n-1) = (5)(2)^(5-1) = (5)(2)^(4) = 5(16) = 80. this is fifth term

ar^(n-1) = (5)(2)^(6-1) = (5)(2)^(5) = 5(32) = 160. this is sixth term

The proportion of carrying loads in the sample that are less than or equal to 880 pounds per square foot is 0.12.

To find the proportion of carrying loads in the sample that are less than NM pounds per square foot, we need to sum up the frequencies of all the bins that have carrying loads less than NM.

Given the histogram data:

Carrying Load (in pounds per sq. ft) | Frequency

860-880 3

880-900 6

900-920 9

920-940 4

940-960 3

Let's assume NM is the upper limit of the desired range for the carrying load. To calculate the proportion of carrying loads less than NM, we need to add up the frequencies of all the bins with carrying loads below NM.

For example, if NM is less than or equal to 880, then all the frequencies of the first bin (860-880) will be included in the calculation. If NM is between 880 and 900, the frequencies of both the first and second bins will be included, and so on.

To find the proportion, we sum up the frequencies of the relevant bins and divide it by the total sample size.

For the given histogram data, the total sample size is:

Total sample size = 3 + 6 + 9 + 4 + 3 = 25

Let's calculate the proportion for NM values less than or equal to 880:

Proportion = (Frequency of bin 1) / (Total sample size) = 3 / 25 = 0.12

Therefore, the proportion of carrying loads in the sample that are less than or equal to 880 pounds per square foot is 0.12.

Note: The exact value of NM was not provided, so we calculated the proportion for NM values less than or equal to 880 as an example. The calculation can be done for any specific NM value by summing up the frequencies of the relevant bins and dividing by the total sample size.

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Answer:

Step-by-step explanation:

F

                 ______________              _______. F f f f f.  F

The initial size of the culture is 464.

The doubling period is 17 minutes approximately.

The population after 65 minutes is 6675.

In 83 minutes the population will reach 14000.

The count of bacteria grows exponentially. So the best suited model for the case is Exponential function.

General form of Exponential model is,

f(t) = A₀ eᵏᵗ, k is growth constant.

We know that count of bacteria was 700 after 10 minutes.

So when t = 10 then f(t) = 700

A₀ e¹⁰ᵏ = 700 ..................... (i)

and again the count of bacteria was 1600 after 30 minutes.

So when t = 30 then f(t) = 1600

A₀ e³⁰ᵏ = 1600 ..................... (ii)

Dividing equation (ii) by equation (i) we get,

(A₀ e³⁰ᵏ)/(A₀ e¹⁰ᵏ) = 1600/700

e²⁰ᵏ = 16/7

20k = ln(16/7)

k = (ln(16/7))/20

k = 0.041 [rounding off to nearest thousandth]

Substituting the value of k in equation (i) we get,

[tex]A_0e^{10\times 0.041}[/tex] = 700

A₀ = 464.55

So the model is,

f(t) = 464.55 [tex]e^{0.041t}[/tex]

At initial stage t = 0, so the initial size is,

f(0) = 464 (approximate to nearest integer)

When the size is doubled then it is double of initial size A₀.

2A₀ = A₀[tex]e^{0.041t}[/tex]

t = 17 (approximate to nearest miniute)

The population after 65 minutes, (t = 65)

f(65) = 6675 (approximate to nearest integer)

Let at t = m time the population will reach 14000.

14000 = 464.55 [tex]e^{0.041m}[/tex]

m = 83 (approximate to nearest minute)

So in 83 minutes the population will reach 14000.

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The conditions for inference are not met. Specifically, the random condition is not met for both samples.

For inference to be valid, the samples should be selected randomly from their respective populations. In this case, the coach selected a random sample of 5 players from his team and 5 players from the rival team. However, since the selection was limited to only 5 out of 11 players in each team, the random condition is not fully satisfied.

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