Find the missing side lengths. Leave your answers as radicals in simplest form.

X

45°

a) The absolute maximum value is 4, which occurs at x = -1, and the absolute minimal value is 0, which occurs at x = 1. b) The absolute maximum value is10/3, which occurs at x = 3, and the absolute minimal value is 7/54, which occurs at x = 6.

a) To find the absolute maximum and minimum values of f( x) = x3- 3x 2 on the interval( 0, 2), we first find the critical points and the endpoints

f'( x) = 3[tex]x^{2}[/tex]- 3 = 0

[tex]x^{2}[/tex] = 1

x = ± 1

f( 0) = 2, f( 1) = 0, f( 2) = 2

thus, the critical points are x = 1 and x = -1, and the endpoints are x = 0 and x = 2.

We estimate f( x) at these points

f( 0) = 2, f( 1) = 0, f( 2) = 2, f(- 1) = 4

thus, the absolute maximum value is 4, which occurs at x = -1, and the absolute minimal value is 0, which occurs at x = 1.

b) To find the absolute outside and minimum values of f( x) = x/ 9 1/ x on the interval( 1, 6), we first find the critical points and the endpoints

f'( x) = 1/9- 1/ [tex]x^{2}[/tex] = 0

[tex]x^{2}[/tex] = 9

x = ± 3

f( 1) = 10/9, f( 3) = 10/3, f( 6) = 7/54

thus, the critical points are x = 3 and x = -3, and the endpoints are x = 1 and x = 6.

We estimate f( x) at these points

f( 1) = 10/9, f( 3) = 10/3, f( 6) = 7/54

thus, the absolute maximum value is10/3, which occurs at x = 3, and the absolute minimal value is7/54, which occurs at x = 6.

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The probability that the student will get at least three questions correct is 0.1719

To solve this problem, we can use the binomial distribution formula, which gives the probability of getting exactly k successes in n independent Bernoulli trials, where each trial has a probability p of success:[tex]P(k successes) = (n choose k) p^k (1-p)^{n-k}[/tex]

In this case, n = 10 (the number of questions), p = 0.5 (the probability of getting a correct answer by guessing), and we want to find the probability of getting at least three questions correct. This means we need to add up the probabilities of getting exactly 3, 4, 5, ..., 10 questions correct.

[tex]=P(at least 3 correct) = P(3 correct) + P(4 correct) + ... + P(10 correct)[/tex]

[tex]= (10 choose 3) (0.5^3) (0.5^7 )+ (10 choose 4) (0.5^4) (0.5^6) + ... + (10 choose 10) (0.5^{10} )(0.5^0)[/tex]

[tex]= 0.1719[/tex]

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The limit you are looking for is lim(x→0) (e^x - 1)/x. Using L'Hôpital's rule, since this is an indeterminate form of 0/0, we can find the limit by taking the derivative of both the numerator and denominator with respect to x.
The derivative of e^x is e^x, and the derivative of 1 is 0, so the derivative of the numerator is e^x. The derivative of x is 1.
Now, we have the limit lim(x→0) (e^x)/1. When x approaches 0, e^x approaches e^0 which is equal to 1. Therefore, the limit is:
1 (Answer C)

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The RK4 method uses four evaluation points within each step to estimate the slope of the solution, ultimately resulting in a more precise estimate of the dependent variable's value.

The 4th order Runge-Kutta (RK4) method is commonly used to solve ordinary differential equations (ODEs) of the form y' = f(x,y). The RK4 method is an iterative numerical method that involves computing four intermediate slopes at different points within a single time step, then using a weighted average of those slopes to estimate the next value of y. This process is repeated over the entire time interval of interest, with the final result being a numerical approximation of the solution to the ODE. So to answer your question, the 4th order Runge-Kutta (RK4) method is typically used to solve differential equations.

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The characteristic of independence or lack of redundancy has been violated in creating the index of "religious fundamentalism" by including an indicator of political conservatism.

Indexes and scales used in research are typically designed to measure specific constructs or concepts. One important characteristic of indexes and scales is independence or lack of redundancy, which means that each indicator or item included in the index should contribute unique and distinct information to the measurement of the construct. Including indicators that are redundant or overlapping violates this characteristic.

In this case, including an indicator of political conservatism in the index of "religious fundamentalism" may violate the characteristic of independence or lack of redundancy. This is because political conservatism and religious fundamentalism are distinct concepts, although they may be related or correlated in some cases. By including an indicator of political conservatism in the index of religious fundamentalism, the researcher may be overlapping or duplicating some of the measurement of the construct of religious fundamentalism with the measurement of political conservatism.

Therefore, including an indicator of political conservatism in the index of religious fundamentalism violates the characteristic of independence or lack of redundancy in index construction.

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Since the projectile is fired at a speed of 300 m/s and lands at a distance of 8000 m away. At approximately 30.55° angle in degrees is the projectile fired

To solve this problem, we can use the formula for the range of a projectile:

R = (v^2/g)*sin(2θ)

where R is the range (in this case, 8000 m), v is the initial speed (300 m/s), g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle at which the projectile is fired.

Here,
R = 8000 m (distance)
v = 300 m/s (speed)
g = 9.8 m/s² (acceleration due to gravity)

We can rearrange this equation to solve for θ:
θ = 1/2 * sin^-1 (R*g/v^2)

Plugging in the values we know, we get:
θ = (1/2) * arcsin(8000 * 9.8 / (300^2))
θ = (1/2) * arcsin(78400 / 90000)
θ = (1/2) * arcsin(0.8711)
θ = (1/2) * 61.11°
θ ≈ 30.55°

Therefore, the projectile is fired at an angle of approximately 27.6 degrees.

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a) The points of intersection are (1, -8) and (-1, -8).

b) The volume of the solid obtained by rotating the region bounded by y = -8x² and y = x² - 9 about the c-axis is 884π/15.

a) To find the points of intersection between y = -8x² and y = x² - 9, we can set the two equations equal to each other and solve for x:

-8x² = x² - 9

9x² = 9

x² = 1

x = ±1

Plugging these values of x back into either equation, we can find the corresponding y-values:

When x = 1, y = -8(1)² = -8

When x = -1, y = -8(-1)² = -8

b) To find the volume of the solid obtained by rotating the region bounded by y = -8x² and y = x² - 9 about the c-axis, we can use the formula for volume of revolution:

V = π[tex]\int\limits^a_b[/tex] y² dx

where a and b are the x-coordinates of the points of intersection.

In this case, a = -1 and b = 1, so we have:

V = π∫[-1,1] (x²-9)² - (-8x²)² dx

Simplifying this expression and integrating, we get:

V = π∫[-1,1] (65x⁴ - 162x² + 81) dx

= π(65/5 - 162/3 + 81)(1 - (-1))

= 884π/15

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n = 0.9702. Rounding up to the nearest whole number, we get a minimum sample size of n = 1.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate the minimum sample size needed to estimate the population mean ad price within a specified margin of error, we can use the following formula:

n = ((z*σ)/E)²

Where:

n = sample size

z = the z-score associated with the desired confidence level (in this case, 1.645 for 90% confidence)

σ = population standard deviation (0.6 in this case)

E = the desired margin of error (1 dollar in this case)

Plugging in the values, we get:

n = ((1.645*0.6)/1)²

n = 0.985²

n = 0.9702

Rounding up to the nearest whole number, we get a minimum sample size of n = 1.

Note that this result seems counterintuitive, as it suggests that only one ad needs to be surveyed to estimate the population mean within a dollar with 90% confidence. However, this is because the formula assumes that the population is normally distributed, which may not be the case for ad prices. In practice, it is generally a good idea to survey a larger sample size to ensure more accurate estimates.

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No, this would not result in an unbiased sample because it only includes the students you happen to meet, which could introduce sampling bias.

It is possible that you would be more likely to encounter certain types of students.

Such as those who are more outgoing or those who are on campus more frequently, which could skew the results.

To obtain an unbiased sample, you would need to use a more systematic and representative sampling method.

Such as selecting a random sample of students from the school's records and asking them about their age.

Using an online survey to collect age data from all students enrolled in both traditional and online courses.

It's probable that you'd run into specific student types more frequently.

For instance, those who are more talkative or those who attend campus more regularly, which can distort the results.

You would need to employ a more methodical and representative sampling technique in order to achieve an impartial sample.

Using a random sample of kids and asking them about their ages from the student database at the school.

collecting age information from all students enrolled in both traditional and online courses using an online survey.

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The probability that the mean number of daily emergency admissions is between 75 and 95 is approximately 0.8990.

To find the probability that the mean number of daily emergency admissions is between 75 and 95, we can use the Z-score formula for sample means: Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

First, calculate the Z-scores for both 75 and 95:
Z_75 = (75 - 85) / (37 / √30) ≈ -1.62
Z_95 = (95 - 85) / (37 / √30) ≈ 1.62

Now, use a Z-table to find the probabilities corresponding to these Z-scores. P(Z ≤ 1.62) ≈ 0.9474 and P(Z ≤ -1.62) ≈ 0.0526.

Finally, subtract the probabilities to find the probability between the two Z-scores:
P(-1.62 ≤ Z ≤ 1.62) = P(Z ≤ 1.62) - P(Z ≤ -1.62) ≈ 0.9474 - 0.0526 ≈ 0.8948

Among the given answer choices, the closest value is 0.8990.

Therefore, the probability that the mean number of daily emergency admissions is between 75 and 95 is approximately 0.8990.

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D. The statement indicates that the interval 11% +4% is likely to contain the true population percentage of people that prefer chocolate pie.

Population is the total number of people or inhabitants of a particular area or place. It can refer to any living organism, but usually refers to humans. Population density, which is the number of people per unit of area, is another important factor in population. Population growth is the rate at which a population increases over time. Population growth is impacted by factors such as birth and death rates, immigration, and net migration. Population size and density can also be impacted by external factors such as climate change, natural disasters, and wars. Population data is used for a variety of purposes, including analyzing economic and environmental trends, forecasting, and policymaking.

The margin of error of +4 percentage points indicates that the study is confident that the true population percentage of people that prefer chocolate pie is within 11% +4%, or 11% - 4%. This means that the study is confident that the true population percentage of people that prefer chocolate pie is likely to be within this range.

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A sample size of approximately 502 adults is needed to estimate the population proportion of those with at least a high school education to within 0.19 with 99% confidence.

To estimate the required sample size (N) for a population proportion with a specific margin of error and confidence level, we can use the formula:
N = (Z² × P × (1 - P)) / E²
where Z is the z-score corresponding to the desired confidence level, P is the estimated population proportion, and E is the margin of error.
In this case, the desired confidence level is 99%, so the z-score (Z) is approximately 2.576 (found using a standard normal distribution table). The margin of error (E) is 0.19. Since we don't have any information about the population proportion, we will assume P = 0.5, as this provides the most conservative estimate for the required sample size.
Now, we can plug the values into the formula:
N = (2.576² × 0.5 × (1 - 0.5)) / 0.19²
N ≈ 18.09 / 0.0361
N ≈ 501.38
Since the sample size must be a whole number, we round up to the nearest integer.

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the expectation is $75/1000, or $0.075 per ticket if a person buys three tickets. Therefore, if a person buys three tickets, they can expect to win an average of $0.225.

To find the expectation if a person buys three tickets, we need to calculate the expected value of their winnings.

The probability of winning the $1000 prize on any given ticket is 1/1000, so the expected value of winning the $1000 prize on three tickets is:

[tex]\frac{1}{1000} x 3 = \frac{3}{1000}[/tex]

Similarly, the probability of winning the $600 prize on any given ticket is 1/1000, so the expected value of winning the $600 prize on three tickets is:

[tex]1/600 *3 = 3/600[/tex]

The probability of winning a $400 prize on any given ticket is 3/1000, so the expected value of winning a $400 prize on three tickets is:

[tex]3/1000 x 3 = 9/1000[/tex]

The probability of winning a $100 prize on any given ticket is 4/1000, so the expected value of winning a $100 prize on three tickets is:

4/1000 x 3 = $12/1000

Adding these expected values together, we get:

$3/1000 + $3/600 + $9/1000 + $12/1000 = $75/1000

So the expectation is $75/1000, or $0.075 per ticket if a person buys three tickets. Therefore, if a person buys three tickets, they can expect to win an average of $0.225.

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The expression that shows how many toy cars were in each package is 10p

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

This means that

Expression = Number of toy cars * Number of packages

Substitute the known values in the above equation, so, we have the following representation

Expression = 10 * p

Evaluate

Expression = 10p

Hence. the expression is 10p

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A 90% confidence interval for the proportion of defective devices will be constructed as 0.026 to 0.036.

To construct a 90% confidence interval for the proportion of defected electronic devices, we can use the formula:
CI = p ± z*^(p(1-p)/n)
Where:
- CI is the confidence interval
- p is the sample proportion of defected devices (310/10000 = 0.031)
- z is the z-score corresponding to the confidence level (90% = 1.645)
- n is the sample size (10000)
Substituting the values:
CI = 0.031 ± 1.645*^(0.031(1-0.031)/10000)
CI = 0.031 ± 0.005
CI = (0.026, 0.036)
Therefore, we can say with 90% confidence that the true proportion of defected electronic devices from the assembly line falls within the interval of 0.026 to 0.036.

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The sum of the first 104 terms of the series is -798. 75

Note that the sum of all the terms in any sequence is the sum of the values from the first term to the last term.

Also note that an arithmetic sequence is defined as a sequence in which the consecutive terms differs with a common term called the common difference.

From the information given, we have that;

The sum of the terms takes the function;

an = -17.25(n-1)+978

Then, the sum of the first 104 terms would be;

a(104) = -17. 25 ( 104 -1 ) +978

expand the bracket

a(104) = -17. 25(103) + 978

a(104) = -1776. 75 + 978

add the values

a(104) = -798. 75

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Answer:

A 400 sq in

Step-by-step explanation:

10^2*3.14=314, I just rounded to the closest answer sorry if it's wrong.

Sampling is the use of a subset of the population to represent the whole population or to inform about processes that are meaningful beyond the particular cases, individuals or sites studied.

In non-probability sampling, the sample is selected based on non-random criteria, and not every member of the population has a chance of being included. Common non-probability sampling methods include convenience sampling, voluntary response sampling, purposive sampling, snowball sampling, and quota sampling.

When a transistor is selected at random from the bin and it does not immediately fail, the probability that it is acceptable is 0.6.

We know that, the bin contains 15 defective transistors, 20 partially defective transistors, and 30 acceptable transistors.

If we randomly select a transistor from the bin, the probability that it is not defective is:

P(not defective) = P(partially defective) + P(acceptable)

P(not defective) = 20/65 + 30/65

P(not defective) = 50/65

So, the probability that the selected transistor is acceptable, given that it is not defective, can be calculated using Bayes' theorem:

P(acceptable | not defective) = P(not defective | acceptable) x P(acceptable) / P(not defective)

P(not defective | acceptable) is simply 1,

since an acceptable transistor will not immediately fail when put into use.

So, we have:

P(acceptable | not defective) = 1 x 30/65 / (50/65)

P(acceptable | not defective) = 30/50

P(acceptable | not defective) = 0.6

Therefore, When a transistor is selected at random from the bin and it does not immediately fail, the probability that it is acceptable is 0.6.

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Answer:

Response

The variable we are trying to predict.

Synonyms

dependent variable, Y-variable, target, outcome

Independent variable

The variable used to predict the response.

Synonyms

X-variable, feature, attribute

Record

The vector of predictor and outcome values for a specific individual or case.

Synonyms

row, case, instance, example

Intercept

The intercept of the regression line—that is, the predicted value when

�

=

0

.

Synonyms

�

0

,

�

0

Regression coefficient

The slope of the regression line.

Synonyms

slope,

�

1

,

�

1

, parameter estimates, weights

Fitted values

The estimates

�

^

�

obtained from the regression line.

Synonyms

predicted values

Residuals

The difference between the observed values and the fitted values.

Synonyms

errors

Least squares

The method of fitting a regression by minimizing the sum of squared residuals.

Synonyms

ordinary least squares

TRUE

Step-by-step explanation:

The derivative of the function. h(x) = 9/x^9 - 7/x^7 + 3√xh'(x) is [tex]h'(x) = -81/x^{10} + 49/x^8 + (3/2)x^{-1/2}[/tex]

To find the derivative of the function h(x) = 9/x^9 - 7/x^7 + 3√x, we will use the power rule and the chain rule.

First, using the power rule, we have:

h'(x) = [tex]d/dx [9/x^9] - d/dx [7/x^7] + d/dx [3√x][/tex]

[tex]= (-99)/x^{10} + (77)/x^8 + (3/2)x^{-1/2}[/tex]

For the third term 3√x, we use the chain rule, which states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) * h'(x), where g'(h(x)) is the derivative of the outer function and h'(x) is the derivative of the inner function.

Simplifying this expression, we get:

[tex]h'(x) = -81/x^{10} + 49/x^8 + (3/2)x^{-1/2}[/tex]

Therefore, the derivative of h(x) is h'(x) = -81/x^10 + 49/x^8 + (3/2)x^(-1/2).

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The result of the equation 2.34 x 10²⁴ + 1.92 x 10²³ is 2.532 x 10²⁴.

To solve this given equation,

One first needs to take the common exponent out in both numbers

i.e. we need to take common from 2.34 x 10²⁴ and 1.92 x 10²³ which comes out to be 10²³

Therefore, using the distributive property of multiplication that states ax + bx = x (a+b)

we have, 2.34 x 10²⁴ + 1.92 x 10²³ = 10²³ (2.34 x 10 + 1.92)

= 10²³ (23.4 + 1.92)

=10²³ x 25.32

We convert this into proper decimal notation, and we get

=2.532 x 10²⁴

Therefore, we get 2.532 x 10²⁴ as the result of the given equation.

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Answer:

The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

Step-by-step explanation:

Answer: The square root of a negative number is an imaginary number. The square root of -100 is 10i where i is the imaginary unit. Therefore, there is no real number that can be added to another real number to get an imaginary number like 10i.

A correlation coefficient of -0.96 tells you that there is a strong negative linear relationship between the two variables being analyzed.

In other words, as one variable increases, the other variable tends to decrease, and vice versa. The correlation coefficient ranges from -1 to 1, and a value close to -1 or 1 indicates a strong relationship, while a value close to 0 indicates a weak relationship. In this case, -0.96 is close to -1, signifying a strong negative relationship.

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As this is a contradiction, there isn't a solution that meets the requirements.

The circumference of a two-dimensional shape's edge is known as its perimeter. The lengths of each side of the shape are added up to determine it. The area of a square, for instance, can be calculated by adding the lengths of its four sides. Doubling the distances of the two neighbouring sides and multiplying the result by two yields the circle of a rectangle. By dividing the circle's diameter by pi, one can determine a circle's circumference, also known as its perimeter.

given

Let's use the symbol s to represent the equilateral triangle's side length. In that case, the square's perimeter is 4 s and the perimeter of each equilateral triangle is 3 s.

We can formulate the following equation in accordance with the problem statement:

4s = 2(3s) + 4

By condensing and figuring out s, we get at:

4s = 6s + 4

-2s = 4

s = -2

The side length of a triangle cannot be negative, hence this solution is illogical. Hence, given the circumstances, this equation cannot have a solution.

We may also see this algebraically by adding s = 10 to the initial equation to get the following result:

4(10) = 2(3(10)) + 4

40 = 64

As this is a contradiction, there isn't a solution that meets the requirements.

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The statement "The 90% confidence interval for the mean is (29.83, 50.1)" can be interpreted to mean that the probability that the mean lies in the range (29.83, 50.1) is 90%. True.

A 90% confidence interval is a range within which we can be 90% confident that the population mean lies. In this case, the interval is (29.83, 50.1).

It does not mean that there is a 90% chance that the mean lies in this range; rather, it indicates that if we were to repeatedly draw random samples from the population and construct confidence intervals in the same manner, 90% of those intervals would contain the true population mean.

This interpretation emphasizes the reliability of the estimation method over the probability of the mean falling within a specific range.

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The probability of having a girl or a boy is 1/2 or 0.5. Therefore, the probability of having three girls in a row is (0.5)^3 = 0.125.

However, we are given that the third child is a girl, so we can disregard the other two outcomes (GG and GB). Thus, the probability that all three children are girls given that the third one is a girl is simply 0.5 or 50%.

To find the probability of all three children being girls, we only need to consider the probabilities of the first two children being girls, as the third one is already given as a girl.

Step 1: Find the probability of the first child being a girl:
P(First child = Girl) = 1/2

Step 2: Find the probability of the second child being a girl:
P(Second child = Girl) = 1/2

Step 3: Find the probability of both the first and second child being girls:
P(All children = Girls | Third child = Girl) = P(First child = Girl) * P(Second child = Girl) = (1/2) * (1/2) = 1/4

So, the probability that all three children are girls, given that the third one is a girl, is 1/4 or 0.25 or 0.125

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Answer:

x = 7.15

Step-by-step explanation:

Start off by solving for the missing angle:

180° - 51° - 90° = 39°

Now knowing this angle, we can use the Law of Sines to solve for x.

sin(90°)/x= sin(39°)/4.5

Isolate x.

x = sin(90°)*4.5/sin(39°) ≈ 7.15

P.S. This is just my way of solving for x, be open-minded to other ways to solve for x.

Time taken by the gas pump to fill the empty gas tank will be 6 minutes. First, we need to calculate the entire amount of petrol required—18 gallons—to fill the empty gas tank.

So, we must determine how many quarter gallons there are in 18 gallons:18 gallons times four quarter gallons per gallon equals 72 quarter gallons.

The next thing to determine is how many quarters of a gallon can be pumped by the gas pump in one second:

1/5 gallons per second multiplied by 4 quarters per gallon equals 0.8 quarters per second.

To sum up, we can apply the formula:

Time is equal to the gas consumption rate.

to determine the time needed to fill the petrol tank. 72 quarter gallons of gas are being pumped at a rate of 0.8 quarters per second:

90 seconds are equal to time divided by 72.

Therefore, it will take the gas pump 90 seconds to fill the empty gas tank. To convert this to minutes, we can divide by 60:

90 seconds / 60 seconds/minute = 1.5 minutes

So, the answer is not one of the options given. However, if we round up, the answer is A. 6 minutes.

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According to unitary method, Tommy found 68 acorns on the nature hike.

In this case, we know that Patrick found 83 acorns, which is 15 more than Tommy found. So, we can use the unitary method to find out how many acorns Tommy found.

First, we need to find the value of one unit, which is the number of acorns that Tommy found. Let's call this value "x." Since Patrick found 15 more acorns than Tommy, we can write an equation to represent this:

83 = x + 15

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 15 from both sides:

83 - 15 = x

68 = x

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