What is the chance of drawing two Jacks one after another, when drawing without replacement from an incomplete deck of 48 cards that contains 4 Jacks

The % Cold Work for the sample of 1040 steel is approximately 30.54%.

To calculate the % Cold Work (% C W) for a sample of 1040 steel with an original diameter of 12 mm and a final diameter of 10 mm, we will use the following formula:

%CW = [(A o - A f) / A o] x 100

Where:
%CW = Percentage of Cold Work
A o = Original area of the sample
A f = Final area of the sample

Since the cross-sectional area of a cylindrical sample is given by A = π(d/2)^2, we will calculate the original and final areas using the given diameters:

A o = π(12 mm / 2)^2

= π(6 mm)^2

= 113.097 mm²
A f = π(10 mm / 2)^2

= π(5 mm)^2

= 78.54 mm²

Now, we can calculate the % CW:

%CW = [(113.097 mm² - 78.54 mm²) / 113.097 mm²] x 100
%CW = [34.557 mm² / 113.097 mm²] x 100
%CW ≈ 30.54

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Therefore, the water balloon will be on the fourth story in one more second.

The acceleration due to gravity is approximately 9.8 m/s^2. Since the water balloon falls one story down (which is approximately 6 meters) in one second, we can calculate its initial velocity using the equation: d = 1/2at^2. Plugging in the values, we get: 6 = 1/2(9.8)t^2, which simplifies to t = sqrt(1.2245) ≈ 1.11 seconds. Therefore, in one more second, the water balloon will have fallen another story down, i.e., it will be on the fourth story.
The water balloon dropped by the bored college student falls one story down from the top in one second. To calculate how long it will take for it to fall another story down, we can use the equation: d = 1/2at^2, where d is the distance, a is the acceleration due to gravity, and t is time. Plugging in the values, we get t = sqrt(1.2245) ≈ 1.11 seconds.

Therefore, the water balloon will be on the fourth story in one more second.

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If the mean seasonal factor for June was 96.9, and the sum for all twelve months is 1195, the adjusted seasonal index for June is 8.11

To calculate the adjusted seasonal index for June, we need to divide the mean seasonal factor for June by the sum of the seasonal factors for all twelve months and then multiply the result by 100.

Adjusted seasonal index for June = (Mean seasonal factor for June / Sum of seasonal factors for all twelve months) × 100

Adjusted seasonal index for June = (96.9 / 1195) × 100 ≈ 8.11

The adjusted seasonal index for June is approximately 8.11.

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The smallest number of seats that must be occupied in order to be certain that at least three people in attendance have the same first and last initials is 677. The answer to this question requires a bit of mathematical reasoning.

If we assume that there are 26 letters in the alphabet (one for each initial), and that each person in attendance has a unique first and last initial, then the maximum number of people that can be in the auditorium without any two people having the same initials is 52 (since there are 26 possible first initials and 26 possible last initials).

However, we are looking for the smallest number of seats that must be occupied in order to guarantee that at least three people have the same initials. To solve this, we can use a formula called the pigeonhole principle, which states that if n items are placed into m containers, and n is greater than m, then there must be at least one container with more than one item.

In this case, the "items" are the people in attendance, and the "containers" are the possible combinations of first and last initials. We know that there are 26 possible first initials and 26 possible last initials, which gives us a total of 26 x 26 = 676 possible combinations.

Using the pigeonhole principle, we can determine that if we have 677 people in the auditorium, there must be at least three people with the same first and last initials. Therefore, the smallest number of seats that must be occupied in order to be certain that at least three people in attendance have the same first and last initials is 677.

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Cici performed the logistical function of procurement by collecting all the necessary ingredients from different sources such as the farmers' market, grocery store, and dairy. This involved planning and coordinating the sourcing and transportation of the items to ensure they were available for her to use in baking the strawberry pies.
Hi! Cici performed the logistical function of procurement in collecting all of these ingredients. Procurement is the process of finding, acquiring, and transporting goods and services. In this case, Cici procured strawberries from a farmers' market, flour and sugar from the grocery store, and milk from a dairy. By visiting these different locations, she ensured she had all the necessary ingredients to bake her strawberry pies at home.

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The probability that the sample mean would be less than $51.3 when a sample of 40 bags is randomly selected is 55.71%.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the sample mean of a sufficiently large sample size drawn from any population with a finite mean and variance will be approximately normally distributed.

The first step is to calculate the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. The SEM can be calculated using the formula:

[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]

where σ is the population standard deviation, and n is the sample size.

Substituting the values, we get:

[tex]SEM = \frac{66}{\sqrt{40}} = 10.45[/tex]

Next, we need to calculate the z-score corresponding to the sample mean of $51.3:

[tex]z = \frac{51.3 - 50}{10.45} = 0.1435[/tex]

Using a standard normal distribution table, we find that the area to the left of z = 0.1435 is 0.5571. This means that the probability of obtaining a sample mean of $51.3 or less from a sample of 40 bags is 0.5571 or 55.71%. It is important to note that this result is based on the assumption that the population is normally distributed. Additionally, the CLT only holds for sufficiently large sample sizes (typically n > 30).

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By completing squares we will get:

y = (x - 5)^2 - 16

Then the minimum of the quadratic is at y = -16.

Remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the quadratic:

y = x^2 - 10x + 9

We can rewrite that to get:

y = x^2 - 2*5*x + 9

Add and subtract 5^2 in both sides:

y + 5^2 = x^2 - 2*5*x + 5^2 + 9

Now we can complete squares:

y + 25 = (x - 5)^2 + 9

y = (x - 5)^2 + 9 - 25

y = (x - 5)^2 - 16

Then the vertex is at the point (5, -16), and thus the minimum is y = -16.

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Answer:

[tex](5, -16)[/tex]

Step-by-step explanation:

1.) [tex]y=x^2[/tex] [tex]-10x+9[/tex]

2.) [tex]y=x^2[/tex] [tex]-10x+25+9-25[/tex]

3.) [tex]y=x^2-10x+25 -16[/tex]

4.) [tex]y=(x-5)^2-16[/tex]

Therefore, the minimum point Is [tex](5, -16)[/tex]

There are 10,077,696 possible outcomes when rolling 9 regular six-sided dice in this experiment.

You are rolling 9 regular six-sided dice. To determine the total number of outcomes for this experiment, you will use the concept of permutations in combinatorics. Since each die has 6 sides with distinct numbers (1 to 6), each die has 6 possible outcomes.

To find the total number of outcomes for all 9 dice combined, you simply multiply the possible outcomes for each die together. This is because the outcomes of each die roll are independent events, and the overall outcome depends on the combination of all 9 dice. So, you'll calculate the outcomes as follows:

Number of outcomes = (Outcomes for Die 1) x (Outcomes for Die 2) x ... x (Outcomes for Die 9)

Since there are 6 possible outcomes for each die, the equation becomes:

Number of outcomes = 6^9

By calculating 6 raised to the power of 9, you'll get:

Number of outcomes = 10,077,696

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The population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

To find out when the population will be twice what it was in 1980, we need to set up an equation and solve for t.

Let's first determine the population in 1980:

N(0) = 217e0.0102(0) = 217

So, the population in 1980 was 217 million.

Now, we want to find out when the population will be twice that amount:

2(217) = 434

We can set up an equation:

434 = 217e0.0102t

Divide both sides by 217:

2 = e0.0102t

Take the natural logarithm of both sides:

ln(2) = 0.0102t

Solve for t:

t = ln(2)/0.0102

t ≈ 67.8

Therefore, the population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

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In a well-constrained problem space:

a. There are relatively a small number of states.

b. Subgoal decomposition is not required.

c. The solution is not always straightforward.

d. All of the states and operators are known.

A well-constrained problem space refers to a problem-solving environment that has clear boundaries and limitations, with well-defined rules, goals, and constraints. In such a space, there are typically a limited number of possible states or configurations that the system can be in, and the problem solver has access to all of the relevant information about the problem and its solution.

However, while a well-constrained problem space may have a relatively small number of states, it does not necessarily mean that the solution is always straightforward or that subgoal decomposition is not required. In fact, in some cases, even a well-constrained problem space can be complex and require considerable effort to solve. Nevertheless, having all of the states and operators known can help simplify the problem-solving process and enable more efficient and effective problem solving.

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The time it takes to wash dishes on a randomly selected night. The height is 1/10. The probability is 3/5 or 0.600. The probability of an exact value (like exactly 9 minutes) is always 0.

a) The random variable (rv) X in this context represents the time it takes to wash dishes on a randomly selected night.
b) The height of the uniform distribution can be calculated as the reciprocal of the range of the distribution. In this case, the range is (18 - 8) = 10 minutes. Therefore, the height is 1/10.
c) To find the probability that washing dishes tonight will take between 9 and 15 minutes, we need to calculate the area under the uniform distribution curve within this interval. Since it's a uniform distribution, the area can be calculated as the product of the height and the length of the interval. The length of the interval is (15 - 9) = 6 minutes. So, the probability is (1/10) * 6 = 3/5 or 0.600 (accurate to three decimal places).
d) In a continuous uniform distribution, the probability of an exact value (like exactly 9 minutes) is always 0, as there are infinite possible values within the range of the distribution.

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Answer:

Option (B) 0.00076

Step-by-step explanation:

Surface area of a sphere = 4πr²

Volume of a sphere = 4π/3 (r³)

Surface area : Volume = 4πr² : 4π/3 (r³)

                                      = r² : 1/3 (r³)

                                      = 3 r² : r³

                                      = 3/r

                                      = 3/3960

                          (AFTER SIMPLIFICATION)

                                      = 0.00076

Hence the answer is option (B) 0.00076

Hope my answer help you ✌️

The correct option is B) 0.00076. The surface-area-to-volume ratio is 0.00076.

To find the approximate surface-area-to-volume ratio of the Earth with a radius of approximately 3,960 miles, we will use the following formulas:

Surface area (A) of a sphere: A = 4πr²
Volume (V) of a sphere: V = (4/3)πr³

Step 1: Calculate the surface area:
A = 4π(3,960)² ≈ 197,392,088 square miles

Step 2: Calculate the volume:
V = (4/3)π(3,960)³ ≈ 260,625,332,197 cubic miles

Step 3: Calculate the surface-area-to-volume ratio (A/V):
A/V ≈ 197,392,088 / 260,625,332,197 ≈ 0.000757

The best answer from the choices provided is B. 0.00076.

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The value of the number is 97432.

Let us denote the number by ABCDE, where A is the first digit, B is the second digit, and so on. Since the first digit is not zero, A can only take on values from 1 to 9.

The sum of the digits is given as 36, so we have:

A + B + C + D + E = 36

Since all the digits are different, we have 9 choices for the first digit (A), 9 choices for the second digit (since one digit has been used up), 8 choices for the third digit, and so on. Therefore, the total number of such numbers is:

9 x 9 x 8 x 7 x 6 = 27,648

To find the value of the number, we can simply list out all the possible combinations of the digits, keeping in mind that the first digit cannot be zero. One such number is:

97432

So the value of the number is 97432.

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Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.

The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch. Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.
The probability that a randomly selected fertilized chicken egg takes between 19 and 21 days to hatch depends on several factors such as the breed of the chicken, temperature, and humidity. However, on average, most chicken eggs take around 21 days to hatch.

Therefore, the probability of a fertilized chicken egg taking between 19 and 21 days to hatch is relatively high. However, it is important to note that there may be some variation in the time it takes for eggs to hatch based on individual circumstances.

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We can add the remaining terms of the polynomial: f(x) = 8(x+2) + 2(x+2)(x+1) - 4(x+2)(x+1)(x-1) - 1(x+2)(x+1)(x-1)(x-3) + 0.0416667(x+2)(x+1)(x-1)(x-3)(x-4.9). This is the polynomial of lowest degree (4) that passes through the given points.

To use Newton's divided differences to find the polynomial of lowest degree that passes through the given points, we first need to construct a divided difference table. The table will show the differences between the y-values of the given points, and then the differences between those differences, and so on until we have a single value.

Here is the divided difference table:

|-2 -9  |   -1 -1   |  1 -9  |   3 -9  |  4.9
---------------------------------------
|-9     |   8       | -16     |   0     |
|       |-0.5      |  2      |         |
|       | 0.25     |         |         |
|       |-0.125    |         |         |
|       | 0.0416667|         |         |

The first column lists the x-values of the given points, and the second column lists the corresponding y-values. The remaining columns show the divided differences. For example, the entry in row 2, column 2 (-0.5) is the divided difference between the y-values -9 and -1.

Now we can use the divided differences to construct the polynomial of lowest degree that passes through the points. We start with the first divided difference in the second column, which is 8. This gives us the linear term of the polynomial:

f(x) = 8(x+2) + ...

Next, we use the second divided difference in the third column, which is 2. This gives us the quadratic term of the polynomial:

f(x) = 8(x+2) + 2(x+2)(x+1) + ...

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The probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires is approximately 0.994 or 99.4%.

We can use the central limit theorem to find the probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires.

According to the central limit theorem, the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, we can calculate the z-score as follows:

z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)

where [tex]\bar{X}[/tex] is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we want to find the probability that the sample mean would differ from the population mean by less than 170 miles, which means we need to find the probability that the z-score is between -170/ (σ / √n) and 170/ (σ / √n).

Plugging in the given values, we get:

z = ([tex]\bar{X}[/tex] - μ) / (σ / √n)

z = (170) / (4693 / √211)

z ≈ 8.13

Using a calculator, we can find that the probability of getting a z-score less than 8.13 or greater than -8.13 is approximately 1.0.  Therefore, the probability is approximately 0.994 or 99.4%.

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The horizontal and vertical asymptotes of the function are given below.

We have,

The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (both are 2), and the leading coefficients of both are the same.

The vertical asymptotes are given by setting the denominator equal to zero and solving for x.

In this case, 2x² - 1 = 0, which gives x = ±√(1/2).

Therefore, the vertical asymptotes are x = √(1/2) and x = -√(1/2).

The function g(x) has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator (2 > 0).

The vertical asymptote is at x = 0 because the denominator is equal to zero when x = 0.

The function g(t) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.

The function has no vertical asymptotes because the denominator is never equal to zero.

The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.

The function has no vertical asymptotes because the denominator is never equal to zero.

The function f(x) has no horizontal asymptote because the degree of the numerator is equal to the degree of the denominator (1), and the leading coefficients of both are the same.

The function has a vertical asymptote at x = -1 because the denominator is equal to zero when x = -1.

The function h(x) has no horizontal asymptote because the degree of the numerator is greater than the degree of the denominator (3 > 2).

The function has no vertical asymptotes because the denominator is never equal to zero.

The function g(t) has a horizontal asymptote at y = 2 because as t approaches infinity, the expression (1 - 2)^2 approaches zero, so the function approaches 2.

The function has no vertical asymptotes because the denominator is never equal to zero.

Thus,

The horizontal and vertical asymptotes of the function are given above

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The correct option is A, The error of rejecting a true null hypothesis is known as a Type I error in hypothesis testing.

A hypothesis is an educated guess or a tentative explanation for a phenomenon that can be tested through empirical research. It is a statement that provides a proposed explanation for a phenomenon based on limited evidence or observations. The goal of a hypothesis is to provide a framework for empirical testing, and to determine whether the data collected supports or disproves the hypothesis.

In science, a hypothesis is a crucial part of the scientific method. It helps scientists to define and clarify their research questions, to design experiments or studies, and to make predictions about the outcomes. A hypothesis should be testable, falsifiable, and based on previous research or observations.

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It would take less than 10 minutes for the block of metal to reach the specified temperatures.

To solve this problem, we need to calculate the time it took for the block of metal to cool from 99 degrees Fahrenheit to the specified temperatures.

For the first temperature of 90 degrees Fahrenheit, it would take 9 minutes for the block of metal to cool from 99 degrees Fahrenheit to 90 degrees Fahrenheit, since 9 x -1.4 = -12.6, and 99 - (-12.6) = 90.4.

For the second temperature of 85 degrees Fahrenheit, it would take 14 minutes for the block of metal to cool from 99 degrees Fahrenheit to 85 degrees Fahrenheit, since 14 x -1.4 = -19.6, and 99 - (-19.6) = 85.4.

For the third temperature of 80 degrees Fahrenheit, it would take 19 minutes for the block of metal to cool from 99 degrees Fahrenheit to 80 degrees Fahrenheit, since 19 x -1.4 = -26.6, and 99 - (-26.6) = 80.4.

For the fourth temperature of 75 degrees Fahrenheit, it would take 24 minutes for the block of metal to cool from 99 degrees Fahrenheit to 75 degrees Fahrenheit, since 24 x -1.4 = -33.6, and 99 - (-33.6) = 75.4.

Therefore, it would take less than 10 minutes for the block of metal to reach the specified temperatures.

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Thus,  the higher the test statistic, the stronger the evidence against the "null hypothesis" (i.e., no relationship between Alcohol and Calories).

To calculate the test statistic for the relationship between Alcohol (X) and Calories (Y) in the Beer Large data set, you'll need to perform a linear regression analysis.

1. Access the Beer Large data set in StatCrunch and load it into the platform.
2. Select 'Stat' > 'Regression' > 'Simple Linear' from the menu.
3. Choose 'Alcohol' as the explanatory variable (X) and 'Calories' as the response variable (Y).
4. Click 'Compute' to run the linear regression analysis.

The output will provide you with the test statistic value (rounded to 1 decimal place) for the relationship between Alcohol and Calories.

This value is important when assessing the significance of the relationship between the two variables, as it helps you determine if the relationship is statistically significant or not.

Remember, the higher the test statistic, the stronger the evidence against the null hypothesis (i.e., no relationship between Alcohol and Calories).

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The sample in this argument is "People interviewed in the 10 city survey who watched a 3-D movie".

This is because the researchers selected a random sample of people who watched 3-D movies in the ten major cities, and then interviewed them about their experience of physical discomfort. The 893 people who were interviewed constitute the sample, and their responses were used to draw conclusions about the broader population of people who watch 3-D movies.

Therefore, the sample is a subset of the population of all people who watch 3-D movies, and the researchers used this sample to make inferences about the larger population. The sample in this argument is the people interviewed in the 10 city survey who watched a 3-D movie.

The researchers conducted their study by interviewing a total of 893 individuals across ten major cities at randomly selected movie theaters showing 3-D movies. This sample was used to draw conclusions about the broader population of people who watch 3-D movies and their experiences with physical discomfort, motion sickness, or headaches.

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The probability that the lifespan of a set of tires will be between 32,000 and 44,000 miles is approximately 0.99994 or 99.994%.

To solve this problem, we'll use the concepts of normal distribution, z-scores, and the z-table.

Calculate the z-scores for the given mileage values.
To calculate the z-score, use the formula: z = (X - μ) / σ
For 32,000 miles:
z1 = (32,000 - 38,000) / 1,500 = -6,000 / 1,500 = -4
For 44,000 miles:
z2 = (44,000 - 38,000) / 1,500 = 6,000 / 1,500 = 4
Look up the z-scores in the z-table and find the corresponding probabilities.
For z1 = -4, the z-table gives a probability of approximately 0.00003 (essentially 0).
For z2 = 4, the z-table gives a probability of approximately 0.99997.

Calculate the probability of the lifespan being between 32,000 and 44,000 miles.
Subtract the probability of z1 from the probability of z2:
P(32,000 < X < 44,000) = P(z2) - P(z1) = 0.99997 - 0.00003 = 0.99994.

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The point (-2, -10) does not lie on the line y = 3x - 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question:

y = 3x - 3

To check if the point (-2, -10) lies on the line y = 3x - 3, we need to substitute the values of x and y into the equation and see if it is true.

y = 3x - 3

Plug in x = -2 and y = -10

-10 = 3(-2) - 3

Simplify

-10 = -6 - 3

-10 = -9

But we know that -10 ≠ -9, hence, this is not a true statement.

Therefore, the point does not lie on the line.

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The difference between the largest and smallest numbers is 7173.

To create the largest possible number, we can arrange the digits in decreasing order:

8531

To create the smallest possible number, we can arrange the digits in increasing order:

1358

The difference between the largest and smallest numbers is:

8531 - 1358 = 7173

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Step-by-step explanation:

x = integer     now 'quarter it'

1/4 x       Now square it

(1/4x)^2      add five

(1/4x)^2 + 5     = 9         solve for x

(1/4 x)^2 ) = 4

 1/16  x^2 = 4

         x^2  = 64

            x = ± 8

The function f(x)=150x/100-x models the cost, f(x), in millions of dollars, to remove x% of a river's pollutants. In this equation, x represents the percentage of pollutants that will be removed. The cost of removing pollutants decreases as more pollutants are removed. For instance, if 50% of pollutants are removed, the cost will be $75 million. If 90% of pollutants are removed, the cost will be $450 million. This function is useful in calculating the cost of removing pollutants from a river.

Now, if the government commits $50 million for this project, we can calculate the percentage of pollutants that can be removed using this equation. To do this, we need to solve the equation for x. We can write:

50 = 150x / (100 - x)

Multiplying both sides by (100-x), we get:

50(100-x) = 150x

Expanding and simplifying, we get:

5000 - 50x = 150x

200x = 5000

x = 25

Therefore, the government can remove 25% of the pollutants from the river with the budget of $50 million.

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The requreid electricians must rough in a total of 591 outlets for the eight houses.

To find the total number of outlets, we need to add up the number of outlets for each house:

Total outlets = 68 + 87 + 57 + 74 + 49 + 101 + 99 + 56

Total outlets = 591

Therefore, the electricians must rough in a total of 591 outlets for the eight houses.

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Answer: just add all of the nmber in get a nmber

Step-by-step explanation:

The type of sampling used in this scenario is called random sampling. Random sampling is a method of selecting a sample from a population in which every member of the population has an equal chance of being selected.

In this case, the computer generated 100 random numbers, which means that each number had an equal chance of being selected. Then, 100 people whose names corresponded with the numbers on the list were chosen, which means that each person whose name was on the list also had an equal chance of being selected.

Random sampling is a common method of sampling because it helps to ensure that the sample is representative of the population and reduces the risk of bias

The type of sampling used in this scenario is Simple Random Sampling. This is because each person has an equal chance of being chosen, as their selection is based on random numbers generated by the computer.

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The actual duration of the experiment may vary depending on various factors, such as dropout rates, compliance, and unexpected events.

To determine the number of days needed for the experiment to have a power of 95%, we need to have some additional information about the experiment, such as the sample size, effect size, significance level, and variability in the data.

Assuming that the experiment involves comparing the running time of a group of participants who eat oatmeal with a group of participants who do not eat oatmeal, we can estimate the sample size, effect size, and variability based on previous studies or pilot data.

Let's say that the effect size is 1 minute, the standard deviation of the running time is 5 minutes, and the significance level is 0.05 (i.e., alpha = 0.05). The power of the experiment can be calculated using a power analysis tool, such as G*Power or R.

Using G*Power with a one-tailed t-test, we can calculate the required sample size to achieve a power of 0.95, given the effect size, alpha, and standard deviation. Assuming equal sample sizes in the two groups, we get a required sample size of about 64 participants per group.

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