a researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. a random sample of 28 workers at a large department store had a mean of . the standard deviation of the population is . is there enough evidence to support the researcher's claim at ? assume that the variable is normally distributed. use the -value method with tables.

Answer:x= -67 over 24

Step-by-step explanation:

Answer: 4545 yards

Step-by-step explanation:

We can use similar triangles to solve this problem. Let's represent the height of the flagpole with the variable "x".

Using the triangle formed by Carla's line of sight, the height of the apartment building, and the top of the flagpole, we can set up the following proportion:

x / (x + 1515) = 15 / 20

Simplifying this proportion, we get:

4x = 3(x + 1515)

4x = 3x + 4545

x = 4545

Therefore, the height of the flagpole is 4545 yards.

Answer:

$481

Step-by-step explanation:

37×$17=$481

he made $481

The measure of the angle m∠FGH is 83°.

Since the measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the the difference of the intercepted arcs.

Thus, we can say:

m∠FGH = 1/2 * (∠FIH - 97°)

∠FIH = 360 - 97 = 263° (sum of angle in a circle)

m∠FGH = 1/2 * (263 - 97°)

m∠FGH =  1/2 * 166

m∠FGH = 83°

Learn more about arcs on:

https://brainly.com/question/31152916

#SPJ1

Answer:

5x

6xy

2x3y

hope it's helpful

True.  

The decision that would result from a Type I error is:

Closing the park when the lead levels are within the allowed limit. C

In this scenario, the null hypothesis is that the lead levels are okay, and the alternative hypothesis (Ha) is that lead levels exceed the limit.

The decisions that would result from the Type I error are:

Closing the park when the lead levels are in excess of the allowed limit.

This decision would be a false positive, as the park would be closed even though the lead levels are actually within the allowed limit.

This is a Type I error.

Closing the park when the lead levels are within the allowed limit.

This decision would be a correct decision as the park should be closed if the lead levels are not within the allowed limit.

This is not a Type I error.

Keeping the park open when the lead levels are in excess of the allowed limit.

This decision would be a false negative, as the park would remain open even though the lead levels are actually above the allowed limit.

This is a Type II error.

Closing the park because of the increased noise level in the neighborhood.

This decision is not related to the hypothesis testing for lead levels in the park, and therefore, it is not a Type I error.

For similar questions on Error

https://brainly.com/question/28771966

#SPJ11

The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

know more about circumference visit :

https://brainly.com/question/28757341

#SPJ1

Answer:

$21.28

Step-by-step explanation:

We Know

Dylan bought 3 identical shirts online for a total cost of $71.83

$7.99 for shipping

We have the equation:

71.83 = 3s + 7.99

63.84 = 3s

s = $21.28

So, each shirt cost $21.28

The length created by a central angle is 0.04 feet.

What is radius of circle?

The radius of a circle is the distance from the center of the circle to any point on the circle's edge. It is typically denoted by the letter "r" and is one of the fundamental measurements used to describe the geometry of a circle.

First, we need to convert the central angle from degrees to radians. Since there are 60 minutes in a degree, we can divide 18 by 60 to get the angle in degrees as a decimal,

18/60 = 0.3 degrees

Next, we convert this to radians by multiplying by π/180,

0.3 × π/180 ≈ 0.00524 radians

To find the length of the arc created by this central angle, we use the formula,

arc length = radius × central angle

So, for a circle of radius 8 feet and a central angle of 0.00524 radians, the arc length is arc length = 8 × 0.00524 ≈ 0.04192 feet

Rounded to the nearest hundredth, the length of the arc is approximately 0.04 feet.

Learn more about radius of the circle here,

https://brainly.com/question/28162977

#SPJ1

The total number of non-empty subsets s of[tex]{1, 2, 3, . . . , 8}[/tex] such that the product of the elements of s is at most 200 is:
[tex]255 - (127 + 63 + 31) + 2 = 36.[/tex]
So, there are 36 such subsets.

Number of non-empty subsets s of[tex]{1, 2, 3, . . . , 8}[/tex] such that the product of the elements of s is at most 200, we can use a method called inclusion-exclusion principle.
First, we need to count the total number of non-empty subsets of the given set.

Since each element can either be included or excluded, there are [tex]2^8 - 1 = 255[/tex] non-empty subsets.
Next, we need to count the number of subsets whose product is greater than 200.

We can start by considering the subsets that contain 8, since 8 is the largest element in the set.

There are only two such subsets: {8} and {1, 8}.

Both of these subsets have a product greater than 200. Similarly, we can consider subsets that contain 7, and so on. We find that there are[tex]2^7 - 1 = 127[/tex] subsets that contain 7, and each of these subsets has a product greater than 200. Similarly, there are [tex]2^6 - 1 = 63[/tex] subsets that contain 6, and each of these subsets has a product greater than 200.
Double-counted the subsets that contain both 6 and 7, as well as those that contain both 6 and 8, and those that contain both 7 and 8.

Subtract the number of subsets that contain both 6 and 7, both 6 and 8, and both 7 and 8.

There are [tex]2^5 - 1 = 31[/tex] subsets that contain both 6 and 7, and each of these subsets has a product greater than 200.

Similarly, there are[tex]2^5 - 1 = 31[/tex] subsets that contain both 6 and 8, and each of these subsets has a product greater than 200.

Finally, there are [tex]2^5 - 1 = 31[/tex] subsets that contain both 7 and 8, and each of these subsets has a product greater than 200.
However, we have subtracted too much, since we have now excluded subsets that contain all three of 6, 7, and 8. There are only two such subsets: {6, 7, 8} and {1, 6, 7, 8}. Both of these subsets have a product greater than 200.

For similar questions on subsets

https://brainly.com/question/28705656

#SPJ11

To find the number of non-empty subsets s of {1, 2, 3, . . . , 8} such that the product of the elements of s is at most 200, we can use the concept of power set and combinatorics. By analyzing the pattern, we can determine that there are a total of 120 subsets whose product is at most 200.

To find the number of non-empty subsets s of the set {1, 2, 3, . . . , 8} such that the product of the elements of s is at most 200, we can use the concept of power set and combinatorics. The power set of a set is the set of all its subsets. We know that the number of elements in the power set of a set with n elements is 2n. In this case, we have 8 elements in the set, so the power set will have 28 = 256 subsets. However, we need to find the number of subsets with a product at most 200.

We can analyze the products of all subsets to determine the count.

By analyzing the pattern, we can determine that there are a total of 120 subsets whose product is at most 200. This can be calculated by summing the total number of subsets for each number of elements (1-element subsets + 2-element subsets + 3-element subsets + ... + 8-element subsets).

https://brainly.com/question/33319261

#SPJ12

Sampled 200 delinquent credit card accounts instead of 100, the margin of error would decrease.

Sampled 200 delinquent credit card accounts, the margin of error for the sample mean at a 95% confidence level would be $80.164.

Smaller than the margin of error we found earlier for a sample size of 100.

The margin of error for the sample means at a 95% confidence level, we need to use the formula:
[tex]Margin of error = z\times (standard deviation / square root of sample size)[/tex]
[tex]z\times[/tex] is the z-score for the 95% confidence level, which is 1.96.
So, plugging in the given values, we get:
[tex]Margin of error = 1.96 \times  (578 / \sqrt 100)[/tex]
[tex]Margin of error = 1.96 \times 57.8[/tex]
Margin of error = 113.008
Therefore, the margin of error for the sample mean at a 95% confidence level is $113.008.
Repeated samples of 100 delinquent credit card accounts and computed the sample mean each time, we would expect the true population mean to be within $113.008 of our sample mean about 95% of the time.
The margin of error is inversely proportional to the square root of the sample size. So, as the sample size increases, the margin of error decreases.
To see this, let's plug in the new sample size into the margin of error formula:
[tex]Margin of error = 1.96 \times (578 / \sqrt 200)[/tex]
[tex]Margin of error = 1.96 \times 40.9[/tex]
Margin of error = 80.164

For similar questions on Margin

https://brainly.com/question/30404882

#SPJ11

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=2827.43\\ h=4 \end{cases}\implies 2827.43=\pi r^2(4)\implies \cfrac{2827.43}{4\pi }=r^2 \\\\\\ \sqrt{\cfrac{2827.43}{4\pi }}=r\hspace{5em}\stackrel{\textit{twice that is the \underline{diameter}}}{2\sqrt{\cfrac{2827.43}{4\pi }}} ~~ \approx ~~ \text{\LARGE 30}[/tex]

The required sample size of the given estimate is 1090.9809

The population standard deviation is approximately σ = 50.2. You would like to be 90% confident that your estimate is within 1.5 of the true population mean.

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,

For the 90% confidence the value of the z = 1.645

Now the sample size is given as,

n = [z × σ/2.5]²

Substitute values in the above equation,

n = [1.645×50.2/2.5]²

n = 1090.9809

Thus, the required sample size of the given estimate is 1090.9809.

Learn more about statistic here :-

https://brainly.com/question/29093686

#SPJ4

The output of the LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input[tex]x(t)[/tex], is:

[tex]y(t)[/tex]= inverse Fourier transform of [tex][1/(jw^3) X(w)][/tex]

To compute the output of an LTI system with frequency response function [tex]h(w) = 1/(jw^3)[/tex], given an input x(t), we can use the Fourier transform:

[tex]H(w)[/tex] = Fourier transform of [tex]h(t)[/tex]

[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]

[tex]Y(w) = H(w) X(w)[/tex]

[tex]Y(w)[/tex] is the Fourier transform of the output [tex]y(t)[/tex].

Using the given frequency response function, we have:

[tex]H(w) = 1/(jw^3)[/tex]

Taking the Fourier transform of the input [tex]x(t)[/tex], we have:

[tex]X(w)[/tex] = Fourier transform of [tex]x(t)[/tex]

And multiplying [tex]H(w)[/tex] and[tex]X(w)[/tex], we get:

[tex]Y(w) = H(w) X(w) = 1/(jw^3) X(w)[/tex]

Taking the inverse Fourier transform of [tex]Y(w)[/tex], we get the output [tex]y(t)[/tex]:

[tex]y(t)[/tex] = inverse Fourier transform of [tex]Y(w)[/tex]

For similar questions on frequency

https://brainly.com/question/30466268

#SPJ11

As likely as not (assuming the bag contains an equal number of magnets for each letter in the alphabet).

Probability is a measure of the likelihood or chance that a particular event will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

In probability theory, the probability of an event is calculated by dividing the number of ways that the event can occur by the total number of possible outcomes. This is known as the probability formula:

probability = Number of favorable outcomes / Total number of possible outcomes

Probability is used in a wide range of fields, including statistics, finance, physics, and engineering, to model and analyze uncertain situations and make predictions.

B. Likely (assuming the bag contains an equal number of magnets for each letter in the alphabet, and that there are more consonants than vowels in the alphabet).

C. Unlikely (assuming the deck contains an equal number of red and black cards).

D. Impossible (assuming the deck contains only standard playing cards with 52 cards, including 13 cards for each of the four suits).

E. Unlikely (assuming the deck contains only standard playing cards with 52 cards, including 4 cards for each number or face value).

To learn more about probability, visit

https://brainly.com/question/30034780

#SPJ1

76.74 milligrams will remain after 32 hours.

N(t) = N₀e^(-kt)

where:

N(t) is the amount of substance remaining after time t

N₀ is the initial amount of substance

k is the decay constant

To solve for the decay constant, use the information given in the problem:

100 = 200e^(-22k)

Dividing both sides by 200, we get:

0.5 = e^(-22k)

Taking the natural logarithm of both sides, we get:

ln(0.5) = -22k

Solving for k, we get:

k = ln(0.5)/(-22) = 0.0316

Use this value of k to find the amount of substance remaining after 32 hours:

N(32) = 200e^(-0.0316*32) = 76.74 mg

Therefore, approximately 76.74 milligrams of the substance will remain after 32 hours.

Learn more about radioactive decay, here:

https://brainly.com/question/1770619

#SPJ1

76.4 milligrams will remain after 32 hours.

Exponential refers to a mathematical function in which a constant base is raised to a variable exponent. The value of the function increases or decreases rapidly as the exponent increases, depending on whether the base is greater than 1 or between 0 and 1. Exponential functions are commonly used to model situations where a quantity grows or decays at a constant percentage rate over time.

Decay is the natural process of deterioration or rotting of a substance over time. It can occur in both organic and inorganic materials and is often caused by the activity of microorganisms, exposure to oxygen or other environmental factors.

To determine the amount of radioactive substance that remains after 32 hours, we can use the formula A = A₀ ×[tex]e^{-kt}[/tex], where A is the amount remaining, A₀ is the initial amount, k is the decay constant, and t is the time elapsed.

we can use the same formula for exponential decay to find the value of k:

100 = 200 × [tex]e^{(-k*22)}[/tex]

0.5 = [tex]e^{(-k*22)}[/tex]

ln(0.5) = -k×22

k = ln(2)/(22)

Now we can use this value of k to find the amount of substance remaining after 32 hours:

N(32) = 200 [tex]e^{(-k*32)}[/tex]

N(32) = 200 [tex]e^{(-(ln(2)/(22))32)}[/tex]

N(32) ≈ 76.4 mg

Therefore, approximately 76.4 milligrams of the substance will remain after 32 hours.

Learn more about function here:

https://brainly.com/question/12431044

#SPJ1

These investments do indeed produce a net return of $133.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

Let's call the amount Devon invested in the real estate fund "x". Then, we know that the amount invested in the large cap stock fund is twice that, or "2x". The total amount invested is $9500, so we can write:

x + 2x + y = 9500

where "y" is the amount invested in the bond fund.

We also know the returns of each fund, so we can calculate the total return on the investments:

0.047(2x) - 0.122x + 0.054y = 133

Simplifying this equation, we get:

0.998x + 0.054y = 133

We have two equations and two unknowns (x and y), so we can solve for them. Let's start by solving the first equation for y:

y = 9500 - 3x

Now we can substitute this expression for y into the second equation:

0.998x + 0.054(9500 - 3x) = 133

Simplifying and solving for x, we get:

0.888x = 459.8

x = 517.57

So Devon invested $517.57 in the real estate fund. The amount invested in the large cap stock fund is twice that, or $1035.14. The amount invested in the bond fund is:

y = 9500 - 3x = 8464.29

To check that these investments produce a net return of $133, we can calculate the total return on each investment and add them up:

0.047(2x) - 0.122x + 0.054y = 0.047(2517.57) - 0.122517.57 + 0.054*8464.29 = 133.00

So these investments do indeed produce a net return of $133.

To learn more about algebra from the given link:

https://brainly.com/question/24875240

#SPJ1

The answer is A. Evaluation researchers encounter more logistical problems than other researchers because evaluation research occurs in the context of real life.

Evaluation research often takes place in real-world settings, which can present logistical challenges such as accessing participants, coordinating schedules, and dealing with unexpected events. Additionally, evaluation research often involves multiple stakeholders and requires collaboration and communication among various groups, which can further complicate logistical issues. While evaluation research may also involve longer timelines, higher costs, measurement problems, and examination of multiple variables, these factors do not necessarily contribute to greater logistical challenges.

This means that evaluation researchers have to navigate complex, real-world situations, adapt to unforeseen challenges, and work with various stakeholders, making the research process more logistically challenging compared to controlled laboratory settings or theoretical research.

to learn more about theoretical research. click here:

https://brainly.com/question/29220441

#SPJ11

Evaluation research is a type of research that focuses on assessing the effectiveness, efficiency, and impact of programs, policies, or interventions in real-life settings.

The correct answer is A. occurs in the context of real life.

This often involves evaluating the outcomes and impacts of interventions in complex and dynamic environments, such as organizations, communities, or systems. As a result, evaluation researchers may encounter more logistical problems compared to other types of researchers because they need to navigate real-life contexts, deal with multiple stakeholders, collect data from diverse sources, and address issues such as ethics, confidentiality, and validity in the evaluation process. Logistical problems may include challenges related to data collection, measurement, sample selection, data quality, and managing time and resources.

Learn more about “ Logistical problems “ visit here;

https://brainly.com/question/31087596

#SPJ4

Answer:

The amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Step-by-step explanation:

The given function is:

f(t) = -1/2(4t - 2π)

We can rewrite this function in the form:

f(t) = A cos(B(t - C)) + D

where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

Comparing this with the given function, we can see that:

A = 1/2

B = 4

C = π/2

D = 0

Therefore, the amplitude is 1/2, the period is 2π/4 = π/2, and the phase shift is π/2.

Note that the negative sign in front of the function does not affect the amplitude, period, or phase shift. It simply reflects the function across the x-axis.

a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

To learn more about frequency distribution visit;

https://brainly.com/question/14926605

#SPJ11

If we consider grade "C" or above as a pass grade, then the number of  students who successfully passed the course are 10 students.

The Number of students who got grade "A" = 8,

The Number of students who got "B" grade is 2,

The Number of students who got grade "C" = 0,

The Number of students who got grade "D" = 0,

The Number of students who got grade "F" = 1,

Since the question asks for the number of students who successfully passed the course (i.e., grade "C" or above is considered a pass grade),

We add the number of students who got grades "A" and "B".

So, total number of students who successfully passed course are :

⇒ 8 (students who got grade "A") + 2 (students who got grade "B")

⇒ 10

Therefore, 10 students successfully passed the course.

Learn more about Student here

https://brainly.com/question/11898827

#SPJ4

The given question is incomplete, the complete question is

If 8 students of the class got grade "A", 2 student got grade "B", No student got grade "C" and "D", 1 student got grade "F".

Considering grade "C" or above as a pass grade, how many students from this data successfully passed the course?

Answer: 94 square inches 2

Step-by-step explanation:

2×(5×4 + 5×3 + 4×3) = 94 sq in 2

length x width x height

if you need more help with your ixl I am free to help!

have a good day!

The bigger engine is larger than the smaller one by 235.4724 cubic centimeters.

We know that 1 inch=2.54 centimeters

Then 1 cubic inches-(2.54)^3 cubic centimeters

We have that:

⇒ 1 cubic inches=(2.54)3 = 16.3870 cubic centimeters

⇒350 cubic inches= 350 x 16.3870 = 5735.4724 cubic centimeters

Since, the other displaces 5,500 cubic centimeters  and 5735.4724< 5500. The difference between them is:

= 5735.4724 - 5500

= 235.4724

Hence, the bigger engine larger than the smaller one by 235.4724 cubic centimeters.

Read more about Engine size

brainly.com/question/14439953

#SPJ1

Point A = (5,4). If you rotated A 90 degrees about the point (2,-1), the coordinates of A' is (-1,2).

Rotation is the process of rotating an object or a point around a fixed point or axis. In mathematics, rotation refers to a transformation that preserves the size and shape of an object while changing its orientation. It is a basic geometric transformation that is used in various fields, including mathematics, physics, engineering, and computer graphics.

In a two-dimensional space, a rotation is typically described by an angle of rotation and a fixed point, which is known as the center of rotation. The angle of rotation represents the amount by which the object is rotated, while the center of rotation is the point around which the object is rotated. In a three-dimensional space, a rotation is described by an axis of rotation and an angle of rotation.

To rotate point A 90 degrees counterclockwise about the point (2,-1), we can use the following formula:

A' = (x', y') = (a + (x - a) cosθ - (y - b) sinθ, b + (x - a) sinθ + (y - b) cosθ)

where (a,b) is the center of rotation and θ is the angle of rotation (90 degrees in this case).

Substituting the given values, we get:

a = 2, b = -1, x = 5, y = 4, θ = 90 degrees

x' = 2 + (5 - 2) cos(90) - (4 + 1) sin(90) = 2 - 3 = -1

y' = -1 + (5 - 2) sin(90) + (4 + 1) cos(90) = -1 + 3 = 2

Therefore, the coordinates of A' are (-1, 2).

To know more about coordinates visit:

https://brainly.com/question/18596983

#SPJ9

The probability that a randomly selected can in the box is dented or contains vegetables is 19/20.

To solve the problem, we need to use the formula for the probability of the union of two events:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events.

In this case, we want to find the probability that a randomly selected can is dented or contains vegetables. Let's call these events D and V, respectively.

We are given that there are 20 cans in total, 12 of which contain vegetables, and 5 of which are dented, with 2 of the dented cans containing vegetables. This information allows us to calculate the probabilities of the individual events

P(D) = 5/20 = 1/4

P(V) = 12/20 = 3/5

P(D and V) = 2/20 = 1/10

To find the probability of the union of these events, we plug these values into the formula

P(D or V) = P(D) + P(V) - P(D and V)

= 1/4 + 3/5 - 1/10

= 19/20

Learn more about probability here

brainly.com/question/11234923

#SPJ4

Answer:

1.504 x 10^4

Step-by-step explanation:

"It can vary - it really depends on the distribution of the variable."

The number of intervals, or bins, to choose when creating a histogram can vary depending on the distribution of the variable.

Most often, about 8-10 intervals are used, but there is no set rule. It is generally recommended to have at least 5 intervals, but if the data is highly skewed or has outliers, more intervals may be needed to accurately represent the distribution.

Ultimately, the goal is to choose a number of intervals that provides a clear visual representation of the data without oversimplifying or overcomplicating the histogram.

The number of intervals or bins to be chosen when creating a histogram can vary and it really depends on the distribution of the variable.

While most often, about 8-10 bins are used, there is no hard and fast rule for the number of bins to be used in a histogram.

In general, the number of bins should be large enough to display the shape of the distribution clearly, but not so large that it obscures important features of the distribution or leads to overfitting.

A minimum of 5 bins is recommended to display the basic shape of the distribution, but more bins may be necessary for complex or multi-modal distributions.

Depending on the distribution of the variable, a histogram's number of intervals or bins can be altered.

There is no established guideline, however 8–10 intervals are typically utilized.

A minimum of five intervals are often advised, however if the data is extremely skewed or contains outliers, more intervals could be required to correctly depict the distribution.

For similar questions on variable.

https://brainly.com/question/27894163

#SPJ11

Answer:√2/2

Step-by-step explanation:

Let's label the sides of the right triangle as follows:

The side adjacent to the angle θ (cosine is adjacent/hypotenuse): 6

The hypotenuse (the longest side): 6√2

The side opposite to the angle θ (sine is opposite/hypotenuse): 6√3

Using the Pythagorean theorem, we can find the length of the missing side:

a² + b² = c²

6² + (6√3)² = (6√2)²

36 + 108 = 72

144 = 72

√144 = √72

12 = 6√2

Now that we know the length of all three sides, we can use the cosine ratio to find the value of cos(θ):

cos(θ) = adjacent/hypotenuse = 6/6√2 = √2/2

Therefore, the value of cos(θ) in the right triangle with sides of 6, 6√2, and 6√3 is √2/2.

The sample mean for 100 pell grant recipients is more likely to be within $80 of $2,600 for State A, given the relatively smaller population size and the use of the t-distribution.

To compare the two states, we need to calculate the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 for each state.

For State A, with only 4,000 pell grant recipients, the sample size of 100 is relatively large, but not enough to use the normal distribution. Therefore, we need to use the t-distribution, which has fatter tails than the normal distribution, making it more likely to produce extreme values. This means that the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is higher for State A than for State B.

For State B, with a larger population of 200,000 pell grant recipients, the sample size of 100 is a small fraction of the population, allowing us to use the normal distribution. However, as the distribution is narrower than the t-distribution, the probability of the sample mean for 100 pell grant recipients being within $80 of $2,600 is lower for State B than for State A.

You can learn more about sample mean at: brainly.com/question/14127076

#SPJ11