shoko bought a box of popcorn for $3.50 and three medium drinks. define a variable and write an expression to represent the total they spent.

Answer: You will pay 144 to order a 3 year subscription to the magazine.

Step-by-step explanation:

Answer:

2 and 1/3 of a gallon

Step-by-step explanation:

since a third of a wall requires 3/4 gallons, then two thirds of a wall would require 3/4 + 3/4 gallons since painting two thirds is like painting one thirds two times. similarly, painting three thirds of a wall would be like painting one thirds of a wall three times. 3/4 + 3/4 + 3/4 equals 3 * 3/4 (by the definition of multiplication) which would equal 9/4. 9/4 also equals 2 1/3/

Answer:

I think it is 2 1/4 Gallons

Step-by-step explanation:

3/4 + 3/4 + 3/4 = 9/4

or

3/4 × 3 = 9/4

9/4 = 2 1/4

Answer:

since the decay rate constant of0.0 250 min.

hence the time required for the sample to decay to one forth of it's initial value is

Step-by-step explanation:

Answer:

Step-by-step explanation:

The cross section of a right circular cone parallel to its base is a circle.

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top

The cross section of a right circular cone parallel to its base is a circle.

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To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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The measure of the indicated central angle is 27.

We are given that;

The figure

Now,

Arc length = fraction of the circle x circumference;

Arc length =2 x pi x r x fraction of the circle

3/4 pi  = 2 x pi x 5 x fraction of the circle

3/4 pi  = 10 pi x fraction of the circle

Divide each side by 10 pi

3/4 pi

3/40 = fraction of a circle

A circle is 360 degrees;

3/40 = x/360

Multiply by 360

3/40 *360 = x

x=27

Therefore, by the angle the answer will be 27.

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Answer:

X = 7.633 and Y = 7.638

Step-by-step explanation:

See attached worksheet.

In the expression f(x)=23, x is not a variable. f(x) means “a function of x” or “f of x” and is in practice another way of substituting for the variable y, that is, we are saying:

y=23.

That means x is unspecified and could be anything. So on the xy plane, this is a straight horizontal line, 23 units above the x axis. That would be the best way to interpret this, although it is a little ambiguous.

Usually functions of x are expressed in terms of x, such as:

f(x) = x^2

The value of cos I as a fraction in simplest terms is 4/5.

This is a problem based on trigonometry. Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles. The length of the hypotenuse is 25. The length of the perpendicular is 15. The length of the base is unknown. We know that the angle ∠IJK = 90°.

We need to find the value of Cos(I). But we don't know the value of the length of the base of the triangle. So, we will first find Sin(I).

Sin(I) = 15/25

Sin(I) = 3/5

We know the trigonometric identity that Sin²θ + Cos²θ = 1.

Sin²I + Cos²I = 1

Cos²I = 1 - Sin²I

Cos²I = 1 - (3/5)²

Cos²I = 1 - (9/25)

Cos²I = (25 - 9)/25

Cos²I = 16/25

Cos(I) = √(16/25)

Cos(I) = 4/5

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The first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

Given function is f(x) = x³ - 3x + 1. We have to compute the first derivative of the function at the point x0 = 2 using a five-point formula with h = 5.

Here, we use the five-point formula for differentiation. The five-point formula is given by

\(f′(x) = (-f(x+2h) + 8f(x+h) − 8f(x−h) + f(x−2h))/(12h)\)

Using h = 5 and x0 = 2, we have, h = 5, x = 2

Therefore, x−2h = −8, x−h = −3, x+h = 7, x+2h = 12

Now substitute these values in the above formula:

\(f′(2) = (-f(12) + 8f(7) − 8f(−3) + f(−8))/(12×5)f′(2) = [-1993 - 8(359) + 8(13) + 1349]/60f′(2) = −31.17\) (approx)

Now, we need to find the differentiation error. To find differentiation errors, we use the error formula

|E| = K * h⁴,

where K is a constant, h is the step size and |E| is the maximum error|E| = K * h⁴. Since h = 5, we get|E| = K * 5⁴. To find K, we need to find the maximum value of

\(|f⁽⁵⁾(x)|.f(x) = x³ - 3x + 1\)

∴ \(f′(x) = 3x² - 3\)

∴ \(f′′(x) = 6x\)

∴ \(f′′′(x) = 6\)

∴ \(f⁽⁴⁾(x) = 0\)

∴ \(f⁽⁵⁾(x) = 0\)

So, the maximum value of \(|f⁽⁵⁾(x)| = 0\).

∴ K = 0|E| = K * h⁴ = 0.

f′(2) = -31.17 (approx). The differentiation error is 0.

We are given a function f(x) = x³ - 3x + 1 and we have to find the first derivative of the function at the point x0 = 2 using the five-point formula with h = 5.

The five-point formula is

\(f′(x) = (-f(x+2h) + 8f(x+h) − 8f(x−h) + f(x−2h))/(12h)\)

Using h = 5 and x0 = 2, we have h = 5 and x = 2.

Substituting these values in the formula for the five-point formula for differentiation, we get

\(f′(2) = (-f(12) + 8f(7) − 8f(−3) + f(−8))/(12×5)\)

Substituting the values of f(12), f(7), f(-3) and f(-8) from the given function, we get

\(f′(2) = [-1993 - 8(359) + 8(13) + 1349]/60= −31.17\)(approx)

Now, we need to find the differentiation error. To find the differentiation error, we use the error formula

|E| = K * h⁴,

where K is a constant, h is the step size and |E| is the maximum error.

|E| = K * h⁴

Since h = 5, we get|E| = K * 5⁴. To find K, we need to find the maximum value of |f⁽⁵⁾(x)|.

Differentiating f(x) five times, we get

\(f′(x) = 3x² - 3f′′(x) = 6xf′′′(x) = 6f⁽⁴⁾(x) = 0f⁽⁵⁾(x) = 0\)

The maximum value of |f⁽⁵⁾(x)| = 0. Therefore, K = 0|E| = K * h⁴ = 0. Therefore, the differentiation error is 0. Hence, the first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

The first derivative of the function f(x) = x³ - 3x + 1 at the point x0 = 2 using a five-point formula with h = 5 is -31.17 (approx) and the differentiation error is 0.

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Answer:

25 a week.

Step-by-step explanation:

100+25= 125

125÷5 = 25

The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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Answer:

I think it's 41

Step-by-step explanation:

The Fitness Gram Pacer Test is a multistage aerobic capacity test that progressively gets more difficult as it continues. The 20 meter pacer test will begin in 30 seconds. Line up at the start. The running speed starts slowly, but gets faster each minute after you hear this signal. A single lap should be completed each time you hear this sound. Remember to run in a straight line, and run as long as possible.

if your problem is x = 5, x+6, the answer is 11

but if your problem is x=5x+6

x = -3/2 or -1.5, give me brainliest if correct pleaseee

Answer:

\text{The area of the trapezoid is 92.4 m}^{2}.

The area of the trapezoid is 92.4 m 2.

Step-by-step explanation:

\text{The area of the trapezoid is 92.4 m}^{2}.

The area of the trapezoid is 92.4 m 2.

The weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

To determine the percentage of newborn African lions that weigh less than 3 pounds and the percentage that weigh more than 3.8 pounds, we would need statistical data on the weight distribution of newborn African lions. Since we don't have that information, we cannot provide the exact percentages.

However, if we assume that the weights of newborn African lions follow a normal distribution, we can use the properties of the standard normal distribution to make an estimation.

For the percentage of newborn African lions weighing less than 3 pounds:

We would need to know the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3 pounds and then find the corresponding percentage using a standard normal distribution table. Without this information, we cannot provide an accurate estimation.

For the percentage of newborn African lions weighing more than 3.8 pounds:

Similarly, we would need the mean and standard deviation of the weight distribution to calculate the Z-score for a weight of 3.8 pounds and find the corresponding percentage using a standard normal distribution table. Without the required information, we cannot provide a specific estimation.

Please note that the weight distribution of newborn African lions may not necessarily follow a normal distribution, and the actual percentages can vary based on the specific data available.

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Answer:

9/14

Step-by-step explanation:

The question is not clear enough. Here is a similar question as shown in the attachment

Given the expression

-3/2 ÷ -7/3

= -3/2 ×-3/7

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

= 9/14

Hence the equivalent result expressed as a fraction is 9/14

The ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

Based on the given description, we can identify the following relationships and their characteristics:

1. Book - Publisher Relationship:

  - Degree: 1-to-1 (One book has exactly one publisher)

  - Cardinalities: Each book is associated with one publisher, and one publisher can publish multiple books over time.

  - Graphical Representation: The Book entity will have a foreign key referencing the Publisher entity.

2. Book - Author Relationship:

  - Degree: Many-to-Many (One book can have multiple authors, and one author can write multiple books)

  - Cardinalities: Each book can have one or multiple authors, and each author can write one or multiple books.

  - Graphical Representation: To represent the many-to-many relationship between Book and Author, we will introduce a junction table or associative entity, commonly known as the "BookAuthor" entity. It will have foreign keys referencing both the Book and Author entities.

3. Author - Prospect Relationship:

  - Degree: 1-to-0 or 1 (One author can have either zero or one prospect status)

  - Cardinalities: Each author can either have no prospective status (if they have published books) or have a prospective status (if they haven't published any books yet).

  - Graphical Representation: The Author entity will have an attribute indicating the prospect status, such as a boolean flag.

Overall, the ERD (Entity-Relationship Diagram) representing these relationships will include entities such as Book, Publisher, Author, and BookAuthor (associative entity). The relationships between these entities will be depicted using appropriate connectors and cardinality indicators. Please refer to the attached ERD screenshot for a visual representation of the relationships.

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Answer:

It's $32.39.

Step-by-step explanation:

35.99 - 35.99*10% =

=35.99 - 35.99*0.1

=35.99 - 3.599

=32.391

32.391 is close to 32.39 so we will round it to that number.

The answer is $32.39.

The fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

Given,

The area of the top side of a piece of sheet metal = 4 square feet

The sheet metal is submerged horizontally in 7 feet of water.

Fluid Force on the top side can be found as follows,

Formula used:

Fluid Force = weight-density × volume × depth of fluid

Fluid Force = 62.4 × volume × 7

As the sheet metal is completely submerged, the volume is equal to the area of the sheet metal.

Volume = Area × Depth

= 4 × 7

= 28

Fluid Force = 62.4 × 28 × 7

                   = 12441.6 lb

Thus, the fluid force on the sheet metal's top side when submerged horizontally in 7 feet of water is 12441.6 lb.

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Therefore, the fluid force on the top side is 55838.08 lb.

Given, the area of the top side of a piece of sheet metal is 4 square feet and it is submerged horizontally in 7 feet of water.

The weight-density of water is 62.4 pounds per cubic foot.To find: the fluid force on the top side.Solution:Fluid force formula is given by,

F = ρ * g * V

Where, ρ is the density of the fluidg is the acceleration due to gravityV is the volume of the fluid displaced.Furthermore, the volume of fluid displaced is equal to the volume of the metal sheet submerged in the water.

Therefore,Volume of fluid displaced = Volume of metal sheet submerged in the water = area of metal sheet * depth submerged

Volume of metal sheet submerged in the water = 4 square feet * 7 feet

= 28 cubic feet

Now, calculate the fluid force on the top side of the metal sheet by using the fluid force formula.

F = ρ * g * V

Here, the density of water,

ρ = 62.4 pounds per cubic foot

g = 32.2 ft/s² (the acceleration due to gravity)

V = 28 cubic feet∴

F = 62.4 * 32.2 * 28 lb

= 55838.08 lb

Therefore, the fluid force on the top side is 55838.08 lb.

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Answer:

The equation of the given circle is (x-2)^2 + (y+3)^2 = 9, which is in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Comparing the given equation with the standard form, we can see that the center of the circle is (2, -3) and the radius is 3.

Therefore, the radius of the circle is 3 units.

Answer:

Step-by-step explanation:

The area of a triangle is given by the formula:

● A = (b×h)/2

b is the base and h is the heigth.

■■■■■■■■■■■■■■■■■■■■■■■■■■

Draw the heigth. This gives you two small right triangles.

Let's focus on the right one containing 45°.

● sin 45° = h/8

● h = sin 45° × 8 = 4√(2)

■■■■■■■■■■■■■■■■■■■■■■■■■■

Replace h by its value in the area formula. The base is 17

● A = (17× 4√(2))/ 2

● A = 34√(2)

● A = 48.08

Round to the nearest unit

● A = 48

Answer:

Area = 48 sq. units

Step-by-step explanation:

will make it short and simple.

area of a triangle = 1/2 * a * b * sinФ

area = 1/2 * 17 * 8 * sin(45°) = 48 sq. units

There were 14 participants in each condition in the study, with a total sample size of 28. To determine the number of participants in each condition, we need to look at the degrees of freedom in the one-way ANOVA output.

In this case, the degrees of freedom for the numerator is 1 and the degrees of freedom for the denominator is 26. Since the ANOVA assumes equal sample sizes across conditions, we can calculate the total number of participants by multiplying the sample size by the number of conditions. Using the formula for degrees of freedom, we can calculate the sample size for each condition as follows:
df_between = k - 1
df_within = N - k
Where k is the number of conditions and N is the total number of participants.
In this case, df_between = 1 and df_within = 26. Thus,
1 = k - 1
k = 2
Substituting k = 2 into the df_within equation, we get:
26 = N - 2
N = 28
So, the total number of participants across both conditions is 28. Since we assume equal sample sizes, each condition has 14 participants. Therefore, the number of participants in each condition is 28 / 2 = 14.Therefore, we can conclude that there were 14 participants in each condition in the study, with a total sample size of 28. In summary, given the one-way ANOVA output and assuming equal sample sizes across conditions, we can use the formula for degrees of freedom to calculate the sample size for each condition and determine that there were 14 participants in each condition in the study.

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The best description of the standard deviation is "Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries."

Standard deviation, denoted by σ, is defined as the measure which indicates the average distance of the observations from the mean of the data set. It tells how spread out numbers are. It is equal to the square root of the variance. Variance is the average of the squared differences from the mean.

For the given problem, the standard deviation can be describe as the average(mean) distance of the individual salaries of employees from the mean of all employees' salaries.

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Answer:

Step-by-step explanation:

200 Items were sold

For A total of $130

The Items sold were 0.50

and 0.75.

130 Cans of soda were sold

86 Bags Of popcorn were sold.

The mean number of infected children per sample can be calculated by multiplying the sample size (224) by the probability of a child being HIV positive (25%). Therefore, the mean number of infected children per sample would be 56.

To determine the mean number of infected children per sample, we use the concept of expected value. The probability of a child being HIV positive is given as 25%. This means that in a sample of children born to mothers with HIV antibody, we can expect 25% of them to be infected.

By multiplying this probability by the sample size (224), we obtain the mean number of infected children per sample, which is 56. This value represents the average number of infected children we would expect to find in repeated samples of the same size.

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The critical numbers of the function f(x) = 5x⁴ – x² +1 are 0, 1/√10, and -1/√10. The intervals of increase or decrease are x < -1/√10, -1/√10 < x < 1/√10, and x > 1/√10. The local maximum and local minimum values are f(1/√10) = 4/5√10 + 1 and f(-1/√10) = -4/5√10 + 1 respectively.

Given function f(x) = 5x⁴ – x² + 1(a) Critical Numbers :Critical numbers are the values where the derivative of the function is zero or undefined.

f(x) = 5x⁴ – x² + 1

f'(x) = 20x³ – 2x= 2x(10x² – 1)0 = 2x(10x² – 1)x = 0, or x = ±√(1/10)

Therefore, the critical numbers are 0, 1/√10, and -1/√10.

(b) Increasing and decreasing intervals:

For finding the increasing and decreasing intervals, we need to use the test points. f(x) = 5x⁴ – x² + 1f'(-2) = -72 ( < 0 ).

So, f(x) is decreasing for x < -1/√10.f'(1/2) = 44 ( > 0 )So, f(x) is increasing for -1/√10 < x < 1/√10.f'(2) = 72 ( > 0 )So, f(x) is decreasing for x > 1/√10.(c) Local Maximum and Minimum Values:

For finding the local maximum and minimum values, we need to use the critical numbers.

f(x) = 5x⁴ – x² + 1x = 0, f(0) = 1x = 1/√10, f(1/√10) = 4/5√10 + 1x = -1/√10, f(-1/√10) = -4/5√10 + 1.

Therefore, the function has local maximum at x = 1/√10 and local minimum at x = -1/√10.

To summarize, the critical numbers of the function f(x) = 5x⁴ – x² +1 are 0, 1/√10, and -1/√10.

The intervals of increase or decrease are x < -1/√10, -1/√10 < x < 1/√10, and x > 1/√10.

The local maximum and local minimum values are f(1/√10) = 4/5√10 + 1 and f(-1/√10) = -4/5√10 + 1 respectively.

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\(-0.75(-4f+12)\\\\=-\dfrac 34(-4f +12)\\\\=-\dfrac 34 \cdot (-4f) - \dfrac 34\cdot(12)\\\\=3f-9\\\\\\(5f+9)-(2f+18)\\\\=5f+9-2f-18\\\\=3f-9\\\\\text{Hence, the expressions are equivalent.}\)

Answer:The cordinates of A and B are (-3.8, 5.2) and (7, -2).

Step-by-step explanation:From (1), we get x = (8 - 3y) / 2 ––(3)

Substitute (3) into (2),

2 [(8 - 3y) / 2]² + 3y² = 110

(8 - 3y)² + 3y² = 220

15y² - 48y - 156 = 0

Therefore y = 5.2, then x = (8 - 3×5.2) / 2 = -3.8

OR y = -2, then x = [8 - 3×(-2)] / 2 = 7

Answer:

The coordinates are A. (-3.8, 5.2) and B. (7, -2).

Step-by-step explanation:

At A and B the coordinates satisfy both equations so we solve simultaneously using substitution:

2x^2 + 3y^2 = 110

2x + 3y = 8

From the above equation

x = (8 - 3y)/2

So substituting for x in the first equation:

2 [(8-3y)/2]^2 + 3y^2 = 110

(8-3y)^2 / 2 + 3y^2 = 110

Multiply through by 2:

(8 - 3y)^2 + 6y^2 = 220

64 + 9y^2 - 48y + 6y^2 - 220 = 0

15y^2 - 48y - 156 = 0

3(5y^2 - 16y - 52) = 0

(5y - 26)(y + 2) = 0

y = 26/5, 2

y = 5.2,  -2.

So substituting in 2x + 3y = 8

When y = -2:

2x - 6 = 8

2x = 14

x = 7.

When y = 5.2

2x + 3(5.2) = 8

2x = 8 - 15.6 = -7.6

x = -3.8.

The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000

formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

I bedroom = x

2 bedroom = y

3 bedroom = z

All the condition s gjvbbs'

500x + 900y + 1500z = 750,000 - - - (1)

x + y + z = 1000 - - - - (11)

x = 200 + y + z - - - - (111)

x + 2y + 3z = 1550 - - - (1V)

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the p-value for the given left-tailed test with a test statistic of z = -2.097 is approximately 0.0189. This indicates that if the null hypothesis is true, there is a 1.89% chance of observing a test statistic as extreme as or more extreme than -2.097.

The p-value for a left-tailed test with a test statistic of z = -2.097 can be found by determining the probability of observing a value as extreme as or more extreme than the given test statistic under the null hypothesis. To find the p-value, we look up the corresponding area in the left tail of the standard normal distribution.

Using a standard normal distribution table or a statistical software, the p-value corresponding to a test statistic of z = -2.097 is approximately 0.0189 when rounded to four decimal places. This means that the probability of observing a test statistic as extreme as or more extreme than -2.097, assuming the null hypothesis is true, is approximately 0.0189 or 1.89%.

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