find the mass of the region bounded by y=5-x and with the density function .p(x,y)=5xy

Answer:

\(7-8x+4y=-21\)

Step-by-step explanation:

\(2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21\)

In a random walk, the probability of escape on top at a is the probability that the walk will reach the upper bound of a=8 before hitting the lower bound of b=-4, starting from a initial position between a and b.The answer is (a) 0%.

The probability of escape on top at a can be calculated using the reflection principle, which states that the probability of hitting the upper bound before hitting the lower bound is equal to the probability of hitting the upper bound and then hitting the lower bound immediately after.

Using this principle, we can calculate the probability of hitting the upper bound of a=8 starting from any position between a and b, and then calculate the probability of hitting the lower bound of b=-4 immediately after hitting the upper bound.

The probability of hitting the upper bound starting from any position between a and b can be calculated using the formula:

P(a) = (b-a)/(b-a+2)

where P(a) is the probability of hitting the upper bound of a=8 starting from any position between a and b.

Substituting the values a=8 and b=-4, we get:

P(a) = (-4-8)/(-4-8+2) = 12/-2 = -6

However, since probability cannot be negative, we set the probability to zero, meaning that there is no probability of hitting the upper bound of a=8 starting from any position between a=8 and b=-4.

Therefore, the correct answer is (a) 0%.

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The expression equivalent to the 5ⁿ/2ⁿ will be (5/2)ⁿ , (2/5)⁻ⁿ ,  (2.5)ⁿ , 2⁻ⁿ/5⁻ⁿ.Options A, B, D, and F are correct.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the expression is, 5ⁿ/2ⁿ

The expression can be written in different ways as,

5/2)ⁿ

(2/5)⁻ⁿ

(2.5)ⁿ

2⁻ⁿ/5⁻ⁿ

Thus, the expression equivalent to the 5ⁿ/2ⁿ will be (5/2)ⁿ , (2/5)⁻ⁿ ,  (2.5)ⁿ, 2⁻ⁿ/5⁻ⁿ. Options A, B, D, and F are correct.

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Answer:

#1) Write a function to model population growth. Use a graph to predict when the population will reach 20, 000.

Answer: In this case what you have to do is use an exponential growth equation. In short the correct function that will model this population growth of 14% each year is P(t) = 350(1.14)^t and the population will reach 20,000 in about 31 years.

I hope it helps,

Step-by-step explanation:

plz mark brainlyest

We conclude that the data are consistent with Mendel's prediction of a 3:1 ratio of smooth to wrinkled peas.

To carry out a chi-square goodness-of-fit test, we need to calculate the expected number of smooth and wrinkled peas based on Mendel's prediction of a 3:1 ratio.

The total number of peas observed in the experiment is:n = 423 + 133 = 556The expected number of smooth peas is 3/4 of the total number of peas, and the expected number of wrinkled peas is 1/4 of the total number of peas.

Therefore, we have: Expected number of smooth peas = 3/4 × 556 = 417Expected number of wrinkled peas = 1/4 × 556 = 139

We can now calculate the chi-square statistic as follows:chi-square = Σ[(observed - expected)² / expected]where the sum is taken over the two categories (smooth and wrinkled).

For the observed values of 423 smooth and 133 wrinkled peas, we have: chi-square = [(423 - 417)^2 / 417] + [(133 - 139)^2 / 139]= 0.84 + 0.84= 1.68

The degrees of freedom for this test are (number of categories - 1), which is 2 - 1 = 1.

Using a significance level of 0.05 and a chi-square distribution table with 1 degree of freedom, we find that the critical value of chi-square is 3.84.

Since our calculated chi-square value of 1.68 is less than the critical value of 3.84, we fail to reject the null hypothesis that the observed frequencies do not differ significantly from the expected frequencies based on Mendel's prediction.

Therefore, we conclude that the data are consistent with Mendel's prediction of a 3:1 ratio of smooth to wrinkled peas.

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it is not a universal rule that the sum of two repeating decimals will always be a repeating decimal. There are instances where their sum can result in a terminating decimal or an integer, as demonstrated in the examples above.

It is not always true that the sum of two repeating decimals must be a repeating decimal.

There are cases where their sum can result in a terminating decimal or even an integer.
Let me provide you with a step-by-step explanation:
Firstly, understand what a repeating decimal is. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point, such as 0.333... or 0.272727...
Now, let's consider two repeating decimals as examples: 0.333... and 0.666...
Add these two repeating decimals together:
  0.333...
+ 0.666...
---------
= 0.999...
Observe that the result, 0.999..., is also a repeating decimal. In fact, it is mathematically equal to the integer 1. This demonstrates that the sum of two repeating decimals can be an integer.
Let's consider another example: 0.333... and 0.467467...
Add these two repeating decimals together:
  0.333...
+ 0.467467...
------------
= 0.800467...
In this case, the sum of the two repeating decimals is a mixed decimal with a terminating part (0.800) and a repeating part (467).

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Answer: Your answer is 25

Step-by-step explanation:

To start off, add 16 positive to -116 negative. That gives us a baseline of -100

Now since we did -4 times a number to get to it, the opposite of multiplying is dividing.

A quarter is 25. 4 quarters makes a dollar, or 100 cents. 4 times 25 is 100 so -4 times 25 is -100. Add 16 to your number to get a result of 25! Since you already subtracted 16 we can forget about adding it back. 100/4 = 25

To check our work, -116+10= -100

4 times 25 is 100

-4 times 25 is -100

-100=-100

Answer:

A

Step-by-step explanation:

Find the ratio of pounds to dollars, \(\frac{3}{2}\) or 1.5.

Next test each option by multiply the pounds by that ratio.

A: 28*1.5=42

B: 23*1.5=34.5

C: 11*1.5=16.5

D: 10*1.5=15

You can see A is the incorrect answer as 28 pounds would be 42 dollars, not 44.

Total of all frequencies:

5+8+1213+11= 49

Divide the frequency of 59-61 by total frequencies:

13/49 = 0.265 which rounds to 0.27

The answer is 0.27

To analyze the variances in April, we need to compare the actual costs with the standard costs for materials, labor, and manufacturing overhead.

By calculating the price and quantity variances for materials, rate and efficiency variances for labor, and spending and efficiency variances for variable manufacturing overhead, we can assess the deviations from the standard costs. Additionally, the fixed manufacturing overhead budget and volume variances can be determined by comparing the actual fixed overhead costs with the budgeted amount.

1. Materials Price and Quantity Variances:
The materials price variance measures the difference between the actual cost of materials and the standard cost based on the quantity purchased. It can be calculated as (Actual Price - Standard Price) x Actual Quantity. In this case, the materials price variance is ($18.00 - $18.20) x 6,000 meters.

The materials quantity variance assesses the difference between the actual quantity used and the standard quantity allowed. It can be calculated as (Actual Quantity - Standard Quantity) x Standard Price. Here, the materials quantity variance is (6,000 meters - (2,000 robes x 2.8 meters per robe)) x $18.20.

2. Labour Rate and Efficiency Variances:
The labor rate variance measures the difference between the actual hourly rate and the standard hourly rate, multiplied by the actual hours worked. It can be calculated as (Actual Rate - Standard Rate) x Actual Hours. In this case, the labor rate variance is ($3.80 - $3.60) x 760 hours.

The labor efficiency variance assesses the difference between the actual hours worked and the standard hours allowed, multiplied by the standard rate. It can be calculated as (Actual Hours - Standard Hours) x Standard Rate. Here, the labor efficiency variance is (760 hours - (2,000 robes x 1.5 hours per robe)) x $3.60.

3. Variable Manufacturing Overhead Spending and Efficiency Variances:
The variable manufacturing overhead spending variance measures the difference between the actual variable overhead costs and the standard variable overhead costs. It can be calculated as Actual Variable Overhead - (Standard Variable Rate x Actual Hours). In this case, the variable overhead spending variance is $3,800 - ($1.20 x 760 hours).

The variable manufacturing overhead efficiency variance assesses the difference between the actual hours worked and the standard hours allowed, multiplied by the standard variable overhead rate. It can be calculated as (Actual Hours - Standard Hours) x Standard Variable Rate. Here, the variable overhead efficiency variance is (760 hours - (2,000 robes x 1.5 hours per robe)) x $1.20.

4. Fixed Manufacturing Overhead Budget and Volume Variances:
The fixed manufacturing overhead budget variance measures the difference between the actual fixed overhead costs and the budgeted fixed overhead costs. It can be calculated as Actual Fixed Overhead - Budgeted Fixed Overhead. In this case, the fixed overhead budget variance is $4,600 - $4,680.

The fixed manufacturing overhead volume variance assesses the difference between the standard hours allowed and the budgeted fixed overhead rate, multiplied by the standard fixed overhead rate. It can be calculated as (Standard Hours - Budgeted Hours) x Standard Fixed Overhead Rate. Here, the fixed overhead volume variance is ((2,000 robes x 1.5 hours per robe) - 780 hours) x $2.40.

By calculating these variances, we can analyze the deviations from the standard costs and identify areas where the actual costs differ from the expected costs.

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Answer: If im right the distance she covered is 111 kilometers

Step-by-step explanation:

The volume of the pyramid is 189 cubic units.

Triangular Pyramid. If the base of a pyramid is in the shape of a triangle, it is said to be a triangular pyramid. ...

Pentagonal Pyramid. ...

Right Pyramid vs Oblique Pyramid. ...

Regular vs Irregular Pyramid.

The typical formula for calculating the total surface area of a regular pyramid is provided as follows: The Total surface area of a pyramid formula = 12 pl + B, where "p" denotes the base's perimeter, "l" denotes the pyramid's slant height, and "B" is the base's area.

The value of the volume of pyramid is

1/3*9*9*7

=189 cu units

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Answer:

Volume of pyramid = \( \sf 189 \: {in}^{3} \)

Step-by-step explanation:

Now we have to,

→ find the volume of pyramid.

Formula we use,

→ Volume = (1/3) × b² × h

Then required volume will be,

→ (1/3) × b² × h

→ (1/3) × (9)² × 7

→ (1/3) × 81 × 7

→ (81/3) × 7

→ 27 × 7

→ 189 in³

Hence, the volume is 189 in³.

There are 36 students in Ms. Oaks' class. The number of students who wear each type of item is: Glasses: 15 students, Earrings: 8 students, Hats: 4 students and Watch: 9 students

Let the total number of students in Ms. Oaks' class be x.

a) We know that 2/18 of the students wear hats, which is equivalent to 1/9 of the students. We are also told that 4 students wear hats. So, we can set up an equation:

1/9 * x = 4

Solving for x, we get:

x = 36

Therefore, there are 36 students in Ms. Oaks' class.

b) We can now use the information given to determine how many students wear each type of item.

- Glasses: 5/12 of the students wear glasses, which is equivalent to:

(5/12) * 36 = 15 students

- Earrings: 2/9 of the students wear earrings, which is equivalent to:

(2/9) * 36 = 8 students

- Hats: We are told that 4 students wear hats.

- Watch: 1/4 of the students wear a watch, which is equivalent to:

(1/4) * 36 = 9 students

Therefore, the number of students who wear each type of item is:

Glasses: 15 students

Earrings: 8 students

Hats: 4 students

Watch: 9 students

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Answer:

-4

Step-by-step explanation:

The price of Groupon for revenue of $300 is $4 if the expected revenue is at least $390 per day.

Probability is assigned as

x =30, 60, 120, 180

P(x) = 0.10,0.40, 0.40, 0.10

Expected sales volume:

Number of tubes x =30, 60, 120, 180

Probability P(x)= 0.10,0.40, 0.40, 0.10

Expected values are 3, 24,48,18

Total = 93 tubes

Groupon price = $390/$93 = $4.19

Jane's price for each Groupon is the daily rental income divided by the expected number of tubes rented per day. The expected number of tubes is derived by multiplying the expected number of each tube by its probability and then summing the results. 

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Answer:

median = 9.5

range = 11

Step-by-step explanation:

mean = (sum of numbers)/(number of numbers)

(18 - x + x - 3 + x + x/2 + 5 + 4x - 10 + 2x - 1)/6 = 9

9 + 7x + x/2 = 54

7x + x/2 = 45

14x + x = 90

15x = 90

x = 6

Now we can write the 6 numbers.

12, 3, 6, 8, 14, 11

We write the numbers is increasing order.

3, 6, 8, 11, 12, 14

The median is the mean of the 2 middle numbers.

median = (8 + 11)/2 = 19/2 = 9.5

The range is the difference between the larges and smallest of the numbers.

range = 14 - 3 = 11

Answer:

75% decrease

Step-by-step explanation:

88 - 66 = 22

66 is 75% of 88

\(\huge\text{Hey there!}\)

\(\mathsf{Percentage\ change \ formula\ is: \bf \dfrac{(v_2 - v_1)}{|v_2|}\times 100 = \boxed{\mathsf{\bf percentage \ change}}}\)

\(\textsf{Your equation:} \mathbf{\dfrac{(22 - 88)}{|88|}\times 100}\)

\(\mathbf{\dfrac{(22 - 88)}{|88|}\times 100}\)

\(\mathsf{= \mathbf{\dfrac{(22 - 88)}{|88|}\times \dfrac{100}{1}}}\)

\(\mathbf{= \dfrac{-66}{88}\times\dfrac{100}{1}}\)

\(\mathbf{= \dfrac{-66\div 11}{88\div11}\times\dfrac{100}{1}}\)

\(\mathbf{= \dfrac{-6}{8}\times \dfrac{100}{1}}\)

\(\mathbf{= \dfrac{-6\div2}{8\div2}\times \dfrac{100}{1}}\)

\(\mathbf{= \dfrac{-3}{4} \times \dfrac{100}{1}}\)

\(\mathbf{= \dfrac{-3\times100}{4\times1}}\)

\(\mathbf{= \dfrac{-300}{4}}\)

\(\mathbf{= -300\div4}\)

\(\mathbf{= -75}\)

\(\mathbf{\rightarrow -75\%\ will\ be\ your\ change}\)

\(\mathbf{\rightarrow 75\%\ will \ be\ your\ percentage\ change\ that\ decreased}\)

\(\huge\text{Therefore your answer should probably be:}\)

\(\huge\boxed{\mathsf{75\% \ decrease}}\huge\checkmark\)

\(\huge\text{So, your I guess the answer with the choices}\\\\\huge\text{you have provided we will be: }\\\\\huge\boxed{\textsf {77.3\% (Option C.)}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

The "errors-in-variables" problem, also known as measurement error, occurs in econometrics when one or more variables in a regression model are measured with error. In other words, the observed values of the variables do not perfectly represent their true values.

Consequences for the least squares estimator:

Attenuation bias: Measurement error in the independent variable(s) can lead to attenuation bias in the estimated coefficients. The least squares estimator tends to underestimate the true magnitude of the relationship between the variables. This happens because measurement errors reduce the observed variation in the independent variable, leading to a weaker estimated relationship.

Inconsistent estimates: In the presence of measurement errors, the least squares estimator becomes inconsistent, meaning that as the sample size increases, the estimated coefficients do not converge to the true population values. This inconsistency arises because the measurement errors affect the least squares estimator differently compared to the true errors.

Biased standard errors: Measurement errors can also lead to biased standard errors for the estimated coefficients. The standard errors estimated using the least squares method assume that the independent variables are measured without error. However, in reality, the standard errors will be underestimated, leading to incorrect inference and hypothesis testing.

To mitigate the errors-in-variables problem, econometric techniques such as instrumental variable (IV) regression, two-stage least squares (2SLS), or other measurement error models can be employed. These methods aim to account for the measurement errors and provide consistent and unbiased estimates of the coefficients.

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The matched pairs were identified using sampling techniques as follows:

Convenient: The most convenient way to sample, for example, all people in one location.

Random: A selection of options drawn at random from a set of all.

Systematic: Every k element is sampled for one option.

Cluster: Divide into groups, and survey all elements of each group.

Stratified: Divided into groups, with a percentage of each group surveyed.

So,

Item a:

Item b:

Item c:

Item d:

Item e:

Therefore, the matched pairs were identified using sampling techniques as follows:

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The correct question is given below:

A college administrator wants to survey 250 students that attend her college to see if students are satisfied with the course offerings. Match the strategies to their corresponding sampling techniques.

a. 12345 The administrator gets the complete list of students at the college and then uses a computer to randomly select 250 students. She then surveys these 250 students.

b. -12345 The administrator gets the complete list of students at the college and surveys every 50th students on the list.

c. -12345The administrator researches the ethnic make-up of the college and makes sure that the proportion of each ethnic group represented in the sample is the same as the corresponding proportion of that ethnic group at the college.

d. -12345 The administrator goes into 9 classes from many subject areas and asks all the students in each of these 9 classes.

e. -12345 The administrator stands by the front door of the admissions department and asks the first 250 students who walk in.

1. Stratified Sampling

2. Systematic Sampling

3. Simple Random Sampling

4. Cluster Sampling

5. Convenience Sampling

Answer:

$36

Step-by-step explanation:

2/3 = $24

divide 24 by 2 to find 1/3

1/3 = $12

3/3 = (12 + 12 + 12 )

3/3 = 36

A11. Find the solution z(t) to the differential equation d²z/dt² + t(dz/dt)= 3t, dz/dt(0)=1.

The first thing we need to do is solving the characteristic equation,

given by:r² + tr = 0r (r + t) = 0r 1 = 0r 2 = -t

Thus, the general solution of the homogeneous equation is given by:

Now, we need to find a particular solution.

We can assume zp (t) = at + b, for simplicity.

Therefore,d²z/dt² = \(0dz/dt = adz/dt = a = 1∴ zp\)(t) = t + b Substituting this into the original differential equation,

we have: 2a + t(a) = 3tt + 1 Solving for a, we get:a = 1

Now, we know that zp(t) = t + b.

We can solve for b by substituting into the original equation and using the initial condition of dz/dt(0) =

1. We have:2 + 0b = 3(0)b = -2 Thus, zp(t) = t - 2

Therefore, the general solution of the differential equation is given by

:z(t) = zh(t) + zp(t)z(t) = c1 + c2exp(-t²/2) + t - 2

The last step is to use the initial condition of dz/dt(0) = 1.

We have:dz/dt = c2(-t)exp(-t²/2) + 1 Equating this to 1 and solving for c2, we get:c2 = -exp(t²/2)

Therefore, the final solution is given by:

z(t) = c1 - exp(t²/2) + t - 2exp(-t²/2)

Sketch a graph of the solution for t >0.

The graph is shown below:Graph of z(t) = c1 - exp(t²/2) + t - 2exp(-t²/2)

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The inverse Laplace transform, we have C-1 3s – 20 s(s+4) = f(t), where the correct choice is Of( t) = -5 8e4t.

To determine the inverse Laplace transfigure, we first need to simplify the expression on the left- hand side of the equation. Expanding the equation gives C- 1/( 3s) 20/( s 4) = f( t).

Taking the inverse Laplace transfigure of each term, we get

 L- 1{ C}- L- 1{ 1/( 3s)} L- 1{ 20/( s 4)} = f( t).

The inverse Laplace transfigure of 1/( 3s) is(1/3) u( t),

where u( t) is the unit step function.

The inverse Laplace transfigure of 20/( s 4) is 20e(- 4t) u( t).

the equation becomes

C-(1/3) u( t) 20e(- 4t) u( t) = f( t).

Simplifying further,

we have C( 20e(- 4t)-1/3) u( t) = f( t).

Comparing this with the given options, the correct choice is Of( t) = -5 8e4t, as it matches the form of the equation we deduced.

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Answer:

27%

Step-by-step explanation:

3000 + 3500 + 4000 + 4200 = 14700

4000 / 14700 ≈ 0.27

0.27 = 27%

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Using the Law of Sines, the value of angle A in the triangle with angles B = 52°, C = 20°, and side length b = 40 is approximately 108°

Given:

Angle B = 52°

Angle C = 20°

Side b = 40

To find angle A, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Apply the Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

Substitute the given values:

sin(A)/a = sin(52°)/40 = sin(20°)/c

Rearrange the equation to solve for A:

sin(A) = (a * sin(52°)) / 40

A = arcsin((a * sin(52°)) / 40)

Substitute the known values into the equation:

A = arcsin((a * sin(52°)) / 40)

Use the given information to find the value of side a:

Angle B + Angle C + Angle A = 180° (sum of angles in a triangle)

52° + 20° + A = 180°

A = 180° - 52° - 20°

A = 108°

Substitute the value of A into the equation from step 4:

a = (40 * sin(52°)) / sin(108°)

Calculate the value of a using the given values and trigonometric functions.

Therefore, using the Law of Sines, we find that angle A is approximately 108°.

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The area of the sector is evaluated to be equal to 274.40 square inches rounded to two decimal place.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

the angle of the sector = 260°

the radius = 11 in

hence the area of the sector is calculated as follows:

(260°/360°) × 3.14 × 11 in × 11 in

we simplify by multiplication and division

13/18 × 3.14 × 11 in × 11 in

13/18 × 3.14 × 121 in²

4939.22 in²/18

274.4011 in²

Therefore, the area of the sector is evaluated to be equal to 274.40 square inches rounded to two decimal place.

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The maximum profit from the profit function along the given constraints is 96.

To solve this problem, we can use the graphical method. First, we need to graph the constraints. The first constraint, 4x + 2y ≤ 40, is a line. The second constraint, -3x + y ≥ -4, is a line. The third constraint, x ≥ 3, is a vertical line. The fourth constraint, y ≥ 0, is a horizontal line.

The feasible region is the area of the graph that is shaded in. The maximum profit occurs at the vertex of the feasible region. The coordinates of the vertex are (12.5, 9). The profit at this point is 4(12.5) + 5(9) = 96.

We can also solve this problem algebraically. First, we need to rewrite the constraints as equations. The first constraint becomes 4x + 2y = 40. The second constraint becomes -3x + y = -4. The third constraint becomes x = 3. The fourth constraint becomes y ≥ 0.

We can now solve the system of equations. We can do this by substituting the third equation into the first and second equations. This gives us 4(3) + 2y = 40 and -3(3) + y = -4. Solving these equations gives us y = 9 and x = 12.5.

The profit at this point is 4(12.5) + 5(9) = 96.

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The 95% confidence interval for the difference in mean BMI between vegetarian and omnivorous children, based on the given data, is (a) –1.433 to 0.713, with a margin of error of 0.360.

To calculate the confidence interval, we use the formula:

difference in means ± t * standard error of the difference in means

where t is the critical value from the t-distribution with (n1 + n2 – 2) degrees of freedom and a confidence level of 95%, n1 and n2 are the sample sizes, and the standard error of the difference in means is given by:

sqrt(s1^2/n1 + s2^2/n2)

where s1 and s2 are the sample standard deviations. Using the given data, we get a t-value of 1.984, a standard error of 0.180, and a difference in means of –0.36. Plugging these values into the formula, we get a confidence interval of (–1.433, 0.713). The margin of error is the half-width of the confidence interval, which is 0.360. Therefore, the answer is (a) –1.433 to 0.713 with a margin of error of 0.360.

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