A journal published an article on vocalized laughter among deaf users of American Sign Language​ (ASL). In videotaped ASL conversations among deaf​ participants, 26 laughed at least once. The researchers wanted to know if they laughed more as speakers​ (while signing) or as audience members​ (while listening). For each of the 26 deaf​ participants, the number of laugh episodes as a speaker and the number of laugh episodes as an audience member were determined. One goal of the research was to compare the mean numbers of laugh episodes of speakers and audience members. Complete parts a through d below.
a. Explain why the data should be analyzed as a paired difference experiment.
Choose the correct answer below.
A. Since the samples are​ large, the central limit theorem guarantees a normal distribution.
B. A paired difference experiment is easier to conduct.
C. Since the samples are​ paired, they are not independent.
D.Comparing paired differences is better than comparing the population means.
b. Identify the​ study's target parameter.
Choose the correct answer below.
A. mu Subscript dμd
B. left parenthesis x overbar 1 minus x overbar 2 right parenthesisx1−x2
C. x overbar Subscript dxd
D. σx1−x2
c. The study yielded a sample mean of 3.5 laughter episodes for speakers and a sample mean of 1.4 laughter episodes for audience members. Is this sufficient evidence to conclude that the population means are​ different? Explain.

Volume of the cube  is 840 cubic centimeters and volume of cylinder is 904.32 cubic feet

Let us calculate the volume of the cube which has a length of 7 cm , width is 8 cm and height is 15 cm

Volume = Length×width×height

=7×8×15

=840 cubic centimeters

Now let us find the volume of cylinder which has diameter 12 ft and height of 8 ft

Radius of cylinder is 6 ft

Volume of cylinder= πr²h

=3.14×6²×8

=3.14×36×8

=904.32 cubic feet

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If the central angle is made by the chords and the distance between the center of the circle and the chords are the same, then the chords will be equal.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

In the first part, the measure of the central angle made by the chords is the same. Then the measure of chords will be equal. Then we have

AB ≅ BC

In the second part, the distance between the center of the circle and the chords are the same. Then the chords are of equal length. Then we have

AB ≅ BC

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The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.

A dimensions of a rectangle is the length of each side.

Let x = length of the shorter side

y = length of the longer side

If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is

2x + y = 760

y = 760 - 2x

The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,

A = xy

A = x(760 - 2x)

A = 760x - 2x²

To obtain the largest area possible, the first derivative of the area should be equal to zero.

A(x) = 760x - 2x²

A'(x) = 0

760 - 4x = 0

Solve for x.

760 - 4x = 0

4x = 760

x = 190

length of the shorter side = 190 feet

y = 760 - 2x

y = 760 - 2(190)

y = 380

length of the longer side = 380 feet

Solve for the greatest possible area.

A = xy

A = 190 feet(380 feet)

A = 72,200 square feet

" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "

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Answer:

385000 rupees

Step-by-step explanation:

50x50 = 2500sq. m

2500 x 154 = 385000 rupees

Answer:

Here is your answer with solutions!

Answer:

3

Step-by-step explanation:

For one batch there is 2 cups so for one person it's one serving so you will need 3 batches for 6 people.

Answer:

Step-by-step explanation:

EX.  in function f(x) = 2 cos x -2  

The first 2 is your amplitute, how high from middle line it goes

the last 2 is the shift in y direction.  

For f(x) = 2 cos x -2   (see image for this function)

it has been shifted down 2 and has a period

At \(\pi\) your function has a solution of -4

The first blank is  f(x) = cos x+2

Second blank is f(x) =  cos x -2

The correct solution graph to the inequalities are

\(4(9x-18)>3(8x+12)\)  →  C

\(-\frac{1}{3}(12x+6) \geq -2x +14\)  → A

\(1.6(x+8)\geq 38.4\)  →  B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

\(4(9x-18)>3(8x+12)\)

First, clear the brackets,

\(36x-72>24x+36\)

Then, collect like terms

\(36x-24x>36+72\\12x >108\)

Now divide both sides by 12

\(\frac{12x}{12} > \frac{108}{12}\)

∴ \(x > 9\)

For the second inequality

\(-\frac{1}{3}(12x+6) \geq -2x +14\)

First, clear the fraction by multiplying both sides by 3

\(3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)\)

\(-1(12x+6) \geq -6x +42\)

Now, open the bracket

\(-12x-6 \geq -6x +42\)

Collect like terms

\(-6 -42\geq -6x +12x\)

\(-48\geq 6x\)

Divide both sides by 6

\(\frac{-48}{6} \geq \frac{6x}{6}\)

\(-8\geq x\)

∴ \(x\leq -8\)

For the third inequality,

\(1.6(x+8)\geq 38.4\)

First, clear the brackets

\(1.6x + 12.8\geq 38.4\)

Collect likes terms

\(1.6x \geq 38.4-12.8\)

\(1.6x \geq 25.6\)

Divide both sides by 1.6

\(\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}\)

∴ \(x \geq 16\)

Let the graphs be A, B and C from left to right

The first graph (A) shows \(x\leq -8\) and this matches the 2nd inequality

The second graph (B) shows \(x \geq 16\) and this matches the 3rd inequality

The third graph (C) shows \(x > 9\) and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

\(4(9x-18)>3(8x+12)\)  →  C

\(-\frac{1}{3}(12x+6) \geq -2x +14\)  → A

\(1.6(x+8)\geq 38.4\)  →  B

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Answer:

4(9x − 18) > 3(8x + 12) = x > 9

(12x + 6) ≥ -2x + 14 = x ≤ -8

1.6(x + 8) ≥ 38.4 = x ≥ 16

Just follow the numbers with the dotted thing and see the numbers I underlined.

Step-by-step explanation:

Use the properties of inequality and real numbers to solve each inequality.

4(9x − 18) > 3(8x + 12)

36x − 72 > 24x + 36

12x − 72 > 36

12x > 108

x > 9

The graph has an open circle at 9, and moves toward the right on the number line.

(12x + 6) ≥ -2x + 14

12x + 6 ≤ 6x − 42

6x + 6 ≤ -42

6x ≤ -48

x ≤ -8

The graph has a closed circle at -8, and moves toward the left on the number line.

1.6(x + 8) ≥ 38.4

x + 8 ≥ 24

x ≥ 16

The graph has a closed circle at 16, and moves toward the right on the number line.

Hello!

b = 3 - 2a

b = 3 - 2*4

b = 3 - 8

b = -5

Perimeter is the sum of length of the sides used to made the given figure. The length of each side of the yield sign is 78 centimeters.

Perimeter is the sum of length of the sides used to made the given figure.

Given that the sides of a yield sign all have the same length (see figure). Therefore, if the perimeter of the yield sign is calculated then it will be,

Perimeter of the yield sign = x + x + x

Perimeter = 3x

Now, if the perimeter of a roadway yield sign is 234 centimeters, therefore, we can rewrite the perimeter as,

Perimeter = 3x

234 centimeter = 3x

x = 234 centimeter / 3

x = 78 centimeter

Hence, the length of each side of the yield sign is 78 centimeters.

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On average, Italians spend 7.9 weeks on vacation, while Americans spend 3.9 weeks. Italians have a longer average vacation time than Americans by 4 weeks.

To find the average vacation time for Americans and Italians, we can set up a system of equations. Let's assume that the average vacation time for Americans is represented by 'A' and the average vacation time for Italians is represented by 'I'.

Given that the average time Italians spend on vacation exceeds the average American vacation time by 4 weeks, we can write the equation: I = A + 4.

The combined average vacation time for Americans and Italians is 11.8 weeks, which gives us another equation: A + I = 11.8.

We can substitute the first equation into the second equation to eliminate 'I'. By substituting A + 4 for I in the second equation, we get A + (A + 4) = 11.8.

Simplifying the equation gives us 2A + 4 = 11.8. Subtracting 4 from both sides gives 2A = 7.8. Dividing by 2, we find that A = 3.9.

Therefore, the average vacation time for Americans is 3.9 weeks. Since I = A + 4, the average vacation time for Italians is 7.9 weeks.

In conclusion, Italians spend an average of 7.9 weeks on vacation, exceeding the average American vacation time by 4 weeks. Americans, on the other hand, have an average vacation time of 3.9 weeks.

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Answer:

-3 2 3 7

Step-by-step explanation:

The answer is above

x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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(a) There are not enough information to determine the total number of students in Mr. Garal's class.

The given information only tells us that there are 36 seniors in the class and that 30 students went on a field trip, but it doesn't provide any information about the total number of students in the class or the number of juniors in the class.

(b) We can calculate the number of students from the class who did not go on the field trip by subtracting the number of students who went on the field trip from the total number of students in the class (which we don't know). Therefore, we cannot answer this question with the given information.

(c) We know that there are 36 seniors in the class and that 5 seniors went on the field trip. Therefore, the number of seniors from the class who did not go on the field trip is 36 - 5 = 31.


In summary, we can determine that there are 36 seniors in Mr. Garal's class and that 5 of them went on a field trip, but we cannot determine the total number of students in the class or the number of students who did not go on the field trip. We can also determine that 31 seniors from the class did not go on the field trip.

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Kimberly sent approximately 34 cylindrical boxes that contained soap

Let's assume Kimberly sent a total of 100 gift boxes. Since half of the boxes were cylindrical, that means she sent 50 cylindrical boxes.

If a third of the rectangular boxes contained soap, then 1/3 * (100 - 50) = 1/3 * 50 = 50/3 ≈ 16.7 rectangular boxes contained soap. Since we cannot have a fraction of a box, let's round it down to 16 rectangular boxes containing soap.

Now, since each box contains exactly one gift, the remaining cylindrical boxes must contain the pack of spicy roasted almonds. Therefore, out of the 50 cylindrical boxes, 50 - 16 = 34 cylindrical boxes contain soap.

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.

We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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The implicit solution to the initial value problem is \(\( v = \frac{C_2}{3 + x} \).\)

To solve the initial value problem \(\(v\frac{{dy}}{{dx}} + (3 + x)\,dx = 0\) with \(y(-2) = 1\)\), we can separate the variables and integrate.

Rearranging the equation, we have:

\(\[\frac{{dy}}{{dx}} = -\frac{{(3 + x)}}{{v}}\]\)

Now, we can separate the variables:

\(\[\frac{{dy}}{{(3 + x)}} = -\frac{{dx}}{{v}}\]\)

Integrating both sides with respect to their respective variables, we get:

\(\[\int\frac{{dy}}{{(3 + x)}} = -\int\frac{{dx}}{{v}}\]\)

Integrating the left side gives:

\(\[\ln|3 + x| = -\ln|v| + C_1\]\)

Where \(\(C_1\)\) is the constant of integration.

Simplifying the equation further, we have:

\(\[\ln|3 + x| + \ln|v| = C_1\]\)

Combining the logarithms, we get:

\(\[\ln|v(3 + x)| = C_1\]\)

Now, exponentiating both sides, we have:

\(\[|v(3 + x)| = e^{C_1}\]\)

Simplifying the equation, we get:

\(\[v(3 + x) = C_2\]\)

Where \(\(C_2\)\) is the constant of integration.

Finally, solving for v, we have:

\(\[v = \frac{{C_2}}{{(3 + x)}}\]\)

This is the implicit solution to the initial value problem.

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Answer:

0.0000889

Step-by-step explanation:

Conversion : -

1 mg = 0.00001 hg

8.90 mg

Multiply 8.90 with 0.00001 to convert to hg,

8.90 x 0.00001

= 0.000089 hg

To find the critical points of the function f(x,y)= x² + 18y² + 96x - 18y subject to the constraint 6x - 18y = 30, we can use the method of Lagrange multipliers.



Solving these equations simultaneously, we get:

x = -9, y = 1/2, λ = 7/4

Therefore, the critical point of the function is (-9, 1/2).
To find the critical points of the function f(x, y) = x² + 18y² + 9, subject to the constraint 6x - 18y = 30, using the method of Lagrange multipliers, follow these steps:

Step 1: Define the function and constraint.
Function: f(x, y) = x² + 18y² + 9
Constraint: g(x, y) = 6x - 18y - 30 = 0

Step 2: Set up the Lagrange multiplier equation.
∇f(x, y) = λ∇g(x, y)

Step 3: Compute the gradient of the function and the constraint.
∇f(x, y) = (df/dx, df/dy) = (2x, 36y)
∇g(x, y) = (dg/dx, dg/dy) = (6, -18)

Step 4: Set up the system of equations.
2x = λ(6)         (1)
36y = λ(-18)      (2)
6x - 18y - 30 = 0  (3)

Step 5: Solve the system of equations.
From (1): x = 3λ
From (2): y = -2λ
Plug x and y values from (1) and (2) into (3):
6(3λ) - 18(-2λ) - 30 = 0
18λ + 36λ - 30 = 0
54λ = 30
λ = 30/54 = 5/9

Step 6: Find the critical points.
x = 3λ = 3(5/9) = 5
y = -2λ = -2(5/9) = -10/9

The critical point of the function f(x, y) subject to the given constraint is (5, -10/9).

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Answer:

Step-by-step explanation:

½(x-2) = 8 + 5x

Multiply both sides by 2

2⋅½(x-2) = 2(8 + 5x)

1(x-2) = 2(8 + 5x)

Apply the distributive rule

x - 2 = 16 + 10x

Subtract x from both sides

-2 = 16 + 9x

Subtract 16 from both sides

-18 = 9x

Divide both sides by the coefficient of x

-18 ÷ 9 = 9x ÷ 9

-2 = x

Answer:

if x=-4 & y=-14...then x=9 & Y= -1. which is minus 10

Step-by-step explanation:

-4 is 10 under -14. If X=9 then Y= -1.

A heptagon is a seven-sided polygon. It is also sometimes called a septagon, though this usage mixes a Latin prefix sept- (derived from septua-, meaning "seven") with the Greek suffix -gon (from gonia, meaning "angle"), and is therefore not recommended.

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The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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Answer:

Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.

If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.

To improve your chances of solving the equation successfully, consider the following steps:

Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.

Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.

Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.

Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.

Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.

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Answer:

88

Step-by-step explanation:

The original number ⇒ 100

100 is increased by 10%

The result is 20% reduced.

Calculate increase.

100 × (1 + 10%)

100 × (1.1)

= 110

Calculate decrease.

110 × (1 - 20%)

110 × 0.8

= 88

The relationship between the ages of drivers and the number of violations is a strong negative correlation. The correct option is E.

Correlation is the relationship between any set of data when taken as a whole because the term "co" signifies together. The correlation coefficient, which in statistics is a number between -1 and +1, measures the linear dependency of the collection of data.

A correlation coefficient is always a value between -1 and 1. The closest coefficient to -1, the correlation is a strong negative correlation. The closest coefficient to 1, the correlation is a strong positive correlation. The closest coefficient to 0, there is no correlation at all. The coefficient -0.61 shows a strong negative correlation.

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the following expressions are defined:

b) BC

c) \(B^T\)

d) B-C

e) A+B

f) \(BA^T\)

To determine which of the given expressions are defined, we need to consider the compatibility of matrix dimensions.

a) CA: Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. In this case, A is a 7x6 matrix and C is an 8x7 matrix. The number of columns in A (6) does not match the number of rows in C (8), so CA is not defined.

b) BC: Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. Both B and C are 7x6 matrices, so the number of columns in B (6) matches the number of rows in C (6). Therefore, BC is defined.

c) \(B^T\): The transpose of a matrix is defined for any matrix. So, \(B^T\)is defined.

d) B-C: Matrix subtraction is defined when the matrices have the same dimensions. Both B and C are 7x6 matrices, so B-C is defined.

e) A+B: Matrix addition is defined when the matrices have the same dimensions. Both A and B are 7x6 matrices, so A+B is defined.

f) \(BA^T\): Matrix multiplication is defined when the number of columns in the first matrix matches the number of rows in the second matrix. A is a 7x6 matrix, and \(A^T\)is a 6x7 matrix. The number of columns in A (6) matches the number of rows in \(A^T\) (6). Therefore, \(BA^T\) is defined.

So, the following expressions are defined:

b) BC

c) \(B^T\)

d) B-C

e) A+B

f) \(BA^T\)

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