A regular hexagon is rotated in a counterclockwise direction about its center. Determine and state the minimum number of degrees in the rotation such that the hexagon will coincide with itself.​

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

Analytics is often described as the study of historical data to extract insights and make informed decisions. It involves the collection, processing, and analysis of data to discover patterns, identify trends, and gain insights into business operations. By examining data sets, analytics can help businesses identify areas of improvement, optimize performance, and increase efficiency. Analytics tools and techniques can be used across many different fields, including finance, marketing, healthcare, and sports. In finance, analytics can be used to analyze market trends and predict future outcomes. In marketing, analytics can help businesses identify customer behavior patterns and optimize marketing campaigns. In healthcare, analytics can help identify patterns in patient data and improve healthcare outcomes. In sports, analytics can be used to analyze player performance and predict game outcomes.

Therefore, analytics is a critical tool for businesses and organizations looking to gain a competitive advantage and improve their operations.

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The function f(x) = 3x⁵ - 5x³ + 15 has relative maxima at x = -1 and relative minima at x = 1, so the answer is (d) -1 and 1 only.

To find the relative maximum of the function f(x) = 3x⁵ - 5x³ + 15, we need to find the critical points and then determine whether they correspond to a maximum or minimum.

To find the critical points, we need to find where the derivative of the function is equal to zero

f'(x) = 15x⁴ - 15x²

f'(x) = 15x²(x² - 1)

Setting f'(x) equal to zero, we get

x²(x² - 1) = 0

This equation is true when x = 0, x = 1, and x = -1.

Now we need to determine whether these points correspond to a relative maximum or minimum. To do this, we can use the second derivative test.

f''(x) = 60x³ - 30x

Plugging in x = -1, we get

f''(-1) = -30 < 0

This means that x = -1 corresponds to a relative maximum.

Plugging in x = 0, we get

f''(0) = 0

This test is inconclusive, so we need to use another method to determine the nature of the critical point at x = 0.

Plugging in x = 1, we get

f''(1) = 30 > 0

This means that x = 1 corresponds to a relative minimum.

Therefore, the correct option is (d) -1 and 1 only

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Answer:

1/5

Step-by-step explanation:

You can divide both sides of the fraction by the same number to simplify it

2 and 10 are both multiples of 2, so you can divide both sides by 2

2/2=1

———

10/2=5

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

Front-end estimation is a particular way of rounding numbers to estimate sums and differences.

To use front- end estimation, add or subtract only the numbers in the greatest place value. Then add the decimals rounded to the nearest tenth.

Step-by-step explanation:

In front end estimation we are going to replace the original number with a number that is close by but only has one non zero digit. Examples: {20, 300, -50, 1,000, 80,000}. For example take the number 32, the choices to replace it with are 30 or 40 (they both have only one non-zero digit).

Answer:

b

Step-by-step explanation:

The function \(\(f(x, y) = 4xy - x^2 - 6y^2 + 5x + 5\)\) has a local maximum at \(\(\left(\frac{15}{2}, \frac{5}{2}\right)\)\).

To find the local maxima, local minima, and saddle points of the function \(\(f(x, y) = 4xy - x^2 - 6y^2 + 5x + 5\)\), we need to calculate its partial derivatives and analyze their critical points.

Step 1: Calculate the partial derivatives:

\(\(\frac{{\partial f}}{{\partial x}} = 4y - 2x + 5\)\)

\(\(\frac{{\partial f}}{{\partial y}} = 4x - 12y\)\)

Step 2: Set the partial derivatives equal to zero and solve for x and y to find the critical points:

For \(\(\frac{{\partial f}}{{\partial x}} = 0\)\):

4y - 2x + 5 = 0

For \(\(\frac{{\partial f}}{{\partial y}} = 0\)\):

4x - 12y = 0

Solving these two equations simultaneously, we get:

4y - 2x + 5 = 0

4x - 12y = 0

From the second equation, we have (x = 3y). Substituting this into the first equation:

\(\(4y - 2(3y) + 5 = 0\)\)

\(\(4y - 6y + 5 = 0\)\)

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

\(\(2y = 5\)\)

\(\(y = \frac{5}{2}\)\)

Substituting the value of (y) back into (x = 3y):

\(\(x = 3 \left(\frac{5}{2}\right)\)\)

\(\(x = \frac{15}{2}\)\)

So, the critical point is \(\(\left(\frac{15}{2}, \frac{5}{2}\right)\)\).

Step 3: Analyze the critical points to determine if they are local maxima, local minima, or saddle points.

To classify the critical points, we need to calculate the second-order partial derivatives and evaluate the determinant and the discriminant of the Hessian matrix.

The Hessian matrix is given by:

\(\(H(x, y) = \begin{bmatrix} \frac{{\partial^2 f}}{{\partial x^2}} & \frac{{\partial^2 f}}{{\partial x \partial y}} \\ \frac{{\partial^2 f}}{{\partial y \partial x}} & \frac{{\partial^2 f}}{{\partial y^2}} \end{bmatrix}\)\)

Calculating the second-order partial derivatives:

\(\(\frac{{\partial^2 f}}{{\partial x^2}} = -2\)\)

\(\(\frac{{\partial^2 f}}{{\partial x \partial y}} = 4\)\)

\(\(\frac{{\partial^2 f}}{{\partial y \partial x}} = 4\)\)

\(\(\frac{{\partial^2 f}}{{\partial y^2}} = -12\)\)

Evaluating the Hessian matrix at the critical point \(\(\left(\frac{15}{2}, \frac{5}{2}\right)\)\):

\(\(H\left(\frac{15}{2}, \frac{5}{2}\right) = \begin{bmatrix} -2 & 4 \\ 4 & -12 \end{bmatrix}\)\)

The determinant of the Hessian matrix is:

\(\(\Delta = \frac{{\partial^2 f}}{{\partial x^2}} \cdot \frac{{\partial^2 f}}{{\partial y^2}} - \left(\frac{{\partial^2 f}}{{\partial x \partial y}}\right)^2 = (-2) \cdot (-12) - (4)^2 = 24 - 16 = 8\)\)

The discriminant of the Hessian matrix is:

\(\(D = \frac{{\partial^2 f}}{{\partial x^2}} = -2\)\)

Based on the determinant and discriminant, we can determine the nature of the critical point:

1. If \(\(\Delta > 0\)\) and \(\(D > 0\)\), then the critical point is a local minimum.

2. If \(\(\Delta > 0\)\) and \(\(D < 0\)\), then the critical point is a local maximum.

3. If \(\(\Delta < 0\)\), then the critical point is a saddle point.

4. If \(\(\Delta = 0\)\), further analysis is required (such as higher-order derivatives or other methods).

In this case, we have \(\(\Delta = 8\)\) and \(\(D = -2\)\).

Since \(\(\Delta > 0\)\) and \(\(D < 0\)\), we conclude that the critical point \(\(\left(\frac{15}{2}, \frac{5}{2}\right)\)\) is a local maximum.

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Answer:

distance = 2.6 miles

Step-by-step explanation:

using the Pythagorean theorem:

1²+2.4² = distance²

distance² = 6.76

distance = 2.6 miles

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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The exact value of cos a as required to be determined in the task content is; √57 / 8.

It follows from the task content that sin a = 3 / 8 and the exact value of cos a is to be determined in the task content.

Recall from trigonometric identities that;

cos ² a + sin² a = 1

Therefore, cos² a + (3 / 8)² = 1 since sin a = (3 / 8).

cos²a = 1 - (9 / 64)

cos²a = (64 - 9) / 64

cos²a = 57 / 64

cos a = √57 / 8.

Ultimately, the value of cos a as required to be determined in the task content is; √57 / 8.

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Answer:

  a.  F'(0, 5), G'(1, 0), H'(-3, 3)

Step-by-step explanation:

Reflection across x = -1 gives you the transformation ...

  (x, y) ⇒ (-2 -x, y)

Reflection across y = 1 gives you the transformation ...

  (x, y) ⇒ (x, 2 -y)

Together, these give you the transformation ...

  (x, y) ⇒ (-2 -x, 2 -y)

Applying this to point F, we have ...

  F(-2, -3) ⇒ F'(-2 -(-2), 2 -(-3)) = F'(0, 5) . . . . . . matches choice A

_____

How we found the transformation

In general, if M is the midpoint between A and B, then you have ...

  M = (A+B)/2

  2M = A+B

  B = 2M - A

So, if we want x=-1 to be the midpoint between x' and x, then we have ...

  x' = 2(-1) -x = -2 -x

Likewise, if we want y=1 to be the midpoint between y' and y, then we have ...

  y' = 2(1) -y = 2 -y

So, the transformation is ...

  (x, y) ⇒ (x', y') = (-2 -x, 2 -y)

On solving the linear equations y = 2x - 2 and -4x - y = 26, the value of x is x = -4 and y is y = -10.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two linear equations are -

y = 2x - 2 .... (1)

-4x - y = 26 .... (2)

Substitute the value of y from equation (1) in equation (2) -

-4x - (2x - 2) = 26

Open the brackets -

-4x - 2x + 2 = 26

Combine the like terms -

-4x - 2x = 26 - 2

Use the arithmetic operation of addition and subtraction -

-6x = 24

Use the arithmetic operation of division -

x = 24/-6

x = -4

Substitute the value of x in equation (1) -

y = 2(-4) - 2

y = -8 - 2

y = -10

Therefore, the values of x and y is -4 and -10 respectively.

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A. Hyperbolic paraboloid; xz-trace: \(16x^2-z=0\) (parabola); yz-trace: \(16y^2 + z = 0\) (parabola)

To identify the quadric surface, we can analyze the equation:

\(16x^2 - 16y^2 - z = 0\)

This equation represents a hyperbolic paraboloid.

To find the xy-, xz-, and yz-traces, we set one variable to zero and solve for the other two variables:

1. xy-trace (z = 0):

  \(16x^2 - 16y^2 = 0\)

  Simplifying, we get:

  \(x^2 - y^2 = 0\)

  This is a difference of squares, which factors as:

  (x - y)(x + y) = 0

  So the xy-trace consists of two lines: x = y and x = -y.

2. xz-trace (y = 0):

  \(16x^2 - z = 0\)

  Solving for z, we have:

  \(z = 16x^2\)

  This represents a parabola opening upwards in the xz-plane.

3. yz-trace (x = 0):

  \(-16y^2 - z = 0\)

Solving for z, we get:

  \(z = -16y^2\)

This represents a parabola opening downwards in the yz-plane.

Therefore, the xy-trace consists of two lines (x = y and x = -y), the xz-trace is a parabola opening upwards, and the yz-trace is a parabola opening downwards.

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Answer:

30%

Step-by-step explanation:

Purchases:

Coat £20

Hat £15

Gloves for £5

Total amount of purchases: £20 + £15 + £5 = £40

Sales:

Coat at 50% profit: 150% × £20 = 1.5 × £20 = £30

Hat: £18

Gloves at a 20% loss: 80% of £5 = £4

Total amount of sales: £30 + £18 + £4 = £52

Amount of profit: £52 - £40 = £12

Percent of profit: £12 / £40 × 100% = 30%

Answer: x= 11√3= 19.0525 = 19.1

Step-by-step explanation:

Let the reference angle be 30

so

cos 30 = b/h

√3/2 = x/22

or, 22√3 = 2x

or. x = (22√3)/2

so, x = 11√3

Answer:

x = 19.1 cm

Step-by-step explanation:

→ Find the name of the side you are not given

Opposite

→ Find a formula without opposite in it

Cos = Adjacent ÷ Hypotenuse

→ Rearrange to make adjacent the subject

Adjacent = Cos × Hypotenuse

→ Substitute in the values

Adjacent = Cos ( 30 ) × 22

→ Simplify

Adjacent = 19.1

Answer:

17.5 for perpendicular triangle

Step-by-step explanation:

A= 1/2 ( b*h )

A= 1/2 ( 7*5)

A= 1/2 ( 35)

A= 17.5

Answer: -8.93

Step-by-step explanation:

Given the function:

N(X) = 90(0.86)^x+ 69

X in the interval [0, 6]

For X = 0

N(0) = 90(0.86)^0 + 69

90 + 69 = 159

For X = 6

N(6) = 90(0.86)^6 + 69

90(0.404567235136) + 69

= 105.41105116224

Therefore, average change of change in temperature ;

(temp 2 - temp 1) / ( time 2 - time)

(105.41105116224 - 159) / (6 - 0)

= - 53.58894883776 / 6

= - 8.93149147296

= - 8.93

The  approximate average rate of change of the temperature of the hot chocolate, in  degrees per minute, over the interval [0, 6] is;

Option 1; -8.93

We are given the function;

N(x) = 90(0.86)ˣ + 69

We want to find the average rate of change over the interval (0, 6).

Thus;

N(0) = 90(0.86)⁰ + 69

N(0) = 90 + 69

N(0) = 159°

N(6) = 90(0.86)⁶ + 69

N(6) = 105.411°

Formula for rate of change is;

Rate of change = Δy/Δx

Thus; Rate of change = (159 - 105.411)/(0 - 6)

Rate of change = -8.93

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hi <3

it would be option A and option C, i believe.

hope this helps :)

The AAS congruence rule is valid.

AAS stands for “angle, angle, side” and means that we have two triangles where we know two angles and the non-included side are equal. If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Angle-Angle-Side (AAS or SAA) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two corresponding angles and a non-included side in another triangle, then the triangles are congruent.

AAS stands for “Angle, Angle, Side”, which means two angles and an opposite side. AAS is one of the five ways to determine if two triangles are congruent. It states that if the vertices of two triangles are in one-to-one correspondence such that two angles and the side opposite to one of them in one triangle are congruent to the corresponding angles and the non-included side of the second triangle, then the triangles are congruent. The non-include side is the side opposite to either one of the two angles being used. In simple terms, if two pairs of corresponding angles and the sides opposite to them are equal in both the triangles, the two triangles are congruent.

Thus, the AAS congruence rule is valid.

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No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.

Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.

Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.

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The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are: a) sin(2x) = 2sin(x)cos(x). b) cos(2x) = cos^2(x) - sin^2(x). c) tan(2x) = 2tan(x) / (1 - tan^2(x))

(a) To find the exact value of sin(2x), we can use the double angle formula for sine:

sin(2x) = 2sin(x)cos(x)

Therefore, the exact value of sin(2x) is 2sin(x)cos(x).

(b) To find the exact value of cos(2x), we can use the double angle formula for cosine:

cos(2x) = cos^2(x) - sin^2(x)

Therefore, the exact value of cos(2x) is cos^2(x) - sin^2(x).

(c) To find the exact value of tan(2x), we can use the double angle formula for tangent:

tan(2x) = 2tan(x) / (1 - tan^2(x))

Therefore, the exact value of tan(2x) is 2tan(x) / (1 - tan^2(x)).

The exact values of sin(2x), cos(2x), and tan(2x) without solving for x are:

a) sin(2x) = 2sin(x)cos(x)

b) cos(2x) = cos^2(x) - sin^2(x)

c) tan(2x) = 2tan(x) / (1 - tan^2(x))

These formulas allow us to express the values of sin(2x), cos(2x), and tan(2x) in terms of the values of sin(x) and cos(x) without explicitly solving for x.

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The table or software, we find that the critical t-value is approximately 1.684.

The critical value for the traditional method of testing can be determined by comparing the given sample data and the significance level of α = 0.05. Based on the information provided, we need to find the critical t-value for a one-tailed test with a significance level of 0.05.

The critical value for the traditional method of testing can be obtained from a t-distribution table or by using statistical software. For a one-tailed test with α = 0.05 and degrees of freedom (df) equal to n1 + n2 - 2 = 48 + 44 - 2 = 90, the critical t-value is approximately 1.684.

To find the critical value for the traditional method of testing, we need to consider the significance level (α), the type of test (one-tailed or two-tailed), and the degrees of freedom. In this case, the claim is that μ1 > μ2, indicating a one-tailed test. The given significance level is α = 0.05.

Using the sample data provided, we calculate the degrees of freedom as df = n1 + n2 - 2 = 48 + 44 - 2 = 90. With a one-tailed test and a significance level of α = 0.05, we refer to the t-distribution table or use statistical software to find the critical t-value corresponding to these values. From the table or software, we find that the critical t-value is approximately 1.684.

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The correct answer is option D: 2.66 M. The molarity of the hydrochloric acid (HCl) solution is 2.66 M.

To determine the molarity of the hydrochloric acid (HCl) solution, we can use the given information about the amount of sodium hydroxide (NaOH) used and the volume of the acid solution.

To find the molarity (M) of a solution, we use the formula:

Molarity (M) = moles of solute / volume of solution in liters

Given:

Moles of NaOH used = 0.0665 mol

Volume of HCl solution = 0.025 L

We need to calculate the molarity of the HCl solution.

First, we need to determine the moles of HCl using the balanced chemical equation for the neutralization reaction between NaOH and HCl, which is 1:1.

From the equation, we know that 1 mole of NaOH reacts with 1 mole of HCl.

Since the moles of NaOH used is 0.0665 mol, the moles of HCl would also be 0.0665 mol.

Now, we can calculate the molarity of the HCl solution:

Molarity (M) = moles of HCl / volume of solution in litersMolarity (M) = 0.0665 mol / 0.025 L

Molarity (M) = 2.66 M

Therefore, the molarity of the hydrochloric acid (HCl) solution is 2.66 M.

Hence, the correct answer is option D: 2.66 M.

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Answer:

1, 18, 2, 9, 3, 6

I think

Answer:

Down Below!

Step-by-step explanation:

18 = 1 x 18, 2 x 9, or 3 x 6

Prime Factors: 18 = 2 x 3 x 3

Factors of 18: 1, 2, 3, 6, 9, 18

Answer: c=-1,b=5,a=-5

Step-by-step explanation: If c=-1, substitute it into the second equation first. The second equation becomes -2b-1=-11, simplify it becomes -2b=-10, divide by 2 it becomes -b=-5, so b=5. Then you substitute b and c into the first equation. The first equation becomes a+5+-(-4)=4, simplify it becomes a+5+4=4, Simplify again it becomes a=-5.

Answer:

1st rule: Reflection over the X-axis, (x,y) -> (x , -y)

2nd rule: Horizontal translation to the RIGHT 6 units (x , -y) -> (x+6 , -y)

Step-by-step explanation:

1st rule: Reflection over the X-axis, (x,y) -> (x , -y)

2nd rule: Horizontal translation to the RIGHT 6 units (x , -y) -> (x+6 , -y)

MJS: (4,-4) (-2,-3) (-3,1) -> (-4,4) (-2,3) (-3,-1) -> (2,4) (4,3) (3,-1)

They are congruent!!

The measure of angle 2 and angle3 are 133 ad 47 degrees respectively

From the given diagram, the measure of angle 1 and 2 are congruent. (vertical angles)

Given he following parameters

m<1 = 133 degrees

Since m<1 = m<2, hence m<2 = 133 degrees

Also;

m<2 + m<3 = 180

133 + m<3 = 180

m<3 = 180 - 133

m<3 = 47 degrees

Hence the measure of angle 2 and angle3 are 133 ad 47 degrees respectively

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Answer:

Looks right to me! Great work!

The probability that Sumit actually saw a shark is 1/36.

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

According to the question, we can say

Let us assume that Sumit has actually seen 1 creature.

The probability that it is a Shark and Sumit reports it correctly = (1/8)(1/6) = (1/48)

The probability that it is not a Shark and Sumit claims that it is = (7/8)(5/6) = (35/48)

Therefore,

The probability that Sumit actually sees a Shark, given that he claimed to have seen one = [(1/8)(1/6)] / [(1/8)(1/6) + (7/8)(5/6)] = 1/36

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False. Null and alternative hypothesis are not statements about descriptive statistics.

Null and alternative hypothesis are fundamental concepts in hypothesis testing, a statistical method used to make inferences about population parameters based on sample data. These hypothesis are not directly related to descriptive statistics, which involve summarizing and describing data using measures such as mean, median, standard deviation, etc.

The null hypothesis (H0) represents the default or no-difference assumption in hypothesis testing. It states that there is no significant difference or relationship between variables or groups in the population. On the other hand, the alternative hypothesis (H1 or Ha) proposes that there is a significant difference or relationship.

Both null and alternative hypotheses are formulated based on the research question or objective of the study. They are typically stated in terms of population parameters or characteristics, such as means, proportions, correlations, etc. The aim of hypothesis testing is to gather evidence from the sample data to either reject the null hypothesis in favor of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.

Finally, null and alternative hypotheses are not statements about descriptive statistics. Rather, they are statements about population parameters and reflect the purpose of hypothesis testing in making statistical inferences.

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