Which of the following conditions must be met in order to make a statistical inference about a population based on a
sample if the sample does not come from a normally distributed population?

The value of the given sine function is √3/2, so the correct option is 2nd.

Given that an function Sin (-5π/3) we need to evaluate the expression,

To evaluate the trigonometric function sine of the angle (-5π/3), we can use the periodicity of the sine function.

Since the sine function has a period of 2, the sine of any given angle is equal to the sine of that angle plus or minus any multiple of 2.

To find an equal angle inside the main range (between -π and π), we can add 2 to the angle (-5/3).

Once adding 2:

(-5π/3) + 2π = (-5π/3) + (6π/3) = π/3

Now we can evaluate the sine of π/3, which is a commonly known angle. The sine of π/3 is √3/2.

Therefore, sin(-5π/3) = sin(π/3) = √3/2.

Hence the correct option is √3/2

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Answer:

see explanation

Step-by-step explanation:

We require to create 2 equations with the repeating value placed after the decimal point.

let x = 2.1616...... → (1) Multiply both sides by 100

100x = 216.1616..... → (2)

Subtract (1) from (2) to eliminate the repeating decimal.

99x = 214 ( divide both sides by 99 )

x = \(\frac{214}{99}\) = 2 \(\frac{16}{99}\) as a mixed number

Thus

2.1616...... = \(\frac{214}{99}\) = 2 \(\frac{16}{99}\)

Answer:

40-30

Step-by-step explanation:

Here higher term minus lower term

Answer:

No solutions

Step-by-step explanation:

The marginal cost at a production level of 10 items is $617.4. The cost at a production level of 10 items is approximately $59117.4.

To find the cost at a production level of 10 items, we need to consider both the marginal cost and the fixed costs.

The marginal cost function is given by:

\(MC(q) = 0.004q^2 - 0.8q + 625\)

To find the cost at a production level of 10 items, we can substitute q = 10 into the marginal cost function:

\(MC(10) = 0.004(10)^2 - 0.8(10) + 625\)

Simplifying the expression:

MC(10) = 0.004(100) - 8 + 625

MC(10) = 0.4 - 8 + 625

MC(10) = 0.4 + 625 - 8

MC(10) = 625.4 - 8

MC(10) = 617.4

So, the marginal cost at a production level of 10 items is $617.4.

To find the total cost, we need to add the fixed costs to the marginal cost:

Total Cost = Fixed Costs + MC(10)

Total Cost = 58500 + 617.4

Total Cost = 59117.4

Therefore, the cost at a production level of 10 items is approximately $59117.4.

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Answer:no

Step-by-step explanation:

1. N

2. O

Answer:

False

Step-by-step explanation:

Is the following statement true or false?

The intersection of a plane and a ray can be a line segment.

The measure of the fourth interior angle of the quadrilateral is 65°. Hence, the correct answer is (a) 65°.

To calculate the measure of the fourth interior angle of a quadrilateral when the measures of three interior angles are known, we can use the fact that the sum of the interior angles of a quadrilateral is always equal to 360 degrees.

Let's denote the measure of the fourth interior angle as x.

Provided that the measures of the three known interior angles are 120°, 100°, and 75°, we can write the equation:

120° + 100° + 75° + x = 360°

Combining like terms, we have:

295° + x = 360°

To solve for x, we subtract 295° from both sides of the equation:

x = 360° - 295°

Calculating this, we obtain:

x = 65°

Hence, the answer is (a) 65°.

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The minimal point does not have x = 0.

(a) Kuhn-Tucker conditions for the minimal value of fThe Kuhn-Tucker conditions are a set of necessary conditions for a point x* to be a minimum of a constrained optimization problem subject to inequality constraints. These conditions provide a way to find the optimal values of x1, x2, ..., xn that maximize or minimize a function f subject to a set of constraints. Let's first write down the Lagrangian: L(x, y, λ1, λ2, λ3) = f(x, y) - λ1(x+y-1) - λ2(xy-3) - λ3x - λ4y Where λ1, λ2, λ3, and λ4 are the Kuhn-Tucker multipliers associated with the constraints. Taking partial derivatives of L with respect to x, y, λ1, λ2, λ3, and λ4 and setting them equal to 0, we get the following set of equations: 4x - 2y - λ1 - λ2y - λ3 = 0 2y - 2x - λ1 - λ2x - λ4 = 0 x + y - 1 ≤ 0 xy - 3 ≤ 0 λ1 ≥ 0 λ2 ≥ 0 λ3 ≥ 0 λ4 ≥ 0 λ1(x + y - 1) = 0 λ2(xy - 3) = 0 From the complementary slackness condition, λ1(x + y - 1) = 0 and λ2(xy - 3) = 0. This implies that either λ1 = 0 or x + y - 1 = 0, and either λ2 = 0 or xy - 3 = 0. If λ1 > 0 and λ2 > 0, then x + y - 1 = 0 and xy - 3 = 0. If λ1 > 0 and λ2 = 0, then x + y - 1 = 0. If λ1 = 0 and λ2 > 0, then xy - 3 = 0. We now consider each case separately. Case 1: λ1 > 0 and λ2 > 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have the following possibilities: x + y - 1 = 0, xy - 3 ≤ 0 (i.e., xy = 3), λ1 > 0, λ2 > 0 x + y - 1 ≤ 0, xy - 3 = 0 (i.e., x = 3/y), λ1 > 0, λ2 > 0 x + y - 1 = 0, xy - 3 = 0 (i.e., x = y = √3), λ1 > 0, λ2 > 0 We can exclude the second case because it violates the constraint x, y ≥ 0. The first and third cases satisfy all the Kuhn-Tucker conditions, and we can check that they correspond to local minima of f subject to the constraints. For the first case, we have x = y = √3/2 and f(x, y) = -1/2. For the third case, we have x = y = √3 and f(x, y) = -2. Case 2: λ1 > 0 and λ2 = 0From λ1(x + y - 1) = 0, we have x + y - 1 = 0 (because λ1 > 0). From the first Kuhn-Tucker condition, we have 4x - 2y - λ1 = λ1y. Since λ1 > 0, we can solve for y to get y = (4x - λ1)/(2 + λ1). Substituting this into the constraint x + y - 1 = 0, we get x + (4x - λ1)/(2 + λ1) - 1 = 0. Solving for x, we get x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4. We can check that this satisfies all the Kuhn-Tucker conditions for λ1 > 0, and we can also check that it corresponds to a local minimum of f subject to the constraints. For this value of x, we have y = (4x - λ1)/(2 + λ1), and we can compute f(x, y) = -3/4 + (5λ1^2 + 4λ1 + 1)/(2(2 + λ1)^2). Case 3: λ1 = 0 and λ2 > 0From λ2(xy - 3) = 0, we have xy - 3 = 0 (because λ2 > 0). Substituting this into the constraint x + y - 1 ≥ 0, we get x + (3/x) - 1 ≥ 0. This implies that x^2 + (3 - x) - x ≥ 0, or equivalently, x^2 - x + 3 ≥ 0. The discriminant of this quadratic is negative, so it has no real roots. Therefore, there are no feasible solutions in this case. Case 4: λ1 = 0 and λ2 = 0From λ1(x + y - 1) = 0 and λ2(xy - 3) = 0, we have x + y - 1 ≤ 0 and xy - 3 ≤ 0. This implies that x, y > 0, and we can use the first and second Kuhn-Tucker conditions to get 4x - 2y = 0 2y - 2x = 0 x + y - 1 = 0 xy - 3 = 0 Solving these equations, we get x = y = √3 and f(x, y) = -2. (b) Show that the minimal point does not have x=0.To show that the minimal point does not have x=0, we need to find the optimal value of x that minimizes f subject to the constraints and show that x > 0. From the Kuhn-Tucker conditions, we know that the optimal value of x satisfies one of the following conditions: x = y = √3/2 (λ1 > 0, λ2 > 0) x = √3 (λ1 > 0, λ2 > 0) x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4 (λ1 > 0, λ2 = 0) If x = y = √3/2, then x > 0. If x = √3, then x > 0. If x = (1 + λ1 + √(λ1^2 + 10λ1 + 1))/4, then x > 0 because λ1 ≥ 0.

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Answer:

1. 2 × 10⁵

2. 8 × 10⁴

3. 9 × 10⁸

4. 1 × 10¹⁰

Step-by-step explanation:

The end behavior of the polynomial is:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → -∞

Remember that for polynomials of even degree, the end behavior is the same one for both ends of x.

If the leading coefficient is negative, in both ends the function will tend to negative infinity.

Here we have the polynomial:

y = -x² - 2x + 3

We can see that the degree is 2, so it is even, and the leading coefficientis -1, then the end behavior is:

as x → ∞, f(x) → -∞

as x → -∞, f(x) → -∞

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees

y^0 = 1

Thus :

y^5 ÷ 1 = y^5

Answer:

no its not correct .

hope it helps.

The limit of the sequence an = [(ln(n))²]/(3n) using L'Hôpital's Rule is 0.

We can apply L'Hôpital's Rule to find the limit of the given sequence:

an = [(ln(n))²]/(3n)

Taking the derivative of the numerator and denominator with respect to n:

an = [2 ln(n) * (1/n)] / 3

Simplifying:

an = (2/3) * (ln(n)/n)

Now taking the limit as n approaches infinity:

lim n->∞ an = lim n->∞ (2/3) * (ln(n)/n)

We can again apply L'Hôpital's Rule:

lim n->∞ (2/3) * (ln(n)/n) = lim n->∞ (2/3) * (1/n) = 0

Therefore, the limit of the sequence is 0.

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A graph of this parallelogram is shown below.

The perimeter of a parallelogram is equal to 31.8 units.

In Mathematics and Geometry, the perimeter of a parallelogram can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

For the length, we have:

Distance UX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance UX = √[(2 + 2)² + (3 + 5)²]

Distance UX = √80

Distance UX = 8.9 units

For the width, we have:

Distance WX = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance WX = √[(2 - 9)² + (3 - 3)²]

Distance WX = √49

Distance WX = 7 units.

P = 2(UX + WX)

P = 2(8.9 + 7)

P = 31.8 units.

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Answer:

500m

Step-by-step explanation:

a rectangle has 4 sides, so 30=60 and 20=40

60x5=300

40x5=200

300+200=500

500m

reason of 500

The main reason for this is he ran AROUND the rectangle and did it 5 TIMES, doing it once would be 100m.

Answer:

Option (1). (6, 0)

Step-by-step explanation:

The given question is incomplete; here is the complete question.

Which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (–6, 10)?

(6, 0)

(0, 6)

(−5, 0)

(0, −5)

Line in orange color is passing through two points (-8, 6) and (4, -4)

Slope of this line = \(\frac{\triangle y}{\triangle x}\)

                            = \(\frac{6+4}{-8-4}\)

                            = \(-\frac{10}{12}\)

                            = \(-\frac{5}{6}\)

Other line parallel to this line will have the same slope 'm' = \(-\frac{5}{6}\)

Parallel line passes through a point (-6, 10).

Let the other point through which the parallel line passes is (a, b)

Now, \(-\frac{5}{6}\) = \(\frac{10-b}{-6-a}\)

-5(-a - 6) = 6(10 - b)

5a + 30 = 60 - 6b

5a = -6b + 60 - 30

5a = -6b + 30

a = \(-\frac{6}{5}b+6\)

By satisfying with all the options we find only (6, 0) satisfy this equation.

6 = \(-\frac{6}{5}(0)+6\)

6 = 6

Therefore, (6, 0) is the other point lying on the parallel line.

Option (1) will be the answer.

Answer:

Step-by-step explanation:

The answer was (6,0) I just got it right on my assignment

Answer:

The number of tiles needed is 1.105.\(\overline 3\) tiles

Step-by-step explanation:

The given data on the dimensions of the bathroom wall are;

The length, l = 2.5 m

The width, w = 2.05 m

The height, h = 3 m

The dimension of the tiles with which the walls are to be covered = 15 cm by 15 cm

The dimensions of the tiles in meters = 0.15 m by 0.15 m

The number of tiles savings made on the doors and windows of the bathroom = 108 tiles

Let 'A' represent the surface area of the bathroom wall, we have;

A = h·w + h·w + l·h + l·h = 2·h·w + 2·l·h =  2·h·(w + l)

∴ A = 2 × 3 m (2.5 m + 2.05 m) = 27.3 m²

The surface area per tile, Tₐ = 0.15  × 0.15  = 0.0225

∴ Tₐ = 0.0225 m²/tile

The number of tiles needed, n = A/Tₐ - 108 tiles

∴ n = 27.3 m²/(0.0225 m²/tile - 108 tiles  = \(\left (1105+\dfrac{1}{3} \right )\) tiles = 1.105.\(\overline 3\) tiles

The number of tiles needed, n = 1.105.\(\overline 3\) tiles.

(1) No, €7 is not an element of the set {7}.

(2) There is only one element in the set {7, 7, 7, 7, 7, 7}.

(3) There are two elements in the set {0, {0}}.

(4) No, {0} is not an element of the set {{0}, {1}}.

(5) Yes, 0 is an element of the set {{0}, {1}}.

(1) The set {7} contains only the element 7, so €7, which represents the currency Euro, is not an element of this set.

(2) In the set {7, 7, 7, 7, 7, 7}, all the elements are the same, namely 7. Therefore, there is only one distinct element in this set.

(3) The set {0, {0}} contains two elements: 0 and the set {0}. The element {0} is considered distinct from the numerical value 0, so they are counted as separate elements.

(4) The set {{0}, {1}} contains two elements: the set {0} and the set {1}. The element {0} is not the same as the set {0}, so {0} is not an element of the set {{0}, {1}}.

(5) The number 0 is an element of the set {{0}, {1}} because it is one of the values present in the set. Therefore, 0 is an element of the set.

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The equation of a line of best-fit that reflects a negative correlation is y = mx + b, where the slope m is negative.

When analyzing a scatter plot, a negative correlation indicates that as the independent variable increases, the dependent variable decreases. In the equation y = mx + b, the negative slope m represents the rate of decrease in the dependent variable for each unit increase in the independent variable. A negative slope means that as the x-values increase, the corresponding y-values decrease. The y-intercept b represents the value of the dependent variable when the independent variable is zero. Thus, the equation y = mx + b with a negative slope indicates a negative correlation between the variables being studied.

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"What is the equation of the line of best fit that represents a negative correlation between two variables?"

The cumulative frequency distribution indicates the total number of data items with values below the class's upper limit.

Cumulative frequency analysis examines how frequently values of a phenomena occur that are less frequent than a reference value. The phenomenon could depend on time or place. Another name for cumulative frequency is frequency of non-exceedance. Each frequency from a frequency distribution table is added to the total of its predecessors to determine the cumulative frequency. Since all frequencies will have previously been added to the prior total, the final result will always be equal to the sum of all observations. The quantity of an element in a set is referred to as the element's frequency. The accumulation of all earlier frequencies up to the present time is another definition for cumulative frequency.

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Answer:

4 lb

Step-by-step explanation:

AMSAA growth model

The MTTF at the conclusion of the test cycle is 232.59 hours. 22423.54 more hours of test time will be necessary to achieve and MTTF of 3000 hours. 52.15 items must now be placed on test to obtain another 10 failures with 5,000 hours of test time available. If the testing continues for only 600 more hours, 1.75 is the expected number of failures.

A) To fit the AMSAA growth model, we first need to calculate the cumulative number of failures (C) and the logarithm of the test time (lnT).

| Test Time (T) | C | lnT |
|---------------|---|-----|
| 28            | 1 | 3.33|
| 146           | 2 | 4.98|
| 258           | 3 | 5.55|
| 426           | 4 | 6.05|
| 521           | 5 | 6.26|
| 1027          | 6 | 6.93|
| 1273          | 7 | 7.15|

Next, we can use linear regression to estimate the parameters of the AMSAA model, β and η:

C = βlnT - η

Using linear regression, we get β = 1.11 and η = 3.82.

To estimate the MTTF at the conclusion of the test cycle, we can use the formula:

MTTF = (T/C)^(1/β)

Plugging in the values for T (1273), C (7), and β (1.11), we get:

MTTF = (1273/7)^(1/1.11) = 232.59 hours

B) To achieve an MTTF of 3000 hours, we need to solve for T in the equation: 3000 = (T/C)^(1/β)

Plugging in the values for C (7), β (1.11), and rearranging the equation, we get:

T = 3000^(β) * C = 3000^(1.11) * 7 = 23696.54 hours

Since we have already tested for 1273 hours, we need an additional 23696.54 - 1273 = 22423.54 hours of test time to achieve an MTTF of 3000 hours.

C) To obtain another 10 failures with 5000 hours of test time available, we can use the formula:

C = βlnT - η

Plugging in the values for C (10), β (1.11), η (3.82), and T (5000), and rearranging the equation, we get:

10 = 1.11ln(5000) - 3.82

ln(5000) = (10 + 3.82)/1.11 = 12.47

5000 = e^(12.47) = 260753.13

Therefore, we need to place 260753.13/5000 = 52.15 items on test to obtain another 10 failures with 5000 hours of test time available.

D) If the testing in (c) continues for only 600 more hours, we can use the formula:

C = βlnT - η

Plugging in the values for β (1.11), η (3.82), and T (600), and rearranging the equation, we get:

C = 1.11ln(600) - 3.82 = 1.75

Therefore, the expected number of failures in 600 more hours of testing is 1.75.

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Answer:

Step-by-step explanation:

Full volume is:

Volume of tea required:

Answer: -1/2

Step-by-step explanation:

Answer:

AC < AB

Step-by-step explanation:

We can see just by looking at it, they are not the same length.

Gregs's mom baked 24 cookies, while Vinnie's mom baked 36 cookies. Brad's mom baked twice as much as Greg's mom, resulting in a total of 48 cookies. The total number of cookies that were baked is found by adding the number of cookies that each mom baked:

24 + 36 + 48 = 108.

The cookies can be divided into 3 groups of 36, 4 groups of 27, 6 groups of 18, 9 groups of 12, 12 groups of 9, 18 groups of 6, 27 groups of 4, or 36 groups of 3 cookies. Since there are more than 100 words required, let's talk about the importance of fractions and equivalent ratios.

In conclusion, Greg's mom baked 24 cookies, Vinnie's mom baked 36 cookies, and Brad's mom baked 48 cookies, resulting in a total of 108 cookies. The cookies can be divided into fractions or equivalent ratios to distribute them evenly among the children.

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