t
h)
f(x + h) − f(x)
If f(x) = 3x2 + 11, find f(3) (a) 38 (b) RV11) (c) f(3 + 11 (d) f(3) + f(v (e) f(3x) (f) f(3 - x) (9) f(x + h) (h) flv

The value of derivative dx/dt = 12t³ and dy/dt = 4-2t.

To find the derivatives of x and y as functions of t, we'll calculate dx/dt and dy/dt.

For x=3t⁴, the derivative dx/dt is 12t³. For y=4t-t², the derivative dy/dt is 4-2t.

Now, let's break down the steps in the explanation:
1. Identify the functions x and y: x=3t⁴, y=4t-t².
2. Calculate the derivative of x with respect to t:
  dx/dt = d(3t⁴)/dt = 3 * d(t⁴)/dt = 3 * (4t³) = 12t³.
3. Calculate the derivative of y with respect to t:
  dy/dt = d(4t-t²)/dt = d(4t)/dt - d(t²)/dt = 4 - 2t.
4. Write the final derivatives: dx/dt = 12t³, dy/dt = 4-2t.

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(i) The statement 0(x⁻¹) = 0(2), for all x in every group G, is true.

(ii) The statement "All groups of order 8 are isomorphic to each other" is false.

(iii) The statement "o(xyx⁻¹) = o(y), for all x, y in every group G" is true.

(iv) The statement "HU K is a subgroup of G for all subgroups H, K of every group G" is false.

(i) The statement 0(x⁻¹) = 0(2), for all x in every group G, is true.

Justification: The operation of a group is usually denoted as multiplication, and the identity element of a group is denoted as e or 1. In this case, 0 represents the identity element of the group, and x⁻¹ represents the inverse of x in the group. Since the identity element multiplied by any element in a group gives the same element, the statement 0(x⁻¹) = 0(2) holds for all x in every group G.

(ii) The statement "All groups of order 8 are isomorphic to each other" is false.

Justification: Groups of the same order can have different structures and properties, and not all groups of the same order are isomorphic. The isomorphism between groups depends on the specific group structure, including the group operation and the relations between elements. Therefore, it is not true that all groups of order 8 are isomorphic to each other.

(iii) The statement "o(xyx⁻¹) = o(y), for all x, y in every group G" is true.

Justification: Here, o(x) represents the order of an element x in the group, which is the smallest positive integer n such that xⁿ = e, where e is the identity element of the group. For any elements x, y in a group G, we have o(xyx⁻¹) = o(y). This is because conjugating an element by another element does not change its order. Therefore, the statement holds true for all x, y in every group G.

(iv) The statement "HU K is a subgroup of G for all subgroups H, K of every group G" is false.

Justification: The statement implies that the product of two subgroups H and K, denoted as HU K, is always a subgroup of the original group G. However, this is not generally true. The product of subgroups H and K is a subgroup of G if and only if H and K commute with each other, i.e., hk = kh for all h in H and k in K. If H and K do not commute, then the product HU K may not be a subgroup. Therefore, the statement is false.

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Answer:

Average speed = 100 km/h

Step-by-step explanation:

Given:

Total distance covered = 250 km

Total time taken = 8:30 am - 6:00 am = 2:30 hours = 2.5

Find:

Average speed.

Computation:

⇒ Average speed = Total distance covered / Total time taken

⇒ Average speed = 250 / 2.5

⇒ Average speed = 100 km/h

SS(between) = 11.59, SS(within) = 22.33. SS(total) = 33.92, verifying the relationship SS(total) = SS(between) + SS(within). MS(between) = 5.795, MS(within) = 1.489, s^2(pooled) = 2.261.

(a) To compute SS(between) and SS(within), we first need to calculate the grand mean and the group means. The grand mean is the average of all the data points, while the group means are the averages of each sample.

Grand mean = (9 + 6 + 7 + 5 + 8 + 6)/18 = 6.33

Sample 1 mean = (9 + 6 + 7)/3 = 7.33

Sample 2 mean = (5 + 8)/2 = 6.5

Sample 3 mean = (6 + 6)/2 = 6

SS(between) measures the variation between the sample means and the grand mean:

\($SS_{between} = 3[(7.33 - 6.33)^2 + (6.5 - 6.33)^2 + (6 - 6.33)^2] = 11.59$\)

SS(within) measures the variation within each sample:

\($SS_{within} = \sum\limits_{i=1}^n (x_i - \bar{x})^2 = (9-7.33)^2 + (6-7.33)^2 + (7-7.33)^2 + (5-6.5)^2 + (8-6.5)^2 + (6-6)^2$\)

SS(within) = 22.33

(b) To compute SS(total), we simply sum the squared deviations of all the data points from the grand mean:

\(SS_{total} = \sum\limits_{i=1}^n (x_i - \bar{x}_{grand})^2 = (9-6.33)^2 + (6-6.33)^2 + (7-6.33)^2 + (5-6.33)^2 + (8-6.33)^2 + (6-6.33)^2$\)

SS(total) = 42.33

We can verify the relationship between SS(between), SS(within), and SS(total) by checking that:

SS(total) = SS(between) + SS(within)

In this case, we have:

SS(total) = 11.59 + 22.33 = 33.92

(c) To compute MS(between) and MS(within), we need to divide SS(between) and SS(within) by their respective degrees of freedom (df):

df(between) = k - 1 = 3 - 1 = 2

df(within) = N - k = 18 - 3 = 15

MS(between) = SS(between)/df(between) = 11.59/2 = 5.795

MS(within) = SS(within)/df(within) = 22.33/15 = 1.489

To compute the pooled variance, we first calculate the pooled sum of squares:

SS(pooled) = SS(between) + SS(within) = 11.59 + 22.33 = 33.92

Then, we can compute the pooled variance as:

\($s_{pooled}^2 = \frac{SS_{pooled}}{N-k} = \frac{33.92}{15} = 2.261$\)

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Complete question:

The accompanying table shows fictitious data for three samples. (a) Compute SS(between) and SS(within). (b) Compute SS(total), and verify the relationship between SS(between), SS(within), and SS(total). (c) Compute MS(between), MS(within), and Spooled Sample 2 1 3 23 18 20 29 12 16 17 15 25 23 23 19 Mean 25.00 15.00 19.00 2.74 SD 2.83 3.00 The following ANOVA table is only partially completed. (a) Complete the table. (b) How many groups were there in the study? (c) How many total observations were there in the study? df SS MS 4 Source Between groups Within groups Total 964 53 1123

Since the Mean is of mean daily revenue of $5400

Also, the standard deviation is $54

For the sample mean

The mean and standard deviation will remain unchanged

Hence the answer is

Option A

According to the question the method of undetermined coefficients to find a particular solution is The particular solution to the given system is

\(\(x_p = -2 e^{kt}\)\) , \(\(y_p = e^{kt}\)\).

To apply the method of undetermined coefficients, we assume a particular solution of the form:

\(\(x_p = A e^{kt}\)\\\(y_p = B e^{kt}\)\)

where \(\(A\) and \(B\)\) are undetermined coefficients to be determined and \(\(k\)\) is a constant.

Differentiating the assumed forms of \(\(x_p\) and \(y_p\):\)

\(\(x'_p = Ak e^{kt}\)\\\(y'_p = Bk e^{kt}\)\)

Substituting these into the given system of equations:

\(\(Ak e^{kt} = 7(A e^{kt}) - 10(B e^{kt}) + 12\)\\\(Bk e^{kt} = 2(A e^{kt}) - 5(B e^{kt}) - 4e^{-3t}\)\)

Simplifying the equations:

\(\((Ak - 7A + 10B) e^{kt} = 12\)\)

\(\((Ak - 2A + 5B) e^{kt} = -4e^{-3t}\)\)

Since these equations must hold for all \(\(t\)\), the coefficients multiplying \(\(e^{kt}\)\) must be equal to 0:

\(\(Ak - 7A + 10B = 12\)\)

\(\(Ak - 2A + 5B = 0\)\)

Solving these equations for \(\(A\) and \(B\):\)

\(\(A = -2\)\)

\(\(B = 1\)\)

Therefore, the particular solution to the given system is \(\(x_p = -2 e^{kt}\)\) , \(\(y_p = e^{kt}\)\).

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Given the inequality equations

y < 2x – 3 ....... 1

y > -6x + 9 .........2

We are to find the range of interval of x

Rerrange

y-2x< -3

y+6x > 9

From equation 1, make x = 0 and find y

y < 2(0) - 3

y< 0-3

y < -3

Also make y = 0 and get x

0 < 2x-3

-2x<-3

Multiply through by -1

x>3

Graph the function of y < -3 and x>3

From equation 2, make x = 0 and find y

y > -6(0) + 9

y> 0+9

y > 9

Also make y = 0 and get x

0 > -6x+9

6x>9

Divide through by 3

2x>3

Divide through by 2

x>3/2

Also graph the function of y > 9 and x>3/2

This is for the first inequality. Upper part will be shaded because if you plug x = 0 and y = 0 into the inequality, it will become

0<2(0)-3

0<-3

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is recommended to add the numbers in ascending order (from smallest to largest) to minimize the accumulation of rounding errors and maintain higher precision during intermediate calculations. Thus, starting with 0.01 and ending with 1.00 would provide better accuracy.

To achieve better accuracy when adding the numbers from 0.01 to 1.00, it is generally recommended to use an order that minimizes the accumulation of rounding errors. In this case, it is advisable to start with the smaller numbers and progress towards the larger ones.

By adding the numbers in ascending order (from 0.01 to 1.00), the rounding errors at each step will have a smaller impact on the overall result. This is because adding smaller numbers together first helps maintain a higher level of precision during intermediate calculations.

Therefore, to achieve better accuracy, you should add the numbers in ascending order, starting with 0.01 and ending with 1.00.

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The area of a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola   \(y=c-x^2\)   is   \(4(\frac{c}{3})^\frac{3}{2}\).

A rectangle has a width  \(2x\) ⇒ w= \(2x\)

height of the rectangle is   \(c-x^2\) ⇒    \(y=c-x^2\)

Area=width multiplied by the height

                                       ⇒\(area=width*height\)

we maximize Area by setting   \(\frac{dA}{dx} =0\) .

                                     \(\frac{d(2c-2x^3)}{dx} =0\\\\2c-6x^2=0\\\\x^2=\frac{1}{3}c\\ \\x=\sqrt{\frac{c}{3} }\)

substituting back the value of x in the formula of the area we get  

                                  \(area=2\sqrt{\frac{c}{3} } *2\frac{c}{3} \\\\area=4(\frac{c}{3})^\frac{3}{2}\)

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Answer:

the answer is x=4

Step-by-step explanation:

Answer:

98

Step-by-step explanation:

It would be the same amount because when the lines are parallel, the corresponding angles will also be the same.  

We can tell the difference between the two types of angles (Supplementary and complementary) 98 and 82 would be the two types of angles.

So, the angle measure would be 98.

The probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

We can use Bayes' theorem to calculate the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids. Let A be the event that a randomly selected bicyclist uses steroids, and B be the event that a randomly selected bicyclist tests positive for steroids. Then, we want to find P(A|B), the probability that a bicyclist uses steroids given that they test positive for steroids:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of testing positive given that the bicyclist uses steroids, P(A) is the prior probability of a bicyclist using steroids, and P(B) is the probability of testing positive for steroids.

We are given that P(A) = 0.08, P(B|A) = 0.94, and P(B|not A) = 0.09. We can calculate P(B) using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= 0.94 * 0.08 + 0.09 * 0.92

= 0.0976

where P(not A) = 1 - P(A) = 0.92.

Substituting the values we have:

P(A|B) = 0.94 * 0.08 / 0.0976

= 0.763

Therefore, the probability that a randomly selected bicyclist who tests positive for steroids actually uses steroids is 0.763 (rounded to three decimal places).

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The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

Given i - k and i - 3j + 2k.

Find two unit vectors that are orthogonal to both i −k and i − 3j 2k.

The two unit vectors orthogonal to both i - k and i - 3j + 2k are as follows:

First we find the cross product between i - k and i - 3j + 2k.

(i - k) × (i - 3j + 2k) = i × i - i × 3j + i × 2k - k × i + k × 3j - k × 2k= 0 + 2j - 3j - 0 + 0 + i = i - j

The cross product is (i - j).

Let v be any vector orthogonal to (i - j).

Let v = ai + bj + ck where (a, b, c) is a non-zero vector such that ai + bj + ck is orthogonal to (i - j).

We know that the dot product of two orthogonal vectors is zero. i.e (ai + bj + ck) • (i - j) = 0

(ai + bj + ck) • (i - j) = ai + bj + ck - aj - bj= (a - c)i - (a + b)j + ck

So we need to have (a - c) = (a + b) = 0 since (a, b, c) is non-zero implies ai + bj + ck is non-zero.

Therefore a = c and a = - b and a ≠ 0.

So a = - b and c = a.

Thus v = ai - aj + ak or v = -ai + aj + ak, both of which are unit vectors.

The two unit vectors that are orthogonal to both i −k and i − 3j + 2k are:i - j / √2- i + j / √2

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In general, observational studies are more problematic than randomized controlled trials because they can produce spurious relationships.

Observational studies rely on the natural variation in exposures and outcomes that occur in the population, without any intervention or manipulation by the researcher.

This can lead to confounding variables, which are factors that are associated with both the exposure and the outcome and can produce a false association between them.

Randomized controlled trials, on the other hand, assign participants to different exposure groups at random, which reduces the risk of confounding and allows for a more accurate assessment of causality.

Therefore, researchers must be cautious when interpreting observational studies and consider the potential for spurious relationships.

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First term (a1) = -7

Second term (a2) = -2

Common difference: a2 - a1 = -2-(-7) = 5

Hence, Fifth term = a1 + 4d = -7 + 4(5) = 13

Given:

Weekly wage = $2456

A career starts 24 years and ends in 65 years.

Find-: Lifetime earring.

Sol:

Total years of working is:

In one year 52 weeks

For 41 years total week is:

Lifetime earnings.

So lifetime earning is 5236192.00

Answer:

You will now because the sides are equal. All sides must be equal to be congruent.

Step-by-step explanation:

Answer:

(x−4)2(x2+4x+16)

Step-by-step explanation:

here hope this helpsss

Answer: The third one.

Step-by-step explanation: The hottest time of the day is around 3 p.m. Heat continues building up after noon, when the sun is highest in the sky, as long as more heat is arriving at the earth than leaving.

Answer: All of them

Step-by-step explanation: I think zll of them

You would need to invest approximately $34,175.85 now in one lump sum in order to have $100,000 after 18 years with an annual interest rate of 10% compounded quarterly.

Using the formula for present value of money, you would need to invest approximately $34,175.85 now in one lump sum in order to have $100,000 after 18 years with an annual interest rate of 10% compounded quarterly.

To calculate the present value of an investment, we can use the formula for the present value of money:

PV = FV / (1 + r/n)^(n*t)

Where:

PV = Present Value

FV = Future Value ($100,000 in this case)

r = Annual interest rate (10% or 0.10)

n = Number of compounding periods per year (4 for quarterly compounding)

t = Number of years (18 years in this case)

Plugging in the values into the formula, we get:

PV = 100,000 / (1 + 0.10/4)^(4*18)

Calculating the expression inside the parentheses first:

PV = 100,000 / (1 + 0.025)^(72)

Simplifying the exponent:

PV = 100,000 / (1.025)^(72)

Calculating the value inside the parentheses:

PV = 100,000 / 2.925169596

Calculating the final present value:

PV ≈ $34,175.85

Therefore, you would need to invest approximately $34,175.85 now in one lump sum in order to have $100,000 after 18 years with an annual interest rate of 10% compounded quarterly.

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This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

87.5

Step-by-step explanation:

i think this is only the answer

have a nice time

tell me if the ans is right if wrong then to

the gradients of each of the sides of the triangle are \(m_1=\frac{8}{5}, m_2=\frac{4}{-9} and m_3=-3\)

Given  vertices of triangle ABC are A(2,-3),B(7,5) and C(-2,9).

Let's find out the gradients of each side of the sides of the triangle using given points.

Formula for Gradient  using two points.

Gradient denoted by m.

Gradient can also called as slope.

First gradient using two points are A(2,-3) & B(7,5)

           \(m_1=\frac{y_2-y_1}{x_2-x_1}\)

           \(m_1=\frac{5-(-3)}{7-2}\)

           \(m_1=\frac{8}{5}\)

Second gradient using two points are B(7,5) & C(-2,,9)

            \(m_2=\frac{y_2-y_1}{x_2-x_1}\)

            \(m_2=\frac{9-5}{-2-7}\)

            \(m_2=\frac{4}{-9}\)

Third gradient using two points are   A(2,-3) & C(-2,9)

              \(m_3=\frac{y_2-y_1}{x_2-x_1}\)

              \(m_3=\frac{9-(-3)}{-2-2}\)

              \(m_3=\frac{12}{-4}\)

              \(m_3=-3\)

Therefore, the gradients of each of the sides of the triangle are \(m_1=\frac{8}{5}, m_2=\frac{4}{-9} and m_3=-3\)

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The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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Since, the triangle FGH is a right angle triangle, The angles of the ∠F = 62°, ∠G = 90° and ∠H = 28°.

Right Angle Triangle:

A right triangle (American English) or right triangle (UK), or more formally an orthogonal triangle, formerly known as a right triangle, is a triangle in which one angle is a right angle (i.e. say an angle of 90 degrees), i.e. two of its sides are perpendicular. The relationship between the sides of a right triangle and the other angles is the basis of trigonometry.

According to the Question:

Interior angles of a triangle add up to 90 degrees

∠F + ∠ G + ∠H = 180

⇒ 9x - 1 + 90 + 3x + 7 = 180

⇒ 12x + 96 = 180

⇒ 12x = 180 - 96

⇒ 12x = 84

⇒ x = 84/12

⇒ x = 7

Therefore,

∠F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62

And, ∠G = 90

And, ∠ H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28

If we add the angles :

62 + 90 + 28 = 180°

Complete Question:

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

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Using the properties of arithmetic sequence , we calculate

a) 100 seats in the first row (b) 40 rows are required (c) 22 more seats in each row (d) 958 seats in the last row.

The overlap of any two doubly infinite arithmetic progressions seems to be either empty or another arithmetic progression, according to the Chinese remainder theorem.

If every pair of advancements in a family of twice infinite arithmetic progressions has a non-empty intersection, then there is a number that connects all of the pairs; consequently, an infinite arithmetic progression is a member of the Helly family.

However, rather than being an unending progression in and of itself, the intersection of an infinite number of infinite arithmetic progressions might be a particular number.

We know that the AP has the total number of seats between 18 000 and 22 500.

So if we take first term as 100 common difference as 22 and 40 rows we get :

sum =  \(\frac{40}{2} [2\times 100+(40-1)22] = 21160\)

Therefore the number of seats in the arena matches the required description.

and the last row will have 100+(39)22 = 968 seats.

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Answer:

The Answer should be: 40 49 60 8 54

\

95 82 40 18 39

94 72 23 70 39

24 55 6 48 40

16 100 67 93 83

2 59 97 66 28

51 81 81 6 1

29 59 34 15 65

100 94 100 70 64

87 33 20 79 76

47 56 83 58 1

36 14 71 87 26

13 4 67 26 76

85 44 55 99 64

89 50 13 10 29

62 76 82 51 71

69 13 76 3 46

71 5 51 81 15

53 94 47 55 61

6 23 97 99 46

3 87 45 49 72

87 14 32 29 22

84 60 17 4 95

100 51 39 77 87

31 97 11 80 94

78 61 38 79 35

87 67 11 21 70

82 43 19 74 42

58 90 24 8 3

61 3 63 84 1

15 67 79 31 83

28 27 93 46 39

76 7 57 82 97

35 38 73 6 88

24 95 20 90 73

17 49 4 63 63

100 3 23 52 80

17 61 39 68 63

67 27 16 81 84

81 37 43 82 34

97 54 8 32 78

99 77 20 71 17

21 42 52 48 8

46 75 71 55 74

11 48 80 39 30

76 50 52 89 100

19 10 57 21 79

58 53 99 99 11

24 59 72 16 52

91 84 36 21 22

72 44 52 56 29

96 78 57 91 47

72 42 35 79 99

44 51 76 93 16

16 36 63 82 63

42 36 82 86 30

63 42 78 75 50

65 2 50 21 32

10 23 26 96 96

61 13 16 37 58

3 30 99 93 1

54 43 8 94 13

62 54 76 14 40

12 22 68 57 24

83 16 36 2 66

49 68 65 88 2

19 36 17 89 59

51 68 100 39 75

67 27 50 87 100

12 87 65 2 1

47 61 50 36 29

64 37 68 3 99

20 83 98 91 77

53 35 37 78 89

87 79 73 20 49

19 36 23 58 29

76 4 18 44 61

65 25 84 11 3

99 97 74 92 97

9 47 73 47 8

35 96 15 65 16

93 5 48 53 28

59 23 7 47 50

20 73 26 86 92

21 10 99 91 32

32 35 63 47 25

3 87 75 9 5

4 75 15 79 43

62 33 6 23 70

81 37 96 93 33

49 72 20 47 61

30 51 67 77 16

51 11 66 68 36

49 45 29 10 98

92 39 36 89 57

74 70 77 13 94

78 1 80 33 85

34 82 27 1 97

59 99 72 82 20

73 67 35 69 68

61 83 15 77 72

31 90 77 9 71

96 96 30 75 87

40 97 78 26 16

41 5 4 57 82

50 94 11 1 94

2 72 71 6 77

89 12 22 68 82

2 35 88 11 43

54 46 9 30 95

7 90 63 13 70

10 15 49 97 73

12 7 86 24 69

91 99 40 51 18

2 79 91 19 97

99 9 66 86 92

70 34 77 31 95

89 25 68 70 57

65 36 4 24 95

36 48 92 44 62

69 84 41 52 92

84 20 66 23 73

16 85 44 17 2

9 90 58 28 90

53 41 42 15 37

18 87 53 21 57

55 25 24 5 57

93 24 17 37 63

8 92 68 68 20

100 69 45 73 11

100 79 27 99 36

44 38 10 100 27

35 32 10 28 70

53 67 81 26 97

9 42 22 1 91

61 70 80 16 38

87 91 49 1 12

57 1 22 12 24

71 88 72 42 23

67 41 20 89 14

24 1 40 41 78

86 77 23 57 96

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