Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L = 12, Q = 122) and (L = 13, Q = 132). Then the marginal product of the 13th worker is
a.) 8 units of output.
b.) 10 units of output.
c.) 122 units of output.
d.) 132 units of output.
b.) 10 units of output.

The ordered pair (4, 0) makes both inequalities true.

What is inequality equation?

The mathematical expressions in which both sides are not equal are called inequalities.

Main body:

In inequality, unlike in equations, we compare two values.

The equal to sign in between is replaced by less than, greater than or not equal to sign.

It is given that

y < 3x -1 …. (1)

y > -x + 4 …. (2)

Let us take the point (4, 0)

In inequality (1)

y < 3x-1

0 < 3 (4) - 1

0 < 12 - 1

0 < 11 which is true

In inequality (2)

y ≥ - x + 4

0 ≥ -4 + 4

0 ≥ 0 …. Which is true

Therefore, the ordered pair (4, 0) makes both inequalities true.

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If the mean of a statistic's sample distribution perfectly matches the actual value of the parameter being evaluated, the statistic is said to be unbiased. The population proportion p is best estimated objectively using the sample proportion (p hat) from an SRS.

If the expected value of an estimate for a given parameter is the same as the parameter's true value, the estimator is said to be impartial. To put it another way, an estimator is impartial if it generates parameter estimates that are generally accurate.

The mean of a sample taken from a population is calculated to produce a point estimate of the population mean. The mean is calculated by dividing the total sample values by the total number of values.

Hence we get the required answer.

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The table which shows probability distribution is ,

X    P(X)

0    0.25

1      0.05

2     0.7

What is probability distribution?

   In mathematics, a probability distribution is a function that expresses the likelihood of many possible values for a variable. Utilizing graphs or probability tables, probability distributions are frequently represented. For a specific data generation process, a probability distribution shows the anticipated results of potential values. According to the mean, standard deviation, skewness, and kurtosis, probability distributions can take many different forms and exhibit a variety of properties.

A= Older eaglet survive

B = Younger eaglet survive

Given the older eaglet has 50% of survival ,

P(A) = 50% = 50/100 = 0.5

Now the older eaglet survive , the younger eaglet have only 10% of survival chance,

=> P(B/A)=10% = 10/100 = 0.1

Here P(B/A) = P(B∩A)/P(A)

=> 0.1 = P(B∩A) ×0.5

=> P(B∩A) = 0.05.

Both eaglet survives is P(B∩A) = 0.05. -------> 1

Now if the older eaglet does not have survive , the younger eaglet has 30% of survival chance,

=>P(B/A') = 30% = 0.3

Here P(B/A') = P(B∩A')/P(A')

Here P(A') = 1-P(A) = 1-0.50 = 0.50.

=> P(B∩A') = P(B/A')*P(A')

=> P(B∩A') = 0.3*05

=> P(B∩A') = 0.15

Now P(B) = P(B∩A)+P(B∩A')

=> P(B) = 0.05+0.15

=> P(B) = 0.20

P(only one eaglet survive) = P(A)+P(B)

=> 0.5+0.2 = 0.7 .-------> 2

Let x be the number of eaglet that survive,

Here x takes value of 0,1,2.

P(both eaglet survive ) = 0.05 ( from equation 1)=P(X=2)

P(only one eaglet survive) = 0.7 (from equation 2) =P(x=1)

As we know x takes only 3 values and we want to find probability distribution of x,

=> P(X=0) = 1-P(X=1)-P(x=2)

=> P(X=0) = 1-0.7-0.05

=> P(X=0) = 0.25 .

Therefore the table which shows probability distribution ,

X    P(X)

0    0.25

1      0.05

2     0.7

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The first two events are not independent, with a probability P = 0.0637

The second pair of events are independent, and the probability is P = 0.0625

How is probability obtained?

First, the probability that any card will be picked at random will be the same for all cards in the deck, or p = 1/52.

A) If Lacy draws a diamond card first, there are now fewer cards in the deck (now there are 51 cards on the deck). As a result, there is now a higher chance than before of drawing a spade. In that case, the first two events are not random.

The Probability of getting the first diamond card is:

P = 13/52 (because there are 13 diamonds and a total of 52 cards).

The probability of drawing a spade after is:

Q = (13/51)

The joint probability is the product of the individual probabilities, this will give:p = P×Q = (13/52)×(13/51) = 0.0637

B) Now we replace the first card, then the events are now independent, as the probability of drawing a spade after the first draw is not changed (because the total number of cards will be 52).

The probability of drawing a diamond is:

P = 13/52

Now we replace the diamond card drawn.

The probability of drawing a spade will be:

Q = 13/52

The joint probability is:

p = P×Q = (13/52)² = 0.0625

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Answer:

an obtuse angle are angles that are greater than 90 degrees

Step-by-step explanation:

an obtuse angle are angles that are greater than 90 degrees

The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

Now,

Substitute r = √x² + y² , r sin θ = x, r cos θ = y in above equation, we get;

The polar equation will be;

⇒ r = 4 sin(θ) + 5 cos(θ)

⇒ r² = 4 r sin(θ) + 5 r cos(θ)

⇒ x² + y² = 4x + 5y

⇒ x² + y² - 4x - 5y = 0

Thus, The Cartesian equation will be;

⇒ x² + y² - 4x - 5y = 0

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The minimum height is 6ft and length is 12 ft.

Let  [tex]l[/tex] be side of square base and h be the height.

we know  [tex]l^{2}[/tex] × h  = 864

We have minimize

[tex]l^{2}[/tex] + 4 × [tex]lh[/tex]

=  [tex]l^{2}[/tex] + 4 × 864/l

diffrentitate and equate to 0

2[tex]l[/tex] - 4 × 964/ [tex]l^{2}[/tex]  = 0

[tex]l[/tex] = [tex]\sqrt[3]{2 * 864}[/tex] = 12

so h = 6

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The highest temperature can be increased by any amount without changing the median.

Here, we are given the following data set-

94, 93, 98, 101, 98, 96, and 93

To find the median of the given numbers, we first need to arrange the numbers in an ascending or descending order. Let us arrange them in an ascending order as follows-

93, 93, 94, 96, 98, 98, 101

Now, the median of the middlemost value of a data set.

Here, we have 7 values, thus, the middlemost value will be given by the 4th term in the series.

As we can see from above, the fourth value is 96. Hence, 96 is the median of the data set.

Now, as we can see the highest temperature value is 101. We can increase it by any amount and it will still be the last term in the series, and the median will remain the same middle value, that is, 96.

Thus, the highest temperature can be increased by any amount without changing the median.

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The slope of the line that passes through the points (-3, 3), and (1, -5) is -2.

Steps to finding slope:

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,

m = slope of the line

x₁ = the x-coordinate of the first point

y₁ = the y-coordinate of the first point

x₂ = the x-coordinate of the second point

y₂ = the x-coordinate of the second point

Here, the given points are  (-3, 3), and (1, -5):

y₂ = -5, y₁ =3 , x₂ = 1, x₁ = -3

Substitute the values,

m = (y₂ - y₁) / (x₂ - x₁)

m = (-5 - 3) / (1 - (-3))

= -8 / (1+3)

= -8 / 4

m = -2

Hence, the slope of the line that passes through the points (-3, 3), and (1, -5) is -2.

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The required number of two positive consecutive integers are 35 and 36.

Consecutive integers are the whole numbers that follow each other without gaps. consecutive  integers are even, and odd integers.

consecutive even integers that differ from previous integer by difference of 2 and each integer is divisible by 2.

consecutive odd integers that differ from previous integer by difference of 2 and each integer is an odd number.

let the first positive integer be x

Therefore the second positive integer be (x+1)

Given that the sum of two consecutive positive integer is 71:

x+(x+1)=71

open the bracket

x+x+1=71

Add the similar terms

2x+1=71

2x=71-1

2x=70

x=35

Finding the second integer Substituate the value of x=35 in (x+1):

x+1=35+1

x+1=36

The required number of two positive consecutive integers are 35 and 36.

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None of these ordered pairs work. Each is false for at least one of the 2 equations.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

(1, 0) is false for equation 1.

y > -3x + 3

0 > -3(1) + 3

0 > -3 + 3

0 > 0 (FALSE)

(-1, 1) is false for equation 1.

y > -3x + 3

1 > -3(-1) + 3

1 > 3 + 3

1 > 6 (FALSE)

(2, 2) is false for equation 2.

y > 2x - 2

2 > 2(2) - 2

2 > 4 - 2

2 > 2 (FALSE)

And (0, 3) is false for equation 1.

y > -3x + 3

3 > -3(0) + 3

3 > 3 (FALSE)

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Question:

Which ordered pair makes both inequalities true? y > –3x + 3 y > 2x – 2 (1,0) (–1,1) (2,2) (0,3)

he got the same answer i did

Step-by-step explanation:

The required value of g would be 7.

The slope of a line is defined as the gradient of the line.

We have been given that a line that includes the points (0, – 3) and (g, 3) has a gradient of 6/ 7.

The gradient of line = (3 - (-3))/(g - 0)

⇒ 6/7 = (3 + 3)/g

⇒ 6/7 = 6/g

Apply the cross-multiplication operation,

⇒ 6g = 42

⇒ g = 42/6

Apply the division operation,

⇒ g = 7

Therefore, the required value of g would be 7.

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The equation of the line in slope intercept form is y = 4/3x - 10/3.

What is a line in slope-intercept?

The equation of a line with a slope of m and a y-intercept of (0, b) is y = mx + b. To graph a slope-intercept line, do the following: On the coordinate plane, draw the y-intercept. Find another point on the line using the slope.

We have,

the line that passes through  (-3,-6) and slope m = -2/3.

Now using the slope and the point (-3, -6) the y-intercept is

m = -2/3.

y = mx + b

-6 = -2/3(-3) + b

6 = 6/3 + b

By further calculation,

b = 6 - 2

b = 4

By writing the equation in slope intercept form

y = mx + b

y = -2/3x - 4

Therefore, the equation of the line in slope intercept form is y = -2/3x - 4.

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Okay here is step by step.

2x + 8 = 15

2x = 15 - 8

2x = 7

7/2 = 3.5

3.5 = x

Because we use the laws of substitution switching the numbers to the other side, which is allowed because they still mean the same thing.

Hope this helps.

By using the formula for mean and variance, it can be calculated that

Mean of X = 25

Variance of X = 51.67

What is mean and variance?

Suppose there is a data set. Mean gives the average of the values of the data set

Variance is the square of the sum of deviation from mean.

Let x be the total; of the numbers on the two card

Possible values of X= 15, 20, 25, 30, 35

P(X = 15) = [tex]\frac{2}{12}[/tex]

P(X = 20) = [tex]\frac{2}{12}[/tex]

P(X = 25) = [tex]\frac{4}{12}[/tex]

P(X= 30) = [tex]\frac{2}{12}[/tex]

P(X = 35) = [tex]\frac{2}{12}[/tex]

Mean of X =

[tex]15 \times \frac{2}{12} + 20 \times \frac{2}{12} +25 \times \frac{4}{12} + 30 \times \frac{2}{12} + 35 \times \frac{2}{12}\\\\\frac{300}{12}\\\\25[/tex]

Variance of X =

= [tex](225 \times \frac{2}{12} + 400 \times \frac{2}{12}+625 \times \frac{4}{12}+900 \times \frac{2}{12}+1225 \times \frac{2}{12}) - (25)^2\\\\\frac{8000}{12} - 625}\\\\666.67 - 625\\\\51.67[/tex]

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Complete Question

In a box are four cards numbered 5, 10, 15, 20. two cards are taken out at random without replacement, and X is the total; of the numbers on the two card. Find the mean and variance of X .

The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x).

Given,

Function,

Region = [0,1] × [0,1]

Lˣ = 1/area of region ∫¹₀ ∫₀¹ f(xy) dx dy

Differentiating,

Lˣ

= 1/1 ∫₀¹ tan⁻¹ xy dxdy

= ∫¹₀ [ ∫¹₀ tan⁻¹(xy) dx ] dy

= ∫₀¹ [{x tan⁻¹ (xy) ¹₀ - 1/2 ∫ 2(x+y)/ 1 + xy₂ dx] dy

= ∫¹₀ tan⁻¹ y dy - ¹₀ log(y² + 1) 2y dy

= [ytan⁻¹ y - 1/2 log( y² + 1) ∫¹₀ - [1/4 log (y² +1) log y² +1/4log(y²+1)

= π/4 - 1/2 log 2 -π²/48

L = 1/4( π - log4) - π²/48

The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

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The case mentioned above is resolved via multiplication.

Given information,

Linda can sell 12 magazine subscriptions per week and makes 4$ for each magazine subscription she sells. This means that Linda will make 48$ per week from magazine subscriptions.

To show it mathematically,

1 week ⇒ 12 magazines

Each of them costs $4;

⇒ 12 * 4$ = 48$ per week

By using multiplication we solve the above-given case.

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The Gross profit is $178, in the ending inventory using the periodic inventory.

What is profit?

To determine how much profit has been generated in a transaction, apply the profit formula. A product is said to have made a profit when its selling price is higher than its cost. The profit formula is useful for figuring out how much money is made when a certain product is sold, often in a business, or for figuring out how much money is made in any financial transaction. In situations where the selling price exceeds the cost price, profit can be determined. The following is the formula to calculate the profit:

Selling price minus cost price is referred to as profit (C.P.)

the last-in, first-out principle. According to LIFO, expenses are deducted starting with the costs of the most recent purchases of goods.

The most recent purchases, which were made on January 18 and January 12, resulted in 16 units.

Cost of goods sold = (7*6) + (9*4) = 42 + 36 = $78

Sales = 16*16 = $256

Gross profit = Sales - Cost of goods sold = 256 - 78 = $178

Hence, the Gross profit is $178

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The correct answer is 4 km per hour Lashonda would swim if there were no current.

Here, we'll suppose that Lashonda is moving at x km/hr. in the absence of any current.

Speed of the current is 2 km/hr.

Distance swim against current is 5km

Time taken to swim against current is  5 ÷ (x - 2)

Distance swim with current is 15km

Time is taken to swim with current is 15 ÷ (x + 2)

Now,

Given that  if the time taken in both instances are the same, So, the equation will be 5 ÷ (x - 2) = 15 ÷ (x + 2)

After solving for x we will be solving;

⇒ 5 ÷ (x + 2) = 15 ÷ (x - 2)

⇒ 5x + 10 = 15x - 30

⇒ 10 + 30 = 15x - 5x

⇒ 40 = 10x

⇒ x= 40 ÷ 10 = 4 km per hour

Hence, 4 km per hour Lashonda would swim if there were no current.

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The p-value for this hypothesis test for a proportion p is 0.039.

What is a random sample?

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals is chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

For the null hypothesis,

H0 : p = 0.63

For the alternative hypothesis,

Ha : p < 0.63

This is a left-tailed test

Considering the population proportion, probability of success, p = 0.63

q = probability of failure = 1 - p

q = 1 - 0.63 = 0.37

Considering the sample,

Sample proportion, P = x/n

Where,

x = number of success = 478

n = number of samples = 800

P = 478/800 = 0.6

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.6 - 0.63)/√(0.63 × 0.37)/800 = - 1.76

From the normal distribution table, the area below the test z score in the left tail is 0.039

Thus,

p = 0.039

Hence, the p-value for this hypothesis test for a proportion p is 0.039.

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Answer:

The answer is b

Step-by-step explanation:

One of the two identical halves of a chromosome that has been replicated in preparation for cell division is referred to as a chromatid. The two "sister" chromatids are united at the centromere, a restricted portion.

A chromatid is an individual of two together alike halves of a deoxyribonucleic acid that has been copied imminent for the formation of cells by dividing. The two “twin” chromatids are linked at an inhibited domain of the chromosome named the centromere. The establishment of chromatids is a main become involved in cellular division guaranteeing that each new girl cell has the correct complement of DNA at the end of the formation of cells by dividing.

Cell division is the process by which a person's container divides into two woman cells. Cell division frequently happens as few the best container phase at which point the cell evolves and replicates allure deoxyribonucleic acid before separating.

There are two types of cell division: the formation of cells by dividing and the formation of cells by dividing. Most of the time when nations are concerned with “cellular division,” they mean the formation of cells by dividing, the process of making new carcass containers.

Sister chromatids differ from chromatids in that sister chromatids are two copies of a single chromosome and are products of the S phase of the cell cycle. The centromere links sister chromatids together.

During the early stages of cell division, chromatids are produced. Non-sister chromatids appear during metaphase I of meiosis, whereas sister chromatids replicate from the same chromosome.

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The bearing of the oil rig from the port is 28.61° west by north.

What are the trigonometric identities?

All trigonometric identities are based on the six trigonometric ratios. Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.

We have,

First, the boat travels 55km toward the west,

and then it travels 30km toward the north.

So the boat forms the right triangles, see in the image attached,

tanθ = 33/55

θ = tan⁻¹ (33/55)

θ = 28.61°

28.61° west by north.

Hence, the bearing of the oil rig from the port is 28.61° west by north.

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Answer:

A

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 3, 6 ) and r = 2 , then

(x - (- 3) )² + (y - 6)² = 2² , that is

(x + 3)² + (y - 6)² = 4

When testing a newly installed hydromatic propeller, the propeller is exercised by moving the governor control through its entire travel several times to free the dome of any entrapped air.

A hydromatic propeller uses a double-acting governor control utilizing oil pressure on both sides of the propeller piston. It was introduced in the 1930s as a substantial advancement over the counterweight, controllable pitch propeller. The application of oil pressure to both sides of the actuating piston provided improved capacity and the potential of feathering or unfeathering by a single control knob. It was designed for larger blades, faster rate of pitch change, and wider range of pitch control. A hydromatic propeller should be checked before, during, and after the operation of the engine. A newly installed hydromatic propeller should be checked by moving the governor along its travel numerous times to ensure that no air is entrapped in the dome.

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By using the concept of cryptography, it can be concluded that

A solution that is now widely used to allow two parties to secretly exchange keys is Deffie - Hellman protocol

What is cryptography?

Cryptography refers to secure information and communication techniques derived from mathematical concepts and a set of rule-based calculations called algorithms, to transform messages in ways that are hard to decipher.

This is a concept of Cryptography

Diffie–Hellman key exchange establishes a shared secret between two parties which will be used for secret communication for exchanging data over a public network.

A solution that is now widely used to allow two parties to secretly exchange keys is Diffie - Hellman protocol

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The function has its graph to be represented by graph (a)

Table:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

The equation that represents the function is given as

f(x) = (3/4)ˣ

Next, we extract the x values from the given table

These x values are represented as

x = -2, -1, 0, 1 and 2

Solving further, we need to calculate the function at the x values

So, we have the following computations

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

When these values are presented on a table, we have:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

Some of the points on the table are

(0, 1), (1. 3/4) and (2. 9/16)

The graph that passes through these points is graph (a)

So, the

Hence, the graph of the function is graph (a)

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Yes, you can still get from one city to another even if a road is closed for maintenance.

How is it feasible to get from one city to another if one road is closed for repairs?

It is sufficient to show that even with route AB closed, we can still get from point A to point B. In the connected component that contains vertex A, all the vertices would be even if this weren't the case.

When a connected component has exactly one odd vertex, the "A graph must have an even number of odd vertices" condition is violated.

Therefore, even if one of the roads is closed for maintenance, it is still possible to go from Point A to Point B by another road or city.

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The given question is improper. Proper question is given below;

in a certain country, 40 roads lead out of each city. when all roads are open, it is possible to travel from any city to any other. each road leads from one city to another; there are no dead end roads. if one road is closed for repairs, is it still necessarily possible to travel from any city to any other? prove your answer.

By using the concept of Population and sample, it can be concluded that

The above data would be a population of weights because they represent all of the football players.

The first option is correct

What is population and sample?

Population is the set where all item are the members of the sets and from where the set of items can be drawn for statistical study

Subset of population is called sample

Here the data would be a population of weight because they represent all of the football players .

This is not a subset. So the question of sample will not come into existance here

So the first option is the correct option

The above data would be a population of weights because they represent all of the football players.

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Complete Question

The statistical data has been given below

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year. 176; 202; 212; 212; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265