Calcium is essential to tree growth. In 1990, the concentration of calcium in precipitation in Chautauqua, New York, was 0.11 milligram per liter (mgL). A random sample of 8 participation dates in 2018 results in the following data:
0.087 0.313 0.183 0.07 0.108 0.12 0.262 0.065
H0:μ=.11
H1:μ≠.11
Find the test statistic t0

Answer:

the answer is 1,412

Step-by-step explanation:

all you do is add all the numbers together

Answer:

x = 10[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2x = 20[tex]\sqrt{3}[/tex] ( divide both sides by 2 )

x = 10[tex]\sqrt{3}[/tex]

Answer:

12x^2 + 30x+12    

Step-by-step explanation:

3x+6) (4x+2)

3x          6

12x^2       24x              4x

6x           12                   2

use a punnet square type deal here.

12x^2 + 24x + 6x + 12

12x^2 + 30x+12    

And so your answer should be: 12x^2 + 30x+12  

Answer:

Function notation means to replace y= into f(x)=. So I think that it would be f(x) = 40 +12d.

Step-by-step explanation:

[tex]f+44^{\circ}[/tex] and [tex]71^{\circ}[/tex] are opposite angles.

Therefore

[tex]f+44^{\circ}=71^{\circ}\\f=27^{\circ}[/tex]

27°

Using information about angles, we can create an equation to solve for f.

Verticle Angles

There is a special angle relationship known as vertical angles. Vertical angles are opposite angles made by interesting lines. The left angle  (made up of f and 44°) and the right angle (71°) are vertical angles. We know this because they are opposite each other and formed by the same interesting lines. Verticle angles are always congruent. This means that their measurements are equal.

Solving for f

We can use the information above to create an equation. Since we know that the left and right angles are congruent, we can set the equal to each other.

Now, we can subtract 44 from both sides and solve for f.

So, angle f must equal 27°.

Answer:

808 over 25 as a faraction

Step-by-step explanation

a quarter of 65 is 16 4 over 25

16 4 over 25 times 2 808 over 25 as a fraction

Before the price change, the optimal consumption choice (A) is determined by equalizing the marginal utilities of x and y.

Using the utility function U(x, y) = xy, and considering prices of Px = 1 and Py = 2, along with an income of 40, we find that the utility equalization condition leads to y = x/2.

With the budget constraint of x + 2y = 40, we solve for x = 20 and y = 10, giving the optimal consumption choice (20, 10) labeled as point A on the graph.

After the price change, with the price of y falling to 1, the consumer aims to maintain the same utility level. Setting MUX/Px = MUY/Py, we find x = y, and using the budget constraint x + y = 40, we get x = y = 20, resulting in the optimal consumption choice (20, 20) labeled as point B.

The substitution effect is illustrated by a movement from A to B along the budget constraint. The new optimal consumption choice (C) after the price change is determined by the new budget constraint x + y = 40, where x = 30 and y = 10, labeled as point C on the graph.

The income effect is depicted by the parallel shift of the budget constraint line outward from the origin.

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The probability of Sunshine Delight winning given that it is raining is approximately 0.79. The probability that a document is spam if it contains the word "llwws" is approximately 0.50.

In the case of Sunshine Delight winning, given that it is raining, the probability is directly provided as 0.79.

For the probability of a document being spam if it contains the word "llwws," the information shows that the probability of the word "llwws" appearing in a spam document is 0.50. However, without further information about the overall prevalence of spam and non-spam documents, we cannot directly determine the probability that a document containing "llwws" is spam. Additional context about the overall occurrence of spam and non-spam documents is required to calculate the requested probability.

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Option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.

The accurate translation of the sentence "Only lunatics drive on the autobahn" into the language of PL (Propositional Logic) can be represented as:

b. (Ex)(DxLx)

Let's break down the translation scheme:

Lx: x is a lunatic (Lunatics)

Dx: x drives on the autobahn (Drive on the autobahn)

The sentence states "Only lunatics drive on the autobahn," which implies that there are some individuals who drive on the autobahn and they are lunatics. This can be expressed using existential quantification (Ex) to indicate that there exists at least one individual who satisfies the condition. Therefore, option b. (Ex)(DxLx) accurately translates the given sentence.

Option a. (x)(DxLx) would mean "For all x, x drives on the autobahn implies x is a lunatic." This does not capture the meaning of the original sentence because it suggests that everyone who drives on the autobahn is a lunatic, which is not what the sentence implies.

Option c. (x)(LxDx) would mean "For all x, x is a lunatic implies x drives on the autobahn." Again, this does not capture the intended meaning of the original sentence as it suggests that all lunatics drive on the autobahn.

Option d. (Ex)(LxDx) would mean "There exists an x such that x is a lunatic and x drives on the autobahn." This translation does not capture the sense of the original sentence, which states that only lunatics drive on the autobahn, not that there exists at least one lunatic who drives on the autobahn.

Therefore, option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.

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Answer:

71

93.5

x=15.5

Step-by-step explanation:

(2x+40)+(5x+16)+(x)=180

you have to put all the measures together and equal it to 180. when it comes to triangles, all the angles added together are equal to 180.

now solve the equation and you should get this:

x=15.5

the next step is to solve the give equations separately:

2(15.5)+40=71

5(15.5)+16=93.5

(15.5)=15.5

now to check the work, you have to add all the measures that were just calculated:

71+93.5+15.5=180 so check!

Answer:

The system of this equation is ( -1, 10) which is Option A.

Step-by-step explanation:

Solve for y in the first equation.

[tex]y = - 5x + 5 \\ - 2y = - x - 21[/tex]

Replace all occurrences of yy with -5x+5 in each equation.

[tex]10x - 10 = - x - 21 \\ y = - 5x + 5[/tex]

Solve for x in the first equation.

[tex]x = - 1 \\ y = - 5x + 5[/tex]

Replace all occurrences of x with -1 in each equation.

[tex]y = 10 \\ x = - 1[/tex]

The solution to the system is the complete set of ordered pairs that are valid solutions.

(−1, 10)

Hence, the system of this equation is (-1, 10).

Option A.

Answer:

C and D.

Step-by-step explanation:

For C, 4 * 2x = 8x and 4*1 = 4.

For D, 5x+3x = 8x and 2+2 = 4.

Answer:

A)  8( x + 2 ) is the only equal expression.

Answer:

DON'T LOOK AT THE PICTURE!!

Step-by-step explanation:

a) the Shapley-Shubik Index of the Conservative party is 3360/5040.

b) the Shapley-Shubik Index of the Labour party is 82.142

To calculate the Shapley-Shubik index for a party in a weighted voting system, we need to consider all possible orderings of the parties and determine the party's contribution to the winning coalition in each ordering. The Shapley-Shubik index represents the average contribution across all possible orderings.

(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation:

To calculate the Shapley-Shubik Index of the Conservative party, we consider all possible orderings of the parties and determine the Conservative party's contribution to the winning coalition in each ordering.

The total number of possible orderings of the parties is given by the factorial of the total number of parties: 7! = 5040.

In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Conservative party, with 316 votes, does not reach the threshold alone.

However, if we consider the cumulative votes of the Conservative party and the Labour party (316 + 259 = 575), we reach the winning threshold. Therefore, the Conservative party's contribution to the winning coalition is 575 votes.

Since there are 6 other parties, we need to distribute the remaining votes among them. We can do this in 6! = 720 different ways.

The Shapley-Shubik Index is calculated by summing the contributions of the Conservative party across all possible orderings and dividing by the total number of orderings:

Shapley-Shubik Index of the Conservative party = (575 * 720) / 5040 = 3360 / 5040

Therefore, the Shapley-Shubik Index of the Conservative party is 3360/5040.

(b) To compute the Shapley-Shubik Index of the Labour party, we follow a similar approach:

The Labour party has 259 votes. We consider all possible orderings of the parties and determine the Labour party's contribution to the winning coalition in each ordering.

In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Labour party alone does not reach the threshold.

However, if we consider the cumulative votes of the Labour party and the Conservative party (259 + 316 = 575), we reach the winning threshold. Therefore, the Labour party's contribution to the winning coalition is 575 votes.

Similar to the previous calculation, we distribute the remaining votes among the 6 other parties in 6! = 720 different ways.

The Shapley-Shubik Index of the Labour party is calculated by summing the contributions of the Labour party across all possible orderings and dividing by the total number of orderings:

Shapley-Shubik Index of the Labour party = (575 * 720) / 5040

= 82.142

Therefore, the Shapley-Shubik Index of the Labour party is 82.142.

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Given question is incomplete, the complete question is below

A (simplified representation of) the 2019 British parliament was as a weighted voting system [326 : 316,259,35,12,12,10,6]. The Conservative party had 316 votes, the Labour party had 259 votes, and various other parties had the remaining votes.

(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation.

(b) Compute the Shapley-Shubik Index of the Labour party.

Answer:

2 laborers and 33 ops

Step-by-step explanation:

Given

Let:

L = Laborers

P = Ops

From the statements, we have:

[tex]L + P = 35[/tex] -- total people hired; and

[tex]140P + 100L = 4820[/tex] ---number of hirees

Required

Solve for L and P

Make L the subject in: [tex]L + P = 35[/tex]

[tex]L = 35 - P[/tex]

Substitute [tex]L = 35 - P[/tex] in [tex]140P + 100L = 4820[/tex]

[tex]140P + 100(35 - P) = 4820[/tex]

[tex]140P + 3500 - 100P = 4820[/tex]

Collect like terms

[tex]140P - 100P = 4820 - 3500[/tex]

[tex]40P = 1320[/tex]

Solve for P

[tex]P = 1320/40[/tex]

[tex]P = 33[/tex]

Substitute [tex]P = 33[/tex] in [tex]L = 35 - P[/tex]

[tex]L = 35 - 33[/tex]

[tex]L = 2[/tex]

Answer:

trapazoid

Step-by-step explanation:

.....

Answer:

x²+8x+9=0

Comparing above equation with ax²+bx +c

we get

a=1

b=8

c=9

quadratic equation is

[tex]x = \frac{ - 8± \sqrt{ {8}^{2} - 4×1×9} }{2*1} [/tex]

[tex]x = \frac{ -8± \sqrt{ 64-36} }{2} [/tex]

2x+8=±[tex] \sqrt{ {28}}[/tex]

taking + ve

2x=[tex] \sqrt{ {28}}[/tex]-8

x=[tex] 2\sqrt{ {7}}[/tex]-8/2

x=[tex] \sqrt{ {7}}[/tex]-4

taking -ve

2x=-[tex] \sqrt{ {28}}[/tex]-8

x=-[tex] 2\sqrt{ {7}}[/tex]-8/2

x=-[tex] \sqrt{ {7}}[/tex]-4

As given

General equation

On comparing

Answer: a = 2^12  b= 2^12  c=2^20

d= 2^12   e= 2^64   f= 2^12   g= 2^22   h= 2^40

Step-by-step explanation:

Answer: 1,953

Step-by-step explanation:

23,440 divided by 12

Answer:

$86.94

Step-by-step explanation:

All we need to do is subtract his weekly play from his pay after taxes and his other taxes.

   $625

   $499.61

_ $38.45

____________

   $86.94

Have a nice day, fam. Spread The Love.

Answer:

Step-by-step explanation:

2.3

Probability of exactly one error in 10 forms: Use binomial distribution with n = 10 and p = 0.08..Mean and standard deviation of forms with mistakes: Calculate using expected value and standard deviation formulas for a binomial distribution.

To calculate the probability that exactly one form has an error out of 10 randomly selected forms, we use the binomial probability formula: P(X = k) = (n C k) * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, and k is the number of successes. In this case, n = 10, p = 0.08, and k = 1. Plugging in these values, we can calculate the probability as P(X = 1) = (10 C 1) * (0.08)^1 * (1-0.08)^(10-1).

The mean (expected value) of the number of forms with mistakes can be calculated as μ = n * p, where n is the number of trials and p is the probability of success. In this case, n = 25 and p = 0.08. The standard deviation can be calculated as σ = sqrt(n * p * (1-p)), where sqrt represents the square root. Plugging in the values, we can calculate the mean and standard deviation.

Finding no mistakes in 25 randomly selected forms does not provide strong evidence to conclude that the employee is missing mistakes. The probability of not finding any mistakes in 25 forms can be calculated using the binomial distribution with parameters n = 25 and p = 0.08. If the actual proportion of mistakes is 8%, it is possible to observe a sample without mistakes due to random chance. To draw a more reliable conclusion, a larger sample size or additional evidence would be needed.

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Answer:

B its B

Step-by-step explanation:

Answer:

D. 105°

Step-by-step explanation: