Write an equation of the line in​ point-slope form that passes through the given points in the table. Then write the equation in​ slope-intercept form.x510152025y90120150180210

The null hypothesis and the alternate hypothesis for the set of elementary school children is given by H₀ :  μ₁ = 2 and H₁ : μ₂  ≠ 0 and the p-value is 0.136 .

Given x₁ = 74 , x₂ = 72

s₁ = 9 , s₂ = 11 (standard deviation)

n₁ = 50 ,n₂ = 50

Let μ₁ be the true mean for x₁

Let μ₂ be the true mean for x₂

null and alternate hypothesis:

H₀ :  μ₁ - μ₂  = 0

H₁ : μ₁ - μ₂  ≠ 0

Test statistic ,

Z = (x₁ - x₂ - D₀ ) / (√σˣ₁² /n₁ + √σˣ₂² /n₂ )

Now we will substitute the values to calculate the the test statistic.

D₀ = μ₁ - μ₂

hence Z₀ = (74 - 72) / √(81/80+121/50)

or,  Z₀ = 1.49256..

or,  Z₀ ≈ 1.49

Now we will calculate the p-value using the z-score.

p-value:

= 2P(Z > Z₀)

= 2P(Z>1.49)

= 2 {1-0.93189}

= 0.1362...

≈ 0.136

Hence the p-value is 0.136 .

A hypothesis is presented as a theory to explain a certain phenomenon. A hypothesis cannot be said to as a scientific hypothesis if it cannot be tested using the scientific process.

History-based observations that can't currently be fully explained by existing bodies of knowledge are typically where science starts. A hypothesis is a theory put out to explain an observed occurrence or a proven assertion regarding the relationship between two or more variables in a scientific field.

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Answer:

Slope = 2

Step-by-step explanation:

5-3

over

2-1 is

2 over 1 which is slope of 2

Answer:

There were 40 people total at the party and we assume each had cake of one type.

So, the % of those who had chocolate is:

32/40 = .8 = 80%

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

\(3,10,29,66,127,218\)

Step-by-step explanation:

\(f(n) = n^3 +2\\\\f(1) = 1^3 +2 = 1+2=3\\\\f(2) =2^3 +2 = 8+2=10\\\\f(3)=3^3 +2 = 27+2 = 29\\\\f(4) = 4^3 +2 = 64 +2 = 66\\\\f(5) = 5^3 +2 = 125+2 = 127\\\\f(6) = 6^3 +2 = 216+2 = 218\)

Answer:

-15

Step-by-step explanation:

m/n - 3

-12 / 1 - 3

-12 - 3

-15

Can I get a crown?

For the given expression, the value of x is 263/352

Expression:

Basically, the expression are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Here we have the expression 2-3/4(8x-6)=11.

Now, we need to find the value of x.

Now, we have to write the given expression,

=> 2-3/4(8x-6)=11

Now, we have to simplify the given expression as,

=> -1/ 4(8x - 6) = 11

Now, we have to expand the denominator of the expression, then we get,

=> -1/ 32x - 24 = 11

Cross multiply the expressions, then we get,

=> -1 = 11 (32x - 24)

=> -1 = 352x - 264

=> -1 + 264 = 352 x

=> 263 = 352 x

=> x = 263/352

Therefore, the value of x is 263/352.

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Refer to the images attached.

The length of PQ, as per Pythagoras' theorem, is 20 centimeters.

Given information:

The area of an isosceles triangle is 192 cm².

RQ = 24 cm.

To find PQ:

First, find the height described as h.

Area of isosceles triangle = 1/2 x 24 x h

192 = 12 x h

h = 16 cm.

Therefore, the side length of PQ can be calculated as Pythagoras' theorem,

PQ = √((h)² + (12)²)

PQ  = √(16)² + (12)²

PQ = √(256 + 144)

PQ = 20 cm.

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In response to the question, we may say that In 1.6 micrometres of expression graphite, there are approximately 8,000 layers of graphene.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the depiction of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

To determine the number of graphene layers in 1.6 micrometres (1.6 m), first convert the thickness of a single layer of graphene from picometers to micrometres:

1 picometer equals 110-6 micrometres

As a result, the thickness of a single sheet of graphene is as follows:

200 picometers = 200 tens of metres = 0.2 tens of metres = 0.2 nanometers = 0.2 tens of micrometres

As a result, the number of graphene layers in 1.6 micrometres is:

8,000 layers = 1.6 micrometres / (0.2 10-3 micrometers/layer)

In 1.6 micrometres of graphite, there are approximately 8,000 layers of graphene.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The option (a) 12 ounces of beer (360ml) contain more alcohol

Alcohol content is something that is important to understand, especially if you are of legal drinking age. It can affect your health and your ability to make sound decisions.

First, let's start with 12 ounces of beer. A typical beer has an alcohol content of around 5%, which means that 12 ounces of beer contains 0.6 ounces (18 ml) of alcohol. This is the same as the fourth option.

Next, let's consider 4 ounces of wine. The alcohol content of wine varies depending on the type and brand, but a typical wine has an alcohol content of around 12%. This means that 4 ounces of wine contains 0.48 ounces (14.2 ml) of alcohol.

Finally, we have 1.5 ounces of spirits. The alcohol content of spirits is generally higher than beer and wine, with a typical range of 40-50%. For the sake of this comparison, let's assume the spirits have an alcohol content of 40%. This means that 1.5 ounces of spirits contains 0.6 ounces (18 ml) of alcohol, the same amount as 12 ounces of beer.

So, in summary, 12 ounces of beer and 1.5 ounces of spirits contain the same amount of alcohol, which is 0.6 ounces (18 ml). 4 ounces of wine contains less alcohol, with 0.48 ounces (14.2 ml).

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Answer:

Step-by-step explanation:

The terms of this series may be arranged without changing the value of the series. The sum of the reciprocals of the squares of the odd positive integers is \(\pi ^{2} /8\).

In mathematics, a sequence is the cumulative sum of a given collection of terms. Usually, those phrases are actual or complicated numbers, but plenty of extra generalities are feasible.

A series is described as an arrangement of numbers in a specific order. then again, a chain is described as the sum of the factors of a sequence.

In mathematics, a series is, more or less speaking, a description of the operation of including infinitely many quantities, one after the alternative, to a given beginning quantity. The look at of series is a primary part of calculus and its generalization, mathematical analysis.

k=1

1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.

up to ∞ terms = 2/6

[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+

..∞0] = T²/6

→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+

1/4(3)²+....0] =²/6

[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+

1/(3)²+....x] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6

⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6

=

↑

[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8

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Answer:

B...i'm pretty sure that this Is the right one

Step-by-step explanation:

To solve the inequality:

4x + 8 ≥ -4

4x ≥ -12

x ≥ -3

If this is what you did then I'm not sure how you ended up getting x ≤ -3. You're not dividing by a negative number so the sign never switches.

Hope this helps

Step-by-step explanation:

−4≤4x+8

Subtraction property of inequality with the value 8.

-12≤4x

Division property of inequality with the value of 4.
The reason the sign stays as less than or greater to is because the sign only switches when the DIVISOR is negative, not the dividend.

(Just so the guy who originally answered can get brainliest :).

Answer:

no sé cómo hacer pero para la próxima lo intento

The partial derivative of the utility function \(U(x_1, x_2)\) with respect to \(x_1\) is \(a * x_1^{(a-1)} * x_2^{(1-a)}\), and the partial derivative with respect to \(x_2\) is \((1-a) * x_1^a * x_2^{(-a)}.\)

The utility function  \(U(x_1, x_2)\) represents a consumer's satisfaction or preference for two consumption goods, \(x_1\) and \(x_2\). The partial derivatives provide insights into how the utility function changes as we vary the quantities of the goods.

To calculate the partial derivative with respect to \(x_1\), we differentiate the utility function with respect to \(x_1\) while treating \(x_2\) as a constant. The result is \(a * x_1^{(a-1)} * x_2^{(1-a)}\). This derivative captures the impact of changes in \(x_1\) on the overall utility, taking into account the relative importance of \(x_1\)(determined by the parameter a) and the quantity of \(x_2\).

Similarly, to find the partial derivative with respect to \(x_2\), we differentiate the utility function with respect to \(x_2\) while treating \(x_1\)as a constant. The resulting derivative is \((1-a) * x_1^a * x_2^{(-a)}.\). This derivative shows how changes in \(x_2\) affect the overall utility, considering the relative weight of \(x_2\) (given by 1-a) and the quantity of \(x_1\).

In summary, the partial derivatives provide information about the sensitivity of the utility function to changes in the quantities of the consumption goods, allowing us to understand the consumer's preferences and decision-making.

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The Intersection between set A and set B is empty (A ∩ B = ∅). The intersection between set B and set C is empty (B ∩ C = ∅). The intersection between set A and set C is also empty (A ∩ C = ∅).

Venn diagrams that illustrate the sets A, B, and C for the given conditions:

(a) Venn diagram for condition A:

_____       _____

  |     |     |     |

A  |     |  B  |  C  |

  |_____|_____|_____|

In this diagram, set A is completely separate from set B, indicated by the empty intersection (A ∩ B = ∅). Set A is a subset of set C, indicated by A ⊆ C. Set C does not intersect with set B (C ∩ B = ∅).

(b) Venn diagram for condition B:

___________

  |           |

A  |     B     |

  |___________|

    /         \

   /           \

  |             |

  |      C      |

  |_____________|

In this diagram, set A is a subset of set B (A ⊆ B). Set C is also a subset of set B (C ⊆ B). The intersection between set A and set C is empty (A ∩ C = ∅).

(c) Venn diagram for condition C:

   _______   _______

  |       | |       |

A  |   B   | |   C   |

  |_______| |_______|

In this diagram, the intersection between set A and set B is empty (A ∩ B = ∅). The intersection between set B and set C is empty (B ∩ C = ∅). The intersection between set A and set C is also empty (A ∩ C = ∅).

These Venn diagrams visually represent the relationships between sets A, B, and C based on the given conditions. The empty intersections indicate that the corresponding sets have no elements in common, while the subset relationships show the inclusion of one set within another.

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The probability that at least one customer arrives in a particular one-minute period is approximately 0.393, rounded to three decimal places.

To find the probability that at least one customer arrives in a particular one-minute period, we can use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring within a fixed interval of time or space, given the average rate of occurrence.

In this case, we are given that the average number of customers per hour is 30. To convert this to the average number of customers per minute, we divide by 60 since there are 60 minutes in an hour. Therefore, the average number of customers per minute is 30/60 = 0.5.

The probability of no customers arriving in a particular one-minute period can be calculated using the Poisson distribution formula:

P(X = 0) = (e^(-λ) * λ^0) / 0!

Where λ is the average number of customers per minute.

Let's calculate the probability of no customers arriving in one minute:

P(X = 0) = (e^(-0.5) * 0.5^0) / 0!

= (e^(-0.5) * 1) / 1

= e^(-0.5)

Now, to find the probability that at least one customer arrives in one minute, we can subtract the probability of no customers from 1:

P(at least one customer) = 1 - P(X = 0)

= 1 - e^(-0.5)

Using a calculator, we can evaluate this expression to three decimal places:

P(at least one customer) ≈ 1 - e^(-0.5) ≈ 0.393

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The referee should call a double touch and have the fencers restart the point.

A double touch occurs when both fencers land a valid touch on the opponent at the same time. In this case, fencer X made a feint, which is an attempt to draw the opponent into a reaction. Fencer Y responded with a direct attack. Since both fencers landed a valid touch at the same time, the referee should call a double touch.

A double touch is a situation in which both fencers hit the other at the same time, and the point is not awarded to either fencer. The referee has the power to decide if a double touch occurred, and the fencers will restart the point if a double touch is called. To ensure fairness, the referee should observe both fencers carefully and make a judgment on who initiated the attack and who responded.

If both fencers hit at the same time and the referee cannot determine who initiated the attack, then a double touch should be called.

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The polynomials with coefficients in Z5 are f(x) = 2x² - x + 5 and g(x) = 3x³ - 2x² + x + 4.

Suppose we have polynomials f(x) = 2x² + 4x + 5 and g(x) = 3x³ - 2x² + x - 6.  

Here, we have to find the polynomial with coefficients in Z5, which means we need to perform arithmetic modulo 5. So, we replace all coefficients with their remainder when divided by 5.We have, f(x) = 2x² + 4x + 5 = 2x² - x + 5          (mod 5) g(x) = 3x³ - 2x² + x - 6 = 3x³ - 2x² + x + 4 (mod 5). Therefore, the polynomials with coefficients in Z5 are f(x) = 2x² - x + 5 and g(x) = 3x³ - 2x² + x + 4.

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Answer:

8v+4

This correct because basically what you are doing is multiplying the 2 so if 4v multiply it by 2 and you would get 8v

In a box there are some buttons. 45 are large and the rest are small. Some are yellow and the rest are green. The number of small is 53 of the number of large. The number of green is 300% of the number of yellow. There are 12 small yellow buttons. How many large green buttons are there?

Step-by-step explanation:

22buttons

Answer:

A' = (-2,0)

Step-by-step explanation:

imagine a mirror being along the line y=2.

Then A's mirror image would appear at -2,0.

Answer:

The slope for these to points would be -9/7 (rise/run)

The profit from selling 20 bags of rice is 61.67.e percentage profit from selling 20 bags of rice is approximately 10.54%.

To calculate the profit from selling 20 bags of rice, we need to determine the cost of the bags, the selling price, and subtract the cost from the selling price. Using the given cost equation c = 24x + 105 and the selling price equation s = 33x - x^2/30, we can calculate the profit expression and then determine the percentage profit.

Given that the cost equation is c = 24x + 105, we can substitute the value of x (which represents the number of bags) with 20 to find the cost of 20 bags.

c = 24(20) + 105

c = 480 + 105

c = 585

The cost of 20 bags of rice is 585.

Next, we use the selling price equation s = 33x - x^2/30 to find the selling price of 20 bags.

s = 33(20) - (20^2)/30

s = 660 - 400/30

s = 660 - 400/30

s = 660 - 13.33

s = 646.67

The selling price of 20 bags of rice is 646.67.

To calculate the profit, we subtract the cost from the selling price:

Profit = Selling Price - Cost

Profit = 646.67 - 585

Profit = 61.67

The profit from selling 20 bags of rice is 61.67.

To calculate the percentage profit, we divide the profit by the cost and multiply by 100:

Percentage Profit = (Profit / Cost) * 100

Percentage Profit = (61.67 / 585) * 100

Percentage Profit ≈ 10.54%

Therefore, the percentage profit from selling 20 bags of rice is approximately 10.54%.

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See solution below

Explanation:

a) 5x - 7 ≤ -2

collect like terms:

5x ≤ -2 + 7

5x ≤ 5

Divide through by 5:

x ≤ 1

From the graph above, the inequality has a solution.

b) 2/3b > -8

Cross multiply:

2 > -8(3b)

2 > -24b

Divide through by -24:

Note: when we divide an inequality by a negative number, the inequality sign changes.

2/-24 < b

-1/ 12 < b

Hence, b > -1/12

Note: To make it easier to graph, I represented b with x

From the graph above, the inequality has a solution.

c) 3w - 7 - w < 2w + 4

2w - 7 < 2w + 4

collect like terms:

2w - 2w < 4 + 7

0 < 11

Note: To make it easier to graph, I represented b with x

From the graph, the solution is for all real numbers.



Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].

Explanation:

We can approximate f(x) as a Fourier series, as follows:

\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)

If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.

We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:

\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)

For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.

However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.

Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:

\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)

Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].

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The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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