A scientist planted seeds in 4 sections of soil for an experiment. Not all of the seeds grew into plants. After

20 days, the scientist counted the number of plants in each of the 4 sections. The results are shown in the

table.

Plant Experiment

Section

Size of Section

(square feet)

Number of Plants

1

25

13

2

100

38

3

125

47

4

150

62

.

• Use the data in the table to determine approximately how many plants grew per square foot.

Explain or show how you determined your approximation.

• Lety be the number of plants expected to grow in x square feet. Write an equation the scientist could

use to model the relationship between y and x.

a) The point estimate is 3 thousand dollars.

b) The 9% confidence interval for the difference between the two population means is -1.829 to 7.829 thousand dollars.

The point estimate is given by the mean of the sample data for each type of project. For the first type of project, the mean is (3.3 + 2.7 + 3.5)/3 = 3.17 thousand dollars.

For the second type of project, the mean is (4.3 + 4.6 + 4.2)/3 = 4.37 thousand dollars.

The difference between the means is 4.37 - 3.17 = 1.2 thousand dollars.

To calculate the confidence interval, we need to find the standard error of the difference and the critical value for a t-distribution with n1 + n2 - 2 degrees of freedom. The formula for the standard error is:

SE(d) = sqrt[ (s1^2 / n1) + (s2^2 / n2) ] = sqrt[ ((0.4)^2 / 3) + ((0.2)^2 / 3) ] = 0.282

The critical value for a 9% two-tailed t-test with 4 degrees of freedom is 2.306 (from a t-table or using Excel's TINV function).The margin of error for the 9% confidence interval is:

ME = t(0.09/2, 4) * SE(d) = 2.306 * 0.282 = 0.649

The 9% confidence interval for the difference between the population means is:

d ± ME = 1.2 ± 0.649 = (0.551, 1.849)

Therefore, the 9% confidence interval for the difference between the two population means is -1.829 to 7.829 thousand dollars (rounded to three decimal places).

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Answer:

¼ of the students

Step-by-step explanation:

½×20 = 10

½ × 10 = 5

\( \frac{5}{20} = \frac{1}{4} \)

<3

Answer:

\( \frac{1}{4} \)

Step-by-step explanation:

Refer the attachment for explanation

The following statements is not always true is that a 95% confidence interval may include the hypothesized value under the null hypothesis that is rejected at 99% option D.

Assuming a given standard deviation, it is described as the sampling distribution that follows a roughly normal distribution. estimating the population standard deviation's confidence interval:

We are aware that significance level = confidence level - 1.

Given this, a null hypothesis can only be ruled out at a 5% level of significance.

A null hypothesis cannot be ruled out at the 5% level of significance unless the parameter's hypothesis value is contained within a 95% confidence range.

If the anticipated value is included in the 95% confidence interval, a hypothesis test at the 0.05 level will almost never succeed in rejecting the null hypothesis.

So, a null hypothesis can only be disproved at the 5% level of significance if and only if a 95% confidence interval contains the parameter's postulated value.

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Answer:

-6

Step-by-step explanation:

The function F(x) = x² + 2x - 15 is neither odd nor even.

The function in this problem is defined as follows:

F(x) = x² + 2x - 15.

For F(-x), we have that:

F(-x) = (-x)² + 2(-x) - 15

F(-x) = x² - 2x - 15.

There is no relation between F(x) and F(-x), hence the function is neither even nor odd.

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Using Table E, the probability of a value less than -1.12 is 0.1315. To calculate the probability of a value greater than 1.24, you will need to subtract the probability of a value less than 1.24 from 1. The probability of a value less than 1.24 is 0.8915, so the probability of a value greater than 1.24 is 1 - 0.8915 = 0.1085. Therefore, the probability of a value between -1.12 and 1.24 is 0.1315 + 0.1085 = 0.24. To four decimal places, this probability is 0.2400.

To understand this answer, it is important to understand the concept of normal distributions. Normal distributions are symmetrical and bell-shaped, and all values within the distribution have an equal chance of occurring. The mean of a normal distribution is 0 and the standard deviation is 1. Using Table E, you can look up the probability for values between the mean (0) and any other value. For example, if you look up the probability for a value of 1.24, you will find it is 0.8915. This is because 89.15% of the area under the curve is to the left of the value 1.24. To calculate the probability of a value greater than 1.24, you need to subtract the probability of a value less than 1.24 from 1. This is because the total area under the curve is 1.

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The number 15.74 is nearest to the number 8. Then the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 15.93 - 0.19

Simplify the expression, then we have

⇒ 15.93 - 0.19

⇒ 15.74

The number 15.74 is closest to the number 8. Then, at that point, the right choice is B.

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Answer:

I think x might be 2 i don't know...

Step-by-step explanation:

Answer:

I belive it to be C my guy

Step-by step explanation

Answer:

A the degree of polynomial

The probability that the point P lies outside the square is;1 - (2/π)

If a is the radius of the circle, then;

Area of the inscribed square = 2a²

Now, area of the circle is;

Area of circle = πa²

Thus, probability that the point lies outside the square is;

Area of between circle and square/area of circle

Area between circle and square = πa² - 2a² = a²(π - 2)

Thus;

P(the point lies outside the square) = a²(π - 2)/πa² = (π - 2)/π = 1 - (2/π)

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The expression of the inequality of John profit as per given details is given by  $80,000 ≤ $x ≤ $250,000.

Let us consider the John profit represented by $x.

As per first statement we have,

At least amount of $80,000 John must make to pay bills.

This implies ,

$80,000 is less than or equal to John’s profit.

⇒ $80,000 ≤ John  profit

⇒ $80,000 ≤ $x __(1)

Now, John’s profit is less than or equal to $250,000.

⇒John profit ≤ $250,000

⇒ $x ≤ $250,000 ___(2)

Combine (1) and (2) we get the inequality ,

$80,000 ≤ $x ≤ $250,000

Therefore, the expression used to represents the inequality of John profit is equal to  $80,000 ≤ $x ≤ $250,000.

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The given question is incomplete, I answer the question in general according to my knowledge:

John must make at least $80,000 to pay bills. That can be rephrased as $80,000 is less than or equal to John’s profit. You also know that John’s profit is less than or equal to $250,000 . Write the expression to represents the inequality.

Answer:

3 is right answer

Step-by-step explanation:

see in attached picture

hope it helped you:)

The function represented by the table can be written as:

y = -4x + 3

Here we have a function represented by a table. Notice that for each increase of one unit in the x-value, the y-value decreases by 4.

Then we have a linear function, which can be written in a general form as:

y = a*x +b

Where a isthe slope and b is the y-intercept.

Because of the first pair on the table, (0, 3), we conclude that the y-intercept is 3, then we can rewrite:

y = a*x + 3

Now we can use the second point (1, - 1) and replace the values on the equation above.

-1 = a*1 + 3

-1 = a + 3

-1 - 3 = a

-4 = a

The linear function is:

y = -4x + 3

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Answer:

m = 0

Or Slope intercept form of y = mx+b

y=-5

Step-by-step explanation:

Answer:

The given function is an Absolute value function because its expression is contained within the absolute value symbol.

Explanation:

Given the function;

Recall that Absolute value functions are functions that contains it algebraic expression within the absolute value symbol.

Such as;

Therefore, the given function is an Absolute value function because its expression is contained within the absolute value symbol.

Answer:

Multiplication comes before division.

Step-by-step explanation:

This abbreviation can be used to easily remember the order of operations: PEMDAS

P - Parenthesis (Bracket)

E - Exponent (^)

M - Multiplication (×)

D - Division (÷)

A - Addition (+)

S - Subtraction (-)

This order should be followed accordingly when solving a mathematical problem so as to find the correct answer.

Answer:

Multiplication comes before division.

Step-by-step explanation:

Hope this helps

62.5% or 62.5 out of every 100 students exceeded the minimum standards.

The teacher found that 62 1/2% of the students exceeded the minimum standards. To find the part of the students who exceeded the standards, we need to convert the percentage to a decimal.
To do this, divide 62.5 by 100: 62.5 ÷ 100 = 0.625.
This means that 0.625 represents the decimal form of 62 1/2%.
To find the part of the students who exceeded the standards, multiply 0.625 by the total number of students.
For example, if there are 100 students in total, multiply 0.625 by 100: 0.625 x 100 = 62.5.
Therefore, 62.5 represents the part of the students who exceeded the minimum standards.

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In the present scenario, the angle of Θ= π terminates in the second quadrant, where the x-coordinate is negative and the y-coordinate is positive.

the terminal point (x, y) of Θ= π on the unit circle can be calculated with the help of the following steps:

Step 1: Firstly, let’s recall the unit circle, which is a circle having a radius of 1 unit, and it is centered at the origin of a coordinate plane.

Step 2: Draw the angle of Θ= π on the unit circle. We can see that this angle has been formed by rotating in the clockwise direction along the unit circle from its initial position on the positive x-axis.

Step 3: As we know that the terminal point (x, y) of an angle in standard position is given by (cos Θ, sin Θ). Therefore, we can apply this formula to calculate the coordinates of the terminal point for the given angle of Θ= π on the unit circle.

Here, cos π= -1 and sin π= 0. Thus, the coordinates of the terminal point are (-1, 0). Hence, the correct answer is (-1, 0).Note: The coordinates of the terminal point for an angle in standard position can be negative, positive, or zero, based on the quadrant in which the angle terminates.

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Answer:j

Step-by-step explanation:

Since the value is in the positive y axis,the line is expected to pass through the positive y coordinate.Since the coordinate for x wasn't given,you should look out for the line that doesn't pass through the x axis (positive and negative) and the negative y axis .

(a)For the trigonometric function k(t) = 10sin(6x + 4π), within the interval 0 ≤ x < 3π, there are two x-intercepts  -2π/3 and x = -π/2.

(b)The trigonometric function k(t) = -6sin(26x - 3π) has x-intercepts at x = π/26 and x = 14π/26 within the interval 0 ≤ x < 13π.

(a)To find the x-intercepts of the function k(t) = 10sin(6x + 4π) within the given interval, we need to determine the values of x where the function crosses the x-axis or has a y-value of zero.

The x-intercepts occur when sin(6x + 4π) = 0. Since the sine function is zero at multiples of π, we can set 6x + 4π = nπ, where n is an integer, and solve for x.

For the given interval 0 ≤ x < 3π, we can consider n = 0 and n = 1.

For n = 0:

6x + 4π = 0

6x = -4π

x = -4π/6

x = -2π/3

For n = 1:

6x + 4π = π

6x = -3π

x = -3π/6

x = -π/2

Therefore, within the interval 0 ≤ x < 3π, the x-intercepts of the function k(t) = 10sin(6x + 4π) are x = -2π/3 and x = -π/2.

(b)To find the x-intercepts of the function, we need to determine the values of x for which k(t) equals zero. In this case, k(t) = -6sin(26x - 3π). When the sine function equals zero, the argument inside the sine function must be an integer multiple of π. So we set 26x - 3π = nπ, where n is an integer.

First, let's solve for x when n = 0. We have 26x - 3π = 0, which gives us x = 3π/26. This is the first x-intercept within the given interval.

Next, let's consider n = 14. We get 26x - 3π = 14π, which simplifies to 26x = 17π. Dividing by 26, we find x = 17π/26. However, this value of x is greater than 13π, so it is not within the specified interval.

Therefore, the only x-intercept within the interval 0 ≤ x < 13π is x = 3π/26.

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Answer: \(y=\frac{5}{6}(x-2)(x+3)(x-4)\)

Step-by-step explanation:

Assuming this is a cubic polynomial, the equation in factored form is:

\(y=a(x-2)(x+3)(x-4)\)

Using the point \((1, 10)\) to solve for \(a\),

\(10=a(1-2)(1+3)(1-4)\\\\10=12a\\ \\ a=\frac{5}{6}\\\\\therefore y=\frac{5}{6}(x-2)(x+3)(x-4)\)

In a dispersive medium, a particle is represented by a wave packet propagating. Here, the wave number is dependent on the frequency, and vice versa. In other words, the phase velocity is not the same as the group velocity.The energy of the particle is given by E = ħω. The group velocity of the wave packet can be obtained by differentiating the energy equation with respect to k.

the group velocity is inversely proportional to the mass of the particle. As k increases, vgroup approaches c (speed of light in vacuum). Hence, the wave packet slows down in a dispersive medium. The speed of light in a vacuum can be expressed as c = ω/k. Thus, the phase velocity is greater than the group velocity. This is because the wave packet spreads out in the medium, and not all the waves travel at the same speed.

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Answer:

Step-by-step explanation:

The red line appears to be a good fit for the data because it passes through the center of the data points and follows the general trend of the points reasonably well. It appears to have a positive slope, indicating a positive correlation between the variables represented on the x-axis and y-axis.

Additionally, the red line appears to minimize the overall distance between the data points and the line, which is a common method for determining the line of best fit. This method is often referred to as the least-squares method, and it involves finding the line that minimizes the sum of the squared vertical distances between the data points and the line.

Answer:

2

Step-by-step explanation:

Slope is Y/x. In this case, you could do 4 /2 which would give you a slope of 2/1=2.

Answer:

1

Step-by-step explanation:

rise 1 over run 1 1/1=1

The above Maximum Entropy Model is equivalent to the multi-class logistic regression model as Z(xi) = ∑y=1K exp(θj fj(xi)). This is the softmax function, which is the basis for the multi-class logistic regression model.

The maximum entropy model can be formulated as follows:

Maximize: H(p) = - ∑i=1n ∑y=1K p(y|xi) ln p(y|xi)

Subject to:

∑y=1K p(y|xi) = 1, for i = 1,...,n

∑y=1K p(y|xi) δ(y,yi) fj(xi) = ∑y=1K p(y|xi) fj(xi), for j = 1,...,d and i = 1,...,n

where δ(y,yi) is the Kronecker delta function.

Using the Lagrangian dual theory, we can rewrite the objective function as:

L = - ∑i=1n ∑y=1K p(y|xi) ln p(y|xi) + ∑i=1n λi(∑y=1K p(y|xi) - 1) + ∑i=1n ∑j=1d θj(∑y=1K p(y|xi) δ(y,yi) fj(xi) - ∑y=1K p(y|xi) fj(xi))

where λi and θj are the Lagrange multipliers.

Taking the derivative of L with respect to p(y|xi) and setting it to zero, we get:

p(y|xi) = exp(θj fj(xi)) / Z(xi)

where Z(xi) is the normalization factor:

Z(xi) = ∑y=1K exp(θj fj(xi))

Substituting this into the constraint ∑y=1K p(y|xi) = 1, we get:

∑y=1K exp(θj fj(xi)) / Z(xi) = 1

which can be simplified to:

Z(xi) = ∑y=1K exp(θj fj(xi))

This is the softmax function, which is the basis for the multi-class logistic regression model.

Therefore, we have shown that the maximum entropy model with feature function fj(xi)=[xi]j is equivalent to the multi-class logistic regression model without regularization.

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When 5/9 of the tank is filled in 2 minutes, then it will take 3.6 minutes to fill the entire tank.

The definition of a fraction is a fraction multiplied by another fraction, integer, or a group of variables. Given that the 5/9 tank fills in 2 minutes. The duration of this period in seconds is 60×5= 120 seconds.

So the time taken to fill a 1/9 tank is calculated as follows,

Time taken = 120/5

=24 seconds

The time taken to fill the 9/9 tank (full) is calculated by multiplying 24 seconds and 9, we get,

24×9 = 216 seconds

= 3.6 minutes.

Therefore, the required answer is 3.6 minutes.

The complete question is -

If 5/9 of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?

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Answer:

I think the answer is 3 for 1 length side. And in you need 12 for both length sides. So the total is 36 and one side is 12. Since it's a rectangle,you now know two side lengths since they are the same,just opposite from each other. So 12 + 12 = 24. You do 36 – 24 because you need to get the total number for length which is 12. 12 divided by 2 is 6 which is one length side. You can check by doing 6 + 6 + 12 + 12 and you get 36.

Hope this helped!

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