A 5-ounce container of Greek yogurt contains 135 calories. Find the unit rate of calories per ounce.

Explanation:

The initial expression is:

To know the value of m, we need to solve the equation for m, so adding 7 to both sides of the equation, we get:

Then, we can multiply both sides by 4, so:

The method of least squares of residuals is commonly used to get the best fit with linear regression. The reason why the absolute value of residual's (|y- ypred|) is not used is as follows :

Although least squares purposefully square the error in the belief that it will respond better when values deviate from your projected value, you could run something similar if you so desired.

Consider the following scenario: You plot your data's real values on a graph, and you observe a straight line of numbers with a few outliers that have greater values than you would expect. You could be tempted to believe that the best fit is a straight line along the values. Because the real pattern must take into account all the values that occurred, least squares adapt more to the outliers than other values and purposefully squares values, sort of assuming that the straight line of actual values was a coincidence.

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When dealing with random walk data, Holt's method is preferred due to its ability to capture short-term fluctuations and changing trends without assuming a specific pattern.

A random walk is a time series where the future values are dependent on the previous values and exhibit a random or unpredictable behavior. In such cases, using methods like Moving Average, Holt-Winters, or Logistic Regression may not yield accurate results because they assume certain patterns or trends in the data.

Holt's method, also known as exponential smoothing, is particularly suitable for handling random walk data. It is a forecasting technique that takes into account both the level and the trend of the time series. This method assigns exponentially decreasing weights to past observations, giving more weight to recent data points. By incorporating a level and trend component, Holt's method can capture the short-term fluctuations and gradual changes in the data without assuming a specific pattern.

Unlike Moving Average or Holt-Winters, Holt's method does not rely on a fixed window of past observations, which can be limiting for random walk data. Instead, it adapts dynamically to the changing characteristics of the time series.

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The null hypothesis is rejected at the significance level of 5%. (Round the t-statistic to the second decimal place.)- t-statistic is 2.5, so the null hypothesis is rejected.

Hypothesis

In statistics, hypothesis testing is used to identify the variance in the group of data that results from genuine variation. Based on the presumptions, the sample data are taken from the population parameter. The hypothesis can be divided into many categories. A hypothesis is described in statistics as a formal statement that explains the relationship between two or more variables belonging to the specified population.

It aids the researcher in converting the stated issue into an understandable justification for the study's findings. It provides examples of various experimental designs and guides the investigation of the research procedure.

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Answer: 0.5 Liters

Step-by-step explanation:

1 Liter = 1000 milliliters

500 milliliters = 0.5 Liters

I just need to take 500 divided by 1000 = 0.5 Liters

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

The solution set of the equation 3X=-6/1-X for x # 1 is {-2,1)

3x = -6/(1-x)

3x(1-x) = -6

3x – 3x2 = -6

Taking 3 as common from both sides

x –x2 = -2

x2 – x +2 =0

Using factorisation method we will get two factors

Factoring quadratics is a method of expressing the quadratic equation ax2 + bx + c = 0 as a product of its linear factors as (x - k)(x - h), where h, k are the roots of the quadratic equation ax2 + bx + c = 0. This method is also is called the method of factorization of quadratic equations. Factorization of quadratic equations can be done using different methods such as splitting the middle term, using the quadratic formula, completing the squares, etc.

( x – 2)(x+1)=0

So, x = 2 , -1

Now, when x ≠ 1

The solution of the equation will vary from {-2,1) .

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Answer:

-8

Step-by-step explanation:

(-2)^3 = -2 * -2 * -2 = -8

The probability that a randomly selected balloon animal is green and shaped like a dog is 0.231.

The probability is found using the data table given below:

Purple and giraffe = 3; Purple and dog =  3; Green and giraffe = 4; Green and dog = 3

Out of the total number of balloon animals made, the number of green dog balloon animals is 3.

The probability of randomly selecting a green dog balloon animal is found using the formula:

Probability = 3 / (3 + 3 + 4 + 3) = 3/13

Probability = 0.231

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Answer:

120

Step-by-step explanation:

480 total

1/2 = 240 are cows

1/8 = 60 are goats

remaining = 480-240-60 = 180 are chickens & ducks

33.3333% of 180 = chickens  =180/3 = 60 chickens

so ducks = 180-60 =120

Answer:

120

Step-by-step explanation:

given that out of 480 animals 0.5 of the animals are cows . So ,

no. of cows = 0.5*480 = 240

Again, we are given that 1/8 of the animals are goats , so the number of goats would be ,

no. of goats = 1/8*480 = 60

Total no. of goats and cows ,

= 240 + 60 = 300

No. of remaining animals= 480 -300 = 180

Now out of these 180 animals 33⅓ % animals are chickens and remaining are ducks.

Percentage of ducks = (100 - 33⅓ )% = 66.67%

So the number of ducks would be ,

180 * 66.67/100 = 120

And we are done!

A B C is the correct condition for the researcher to calculate the mean.

When a researcher collects a simple random sample of grade-point averages of statistics students, the sample mean can be treated as a value from a population having a normal distribution under the following conditions:

A. The researcher collects more than 30 samples.

B. If the population of statistics students has a normal distribution.

C. If the population of grade-point averages has a normal distribution.

Hence, options A, B, and C are correct. In order to estimate P(at least 5)

with n = 13 and p = 0.5, the following formula should be used:μ = np = (13)

(0.5) = 6.5σ = sqrt(npq) = sqrt(13 × 0.5 × 0.5) = 1.802P(at least 5) = P(X ≥

5.5)Using continuity correction, P(X ≥ 5.5) is equivalent to:P(Z ≥ (5.5 -

6.5)/1.802)P(Z ≥ -0.555) = 0.2918 (rounded to 4 decimal places)Therefore,

P(at least 5) = 0.2918 (rounded to 3 decimal places).Thus, the correct

choice is option A: P(at least 5) = 0.292 (rounded to 3 decimal places).

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The line of best fit refers to a straight line that represents the trend or relationship between two variables in a scatter plot. It is determined by minimizing the sum of the squared horizontal distances between each data point and the line.

In statistical analysis, the line of best fit, also known as the regression line, is used to approximate the relationship between two variables. It is commonly employed when dealing with scatter plots, where data points are scattered across a graph. The line of best fit is drawn in such a way that it minimizes the sum of the squared horizontal distances from each data point to the line.

The concept of minimizing the sum of squared distances arises from the least squares method, which aims to find the line that best represents the relationship between the variables. By minimizing the squared distances, the line is positioned as close as possible to the data points. This approach allows for a balance between overfitting (fitting the noise in the data) and underfitting (oversimplifying the relationship).

The line of best fit serves as a visual representation of the overall trend in the data. It provides a useful tool for making predictions or estimating values based on the relationship between the variables. The calculation of the line of best fit involves determining the slope and intercept that minimize the sum of squared distances, typically using mathematical techniques such as linear regression.

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Answer:

A 95% confidence interval for μ is (LIL) 4.61.

The confidence interval for the population mean μ is constructed as follows:

Here, x is the sample mean, σ is the population standard deviation,

n is the sample size, and

zα/2 is the z-value

that corresponds to a level of confidence of (1-α)100%.

Given that c = 0.95, x = 4.8, σ = 0.6, and n = 55.

Confidence interval is given by;

(LIL), (UIL) = (x - zα/2*σ/√n), (x + zα/2*σ/√n)

where LIL is the lower limit of the interval and UIL is the upper limit of the interval.

Now, we need to determine the value of zα/2 such that the level of confidence is 0.95.

In the standard normal distribution, the area to the left of

zα/2 is (1-α)/2 or

(1-0.95)/2 = 0.025.

Using the z-table, we can find that the z-value that corresponds to this area is 1.96.

Therefore, the 95% confidence interval for μ is given by;

(LIL), (UIL) = (4.8 - 1.96*0.6/√55), (4.8 + 1.96*0.6/√55)= (4.61, 4.99)

Therefore, a 95% confidence interval for μ is (LIL) 4.61. (Round to two decimal places as needed.)

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Answer:

20x-22y

hope it's helpful ❤❤❤❤❤❤

THANK YOU.

#

Answer:

Step-by-step explanation:

Just the answer.

=20x - 22y

Answer:

\({x}^{2} - 10x + 25\)

Step-by-step explanation:

For this problem, we can break the equation into (x - 5) use FOIL. First, Outer, Inner, Last.

(x - 5) (x - 5)

First, multiply the two Xs together.

X * X =

\( {x}^{2} \)

Now, the outer numbers and values.

X * -5 =

\( - 5x\)

Then, it's the inner numbers and values.

-5 * x =

\( - 5x\)

Finally, multiply the last numbers.

-5 * -5 =

\( 25\)

Now that we have multiplied all of the values, we can put the answers from FOIL together.

\( {x}^{2} - 5x - 5x + 25\)

Now, add any like terms.

\( - 5x - 5x = - 10x\)

The answer is

\( {x}^{2} - 10x + 25\)

Answer:

80 ft

Step-by-step explanation:

hey there,

< We know that the rope is 3 pieces long. To make this into an equation, let's just write x + y + z = 150.

Assuming "y" is our second piece, we can tell y = 2x, because it is two times the size of the first piece, which is "x". We also know "z" (our third piece): z = 30.

We can try inputting all the things we know now. x + (2x) + 30 = 150. From here, we can find that x = 40. Since y is our second piece, y = 2x, so 2 x (40) = 80. The second piece would be 80 feet long. >

Hope this helped! Feel free to ask anything else.

Answer:

The probability of drawing a face card or a 4 is approximately 0.2885, or 28.85%.

Step-by-step explanation:

To find the probability of drawing a face card or a 4 from a well shuffled deck of 52 cards, we need to count the number of cards that are either a face card or a 4, and divide that number by the total number of cards in the deck.

There are 12 face cards in a deck (4 kings, 4 queens, and 4 jacks) and 4 cards with the number 4, but the card with 4 is also a face card (the four of hearts), so we need to subtract one card from the total. Therefore, there are 15 cards in the deck that are either a face card or a 4.

The total number of cards in the deck is 52. Therefore, the probability of drawing a face card or a 4 from a well shuffled deck of cards is:

P = number of desired outcomes / total number of possible outcomes P = 15/52 P = 0.2885 (rounded to four decimal places)

So the probability of drawing a face card or a 4 is approximately 0.2885, or 28.85%.

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Answer:

The area of the circle is":

A = 1017.36 in²

The circumference of the circle is:

C = 113.09 in

Step-by-step explanation:

Given

r = 18 in

We need to determine the area and circumference of the circle

Using the formula to determine the area

A = πr²

   = 3.14 × (18)²

   = 3.14 × 324

   = 1017.36 in²  (Rounded to the nearest 0.01 or  the Hundredths Place)

Thus, the area of the circle is":

A = 1017.36 in²

Using the formula to determine the circumference.

C=2πr

  = 2 × 3.14  ×  18

  = 113.09 in

Thus, the circumference of the circle is:

C = 113.09 in

The statements; (x,y,z(x,y)) is a solution to the equation F(x,y,z)=0 for all (x,y) nearby \((x_{0},y_{0})\), Every point on the level surface F(x,y,z)=0 is on the graph of z=z(x,y), and \(z_{0}\) = z \((x_{0},y_{0})\) are correct.

In the given question have four statement related to the given question. We have to answer which statement is correct.

The given question is;

Suppose that a function z=z(x,y) is defined implicity by a equation F(x,y,z)=0 nearby some point \((x_{0},y_{0},z_{0})\) and all partial derivatives of F(x,y,z) are continuous .

As we know that a function is continuous when it is differentiable. The partial derivatives of a function. Function f:R2→R such that fx \((x_{0},y_{0},z_{0})\) and fy \((x_{0},y_{0},z_{0})\) exist but f is not continuous at \((x_{0},y_{0},z_{0})\).

So the following statement are correct;

1) (x,y,z(x,y)) is a solution to the equation F(x,y,z)=0 for all (x,y) nearby \((x_{0},y_{0})\).

2) Every point on the level surface F(x,y,z)=0 is on the graph of z=z(x,y)

3) \(z_{0}\) = z \((x_{0},y_{0})\)

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To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

We have,

This statement is not entirely correct.

To prove that two functions are inverses of each other, it is indeed necessary to show that both of the following conditions hold:

f(g(x)) = x for all x in the domain of g

g(f(x)) = x for all x in the domain of f

Now,

This does not necessarily mean that the two functions are equal to each other.

For example,

Consider the functions f(x) = x + 1 and g(x) = x - 1.

It can be shown that f(g(x)) = x and g(f(x)) = x for all values of x, which satisfies the conditions for being inverses of each other.

However, it is clear that f(x) and g(x) are not the same functions.

Thus,

To prove that two functions are inverses of each other, it is necessary to show that both of the conditions f(g(x)) = x and g(f(x)) = x hold, but this does not necessarily mean that the two functions are equal.

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Answer:

what do you mean

Step-by-step explanation:

Answer:

48m^2

Step-by-step explanation:

A=LxW=12x4=48

The total harvested area is 232 acres .

To determine the number of acres harvested, we simply have to divide the bushels of soybean by the crop yield.

Mathematically we can write it as,

The total land area = bushels of soybean / bushels per acre

Substituting the known values,

\(Total land area = 9396 / 40.5 = 232\)

Therefore, 232 acres were harvested.

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Answer:The total harvested area is 232 acres

Step-by-step explanation:

Answer:

72 Leafs

Step-by-step explanation:

Answer:

Diagonals linse

Step-by-step explanation:

Answer:

y=5/2x-5

Step-by-step explanation:

The line is interested to the graph is (2,-5)

Answer:

x = 46

Step-by-step explanation:

130 is the exterior angle of the triangle,

Its interior angle

= 180 - 130

= 50

96 is the exterior angle of the triangle,

Its interior angle

= 180 - 96

= 84

Now,

x, 50 and 84 are the interior angles,

Sum of interior angles of a triangle is 180,

50 + 84 + x = 180

134 + x = 180

x = 180 - 134

x = 46

Answer:

x = 46 degrees.

Step-by-step explanation:

The  base angles are 180 - 96 = 84 degrees

and 180 - 130 = 50 degrees.

As there are 180 degrees in a triangle x = 180 - (84 + 50)

= 180 - 134

= 46 degrees,

A population has a mean μ=135 and a standard deviation Ï=28.

The mean of the sampling distribution of sample means is equal to the population mean, that is 135.

The standard deviation of the sampling distribution of sample means can be calculated by using the formula

SE = Ï /\(\sqrt{n}\)

Where Ï is the population standard deviation and n is the sample size.

By putting the given values we get

SE = 28 / \(\sqrt{57}\) = 3.7

Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.

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