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Two classes of elementary school students were asked what activity they want to do during recess. Each student selects one recess option. The table summarizes the recess preference of each student in the class.




What is the probability that a student selected at random prefers to play tag at recess?

The general convention is to reject a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect. This is False.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

After a performing a test, scientists can reject the null hypothesis meaning there is a definite, consequential relationship between the two phenomena

In this case, the convention is to accept a hypothesis if your data analysis indicates that there is a probability that a hypothesis is incorrect.

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Answer:

0.71 weeks

Step-by-step explanation:

To convert 5 days to weeks, we can use the conversion factor:

1 week = 7 days

Therefore, we have:

5 days = 5/7 weeks

Rounding to the nearest hundredth, we get:

5 days ≈ 0.71 weeks

Therefore, 5 days is approximately equal to 0.71 weeks.

Answer:

60

Step-by-step explanation:

f(6) = 60

The function that represents surviving people are X = 2m - d

Given that there are m married couples and d of the 2m of these couples have died, the total people that remain is expressed as:

Total people remaining = Total married couple - those that died

Total married couple = 2m

Total people that died = d

Taking the difference to get the remaining people;

Total people remaining = 2m - d

Hence the function that represents surviving people are X = 2m - d

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Step-by-step explanation:

\(60\% = \frac{60}{100} = \frac{3}{5} \)

and 3/5 is 0,6

Hope I helped :)

Answer:

0.6

Step-by-step explanation:

all you have to do is divide 60 by 100, so 60÷100=0.6

you can do this with any percentage

Answer:

22.25

Step-by-step explanation:

178/8=22.25

Answer:

22.25

Step-by-step explanation:

178 divided by 8

The region is made up of

• a right triangle with short leg 10 m and hypotenuse 26 m

• a parallelogram with sides 40 m and 26 m (the 26-m side corresponds to the aforementioned hypotenuse)

• another triangle with two known legs of length 20 m and 26 m

Find the height of the right triangle using the Pythagorean theorem. If the height is h, then

(10 m)² + h² = (26 m)²   ⇒   h² = 576 m²   ⇒   h = 24 m

This height is common to all three shapes.

Now find the area of each shape.

• right triangle:

1/2 × (10 m) × (24 m) = 120 m²

• parallelogram:

(40 m) × (24 m) = 960 m²

• other triangle:

• 1/2 × (20 m) × (24 m) = 240 m²

Then the total area of the shaded region is 1320 m².

Negative bases are not often used in logarithms because they produce complex results. For example, if the base is negative and the exponent is positive, the result will be a complex number.

Logarithms are generally used to solve equations or simplify complex problems. Having a negative base would complicate this process, as it would introduce complex numbers or even imaginary numbers into the equation. Consequently, it is not feasible to use negative bases with logarithms. Furthermore, if both the base and the exponent are negative, the result is undefined. This means that it is not possible to evaluate the expression. Therefore, for these reasons, it is usually not practical to use negative bases when working with logarithms.

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Answer:

y = -1/2x + 7

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = -1/2

The y-intercept is located at (0, 7)

So, our equation is y = -1/2x + 7

By implementing the strategies of BRAINLEIST, one can enhance their learning effectiveness.

BRAINLEIST is an acronym representing effective learning strategies. Be organized by creating a study plan and maintaining an orderly environment. Actively read by engaging with the material, asking questions, and highlighting key points.

Interact with the material through discussions, group study, or hands-on activities to deepen understanding. Take comprehensive notes to reinforce learning and aid in review. Leverage technology to access educational resources and enhance learning experiences.

Evaluate progress through self-assessment and reflection. Improve learning through practice and active application of knowledge. Space out study sessions to benefit from spaced repetition and improved retention.

Teach others to reinforce understanding and solidify knowledge. Incorporating these strategies can optimize learning, retention, and academic performance.

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a. When evaluating a model, we use R2 as a parameter for performance assessment.

b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.

c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.

When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.

The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.

When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.

Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.

Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.

It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.

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The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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Answer:

25 The number of balls to make an equilateral triangle with the sides of length n is expressed by the formula n(n+1)/2 So to express the number of balls you have is b = n(n+1)/2 + 4 With the larger arrangement you have b = (n+1)(n+2)/2 - 3 Both of those qualities are equal to each other, so set an equation where they're equal. Then solve for n n(n+1)/2 + 4 = (n+1)(n+2)/2 - 3 Distribute the n term on the left (n^2 + n)/2 + 4 = (n+1)(n+2)/2 - 3 Distribute the /2 on the left. 0.5n^2 + 0.5n + 4 = (n+1)(n+2)/2 - 3 Multiply (n+1)(n+2) on right, then distribute the /2 0.5n^2 + 0.5n + 4 = 0.5n^2 + 1.5n + 1 - 3 Subtract 0.5n^2 + 0.5n from both sides 4 = n + 1 - 3 Add 2 to each side 6 = n So the original triangle had sides with a length of 6, for a total number of balls of 6(6+1)/2 = 21 with 4 extra giving 25 balls. Let's check with the next larger triangle 7(7+1)/2 = 28 with 3 balls shortage. Which 25 balls would make happen. So the number of balls in the set is 25

Step-by-step explanation:

Answer:

y=4x³ is not linear

Step-by-step explanation:

All of the equations produce lines, one of the characteristics of a linear function, except for y=4x³ where the graph is a curve. Refer to the graph attached to see this.

The mood of the argument is categorical and the figure is EIO. To determine the mood and figure of the given argument, we'll first identify the premises and conclusion, and then assign the appropriate categorical proposition to each statement.

The argument can be rewritten as:

Premise 1: Some dictators are not warmongers. (Some D are not W)
Premise 2: No dictators are egomaniacs. (No D are E)
Premise 3: Some egomaniacs are warmongers. (Some E are W)
Conclusion: Some dictators are not warmongers. (Some D are not W)

Now, let's assign the categorical propositions to each statement:
Premise 1: I (Some D are not W)
Premise 2: E (No D are E)
Premise 3: I (Some E are W)
Conclusion: O (Some D are not W)

The mood of the argument is IEO.

Next, we'll determine the figure by looking at the placement of the middle term (E) in the premises:
Premise 2: No D are E (subject-middle term)
Premise 3: Some E are W (middle term-predicate)

The figure is 1 because the middle term is the subject of one premise and the predicate of the other premise.

So, the mood and figure of the argument are IEO-1. Therefore, the correct answer is:

IEO - 1

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The information needed to find how much money Mark earned per hour mowing lawns, is the hours that Mark worked to earn that $32

Answer:is 5 ^ -2 ????

Step-by-step explanation:

The definition of slope-intercept form y=mx+b is given below.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.

In geometry, there are two types of lines: straight and curved. Vertical and horizontal straight lines are further divided into categories. Parallel, intersecting, and perpendicular lines are further types of lines.

In the given question:-

The value of the steepness or the direction of a line in a coordinate plane is referred to as the slope of a line, also known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope may be determined using a variety of approaches.

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Answer:

The answer is 98.7

Step-by-step explanation:

Easy! from the millimeter value divide it by 10 for example I have 142mm then the amount of centimeters I have is 14.2

Answer:

the domain is: {−3,0,1,6}

the range is:{2,3,4,−6,4}

the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Explanation:

In the relation:

{(−3,2),(0,3),(1,4),(1,−6),(6,4)}:

The domain:

Is the set of all the first numbers of the ordered pairs.

In other words, the domain is all of the x-values.

So in this case the domain is:

{−3,0,1,6}

The range:

Is the set of the second numbers in each pair, or the y-values.

So in this case the range is:

{2,3,4,−6,4}

A relation is a function if it has only One y-value for each x-value.

So in this case the relation is not a function since it has TWO distinct y values '4' and '-6' for the same x value of '1' .

Step-by-step explanation:

The solution of the system of linear equations is (x, y, z) = (4, 6, - 1).

In this question we are asked to find the solution to the system of linear equations by substitution method, which consist in taking advantage of explicit form of linear equations to reduce the number of variables to one and then determine the value of the remaining variables by evaluating the rest of the expressions in explicit form. We find the following expressions:

- x - y - z = - 8                                 (1)

- 4 · x + 4 · y + 5 · z = 7                  (2)

2 · x + 2 · z = 4                               (3)

First, clear x in (1):

x = 8 - y - z

Second, substitute x in (2, 3):

- 4 · (8 - y - z) + 4 · y + 5 · z = 7

- 32 + 4 · y + 4 · z + 4 · y + 5 · z = 7

- 32 + 8 · y + 9 · z = 7

8 · y + 9 · z = 39                              (2b)

2 · (8 - y - z) + 2 · z = 4

16 - 2 · y - 2 · z + 2 · z = 4

16 - 2 · y = 4

2 · y = 12

y = 6                                                 (3b)

Third, substitute in (2b):

8 · 6 + 9 · z = 39

48 + 9 · z = 39

9 · z = - 9

z = - 1

Fourth, substitute in (1):

x = 9 - 6 - (- 1)

x = 9 - 6 + 1

x = 4

The solution of the system of linear equations is (x, y, z) = (4, 6, - 1).

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Answer:

1/6x - 1/2x does not equal 1/4. They made a mistake in the second to third line.

Step-by-step explanation:

It should have been -1/3x - 3 = 9, which gives you x = -36.

1/6 - 1/2 =  1/6 - 3/6 = -2/6 = -1/3

The mistake is in the third step, the subtraction was done without taking LCM. The value of x is -36.

The numerical expression having two or more operations can be simplified by using ‘BODMAS’ rule, where the letters  B, O, D, M,  A,  S stand for Brackets , orders (powers/indices or roots) , Division, Multiplication,  Addition and Subtraction respectively.

For the given situation,

The expression is 1/3 (1/2x -9) = 1/2 ( x + 18).

We need to simplify the expression to find the mistake done by them.

⇒ \(\frac{1}{3}(\frac{1}{2}x-9 ) = \frac{1}{2}(x+18)\)

⇒ \(\frac{1}{6}x-3 = \frac{1}{2}x+9\)

⇒ \(\frac{1}{6}x-\frac{1}{2}x = 9+3\)

⇒ \(\frac{-2x}{6}=12\)

⇒\(\frac{-1}{3}x=12\)

⇒ \(x=-36\)

Hence we can conclude that the mistake is in the third step, the subtraction was done without taking LCM. The value of x is -36.

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The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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Answer:

prop they're constant inchangeb

Step-by-step explanation:

Answer:

y=1/2x+3, or C

Step-by-step explanation:

1. Find the slope.

To find slope, pick two coordinates and count up and over to find rise over run.

Use (-2, 2) and (0,3) for example.

Counting up and over gives you 1/2. This is your slope.

2. Look to see where the line crosses the y-axis to get the y-intercept.

Here, it crosses it at (0,3). 3 is the y-intercept.

3. The answers are written in slope-intercept form, or y=mx+b. mx represents slope and b represents the y-intercept.

y=1/2x+3

The cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

A Cartesian equation is essential in mathematics. It corresponds to a mathematical formula that expresses the connection between elements as a function of their positions on a plane known as Cartesian.

A two-dimensional coordinate scheme called the Cartesian plane employs a horizontal x-axis and an upward y-axis to identify locations in space.

Given that, \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\).

So, \(csc\hspace{0.1cm}\theta=cosec \hspace{0.1cm}\theta\).

The equation becomes as follows:

\(r=2cosec\hspace{0.1cm} \theta\)

By using the trigonometric equation \(cosec\hspace{0.1cm} \theta=\frac{1}{sin\hspace{0.1cm}\theta}\), we get

\(r= \frac{2}{sin \hspace{0.1cm} \theta}\)

Multiplying both sides by \(sin\hspace{0.1cm}\theta\), we get

\(r \hspace{0.1cm}sin\hspace{0.1cm}\theta =2\hspace{0.1cm}\frac{sin\hspace{0.1cm}\theta}{sin\hspace{0.1cm}\theta}\)

\(rsin\hspace{0.1cm}\theta=2\)

By the parametric equations \(x=rcos\hspace{0.1cm}\theta\) and \(y=rsin\hspace{0.1cm}\theta\), we get

\(y=2\)

It is a horizantal line.

Hence, the cartesian equation of the curve \(r=2 \hspace{0.1cm} csc \hspace{0.1cm} \theta\) is \(y=2\).

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The cartesian equation for the curve is: y = 2 This is a horizontal line passing through the point (0,2).

To find a Cartesian equation for the curve given by the polar equation r = 2 csc(θ), we will convert the polar coordinates (r, θ) into Cartesian coordinates (x, y) using the following relationships:

x = r * cos(θ)
y = r * sin(θ)

Step 1: Express r in terms of θ
r = 2 csc(θ)

Step 2: Since csc(θ) = 1 / sin(θ), rewrite the equation as
r = 2 / sin(θ)

Step 3: Express x and y in terms of r and θ
x = r * cos(θ)
y = r * sin(θ)

Step 4: Substitute r from Step 2 into the y equation
y = (2 / sin(θ)) * sin(θ)

Step 5: Simplify the equation
y = 2

The Cartesian equation for the given polar equation is y = 2, which represents a horizontal line passing through the point (0, 2).

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By strong induction, we have proven that for each n ∈ ℕ, an = 2n - 1 for the given sequence.

To prove that for each n ∈ ℕ, an = 2n - 1 for the given sequence defined by a1 = 3, a2 = 5, and an = an-1 * 2an-2 - 2 for n ≥ 3, we will use strong induction.

*Base Cases:*

For n = 1, we have a1 = 3, and 2^1 - 1 = 2 - 1 = 1. The base case holds.

For n = 2, we have a2 = 5, and 2^2 - 1 = 4 - 1 = 3. The base case holds.

*Inductive Hypothesis:*

Assume that for all k ≤ m, the equation an = 2n - 1 holds, where m is some positive integer.

*Inductive Step:*

We need to show that the equation an = 2n - 1 holds for n = m + 1.

Using the recursive formula, we have:

am+1 = am * 2am-1 - 2

By substituting the inductive hypothesis, we get:

am+1 = (2m - 1) * 2(2m-1) - 2

    = 2m * 2(2m-1) - 2 - (2 - 1)

    = 2m * 2(2m-1) - 2 + 1

    = 2m * 2(2m-1) - 1

Expanding the equation further:

am+1 = 2m * (2 * 2m-1) - 1

    = 2m * 2m - 1

    = 2(m + m) - 1

    = 2(2m) - 1

    = 2(m + 1) - 1

Thus, we have shown that am+1 = 2(m + 1) - 1, which completes the inductive step.

By strong induction, we have proven that for each n ∈ ℕ, an = 2n - 1 for the given sequence.

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Answer:

will do ill ask ur fave color under history in 1 min

Step-by-step explanation:

Answer: my ? and i will

Step-by-step explanation:

The classical errors-in-variables (CEV) assumptions require that the measurement error in tv hours is not related to the true value of television viewing.In other words, the error should be random and not correlated with the actual amount of time spent watching TV.

Additionally, the CEV assumptions require that the measurement error has a mean of zero and a constant variance. Whether or not the CEV assumptions are likely to hold in this application depends on several factors. One important consideration is the accuracy of the survey instrument used to collect data on tv hours.

If the survey is poorly designed or administered, it may introduce systematic measurement error that is correlated with the true value of television viewing.

Another important factor is the population being surveyed. If the population is highly diverse with respect to television viewing habits, it may be difficult to ensure that the CEV assumptions hold for all subgroups.

Overall, while it is possible that the CEV assumptions hold in this application, it is also possible that they do not. Researchers should carefully consider the potential sources of measurement error and take steps to minimize them if possible.

Additionally, sensitivity analyses can be conducted to explore the robustness of study results to violations of the CEV assumptions.

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Answer:

Answer:

Private saving = $3 trillion

National Saving = $2 trillion

Explanation:

Private saving = GDP - Taxes - Consumption + Transfer payments

Private saving = $18 trillion - $2 trillion - $13 trillion + 0

Private saving = $3 trillion

Government runs a deficit of $1 trillion means its spending is $1 trillion more than the tax revenue.

So, National Saving = Private saving + Public saving

National Saving = $3 trillion + ($2 trillion - $3 trillion)

National Saving = $3 trillion + (-$1 trillion)

National Saving = $2 trillion