Your teacher is preparing your classroom when the school reopens. It can only have 12 tables and 12 chairs to ensure the 2 - meter social distancing rule takes place. She is trying to figure out how much space each desk will take up. Can you help her? Include the measurements of everything you want on your desk. You can estimate and measure in centimeters, meters, inches, or feet.

The test statistic (-7.226) is less extreme (i.e., more negative) than the critical value (5.991), we fail to reject the null hypothesis.

To determine whether the "A" students are evenly distributed throughout the classroom, we can perform a chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the "A" students are distributed evenly, while the alternative hypothesis (H₁) suggests that they are not evenly distributed.

We are given the observed frequencies of "A" students in different parts of the classroom:

17 students sat in front

9 students sat in the middle

5 students sat in the back

To conduct the chi-square test, we need to calculate the expected frequencies under the assumption of an even distribution. Since there are three possible locations (front, middle, back), and assuming an equal distribution, we would expect approximately 31.67% of students in each location.

Expected frequencies:

Front: (31.67% * total number of "A" students) = 31.67% * (17 + 9 + 5) = 10.01

Middle: (31.67% * total number of "A" students) = 31.67% * (17 + 9 + 5) = 10.01

Back: (31.67% * total number of "A" students) = 31.67% * (17 + 9 + 5) = 10.01

Now, we can set up the chi-square test:

H₀: "A" students are evenly distributed throughout the classroom.

H₁: "A" students are not evenly distributed throughout the classroom.

We can calculate the test statistic using the formula:

χ² = ∑ ((Observed frequency - Expected frequency)² / Expected frequency)

Plugging in the values, we get:

χ² = [(17 - 10.01)² / 10.01] + [(9 - 10.01)² / 10.01] + [(5 - 10.01)² / 10.01]

= 35.7022 + 0.1009 + 24.3079

= 60.111

Now, with the test statistic of -7.226 provided, we need to determine the critical value or p-value to make a decision. Since the significance level is 0.05, we can look up the critical value for a chi-square distribution with (3-1) = 2 degrees of freedom. The critical value is approximately 5.991.

Since the test statistic (-7.226) is less extreme (i.e., more negative) than the critical value (5.991), we fail to reject the null hypothesis.

Therefore, the correct conclusion is:

Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the "A" students are evenly distributed throughout the classroom.

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The properties used in the given steps include the multiplication property of equality, addition property of equality, subtraction property of equality, and division property of equality.

The steps taken to solve the system of equations and the properties used are as follows:

1.Step 1: 2a + 7b = 0; 3a − 5b = 31

No specific property is used.

Step 2: 10a + 35b = 0; 21a − 35b = 217

Multiplication property of equality: Both sides of the equations are multiplied by 5 and 7 to eliminate coefficients and simplify the expressions.

Step 3: 31a = 217

Addition property of equality

Step 4: a = 7

Division property of equality as both sides are divided by 31 to solve for a.

2. Step 1: 2(7) + 7b = 0

Simplify: the expression is simplified by multiplying 2 and 7 to obtain 14.

Step 2: 14 + 7b = 0

Simplify

Step 3: 7b = −14

Simplify: the equation is simplified by subtracting 14 from both sides.

Step 4: b = −2

Division property of equality: both sides of the equation are divided by the coefficient of 'b' (7) to solve for 'b'.

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Answer:

integer number

Step-by-step explanation:

Fractions and decimals are not integers. All whole numbers are integers (and all natural numbers are integers), but not all integers are whole numbers or natural numbers. For example, -5 is an integer but not a whole number or a natural number.

120

Step-by-step explanation:

if "1 hour is 24 muffins"

you can either use '+' or '×' to find the ans,

for example,

- 24+24+24+24+24 = 120

[formula 1]

using '+' is the longer way to solve the question

the easier way is by using '×', which will solve the question faster (with this you need to memorise the time table!^^)

- 24 × 5 = 120

[formula 2]

Both gives the same amount of ans, but only has a different way of solving it!

Answer:

The answer to your problem is, 120

Step-by-step explanation:

Based on the problem and what is given, formulate the following:

60×2

Calculate. 60 × 2 = 120

Thus the answer to your problem is, 120

Answer:

i have no idea

Step-by-step explanation:

The brightness of the Sun as viewed from a distance of 10 AU compared to its brightness on Earth can be determined using the inverse square law. The Sun would appear approximately 1/100th (or 0.01) as bright as it appears from Earth at this distance.

The inverse square law states that the brightness of a light source decreases as the square of the distance from the source increases. In this case, we are comparing the brightness of the Sun on Earth to its brightness when viewed from a distance of 10 AU (astronomical units). Since AU is a unit of distance used to measure distances within the solar system, 1 AU represents the average distance between the Earth and the Sun, approximately 93 million miles or 150 million kilometers.

Using the inverse square law, we can calculate the relative brightness. If we consider the distance from the Sun on Earth as d1 and the distance from the Sun at 10 AU as d2, the brightness ratio (B(d2)/B(d1)) is equal to (d1/d2)^2. Substituting the values, we find that the Sun would appear approximately 1/100th (or 0.01) as bright when viewed from a distance of 10 AU compared to its brightness on Earth. Therefore, the Sun would appear significantly dimmer when observed from such a distance in the solar system.

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Answer:

D 108

Step-by-step explanation:

YOU CAN MARK ME AS BRAINIEST IF YOU WANT

Answer:

3.85

Step-by-step explanation:

Divide 15.40 by 4.

Answer:

3.85

Step-by-step explanation:

4 ounces = 15.4

4 ounces/ 4= 1 ounce

15.4/4=3.85

Answer:

y = \( \frac{3}{8} x + \frac{5}{2} \)

Step-by-step explanation:

☆Remember: \(m =  \frac{y_2 - y_1}{x_2 - x_1} \)

☆Remember: Slope-intercept form -> y = mx + b

☆Now. We first need to find the slope.

\(m =  \frac{4 - 1}{4 - (- 4)} = \frac{3}{8} \)

☆Now the y-intercept.

\(y = mx + b \\ \\ 4 = \frac{3}{8} (4) + b \\ \\ 4 = \frac{3}{2} + b \\ \frac{ - \frac{ 3}{ 2} = - \frac{ 3}{ 2} \: \: \: \: \: \: \: \: \: \: }{ \frac{5}{2} = b } \)

Let the amount of Tilapia bought be "t" and the amount of Salmon bought be "s"

Since Tilapia costs $3 per pound and Salmon costs $5 per pound, we can say:

Cost of Tilapia = 3t

Cost of Salmon = 5s

Their total cost = 3t + 5s

This total cost should be equal to the total budget, which is $210.

We can equate and write:

TLDR: Your answer is D. 260 square feet.

To find the area of a triangle, you must use the formula "1/2 B ⋅ H."

In this problem, your values are the following:

B = 20

H = 26

Now, you just plug these values in and solve.

1/2 (20) ⋅ 26  >  10 ⋅ 26 = 260 ft

The given vectors are: u = (20 + i, i, 2)v = (1 + i, 2, 41)The dot product of u and v is:u.v = (20 + i)(1 + i) + (i)(2) + (2)(41 - 1)= 20 + 20i + i + i² + 2i + 80= 101 + 22i

To find the imaginary part of u.v, we can simply extract the coefficient of i, which is 22. Hence, the imaginary part of u.v is 22. Therefore, the answer is rounded off to 22.00.

A quantity or phenomenon with two distinct properties is known as a vector. magnitude and course. The mathematical or geometrical representation of such a quantity is also referred to by this term. In nature, velocity, momentum, force, electromagnetic fields, and weight are all examples of vectors.

A movement from one point to another is described by a vector. Direction and magnitude (size) are both properties of a vector quantity. A scalar amount has just greatness. An arrow-labeled line segment can be used to represent a vector. The following describes a vector between two points A and B: A B → , or .

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The image of (-1,7) after a reflection over the line y = x is (7, -1).

What is a line of reflection?

When reflecting a figure in a line or a point, the image and preimage coincide. A reflection converts each point in a figure from a point to an image via a set line. The reflection line is the name given to the fixed line.

Here, we have

Image : (-1.7)

Now,

Reflect over the line y = x:

When reflecting a point across the line y = x, the x-coordinate, and y-coordinate change places.

Thus, the point (-1,7) maps to the point (7,-1) when reflected over y=x.

Hence, The image of (-1,7) after a reflection over the line y = x is (7, -1).

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Answer: 16.8 m - 5m - 84 m area

Step-by-step explanation:

The answer is in numerator = 3 and denominator = 5

Numbers are present in every part οf οur everyday lives, including the number οf laps we cοmplete οn the racetrack, the number οf hοurs we sleep at night, and many οther things.

In math, a number can be even, οdd, prime, cοmpοsite, decimal, fractiοnal, ratiοnal, irratiοnal, natural, integer, real, whοle, οr any cοmbinatiοn οf these.

Numbers are the basis οf mathematics

We must learn abοut numbers if we are tο understand math.

There are many different kinds οf numbers.

There is a lengthy list that includes whοle numbers, οrdinal numbers, οrdinal numbers, natural numbers, οdd numbers, even numbers, cοnsecutive numbers, and sο οn.

3*3 = 9

5*4=20

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Answer:

20

Step-by-step explanation:

The expected value of a toss is:

E(X) = (0.10) (3) + (0.30) (1) + (0.60) (0)

E(X) = 0.6

If she scores an average of 0.6 points per toss, then the expected number of tosses needed to get 12 points is:

12 / 0.6 = 20

Using a random number table, we can assign digit 0 as a 3-point hole, digits 1-3 as a 1-point hole, and digits 4-9 as no points.  Read the digits and add the points until you get 12 points.  The number of digits read is the number of beanbag tosses.

The number of bean bags that we should expect her to toss to get 12 points is 20 bean bags.

Based on the information given, the expected value of the toss will be:

= 10%(3) + 30%(1) + 60%(0)

= 0.10(3) + 0.30(1) + 0.60(0)

= 0.30 + 0.30 + 0

= 0.60

Therefore, the expected number of tosses needed will be:

= 12/0.60

= 20

Therefore, the number of bean bags that we should expect her to toss to get 12 points is 20 bean bags.

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The equation for the function that has the graph with the shape of y = x², but reflected across the x-axis and shifted left 8 units and down 6 units is y = -(x + 8)² - 6.

To write an equation for the given function, we can start with the equation of the graph with the shape of y = x² and apply the necessary transformations.

The graph of y = x² is a parabola that opens upwards with the vertex at the origin (0, 0).

To reflect the graph across the x-axis, we change the sign of the y-coordinate. So, the reflected graph will have the equation y = -x².

To shift the graph left 8 units, we replace x with (x + 8) in the equation. So, the equation becomes y = -(x + 8)².

To shift the graph down 6 units, we subtract 6 from the equation. So, the final equation becomes y = -(x + 8)² - 6.

Therefore, the equation for the function that has the graph with the shape of y = x², but reflected across the x-axis and shifted left 8 units and down 6 units is y = -(x + 8)² - 6.

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Answer:

Step-by-step explanation:

First, let's calculate the volume of the glass sphere:

V_sphere = (4/3) * pi * r^3

V_sphere = (4/3) * 3.14 * 12^3

V_sphere ≈ 7238.23 cm^3

Next, let's find the volume of the cylinder:

V_cylinder = pi * r^2 * h

V_cylinder = 3.14 * 30^2 * 100

V_cylinder ≈ 282,600 cm^3

Since the glass sphere is completely submerged in water, the volume of the water in the cylinder will be the difference between the volume of the cylinder and the volume of the sphere:

V_water = V_cylinder - V_sphere

V_water ≈ 275,362.77 cm^3

Therefore, the approximate volume of the water contained in the cylinder is approximately 275,365 cm^3, which is closest to option D.

To use the splitpts function in Matlab, you will first need to define two sets of points with different arrays for each set. Then, you can use the syntax newSetOfPoints = splitpts(originalSetOfPoints) to split the original set of points into two new sets.

The "splitpts" function in MATLAB is used to split a set of points into two sets based on a specified split point. Here are the steps to use this function:

1. Define the set of points you want to split. For example:
```
points = [1 2 3 4 5 6 7 8 9 10];
```

2. Specify the split point. This can be any number between the minimum and maximum values of the set of points. For example:
```
splitPoint = 5;
```

3. Use the "splitpts" function to split the set of points into two sets. The first set will contain all the points less than or equal to the split point, and the second set will contain all the points greater than the split point. For example:
```
[set1, set2] = splitpts(points, splitPoint);
```

4. The resulting sets will be stored in the variables "set1" and "set2". You can display these sets using the "disp" function:
```
disp(set1);
disp(set2);
```

The output will be:
```
1 2 3 4 5
6 7 8 9 10
```

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The equations (x,y) | x + y > 1 and y (1/2)x + 2 have these solutions as their solutions.

To solve the system of inequalities without using graphs, we can use algebraic methods. First, we can rearrange the second inequality to slope-intercept form y < (1/2)x + 2.

This inequality represents a line with slope 1/2 and y-intercept 2. Next, we can identify the region of the coordinate plane that satisfies the first inequality, x + y > 1. This region is above the line x + y = 1. To check which side of the line satisfies the inequality, we can test a point, such as (0,1),

0 + 1 > 1

This is true, so the region above the line x + y = 1 satisfies the inequality.

Finally, we can combine the regions from the two inequalities to find the solution set. The solution set is the region above the line x + y = 1 and below the line y = (1/2)x + 2.

Therefore, the solution set can be expressed as,

{(x,y) | x + y > 1 and y < (1/2)x + 2}.

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Complete question - solve the given system of inequalities in two variables.

x + y > 1

y < 1/2x + 2

Answer:

10 flowers.

Step-by-step explanation:

Since you have 5 tables and you need two flowers on each table, you would do 2 multiplied by 5 and that gives you 10.

Answer:

(d)

Step-by-step explanation:

1) He multiplied both sides by 2.

2) He combined like terms.

3) He added 4 to both sides.

4) He divided both sides by 8.

The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

The required statement "outlier in a data set can significantly affect the value of the mean but not the median" is true.

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

The average of a group of variables is referred to as the mean in mathematics and statistics.

There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Thus, given statement is true.

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Answer:

quadrant 1

Step-by-step explanation:

b/c quadrant(+,+)

From the origin,

she is 22 units to the right and 1 unit upwards.

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

Given:

Thalia is in the room located at (22,1).

From the origin to this point  (22,1).

In the first quadrant,

From the origin,

she is 22 units to the right and 1 unit upwards.

Therefore, she is 22 units to the right and 1 unit upwards.

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