Matts seat is located at (-2,5) and Beths seat is loacted at (-4,7). How far apart are Matt and Beths seats?​

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

80%

Step-by-step explanation:

Answer: 17.9 km/h

Step-by-step explanation:

Convert 33 minutes and 50 seconds to Hours:

= 33 ⁵⁰/₆₀ minutes

= 33.83 minutes

In hours that would be:

= 33.83 / 60

= 0.56 hours

10,000 meters in kilometers is:

= 10,000 / 1,000

= 10 kilometers

Speed = 10 / 0.56

= 17.9 km/h

Answer:

8,13,21

Step-by-step explanation:

Basically,add the previous number to next number

Answer:8,13,21

Step-by-step explanation:

Answer:

-17/12

Step-by-step explanation:

║5/6 - 7/12║- ║5/3║

= ║10/12 - 7/12║ - ║5/3║

= ║3/12║- ║5/3║

= 3/12 - 5/3

= 3/12 - 20/12

= -17/12

The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

Let x be the hotel charge before tax in the first city, and y be the hotel charge before tax in the second city. Then we have:
y = x + 1500   (the hotel charge before tax in the second city was $1500 higher than in the first)
0.075x + 0.05y = 825   (the total hotel tax paid for the two cities was $825)
We can use the first equation to solve for y in terms of x:
y = x + 1500
Then we can substitute this expression for y into the second equation:
0.075x + 0.05(x + 1500) = 825
Simplifying this equation, we get:
0.075x + 0.05x + 75 = 825
0.125x = 750
x = 6000
So the hotel charge before tax in the first city was $6000. Using the first equation, we can find the hotel charge before tax in the second city:
y = x + 1500
y = 6000 + 1500
y = 7500
So the hotel charge before tax in the second city was $7500.
Therefore, the answer is: The hotel charge in the first city before tax was $6000 and the hotel charge in the second city before tax was $7500.

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Answer:

yes im pretty sure correct me if im wrong. Good luck!!!!!

Step-by-step explanation:

Step-by-step explanation:

k/9 + 76 = 1/3 K

K/9 - 1/3 K = -76

K/9 - 3K/9 = -76

(K-3k)/9 = -76

-2K / 9 = -76

-2K = -76 × 9

-2K = -684

K = -684/-2

K = 342

The proportion is given

After cross product, the proportion becomes

To determine x,

Hence the value of x is 42.

Answer:

a. The positive difference between Nelson's height and the population mean is: \( \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in\).

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: \( \\ z = -1.1739 \approx -1.174\) (Nelson's height is below the population's mean 1.174 standard deviations units).

d. Nelson's height is usual since \( \\ -2 < -1.174 < 2\).

Step-by-step explanation:

The key concept to answer this question is the z-score. A z-score "tells us" the distance from the population's mean of a raw score in standard deviation units. A positive value for a z-score indicates that the raw score is above the population mean, whereas a negative value tells us that the raw score is below the population mean. The formula to obtain this z-score is as follows:

\( \\ z = \frac{x - \mu}{\sigma}\) [1]

Where

\( \\ z\) is the z-score.

\( \\ \mu\) is the population mean.

\( \\ \sigma\) is the population standard deviation.

From the question, we have that:

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

\( \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in\).

That is, the positive difference is 2.7 in.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many standard deviations is that, we need to divide that difference by the population standard deviation. That is:

\( \\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174\)

In words, the difference found in part (a) is 1.174 standard deviations from the mean. Notice that we are not taking into account here if the raw score, x, is below or above the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

\( \\ z = \frac{x - \mu}{\sigma}\)

\( \\ z = \frac{68\;in - 70.7\;in}{2.3\;in}\)

\( \\ z = \frac{-2.7\;in}{2.3\;in}\)

\( \\ z = -1.1739 \approx -1.174\)

This z-score "tells us" that Nelson's height is 1.174 standard deviations below the population mean (notice the negative symbol in the above result), i.e., Nelson's height is below the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

\( \\ -2 < z_{Nelson} < 2\)

\( \\ -2 < -1.174 < 2\)

Then, Nelson's height is usual according to that statement.  

Answer:

0.04

Step-by-step explanation:

Answer:

2,500

Step-by-step explanation:

10% = \(\frac{10}{100} = \frac{1}{10}\)

\(25000\times\frac{1}{10}=2500\)

Answer:have a wonderful Christmas!

Step-by-step explanation:70+95

70=2*5*7

95=5*19

70+95=(5*2*7)+(5*19)=(5*14)+(5*19)=5*(14+19)=5*(33)

5*33=165 and 70+95=165 also

Answer:

The answer is 165, hope this helps.

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

Given:

Total volume = 5.4 L.

We know that 1 L is equivalent to 1000 cubic centimetres; hence:

ANSWER

5400 cm³ of coffee will completely fill the pot

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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Answer:

Yes

Step-by-step explanation:

(-2)^2 is the same as (-2)(-2)

-2^2 is the same as -2*-2

both (-2)^2 and -2^2 = 4

Answer: 14

Tap to view steps...

Step-by-step explanation:

Answer:

1001110₂

Step-by-step explanation:

To convert decimals to binary, you have to divide the decimal by 2 until it meets zero.

Also, while dividing the number by 2 you have to write the remainder in each step.

And then you have to write the remainders from bottom to top.

Let us solve this now

2 |78    

2 |39   - 0

2 | 19   - 1

2 | 9      - 1

2 | 4     -  1

2 | 2      - 0

2 | 1      - 0

    0       - 1

Now write the remainder from bottom to top.

78  ⇒  1001110₂

Answer: k=11

Step-by-step explanation:

A statement which is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals include the following: E. The shortest streak is of length 1.

In this scenario, the distribution of Kobe’s streak lengths from the 2009 NBA finals is plotted on a histogram with the length represented by the x-coordinate (x-axis) while the count is represented by the y-coordinate (y-axis).

By critically observing the histogram, we can reasonably infer and logically deduce the following true statements:

In conclusion, the shortest streak lengths is 0 while the longest streak of baskets is of length 4.

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Complete Question:

Which of the following is false about the distribution of Kobe’s streak lengths from the 2009 NBA finals.

A. The distribution of Kobe’s streaks is unimodal and right skewed.

B. The typical length of a streak is 0 since the median of the distribution is at 0.

C. The IQR of the distribution is 1.

D. The longest streak of baskets is of length 4.

E. The shortest streak is of length 1

Answer:

True:

D.

E.

F

Step-by-step explanation:

First, you should know that the square of any odd number is also odd.

The easiest way to go about this is to plug in an odd number for n. Lets use 3:

Plug 3 into A:

\(3^{2} -1=9-1=8\)

Plug 3 into B:

\(3(3-1)=9-3 = 6\)

Plug 3 into C:

\((3-2)^{2} = 2^{2} = 4\)

Plug 3 into D:

\(3^{2} +2 = 9+2=11\)

Plug 3 into E:

\(3(3-2) = 9-6 = 3\)

Plug 3 into F:

\((3-2)^{2}=1^{2} =1\)

Answer:

We always need an equation relating the given information to what is to be found. With this problem, we must assume that the giant model is proportional to the standard pencil.

3 m: 18 cm :: Vg:9 cm^3 where Vg is the volume of the giant pencil.

Before any calculations are performed all units must be the same.

The 3 m large pencil must be converted to cm. Each meter is 100 centimeters. Therefore: the proportion must be adjusted to:

300 cm : 18 cm :: Vg : 9 vm^3

300/18 = Vg/9 Now solve.

300 x 9 = 18 Vg By cross multiple

2700 = 18 Vg Divide both sides by 18

Vg = 2700/18 = 150 cm^3 = 0.00015 m^3

Conversion Factor: 1 cm^3 = 10^-6 m^3 Divide by 10^6.

Now Double Check

Step-by-step explanation:

Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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The conclusion that is valid are

A valid conclusion is a logical inference or deduction drawn from evidence, facts, or reasoning.

It is a statement or assertion that is supported by sound logic and evidence, making it a reasonable and justifiable interpretation or outcome.

The case of rectangle supports the logic of four right angles and hence a rectangle

Also, that of Alia supports the logic since all vegetarian does not eat meat. then if Alia is a vegetarian, then she should not eat meat

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Answer:

$136.

Step-by-step explanation:

Divide how much they made by the # of hours. 306/18=17. Multiply the amount per hour 17 by the 8 hours of work. 17x8=136.

If you know your derivative rules, then

d/dx [1/x] = -1/x ²

so that when x = 6, the derivative has a value of -1/36.

If you have to use the definition of the derivative, then

d/dx [1/x] = lim {h → 0} (1/(x + h) - 1/x) / h

… = lim {h → 0} (x - (x + h)) / (hx (x + h))

… = lim {h → 0} (-h) / (hx (x + h))

… = lim {h → 0} (-1) / (x (x + h))

… = -1/x ²

and at x = 6, you again get -1/36.

Alternatively, use the definition of the derivative at a point:

d/dx [1/x] (6) = lim {x → 6} (1/x - 1/6) / (x - 6)

… = lim {x → 6} ((6 - x) / (6x)) / (x - 6)

… = lim {x → 6} -(x - 6) / (6x (x - 6))

… = lim {x → 6} (-1) / (6x)

… = -1/36

Answer:

The frequency increases as the pitch increases, and the amplitude increases as the volume increases

Step-by-step explanation:

Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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