In a professional division of a Hockey league, there are 9 total teams. How many different rankings are possible at the end of the year

Answer:

4

Step-by-step explanation:

The Fundamental theorem of algebra states that a polynomial of degree n has n roots, some may be complex.

f(x) = \(x^{4}\) + 5x³ + 2x + 6 ← is a polynomial of degree 4

Thus there are 4 possible roots

Answer:

4 possible roots.

Step-by-step explanation:

This has degree 4.

So it will have one of the following sets of roots.

4 real roots.

2 real and 2 complex roots.

4 complex roots.

The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

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The total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct eigenvalues,

which is at most n.

The reason why a 2x2 matrix can have at most two distinct eigenvalues is because the characteristic equation for a

2x2 matrix is quadratic. This means that there can be at most two distinct solutions for the eigenvalues.

As for an n x n matrix, the reason why it can have at most n distinct eigenvalues is because the characteristic equation

for an n x n matrix is of degree n.

This means that there can be at most n distinct solutions for the eigenvalues. Additionally, the maximum number of

eigenvectors that can be associated with each distinct eigenvalue is equal to the multiplicity of the eigenvalue.

Therefore, the total number of eigenvectors for an n x n matrix is equal to the sum of the multiplicities of its distinct

eigenvalues, which is at most n.

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Answer:

Step-by-step explanation:

Hello!

The experiment consist in "a fair coin is tossed 4 times" the recorded variable is X: number of heads obtained after tossing the coin 4 times

The possible values for this variable: X: 0; 1; 2; 3; 4

The frequencies observed for each possible value of X after repeating the experiment for n=80 times

fi: 4; 8; 36; 20; 12

To create the probability distribution you have to calculate the probability for each value of X, by doing the following calculation \(p(xi)= \frac{fi}{n}\)

p(X=0)= p(0)= 4/80= 0.05

p(X=1)= p(1)= 8/80= 0.10

p(X=2)= p(2)= 36/80= 0.45

p(X=3)= p(3)= 20/80= 0.25

p(X=4)= p(4)= 12/80= 0.15

For this to be a probability of distribution the following conditions are to be met:

All calculated probabilities are at most zero.

∑p(xi)= 0.05+0.10+0.45+0.25+0.15= 1

  xi | 0 | 1 |   2 |  3  | 4

   fi | 4 | 8 | 36| 20 | 12

p(xi)| 0.05| 0.10| 0.45| 0.25| 0.15

F(Xi)|0.05| 0.15 | 0.60| 0.85| 1

I hope this helps!

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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Answer:

d) 5

Step-by-step explanation:

we can observe that the x-value 5 appears twice in the relation. However, in a function or a relation, each x-value should only have one corresponding y-value. Therefore, the repetition of (5, 1) and (5, 2) indicates an inconsistency or ambiguity in the relation. As a result, 5 is not a valid x-value in the domain.

The recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

From the question, we have the following parameters that can be used in our computation:

This means that

Initial, a = 250 bacterial cultures.

Rate = 3

So, the recursive formulas is

f(n) = 3f(n - 1), where f(1) = 250

For the explicit formula, we have

f(n) = 250(3)ⁿ‐¹

Hence, the recursive and the explicit formulas are f(n) = 3f(n - 1), where f(1) = 250 and f(n) = 250(3)ⁿ‐¹

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Answer:

A Euclidean geometry, and theres no parallel lines

Answer:

C = 10

Step-by-step explanation:

\(A^{2}\) + \(B^{2}\) = \(C^{2}\)

\(6^{2}\) + \(8^{2}\) = 100

\(\sqrt{100}\) = 10

Answer: 2. 55/8

Step-by-step explanation: Add the whole numbers first (5+1 = 6), then add the fractions (4/8 + 3/8 = 7/8). Now we have 6 7/8 and since they want the answer in fraction form we will multiply the 6 and the 8 (6x8=48) and then add the 7 to the 48 (7+48 =55) and we leave our answer over the denominator which is 8. This leaves us with the final answer of 55/8

Answer:

  1/3

Step-by-step explanation:

You want to know the ratio of the difference in median wait times to the IQR for the box plots shown.

The median is the line in the middle of the box. The medians are ...

The difference in median wait times is 11 -9 = 2 min.

The IQR is the difference between the upper end of the box and the lower end. The IQRs are ...

The ratio of the difference in medians to the IQR is ...

  (median difference) / (IQR) = (2 min)/(6 min) = 1/3

The difference in medians is 1/3 times the IQR.

__

Additional comment

The problem already tells you the difference of medians and the IQR, so all you need to do is express than as a ratio.

  difference = k × IQR

  k = difference/IQR = 2/6 = 1/3

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Answer:

she profited $35

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Go to this link and your question will be answered.

Answer:

360 in

Step-by-step explanation:

To figure out how many inches the dressmaker has in 10, 3 ft rolls, we can multiply by the conversion ratio:

\(\dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies (10 \cdot 3 \text{ ft}) \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30 \text{ ft} \cdot \dfrac{12 \text{ in}}{1\text{ ft}} \\ \\ \text{} \ \ \implies 30\cdot 12 \text{ in} \\ \\ \text{} \ \ \implies \boxed{360 \text{ in}}\)

So, the dressmaker has 360 in of ribbon.

Answer:

6.7.

Step-by-step explanation:

sin 48 = 5/h

h * sin 48 = 5

h = 5 / sin 48

= 6.73

Answer:

Step-by-step explanation:

the nth term of a geometric sequence is

∙

x

a

n

=

a

r

n

−

1

where a is the first term and r the common ratio

r

=

a

2

a

1

=

a

3

a

2

=

...

...

=

a

n

a

n

−

1

here  

a

=

3

and  

r

=

9

3

=

27

9

=

3

⇒

a

10

=

3

×

3

9

=

3

10

=

59049

yes, actually it is possible. The mathematical expression f(x)=exp or ex denotes the exponential function.

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras. When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.

One of the key mathematical operations is the exponential function (though it would have to admit that the linear function ranks even higher in importance). We allow the exponent to be the independent variable to create an exponential function. The formula f(x)=2x is a straightforward example.

Hence, yes, actually it is possible.

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The three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

To determine the three angles in the triangle ABC, we can use the law of cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The law of cosines states that for a triangle with sides a, b, and c, and angles A, B, and C opposite those sides:

```

a^2 = b^2 + c^2 - 2bc cos(A)

b^2 = a^2 + c^2 - 2ac cos(B)

c^2 = a^2 + b^2 - 2ab cos(C)

```

We can use these equations to solve for the three angles in the triangle ABC.

First, we need to find the lengths of the sides of the triangle. We can use the distance formula to find the lengths of the sides AB, BC, and AC:

```

AB = sqrt((7-2)^2 + (7-2)^2) = sqrt(50)

BC = sqrt((4-2)^2 + (8-2)^2) = sqrt(52)

AC = sqrt((7-4)^2 + (7-8)^2) = sqrt(10)

```

Now we can use the law of cosines to solve for the angles:

```

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (a^2 + c^2 - b^2) / 2ac

cos(C) = (a^2 + b^2 - c^2) / 2ab

```

```

cos(A) = (50 + 10 - 52) / (2 * sqrt(50) * sqrt(10)) = 0.9

cos(B) = (50 + 52 - 10) / (2 * sqrt(50) * sqrt(52)) = 0.2

cos(C) = (10 + 52 - 50) / (2 * sqrt(10) * sqrt(52)) = 0.9

```

Now we can use the inverse cosine function to find the values of A, B, and C:

```

A = acos(0.9) ≈ 0.45 radians

B = acos(0.2) ≈ 1.37 radians

C = acos(0.9) ≈ 0.45 radians

```

Therefore, the three angles in the triangle ABC are approximately 0.45 radians (A and C) and 1.37 radians (B).

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After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

The speed of an object after a certain time can be calculated using the following equation:

v = u + at

Where:v is the final velocity, u is the initial velocity, a is the acceleration of the object, t is the time taken by the object

So, the person is on skis at the top of a 12-degree ski run and starts from rest, which means the initial velocity u is 0 m/s.

The downhill slope creates an acceleration for the person. The acceleration due to gravity is acting down the slope.

The component of gravity along the slope is given by:g = 9.81 × sin (12°) = 2.022 m/s²

Putting all values in the equation:

v = u + atv = 0 + 2.022 × 8.5v = 17.19 m/sTherefore, the person's final velocity after 8.5 seconds down the hill is 17.19 m/s.

After 8.5 seconds down the hill, they will be moving at a velocity of 17.19 m/s.

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Interpreting a correlation requires careful consideration of factors such as causation, confounding variables, nonlinearity, outliers, and sample characteristics.

Interpreting a correlation between two variables can be difficult for several reasons:

Causation vs. correlation: Correlation measures the strength and direction of the relationship between two variables but does not imply causation. Just because two variables are correlated does not mean that one variable causes the other. It is essential to avoid making causal claims based solely on correlation.

Confounding variables: Correlations can be influenced by the presence of confounding variables that affect both variables being studied. Without accounting for these confounding factors, it can be challenging to determine the true nature of the relationship between the variables of interest.

Nonlinear relationships: Correlation coefficients, such as Pearson's correlation coefficient, measure linear relationships between variables. If the relationship is nonlinear, the correlation may not accurately capture the association. It is crucial to consider other types of analysis or transformations to capture more complex relationships.

Outliers and influential observations: Extreme values or outliers in the data can have a significant impact on correlation coefficients. These outliers may distort the correlation and lead to incorrect interpretations. It is important to examine the data for influential observations that may unduly influence the correlation results.

Sample size and representativeness: The size and representativeness of the sample can affect the reliability and generalizability of correlation results. Small or biased samples may not provide a representative picture of the population, leading to misleading interpretations.

Overall, it is important to use correlations as part of a broader analysis and consider additional evidence before drawing definitive conclusions about the relationship between variables.

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The easiest way to solve a system of equations is by using the substitution method.

The substitution method requires you to solve for one variable in one of the equations, substitute the answer into the other equation, and then solve for the remaining variable.

The easiest way to solve a system of equations is to use the substitution method. This method works by substituting one equation into the other to solve for one of the variables. Once the variable is found, it is then substituted back into the other equation to solve for the other variable. For example, if you have two equations: 3x + 2y = 5 and 4x - 2y = 6, you would solve the first equation for y and substitute the answer (y = (5 - 3x)/2) into the second equation. Then, you would solve the second equation for x (x = (6 + 2y)/4). Once you have the values for x and y, you can substitute them into either equation to check your answer.

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Therefore , the solution to the given problem of probability comes out to be dice can even number 14 times.

Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To forecast how likely occurrences are to occur, likelihood has been presented in mathematics. The degree to something which is likely to take place is essentially the definition of probability. The probability distribution is based on this fundamental idea of probability.

Here,

Given : Veronica rolls a six-sided dice 28 times.

Thus,

Dice has 1,2,3,4,5,6 numbers

So ,

There are 3 odds and 3 even numbers

So,

the probability to come even number = 3/6 = 0.5

Or

Rather we can say 50% chances that it will come as even number.

Thus,

50% of 28 = 14

Therefore , the solution to the given problem of probability comes out to be dice can even number 14 times.

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a) By Pythagorean theorem, the value of variable x is equal to 10.2171 meters.

b) By trigonometric functions, the value of variable h is equal to 7.8620 meters.

Herein we have the representation of a geometric system formed by four right triangles, this formation has a known angle and a known side, and two unknown variables as well. The values of the variables can be found by means of trigonometric functions and Pythagorean theorem:

Trigonometric functions

sin 50° = h / x

h = 0.7660 · x

Pythagorean theorem

x² = L² + h²

8² = (0.25 · L)² + h²

64 = 0.0625 · L² + h²

Then, we eliminate L by equalizing second and third equations:

64 = 0.0625 · (x² - h²) + h²

64 = 0.0625 · x² + 0.9375 · h²

And by the first equation:

64 = 0.0625 · x² + 0.9375 · (0.7660 · x)²

64 = 0.0625 · x² + 0.5501 · x²

64 = 0.6126 · x²

8 = 0.783 · x

x = 10.2171 m

And the value of h is:

h = 0.7660 · (10.2171 m)

h = 7.826 m

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Answer:

39

Step-by-step explanation:

11.70 divided by 3 is 3.9, and the unit rate. Multiply by 10 for the answer.

Answer:

Below

Step-by-step explanation:

To find the volume of a rectangular prism find the area of a face and multiply it by the height

V = lwh

  = (12)(5)(12)

  = 720 km^3

Hope this helps!

Answer:

12 in3

Step-by-step explanation: I took the test

Option D is correct, the volume of one paperweight is 12 cubic inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given that glass paperweights in the shape of a square pyramid.

The base of the paperweight is three inches on one side, and it's four inches tall.

Base edge a= 3 inches

Height h = 4 inches.

Volumes =a²h/3

Plug in the values of a and h in the given formula.

=3×3×4/3

=12 cubic inches.

Hence, option D is correct, the volume of one paperweight is 12 cubic inches.

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Answer:

2

Step-by-step explanation:

Estimate 1 2/11 to 1.

Estimate 2.97 to 3.

3 - 1 = 2

Answer:

B

Explanation

I took the quiz

The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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