Suppose Nate loses 38% of all thumb wars.

(a) What is the probability that Nate loses two thumb wars in a row?
(b) What is the probability that Nate loses three thumb wars in a row?
(c) When events are independent, their complements are independent as well. Use this result to determine the probability that Nate loses three thumb wars in a row, but does not lose four in a row.

1. The probability that Nate loses two thumb wars in a row is: _______________
2. The probability that Nate loses three thumb wars in a row is:_____________

According to the question the following scenarios are as follows :

(a) To find the probability that A and B are next to each other in a line of 20 people, we can treat A and B as a single entity. This reduces the problem to arranging 19 entities (A and B together with the other 18 people) in a line. The total number of arrangements of 19 entities in a line is [tex]$19!$[/tex] .

Now, within the 19 entities, A and B can be arranged in [tex]$2! = 2$[/tex] ways (A followed by B or B followed by A). For each arrangement of A and B, the remaining 18 people can be arranged in [tex]$18!$[/tex] ways.

Therefore, the total number of arrangements where A and B are next to each other is [tex]$2 \cdot 18!$[/tex] .

The total number of possible arrangements of 20 people in a line is [tex]$20!$[/tex] .

The probability of A and B being next to each other is given by:

[tex]\[P(A \text{ and } B \text{ are next to each other}) = \frac{2 \cdot 18!}{20!}\][/tex]

(b) If the people are randomly arranged in a circle, we can fix one person (let's say A) at a specific position. Then, we arrange the remaining 19 people in a line, which can be done in [tex]$19!$[/tex] ways.

However, since the circle allows for rotations, each arrangement can be rotated in 20 different ways (corresponding to the different positions of A as the fixed person).

Therefore, the total number of arrangements where A and B are next to each other in a circle is [tex]$20 \cdot 19!$[/tex] .

The total number of possible arrangements of 20 people in a circle is [tex]$(20 - 1)!$[/tex] , since one person is fixed.

The probability of A and B being next to each other in a circle is given by:

[tex]\[P(A \text{ and } B \text{ are next to each other in a circle}) = \frac{20 \cdot 19!}{(20 - 1)!}\][/tex]

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Answer:

8 + (-43) - 1152 =  -1187

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

5/6 of 42 is 35

check to be sure

Answer:

35 tickets

Step-by-step explanation:

Very simple mental division & multiplication.

Divide the total (42) by the denominator (6)

42 ÷ 6 = 7

Then multiply the quotient (7) by the numerator (5)

7 × 5 = 35 tickets

The sum of the series [infinity] (−1)n − 1/n^2 * (13^n), where n starts from 1, can be approximated. The sum of this series is approximately -3.2891 when rounded to four decimal places.

To calculate this approximation, we can use the concept of an alternating series. Since the series alternates between positive and negative terms, we can apply the Alternating Series Test to determine its convergence.

By evaluating the terms of the series, we observe that the absolute value of each term decreases as n increases. This indicates that the series converges.

To approximate the sum, we can calculate the partial sums of the series until we reach a desired level of accuracy. By adding up a significant number of terms, we find that the sum is approximately -3.2891 when rounded to four decimal places.

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To find all real values of x for which f(x) equals zero, we need to solve the equation f(x) = 0. In order to determine the real values of x for which f(x) is equal to zero, we need to solve the equation f(x) = 0.

This means we are looking for the values of x that make the function f(x) equal to zero. To find these values, we can employ various methods depending on the nature of the function. One common approach is to use algebraic techniques such as factoring, completing the square, or applying the quadratic formula for quadratic functions.

For polynomial functions of higher degree, we can use techniques like synthetic division or the rational root theorem to identify potential zeros. Additionally, for transcendental functions, numerical methods or approximation techniques may be necessary. By solving the equation f(x) = 0, we can determine the specific real values of x that satisfy this condition and make the function equal to zero.

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Answer:

7. 8 I think (typing more for the limit)

Answer:

7.8

Step-by-step explanation:

Answer:

The set of numbers that could not represent the three sides of a right triangle are;

{9, 24, 26}

Step-by-step explanation:

According to Pythagoras's theorem, when the lengths of the three sides of a right triangle includes two legs, 'x', and 'y', and the hypotenuse side 'r', we have;

r² = x² + y²

Where;

r > x, r > y

Therefore, analyzing the options using the relationship between the numbers forming the three sides of a right triangle, we have;

Set 1;

95² = 76² + 57², therefore, set 1 represents the three sides of a right triangle

Set 2;

82² = 80² + 18², therefore, set 2 represents the three sides of a right triangle

Set 3;

26² = 24² + 9², therefore, set 3 could not represent the three sides of a right triangle

Set 4;

39² = 36² + 15², therefore, set 4 represents the three sides of a right triangle

Answer:

20

Step-by-step explanation:

4+4+6+6=20

(JUST WHAT SHE SAID)(SORRY FOR THE CAPS HERE)

The formula for the n+1 points where the Chebyshev polynomials Tn(x), for n >= 2, alternate between 1 and -1, can be expressed as follows: x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1.

These points are known as the Chebyshev nodes and are commonly used in polynomial interpolation and numerical analysis. They are distributed in a way that minimizes the interpolation error, making them ideal for approximating functions. The Chebyshev polynomials, denoted as Tn(x), are a set of orthogonal polynomials defined on the interval [-1, 1]. They can be recursively generated using the formula Tn(x) = 2xTn-1(x) - Tn-2(x), with initial values T0(x) = 1 and T1(x) = x. These polynomials have the property that their roots, called the Chebyshev nodes, alternate between 1 and -1.

To find the n+1 Chebyshev nodes, we can use the formula x_k = cos((2k - 1)π / (2n)), where k ranges from 1 to n+1. This formula generates the values of x at which the Chebyshev polynomials Tn(x) alternate between 1 and -1. The nodes are evenly distributed along the interval (-1, 1], with denser clustering towards the endpoints.

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Answer:

event a because you have more out comed multiplying numbers than a set of numbers

The solution to f(x) = g(x) can be found by looking at the point where the graphs of the two functions intersect.

The given functions are: f(x) = 73x - 3g(x) = 2x - 4. To find the solution, we need to set f(x) = g(x) and solve for x.73x - 3 = 2x - 4. Simplifying the above expression, we get: 71x = 1x = 1/71.Therefore, the solution to f(x) = g(x) is x = 1/71. Now let's look at the given graph: From the graph, we can see that the solution x = 1/71 is not listed as one of the answer choices.

However, we can see that the point of intersection of the two lines is at approximately x = 0.02. Therefore, the correct answers are: 0 (since x = 0.02 is rounded to the nearest whole number, which is 0) and2 (since the point of intersection has an x-coordinate of approximately 0.02, which is between 0 and 3).Therefore, the correct answers are:0 and 2.

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a) The expected value of the probability distribution is 1.4

b) The standard deviation of the probability distribution is 1.07.

a) Expected Value:

The expected value, also known as the mean, is calculated by multiplying each value of x by its corresponding probability and then summing them up. Using the provided data:

x:     0    1    2    3

P(x): 0.25 0.3 0.25 0.2

Expected Value = 0(0.25) + 1(0.3) + 2(0.25) + 3(0.2)

              = 0 + 0.3 + 0.5 + 0.6

              = 1.4

Therefore, the expected value of the probability distribution is 1.4 (rounded to two decimal places).

b) Standard Deviation:

The standard deviation measures the dispersion or spread of the probability distribution. It is calculated using the formula:

Standard Deviation = √(∑(x - E(x))^2 * P(x)

where E(x) represents the expected value.

Using the provided data:

x:     0    1    2    3

P(x): 0.25 0.3 0.25 0.2

First, calculate the squared difference between each value of x and the expected value:

(0 - 1.4)^2 = 1.96

(1 - 1.4)^2 = 0.16

(2 - 1.4)^2 = 0.36

(3 - 1.4)^2 = 2.56

Next, multiply each squared difference by its corresponding probability:

1.96 * 0.25 = 0.49

0.16 * 0.3 = 0.048

0.36 * 0.25 = 0.09

2.56 * 0.2 = 0.512

Now, sum up the products:

0.49 + 0.048 + 0.09 + 0.512 = 1.14

Finally, take the square root of the sum to find the standard deviation.

Standard Deviation = √(1.14) ≈ 1.07

Therefore, the standard deviation of the probability distribution is approximately 1.07 (rounded to two decimal places).

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Step-by-step explanation: Tenth is always the first decimal point so 1 rounds down, making it 628.3.

Answer:

628.3

Step-by-step explanation:

A Tenth is the number after the dot. It rounds down 3, therefore, the answer is 628.3.

Answer:

c

Step-by-step explanation:

Answer:

c, rotation

Step-by-step explanation:

where it gives you lets follow them they make a shape everything else dont matter.

Step-by-step explanation:

[tex]1250 - 8 \times 82 = \\ = 1250 - 656 = \\ = 594[/tex]

Answer:

$594

Step-by-step explanation:

since it doesn't seem to be accounting for interest

not going to worry about it

you would start with the initial amount that she had and then subtract 82x

x=8

so 1250-82x or 82(8)

so 1250-656

594

and if your teachers a stickler make sure that you add the dollar sign because they might count it off by half if you do not

Answer:

Here you go.

Step-by-step explanation:

x=25cos10+30cos100

y=25sin10+30sin100

v=√(x^2+y^2)

α=tan(y/x)  

Rounding to two decimal places in intermediate steps...

x≈19.41, y≈33.89

v≈39.05

α=60.20°

So (39.05, 60.20°)

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Answer: 95%

Step-by-step explanation: 0.9 = 90%

Since there are a total of 15 shirts,

5 red shirts+4 white shirts= 9 shirts total

3 blue shirts+3 purple shirts= 6 shirts total

The odds that you would pick a red shirt and then a white are 3:2

3 being the 9 red and white shirts combined.

2 being the 6 purple and blue shirts combined.

9:6 simplified=3:2

9/3=3

6/3=2

3:2

Answer: The odds that you would pick a red shirt then a white shirt would be 3:2 or 60%

Answer:

$772

Step-by-step explanation:

Set it up as

772(1+0.018)^2

Comes out to $800.04

If you need further explanation tell me in comments

Answer:829

Answer:

The distance would be [tex]\sqrt{97[/tex].

Step-by-step explanation:

The least distance between them would be to draw a straight line between them.

By calculating the distance between the y values and the x values, you can calculate the distance.

y values:

|5 - 1| = 4

x values:

|6 - -3| = 9

| | = the absolute value, meaning you change the final sign to positive.

Use the Pythagorean theorem [tex]a^2 +b^2=c^2[/tex] and substitute the numbers in.

[tex]4^2 + 9^2=c^2 \\c^2 = 97\\c=\sqrt{97[/tex]

For W1, W2⊂W1, W2⊂V be finite-dimensional subspaces of a vector space V,

(a) If either W1 or W2 is the zero subspace, the formula holds.

(b) Given a basis S for the intersection W1∩W2, there exist sets T1 and T2 such that their union with S forms bases for W1 and W2, respectively.

(c) The union U = S∪T1∪T2 spans the sum W1 + W2.

(d) The union U = S∪T1∪T2 is linearly independent, and the formula dim(W1 + W2) = dim(W1) + dim(W2) - dim(W1∩W2) holds.

(a) If W1 = {0}, then the dimension of W1 is 0. Similarly, if W2 = {0}, then the dimension of W2 is 0. In both cases, the intersection of W1 and W2, denoted by W1∩W2, is also {0}, and its dimension is 0.

Therefore, we have:

dim(W1 + W2) = dim({0} + W2) = dim(W2) = dim(W1) + dim(W2) - dim(W1∩W2) = 0 + dim(W2) - 0 = dim(W2).

(b) Let S be a basis of W1∩W2. Since W1 and W2 are nonzero, they each have at least one nonzero vector. Let v1 be a nonzero vector in W1, and v2 be a nonzero vector in W2. Then {v1} is linearly independent and can be extended to a basis T1 of W1. Similarly, {v2} is linearly independent and can be extended to a basis T2 of W2.

(c) To show that U = S∪T1∪T2 spans W1 + W2, we need to show that every vector in W1 + W2 can be expressed as a linear combination of vectors in U.

Let w be an arbitrary vector in W1 + W2. By definition, there exist vectors w1 ∈ W1 and w2 ∈ W2 such that w = w1 + w2. Since T1 is a basis of W1, we can express w1 as a linear combination of vectors in T1. Similarly, w2 can be expressed as a linear combination of vectors in T2. Therefore, we can write w as a linear combination of vectors in U = S∪T1∪T2.

(d) To show that U = S∪T1∪T2 is linearly independent, we need to show that the only solution to the equation c1v1 + c2v2 + ... + cnvn = 0, where ci are scalars and vi are vectors in U, is the trivial solution c1 = c2 = ... = cn = 0.

Since S is a basis of W1∩W2, any vector in S can be expressed as a linear combination of vectors in S. Similarly, vectors in T1 can be expressed as a linear combination of vectors in T1, and vectors in T2 can be expressed as a linear combination of vectors in T2. Therefore, the equation c1v1 + c2v2 + ... + cnvn = 0 implies that the coefficients ci must be zero for all vectors in U.

By showing that U is linearly independent, we can deduce that dim(W1 + W2) = |U| = |S∪T1∪T2| = |S| + |T1| + |T2| = dim(W1) + dim(W2) - dim(W1∩W2), which is the claimed identity.

Therefore, we have proved that dimension dim(W1 + W2) = dim(W1) + dim(W2) - dim(W1∩W2).

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k=121 degrees

t=29 degrees

d=30 degrees

Answer:

7/8 if u want more if u want less then it 4/9

Step-by-step explanation:

Answer:

0.3475905 in league

The similarity between the z-test and the one-sample t-test is that they are both statistical tests used to make inferences about population parameters based on sample data.

The z-test and the one-sample t-test are both hypothesis tests used to determine if a sample mean significantly differs from a hypothesized population mean. The main similarity between the two tests is that they are both used when the population standard deviation is known for the z-test or estimated from the sample for the t-test. Both tests involve comparing the observed sample mean to the hypothesized population mean and considering the variability in the data. They both calculate a test statistic that measures the difference between the observed and hypothesized means relative to the variability in the data. The test statistic is then compared to a critical value or p-value to determine the significance of the difference. However, the main difference between the two tests is that the z-test assumes a known population standard deviation, while the one-sample t-test uses the sample standard deviation to estimate the population standard deviation. This makes the t-test more appropriate when the population standard deviation is unknown.

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Answer:

i think its 7/10

Step-by-step explanation: