Find the modulus of the complex number 6-2i

The least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday is 24 people.

(a) An expression in terms of n for the probability that no one shares your birthday is given by;P(A)

= (365/365) * (364/365) * (363/365) *.... * ((365 - n + 1)/365)

= (365 * 364 * 363 * ... * (365 - n + 1))/(365)^n(b) Here, we are supposed to determine the least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday. This is the of the probability that no one shares our birthday, i.e.,1 - P(A) ≥ 0.6 P(A) ≤ 0.4We know that, P(A)

= (365/365) * complement (364/365) * (363/365) *.... * ((365 - n + 1)/365)We can then use trial and error method or any numerical method to find the value of n such that P(A) ≤ 0.4We can use a spreadsheet, a calculator, or a software like R to carry out this calculation.Using R, we can run the following command to get the least value of n that satisfies the condition;> n

= 1while(prod((365 - (0:(n-1)))/365) > 0.4){n

= n + 1} > n [1] 24.The least number of people we need to select so that the probability is at least 0.6 that at least one person shares our birthday is 24 people.

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Answer:

\(w_1=-\frac{1}{4},w_2=-2}\)

Step-by-step explanation:

\(4w^2+9w=-2\)

\(4w^2+9w+2=0\)

\(w^2+9w+8=0\)

\((w+1)(w+8)=0\)

\((4w+1)(w+2)=0\)

\(w_1=-\frac{1}{4},w_2=-2}\)

Answer:

The third side should be more than 7 and  less than 17

Step-by-step explanation:

Sum of lengths any 2 sides of a triangle should be greater than the length of the third side. Here lengths of 2 sides of a triangle are given. So,

5 + 12 > Length of third side

=> 17 > Length of third side

or

=> Length of third side < 17

Let's assume that the side with 12 as length be the longest side of the triangle. So,

5 + length of the third side > 12

(or)

12 < 5 + length of the third side

Here if we gonna add 7 , then it will be equal to 12 . So the length of the third side should be more than 7 .

Answer:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

The given trianagle FAN is an acute triangle.

Step-by-step explanation:

There are three types of triangles on the basis of angle:

(As shown in image attached)

Given:

A triangle FAN with an angle measurement of each angke.

To find:

The name adjoining triangle FAN on the  basis of angle.

Solution:

In ΔFAN

∠A=55°, ∠F=85° ,and ∠C=45​°

∠A<90°, ∠F<90° ,and ∠C<90°

All the given three angles of triangle FAN are less than 90°, which imolies that the given trianagle FAN is an acute triangle.

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Answer:

B- The sales price = the original price - 25% of the originial price

Step-by-step explanation:

According to the information provided, it can be inferred that the conclusion reached by Alex is that there are no advantages to honor roll students.

To calculate the percentages of students who received the requested classes, we must take into account the data in the table. Additionally, we must perform the following operations:

According to the above, the percentage of students who are on the honor roll and receive their classes is 44.44%.

To calculate the percentage of students who are not on the honor roll and receive their classes, we do the following operation.

According to the above, it can be inferred that the students who are on the honor roll do not have advantages over the others because the percentage of students who are not on the honor roll and receive their science classes is greater than the percentage of students who are on the honor roll and receive their classes.

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An indication that the normality condition has been met for a t-test for the slope of a regression model would be a residual plot with no apparent pattern in the residuals and a histogram of the residuals that is centered at 0, unimodal, and symmetric.

The correct option is I and II only.

I. A residual plot with no apparent pattern in the residuals: A residual plot that shows no discernible pattern in the residuals suggests that the errors are randomly distributed and do not follow a systematic pattern. This is consistent with the assumption of normality.

II. A histogram of the residuals that is centered at 0, unimodal, and symmetric: A histogram of the residuals that is centered around 0, has a single peak (unimodal), and is symmetric indicates that the residuals follow a normal distribution.

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The point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Let’s plot the given points E, F and G on the graph and try to find the missing point H:

Now, the length of the side EF will be:

EF = √((3-1)² + (5-5)²)EF = 2 units

The length of the side FG will be:

FG = √((6-3)² + (1-5)²)FG = √10 units

The length of the side EG will be:

EG = √((6-1)² + (1-5)²)EG = √26 units

Therefore, the total length of the three sides of the fence will be:2 + √10 + √26 units

Now, the perimeter of the fenced area with 4 sides EFGH is:16 = 2 + √10 + √26 + EHThe length of EH will be:

EH = 16 - 2 - √10 - √26EH = 11.60 units

We need to plot the missing point H which is at a distance of 11.60 units from point E along the line passing through points E and F.

Using the slope formula we find that the slope of the line passing through points E and F is: m = (y2 - y1)/(x2 - x1) = (5 - 5)/(3 - 1) = 0Therefore the line passing through E and F is a horizontal line as it has zero slope.

The distance between points E and H is 11.60 units and point H will be on the same horizontal line passing through E and F.Therefore, the x-coordinate of point H will be:

EH = √((x2-x1)² + (y2-y1)²)11.60 = √((x-1)² + (5-5)²)

Solving the above equation:

(x-1)² = 134.56(x-1)

= ±√134.56x

= 1 + √134.56 or x = 1 - √134.56

Therefore, the point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

Point H could be (1 + √134.56, 5) or (1 - √134.56, 5).

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Answer: B. 1+2 times 6

Step-by-step explanation:

5 + 2^3 = 13

It can't be A because the answer of A is equal to 11

It can't be C because 3^2 is 9; adding 2 is equal to 11

It can't be D because the answer to D is 343

So, the answer is B. 1+2 times 6

If you can, please give me a Brainliest; thank you!

Answer:

1 + 2 × 6

Step-by-step explanation:

We know that 5 + 2^3 = 5 + 8 = 13

The first answer equals 5 + 2 × 3 = 5 + 6 = 11

The second answer equals 1 + 2 × 6 = 1 + 12 = 13

The third answer equals 3^2 + 2 = 9 + 2 = 11

The fourth answer equals 100 × 3 + 43 = 300 + 43 = 343

Therefore, only the second answer equals 13, which is the correct answer.

I would appreciate it if you mark my answer as brainliest.

One problem we had to solve that required in-depth thought and analysis was how to generate engaging and relevant suggestions for the next user turn after responding.

we had to consider various factors such as the user’s intent, the context of the conversation, the tone and style of the response, and the diversity and novelty of the suggestions. I also had to avoid generating suggestions that were generic, offensive, or out of scope.

The process involved:
1. Identifying the main topic and relevant keywords in the user's question.
2. Comparing these keywords with a database of accurate information.
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Answer:

d

Step-by-step explanation:

The relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

Recall:

Fromm the information given to us about △ZVT and △XWU, we have the following:

Therefore, the relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

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Answer:

13.91 m/s

Step-by-step explanation:

Ave. speed =distance/ time

=100/7.19

=13.91 m/s

So the coordinates of point X' after dilation are (15, 11).

Polygon WXYZ is dilated by a scale factor of 3, with vertex W as the center of dilation. This means that the distances from vertex W to the other vertices are multiplied by 3, while W remains unchanged. Given the coordinates of point W are (3,2) and point X are (7,5), we can find the coordinates of point X' after dilation.

To do this, first determine the change in the x and y coordinates from point W to point X:

Δx =\(7 - 3 = 4\\\)
Δy =\( 5 - 2 = 3\)

Now multiply these changes by the scale factor of 3:

Δx' =\( 4 * 3 = 12\)
Δy' =\( 3 * 3 = 9\)

Now add these new changes to the original coordinates of point W to get the coordinates of point X':

X'(x) =\( W(x) + Δx' = 3 + 12 = 15\)
X'(y) = \(W(y) + Δy' = 2 + 9 = 11\)

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Answer:

19) y = 3/2x + 1

20) y = x + 4

21) a: 4/5 b: y = 4/5x + 4 c: 16 feet d: 4

22) a: y + 1 = 4(x - 6)

The proportion of the team that work part time is 2/13 or 0.154

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

Let the total number of workers in the furniture store be = 13 employees

Let the number of workers who are part time = 2 workers

So , proportion of the team that work part time = number of workers who are part time / total number of workers in the furniture store

On simplifying , we get

The proportion of the team that work part time = 2 / 13

The proportion of the team that work part time = 0.154

Hence , the proportion is 2/13 or 0.154

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Answer:

Step-by-step explanation:

No sol because 37=-3 is false

Answer:

no answer

Step-by-step explanation:

in first equation x-y= 37 make y in the other side then it will be x=37+y

substitute x in the second equation which is x- y= -3

then it will be

37+y-y= -3

there will be no answer

1 1/12 square yards per hour

FIGHTING!

det(MBA) = det(diag(det A, det A, ..., det A)BA) = det(diag(det A, det A, ..., det A)) * det(BA) = det A * det(BA)

Bet AB = det BA, as required.

what is square matrix?

A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.

To show that det AB = det BA, we can use the fact that for any invertible matrix M, we have det(MAB) = det(MBA) = det(M) * det(AB) = det(M) * det(BA). Therefore, it is sufficient to show that there exists an invertible matrix M such that det(MAB) = det(MBA).

Let M be the diagonal matrix with diagonal entries given by the determinant of A, i.e., M = diag(det A, det A, ..., det A). Then, we have:

det(MAB) = det(diag(det A, det A, ..., det A)AB) = det(diag(det A, det A, ..., det A)) * det(AB)

= det A * det(AB)

Similarly, we have:

det(MBA) = det(diag(det A, det A, ..., det A)BA) = det(diag(det A, det A, ..., det A)) * det(BA)

= det A * det(BA)

Therefore, det AB = det BA, as required.

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Answer:

E(X) = $1060.

This shows that the expected value of earnings is greater than the cost of entering the race.

Hence, it is worthwhile to enter the race if it costs $1000.

The horse has a probability of 1/20 of coming in first place,

a probability of 1/10 of coming in second place,

and a probability of 1/3 of coming in third place.

Given that the first place pays $4800 to the winner,

second place $3200,

and third place $1500.

we need to find whether it is worth entering the race if it costs $1000.

Let E be the net profit in the race,

which is calculated as the difference between the total earnings and the cost of entering the race,

i.e., E = Total earnings - Cost of entering the race

Given, The probability of the horse coming in first place = 1/20

The probability of the horse coming in second place = 1/10

The probability of the horse coming in third place = 1/3

Now,

Let us calculate the expected value of the earnings, E(X).

E(X) = (1/20) x 4800 + (1/10) x 3200 + (1/3) x 1500

      = 240 + 320 + 500

      = $1060

Therefore, E(X) = $1060.

This shows that the expected value of earnings is greater than the cost of entering the race.

Hence, it is worthwhile to enter the race if it costs $1000.

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Answer:

B/16

Step-by-step explanation:

if the rotor is spinning 80 reveloutions every 12 seconds and, a minute is 60 seconds

12 divided by 60 = 0.2

0.2 times 80 = 16.

hope this helped

Answer:

b=5

Step-by-step explanation:

\(f(x)=b^{x} \\A(1,5), x=1,y=5=f(x)\\5=b^{1} \\b=5\\f(x)=5^{x}\)

Answer:

Here we answer the question: "What two numbers multiply to -450 and add up to 15?"

The answer to your question is:

-15 and 30

Below we illustrate and prove that -15 and 30 multiply to -450 and add up to 15:

-15 × 30 = -450

-15 + 30 = 15 Are you asking because you are trying to determine how to factor the following quadratic equation? x2 + 15x - 450 = 0 If so, the solution to factor the quadratic equation above is: (x - 15 ) (x + 30) To summarize, since -15 and 30 multiply by -450 and add up 15, you know that the following is true: x2 + 15x - 450 = (x - 15 ) (x + 30)  Multiply To One Number and Add Up To Another

Did you find the information on this page useful? Here you can solve a similar problem. What two numbers multiply to and add to  What two numbers multiply to -450 and up to 35?

Here is the next math problem we have solved for you on our list.

Step-by-step explanation:

Answer:

printer 404 computer 808

Step-by-step explanation:

let the price of computer be c and printer be p

c+p=1212

c=2p

2p+p=1212

3p=1212

p=1212/3 =404

c=2p=2x404=808

Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

The lowest score you can earn and still be qualified for an interview is approximately 67.2.

To find the lowest score you can earn and still be qualified for an interview, we need to determine the score that corresponds to the top 10% of scores.

From the problem statement, we know that the scores are normally distributed with a mean of 80 and a standard deviation of 10. We can use the cumulative distribution function (CDF) of the normal distribution to find the score that corresponds to the top 10%.

Using a table or calculator for the standard normal distribution, we can find the z-score that corresponds to the top 10%:

P(Z > z) = 0.1

Z = invNorm(0.1) ≈ -1.28

Here, P(Z > z) is the probability that a random variable from a standard normal distribution is greater than z, and invNorm(0.1) represents the inverse of the CDF of the standard normal distribution evaluated at 0.1, which gives us the z-score corresponding to the top 10%.

Now, we can use the formula for standardizing a normal distribution to find the score that corresponds to this z-score:

z = (x - μ)/σ

where x is the score we want to find, μ is the mean of the distribution (80), and σ is the standard deviation of the distribution (10).

Substituting the values, we have:

-1.28 = (x - 80)/10

Solving for x, we get:

x = (-1.28 * 10) + 80 ≈ 67.2

Therefore, the lowest score you can earn and still be qualified for an interview is approximately 67.2.

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The direct method of Lyapunov is a technique used in the analysis of the stability of a dynamical system. It involves the use of a Lyapunov function to determine whether a system is stable or not.

A Lyapunov function is a scalar function V(x) that is defined on the state space of a dynamical system, where x is the state of the system. The function is chosen such that it is positive definite, i.e., V(x) > 0 for all x except possibly at the origin, where V(x) = 0. The time derivative of the Lyapunov function along the trajectories of the system, denoted by V'(x), is also chosen to be negative definite or negative semi-definite, i.e., V'(x) < 0 or V'(x) ≤ 0 for all x except possibly at the origin.

The direct method of Lyapunov uses this Lyapunov function to determine the stability of the system. If a Lyapunov function can be found that satisfies the above conditions, then the system is said to be stable or asymptotically stable, depending on whether V'(x) is negative definite or negative semi-definite, respectively. If a Lyapunov function cannot be found, then the stability of the system cannot be determined using this method.

In addition to determining stability, the direct method of Lyapunov can also be used to determine instability. If a Lyapunov function can be found that satisfies the above conditions, but with V'(x) positive definite or positive semi-definite instead of negative definite or negative semi-definite, respectively, then the system is unstable.

Overall, the direct method of Lyapunov provides a powerful tool for analyzing the stability of a wide range of dynamical systems, including linear and nonlinear systems, time-invariant and time-varying systems, and continuous and discrete-time systems.

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We are asked to find the proportion of mild cases that were effectively dealt with using treatment A. First we will find the total number of cases that were dealt with using treatment A, that is:

Fr

Answer:

  19%

Step-by-step explanation:

You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.

The change from February to March is given as 7%.

The change from March to April is 500 bottles. In terms of the February quantity, this is ...

  500/4100 × 100% ≈ 12.2%

Then the total of changes from February to April is ...

  change = 7% +12.2% = 19.2% ≈ 19%.

The number of bottles manufactured increased by about 19% from February to April.

__

Additional comment

When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.

Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.

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Answer:

Step-by-step explanation:

 Let H represent the whole number of hours that the plumber works.

given that the fixed cost is $65

and the hourly cost is $28

also given that Anand has a total of $250 with him

the total cost can be expressed in terms of the number of hours H as

250=65+28H

we can now solve for H

250-65=28H

185=28H

divide both sides by 28

H=185/28

H=6.60714285714

"The plumber only charges for a whole number of hours."

So the number of hours Anand can afford is 6hours

Answer:

Anand can afford is 6hours

Step-by-step explanation:

Let H represent the whole number of hours that the plumber works.

given that the fixed cost is $65

and the hourly cost is $28

also given that Anand has a total of $250 with him

the total cost can be expressed in terms of the number of hours H as

250=65+28H

we can now solve for H

250-65=28H

185=28H

divide both sides by 28

H=185/28

H=6.60714285714

"The plumber only charges for a whole number of hours."

So the number of hours Anand can afford is 6hours