The complex numbers $z$ and $w$ satisfy $|z| = |w| = 1$ and $zw \ne -1.$


(Prove that $\overline{z} = \frac{1}{z}$ and $\overline{w} = \frac{1}{w}.$

To verify that a matrix A satisfies the conditions A € M2x2(R), A = [a b; c d], and det(A) = 0, we can use the formula for the determinant of a 2x2 matrix:

det(A) = ad - bc

In this case, since det(A) = 0, we have:

ad - bc = 0

This formula allows us to check whether a given matrix satisfies the given conditions.

To find three matrices A when a = 5 and det(A) = 27, we can use the formula:

ad - bc = 27

Let's assume b = 1, c = 0, and d = 27/a.

Substituting these values into the formula, we get:

5 * (27/a) - 1 * 0 = 27

135/a = 27

a = 135/27

a = 5

Therefore, one possible matrix A that satisfies the conditions is:

A = [5 1; 0 27/5]

Similarly, we can find two more matrices by choosing different values for b, c, and d, as long as the determinant condition is satisfied.

Now, let's suppose B is a matrix such that det(B) = det(A):

B = [p q; r s]

To show that det(B) = det(A), we can equate their determinants:

det(B) = det(A)

ps - qr = ad - bc

Since we already know that ad - bc = 0, we can conclude that:

ps - qr = 0

This equation shows that the determinant of B is also zero, satisfying the condition det(B) = 0.

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The probability that the sample mean body temperature will be between 36.5° and 37.10° can be determined using the z-score and the standard normal distribution table.

First, we need to calculate the z-scores for both temperatures using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

For the lower temperature of 36.5°:

z1 = (36.5 - 36.8) / (0.62 / √19)

For the higher temperature of 37.10°:

z2 = (37.10 - 36.8) / (0.62 / √19)

Next, we look up the corresponding probabilities associated with these z-scores in the standard normal distribution table. Subtracting the probability of the lower z-score from the probability of the higher z-score will give us the probability of the sample mean body temperature falling between the two values.

Let's calculate the z-scores:

z1 = (36.5 - 36.8) / (0.62 / √19) ≈ -1.350

z2 = (37.10 - 36.8) / (0.62 / √19) ≈ 0.775

Now, we look up the probabilities associated with these z-scores in the standard normal distribution table. The probability corresponding to z1 is approximately 0.0885, and the probability corresponding to z2 is approximately 0.7794.

Finally, we subtract the lower probability from the higher probability:

P(36.5° ≤ sample mean ≤ 37.10°) = 0.7794 - 0.0885 ≈ 0.6909

Therefore, the probability that the sample mean body temperature will be between 36.5° and 37.10° for a sample size of 19 people is approximately 0.6909.

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The average of a sample of high daily temperature, the 90% confidence interval for the average temperature in the desert, based on the given sample data, is within a specific range.

To calculate the 90% confidence interval, we can use the formula:

Confidence Interval = Average ± (Critical Value) * (Standard Deviation / √Sample Size)

Since the sample size is 26 and we want a 90% confidence interval, we need to determine the critical value for a 90% confidence level. By referring to a t-distribution table or using statistical software, we can find that the critical value for a 90% confidence level with a sample size of 26 is approximately 1.708.

Substituting the values into the formula, we get:

Confidence Interval = 114 ± (1.708) * (5 / √26)

Calculating this expression, we obtain the confidence interval for the average temperature. The lower bound of the interval will be 113.36 degrees F, and the upper bound will be 114.64 degrees F. Therefore, we can state that we are 90% confident that the true average temperature in the desert falls within the range of 113.36 to 114.64 degrees F, based on the given sample data.

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Answer:

The equation of the line that passes through the given points is ;

7y = -x + 12

Step-by-step explanation:

Here, we want to get the equation of the line that passes through the given points

The general equation form

is;

y = mx + b

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

Now, let us substitute the x and y coordinate values of each of the points;

for (-2,2); we have

2 = -2m + b

b = 2m + 2 •••••(i)

for F;

1 = 5m + b

b = 1-5m ••••••(ii)

Equate both b

1-5m = 2m + 2

1-2 = 2m + 5m

7m = -1

m = -1/7

Recall;

b = 2m + 2

b = 2(-1/7) + 2

b = -2/7 + 2

b = (-2 + 14)/7 = 12/7

The equation of the line is thus;

y = -1/7x + 12/7

Multiply through by 7

7y = -x + 12

The length M is 12

The measure of the angle BEC is 102

The measure of the arc AB is 128

The length PQ is 18.3

The length M can be calculated using

M² = 8 * (8 + 10)

So, we have

M² = 144

Take the square roots

M = 12

The measure of the angle BEC can be calculated using

BEC = 1/2 * (BC + AD)

So, we have

BEC = 1/2 * (156 + 48)

Evaluate

BEC = 102

The measure of the arc ABcan be calculated using

AB = 180 - 2 * BC

So, we have

AB = 180 - 2 * 26

Evaluate

AB = 128

The length PQ can be calculated using

x² = (12 + 8)² - 8²

So, we have

x² = 336

Take the square roots

x = 18.3

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Answer:

14

Step-by-step explanation:

separate the figure into two  shapes. On the little one is 2x1 which the answer is 2 then on the larger shape is 6x2 which is 12 then you add 12+2 and then you get your answer

Answer:

James will spend $119.94

Step-by-step explanation:

Multiply $19.99 by 6.

$19.99 x 6 = $119.94

The expectation is 0.25.

Poisson distribution is a discrete distribution which is used to model events that occur in the specified interval of time. Parameter of Poisson distribution is [tex]\lambda[/tex], which describes the average number of events occurring in the given interval of time.

The given information is:

E(X) = In 2

X ~ Poi( [tex]\lambda[/tex] ) where  [tex]\lambda[/tex], = In 2

[tex]f(x)=\frac{e^-^\lambda\lambda^x}{x!}[/tex]

It is known that cos([tex]\pi x[/tex])[tex]=(-1)^x[/tex], for x = 1, 2, 3...

To calculate the value of the required expectation.

[tex]E(cos(\pi x))=\sum^\infty_x_=_0 (-1)^xf(x)\\\\E(cos(\pi x))=\sum^\infty_x_=_0(-1)^x\frac{e^-^\lambda(\lambda)^x}{x!}\\ \\E(cos(\pi x))=e^-^\lambda\sum^\infty_x_=_0\frac{(-\lambda)^x}{x!}[/tex]

Expansion of exponential function is as follows

[tex]e^a=\sum^\infty_x_=_0\frac{(a)^x}{x!}[/tex]

Therefore, further calculation can be done as

[tex]E(cos(\pi x))=e^-^\lambda \,e^-^\lambda\\\\E(cos(\pi x))=e^-^2^\lambda\\\\E(cos(\pi x))=e^-^2^(^I^n^ 2^)\\\\E(cos(\pi x))=e^(^I^n^ 2^)^2\\\\E(cos(\pi x))=\frac{1}{4}[/tex]

Therefore, the expectation is 0.25.

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The given question is incomplete, complete question is:

Let X be a Poisson random variable with E(X) =In 2. Calculate [tex]E[cos(\pi x)][/tex].

Answer:

The difference between the absolute values of these two temperatures is 19°F.

Step-by-step explanation:

|-13| = 13

|6| = 6

13 + 6 = 19°F

Answer:

19

Explanation:

an absolute value is the value of a number without considering its sign.

thus, we can calculate the difference as such:

6 - (- 13) = 6 + 13 = 19

the difference between the absolute values of these two temperatures is 19.

i hope this helps! :D

Answer:

Linear: The first and third one. (0,5) & (1,1)

Exponential: The second one (above). (-2, 1/16)

Quadratic function: The last one (below). (-3,35)

Step-by-step explanation:

Answer:

am not sure but

Step-by-step explanation:

since they are similar they must have similar ratio

so 12/4 =3/1

so 3:1

4*3=12

for other sides I think

9*3 =27

and

6*3=18

y=27

x=18

Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

to me when you divide with a farction it already is divsion but when u use it in divson i make nubmer bigger (if it's the 2nd number ) so thats way 2÷1/2=4

There are 30 of the cupcakes are vanilla.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

We have to given that;

Joanne is making 48 cupcakes for a bake sale.

And, 1/4 of the cupcakes are chocolate.

1/8 of the cupcakes are strawberry.

The remainder of the cupcakes are vanilla.

Hence, We get;

Amount of the cupcakes are vanilla is,

⇒ 48 - (1/4 of 48 + 1/8 of 48)

⇒ 48- (12 + 6)

⇒ 48 - 18

⇒ 30

Thus, There are 30 the cupcakes are vanilla.

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Answer: 17.29 cm

Step-by-step explanation:

Given

The dimension of a rectangular prism is [tex]13\ cm\times 9\times \ cm\times 7\ cm[/tex]

The longest line which can be drawn in the rectangular prism is diagonal across the body which is shown in the figure

Length of rectangular is given by

[tex]\Rightarrow L=\sqrt{l^2+b^2+h^2}[/tex]

Putting values

[tex]\Rightarrow L=\sqrt{13^2+9^2+7^2}\\\Rightarrow L\sqrt{169+81+49}=\sqrt{299}\\\Rightarrow L=17.29\ cm[/tex]

Answer:

17.3

Step-by-step explanation:

The dimension of a rectangular prism is 13x9x7

you would normally get 17.29 but  you have to round

which gives us the answer= 17.3

By applying the the FOIL method, which stands for First, Outer, Inner, Last  we obtained the result -84 + 80i for (4 + 10i)^2.

To calculate (4 + 10i)^2, we can:

First, we multiply the first terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Next, we multiply the outer terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Then, we multiply the inner terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Finally, we multiply the last terms of each binomial:

(4 + 10i) * (4 + 10i) = 100i^2

We know that i^2 is equal to -1, so we can substitute that in:

100(-1) = -100

Putting it all together, we get:

(4 + 10i)^2 = 16 + 40i + 40i + (-100)

= -84+80i

Therefore, by applying this method for squaring a complex number, we obtained the result -84 + 80i for (4 + 10i)^2.

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The quotient of (2x^2 + 5x + 8) divided by (x + 2) is 2x + 1, and the remainder is 12.

To divide the polynomial[tex](2x^2 + 5x + 8) by (x + 2)[/tex] using synthetic division, we follow these steps:

1. Set up the synthetic division table by placing the divisor (x + 2) on the left side of the table and writing down the coefficients of the dividend (2x^2 + 5x + 8) in descending order on the top row of the table.

  | 2   5   8

-2 |

2. Bring down the first coefficient, which is 2, from the top row and write it underneath the horizontal line.

 | 2   5   8

-2 | 2

3. Multiply the divisor (-2) by the number beneath the line (2) and write the result in the next column.

  | 2   5   8

-2 | 2  -4

4. Add the result to the next coefficient in the top row and write the sum in the next column.

  | 2   5   8

-2 | 2  -4   4

5. Repeat steps 3 and 4 until all coefficients have been processed.

  | 2   5   8

-2 | 2  -4   4

    ___________

     2   1  12

The last number in the bottom row, 12, is the remainder. The other numbers in the bottom row represent the coefficients of the quotient.

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(a) There are 840 distinguishable permutations of the letters in the word "initial." (b) There are 180 distinguishable permutations of the letters in the word "Hawaii." (c) There are 420 distinguishable permutations of the letters in the word "decreed."

(a) For the word "initial," we have a total of 7 letters, with 2 "I"s, and 1 occurrence of each of the remaining letters. Applying the formula, we get:

n! / (3!1!1!1!1!) = 7! / (3!1!1!1!1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1 ×1 × 1 × 1 × 1) = 840

(b) For the word "Hawaii," we have a total of 6 letters, with 1 "H," 2 "A"s, and 2 "I"s. Applying the formula, we get:

n! / (1!2!1!2!) = 6! / (1!2!1!2!) = (6 × 5 × 4 × 3 × 2 × 1) / (1 × 2 × 1 × 2 × 1 × 1) = 180

(c) For the word "decreed," we have a total of 7 letters, with 2 "E"s, 3 "D"s, and 1 occurrence of each of the remaining letters. Applying the formula, we get:

n! / (2!3!1!1!) = 7! / (2!3!1!1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1 × 3 × 2 × 1 × 1 × 1) = 420

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The general solution to the given differential equation, (x³+ ye^xy) dx + (xe^xy-sin3y) = 0, involves two steps: identifying an integrating factor and then integrating the resulting equation. The integrating factor is found to be e^(3xy).  We find F(x, y) = ∫(e^(x^4/4 + ye^xy) (x³+ ye^xy)) dx + g(y),

To solve the given differential equation, we first determine an integrating factor. Since the coefficient of dx, x³ + ye^xy, is a function of x and y only, we can identify the integrating factor as e^(∫(x³ + ye^xy) dx). Evaluating the integral, we obtain e^(x^4/4 + y∫e^xy dx). Simplifying further, the integrating factor is found to be e^(x^4/4 + ye^xy).

Next, we multiply the entire differential equation by this integrating factor. This step transforms the equation into an exact differential equation, which is easier to solve. Multiplying through, we have e^(x^4/4 + ye^xy) (x³+ ye^xy) dx + e^(x^4/4 + ye^xy) (xe^xy-sin3y) = 0.

After multiplying, we can observe that the left-hand side of the equation is now the total derivative of a function F(x, y). By integrating with respect to x, we find F(x, y) = ∫(e^(x^4/4 + ye^xy) (x³+ ye^xy)) dx + g(y), where g(y) is the constant of integration with respect to x. Finally, the general solution is obtained by solving for y in terms of x and the constant g(y).

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The error of rejecting the null hypothesis when it is actually true is known as a Type I error or alpha error. It represents the incorrect rejection of a null hypothesis that is true in reality.

Type I errors are associated with the significance level (alpha) chosen for a statistical test and occur when the test incorrectly concludes that there is a significant effect or relationship when there isn't one.

In hypothesis testing, the null hypothesis represents the assumption of no effect or no relationship between variables. The alternative hypothesis, on the other hand, suggests the presence of an effect or relationship. The significance level (alpha) is the threshold set by the researcher to determine the probability of rejecting the null hypothesis.

A Type I error occurs when the null hypothesis is true, but the statistical test incorrectly rejects it, leading to a false conclusion of a significant effect or relationship. This error is also known as a false positive. The probability of making a Type I error is denoted by alpha.

Type I errors are considered undesirable because they lead to incorrect conclusions and may result in wasted resources or inappropriate actions based on flawed evidence.

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Answer:

V = 135π in3; S = 105π in2

Step-by-step explanation:

The conditions that are required to validate the use of t for the significance test would be:

D). l and ll only

"Regression Line" is described as the line that most adequately fits the provided data in order to display the efficacy of the model.

In the given situation, the I and II exemplify the conditions which will validate the process for the significance test.

The normal distribution, and among x and y and the independent response of y over x display that it suits the data successfully.

Thus, option D is the correct answer.

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Answer: Answer is THREE only.

Step-by-step explanation: Took the test. Also for the other guy's solution, he said one and two were REQUIRED. Make sure you read the question first ya'll. He still answered it.

what? bro I am confused is this a question?

The probability that exactly ten requests are received during a particular 2-hour period, with a rate of α = 4 requests per hour, is approximately 0.0194 or 1.94%.

Let's denote the random variable X as the number of requests received during a 2-hour period. Since the rate of requests per hour is α = 4, we can calculate the rate for a 2-hour period as λ = α × 2 = 4 × 2 = 8.

The probability mass function (PMF) of a Poisson distribution is given by the formula:

[tex]P(X = k) = (e^{-\lambda} \times \lambda ^k) / k![/tex]

where e is Euler's number (approximately 2.71828), λ is the average number of events (rate) during the given time period, and k is the number of events we are interested in.

In this case, we want to find the probability of exactly ten requests, so k = 10 and λ = 8. Plugging these values into the formula, we get:

P(X = 10) = (e⁻⁸ * 8¹⁰) / 10!

To calculate this probability, we need to evaluate the values of e⁻⁸, 8¹⁰, and 10!.

e⁻⁸ is approximately 0.0003354626 (rounded to 10 decimal places).

8¹⁰ is equal to 1,073,741,824.

10! (10 factorial) is equal to 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, which is 3,628,800.

Plugging these values back into the formula, we have:

P(X = 10) = (0.0003354626 * 1,073,741,824) / 3,628,800

Evaluating this expression gives us the probability that exactly ten requests are received during the two-hour period.

P(X = 10) ≈ 0.0194 or 1.94%.

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Answer:

(x,y) = (-1,3)

Step-by-step explanation:

hope this helps!

Answer:

w = 8, y = 4.

Step-by-step explanation:

i think this is right i am not sure

Answer:

[tex]x = 8 \\ y = 4[/tex]

Step-by-step explanation:

Let x be the number of one point shots, and y the number of two point shots.

We have

[tex]x + y = 12 \\ y = 12 - x[/tex]

And

[tex]x + 2y = 16[/tex]

Substituting the first equation in we get

[tex]x + 2(12 - x) = 16 \\ x + 24 - 2x = 16 \\ - x = - 8 \\ x = 8[/tex]

Since

[tex]y = 12 - x \\ y = 12 - 8 = 4[/tex]

The probability of getting exactly seven fours in ten rolls of a fair die is approximately 0.0574.

To determine the probability of exactly seven fours in 10 rolls of a fair die, we can use the binomial distribution formula:

P(X = k) = (nCk) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k successes (in this case, rolling a four) in n trials (in this case, rolling a die 10 times),

nCk is the number of combinations of n items taken k at a time,

p is the probability of success on a single trial (rolling a four), and

(1-p) is the probability of failure on a single trial (not rolling a four).

In this case, n = 10, k = 7, p = 1/6 (since there is a 1/6 chance of rolling a four on a fair die), and (1-p) = 5/6.

Plugging these values into the formula:

P(X = 7) = (10C7) * (1/6)^7 * (5/6)^(10-7)

Calculating the combinations:

(10C7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120

Substituting the values:

P(X = 7) = 120 * (1/6)^7 * (5/6)^(10-7)

Calculating the probability:

P(X = 7) = 120 * (1/6)^7 * (5/6)^3 ≈ 0.0595

Therefore, the probability that exactly seven fours will appear in 10 rolls of a fair die is approximately 0.0595 (rounded to 4 decimal places).

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Answer:

31 degrees

Step-by-step explanation:

1. since angle x and angle y are congruent, and segment xw and segment yw are congruent, you can assume that angle xzw and angle wzy are also congruent.

2. set angle xzw and angle wzy equal to each other

8x-1 = 5x+11

3. combine like terms

3x = 12

4. simplify to find the value of x

x = 4

5. plug x into the equation to find the degree of angle wzy

5(4)+11

20+11

=31 degrees