Person A wishes to set up a public key for an RSA cryptosystem. They choose for their prime numbers p = 41 and q = 47. For their encryption key, they choose e = 3. To convert their numbers to letters, they use A = 00, B = 01,... 1. What does Person A publish as their public key? 2. Person B wishes to send the message JUNE to person A using two-letter blocks and Person A's public key. What will the plaintext be when JUNE is converted to numbers? 3. What is the encrypted message that Person B will send to Person A? Your answer should be two blocks of four digits each. 4. Person A now needs to decrypt the message by finding their decryption key. What is (n)? 5. Find the decryption key by find a solution to: 3d mod (n) = 1. What is the decryption key? 6. Confirm your answer to the previous part works by computing cd mod n for each block of the encrypted message, and showing it matches the answer to part (b).

Answers

Answer 1

1) Person A publishes their public key as (3, 1927).

2) Converting JUNE to numbers,   J = 09, U = 20, N = 13, E = 04

3) The encrypted message is the pair of blocks: (729, 1121).

4) Person A now needs to decrypt the message by finding their decryption key. The n is 1927.

5) The decryption key is 642

To set up an RSA cryptosystem, Person A needs to perform several steps. Let's go through each step to find the answers to the questions:

1. Finding the public key:

  Person A has chosen prime numbers p = 41 and q = 47.

  Compute n = p * q: n = 41 * 47 = 1927

  The public key consists of the pair (e, n), where e = 3.

  Therefore, Person A publishes their public key as (3, 1927).

2. Converting the message "JUNE" to numbers:

  Using the given conversion scheme A = 00, B = 01, ..., Z = 25:

  J = 09

  U = 20

  N = 13

  E = 04

3. Encrypting the message using Person A's public key:

  To encrypt each two-letter block, we need to calculate c = [tex]m^{e}[/tex] mod n, where m is the plaintext number and e is the encryption key.

  For the first block "JU":

    For J (m = 09): c1 = 09³ mod 1927 = 729

    For U (m = 20): c2 = 20³ mod 1927 = 16000 mod 1927 = 1121

  The encrypted message is the pair of blocks: (729, 1121).

4. Finding the decryption key:

  To decrypt the message, Person A needs to find the decryption key d, where 3d mod n = 1.

  Since n = 1927, we need to solve the equation 3d mod 1927 = 1 for d.

  We can use the Extended Euclidean Algorithm to find the modular inverse of 3 modulo 1927.

  Using the Extended Euclidean Algorithm, we get:

  1927 = 3 * 642 + 1

  1 = 1927 - 3 * 642

  Therefore, the decryption key is d = 642.

5. Computing the decryption key:

  We found that d = 642 in the previous step.

6. Confirming the decryption works:

  To confirm that the decryption works, we need to compute [tex]c^{d}[/tex] mod n for each block of the encrypted message and check if it matches the corresponding plaintext number.

For the first block (c1 = 729):

Compute [tex]c_{1} ^{d}[/tex] mod n: 729⁶⁴² mod 1927 = 09 (which matches the first plaintext number "J").

For the second block (c2 = 1121):

Compute [tex]c_{2} ^{d}[/tex] mod n: 1121⁶⁴² mod 1927 = 20 (which matches the second plaintext number "U").

Therefore, the decryption process works correctly, and the decrypted message is "JUNE," which matches the original plaintext.

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Related Questions

50 POINTS!! Please help tysm :) image is attached (sorry about the quality); find the value of x. the answer key says x=10, but I'm not sure how to get there.

please don't put an unrelated answer or just repeat the answer for the points :) I would like a step by step explanation ​

Answers

Answer:

[tex] \: x = 10[/tex]

Step-by-step explanation:

prefer the attachment

according to the question

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{8 + 6}{17.5} [/tex]

simplify addition:

[tex] \displaystyle \: \frac{6}{17.5-x} = \frac{14}{17.5 } [/tex]

simplify fraction;

[tex] \displaystyle \: \frac{6}{17.5 - x} = 0.8[/tex]

cross multiplication:

[tex]\displaystyle 6 = 14 - 0.8x[/tex]

cancel 14 from both sides:

[tex] \displaystyle - 8= - 0.8x[/tex]

divide both sides by -0.8:

[tex] \therefore \: x = 10[/tex]

Let T : P3 right arrow P3 be the linear transformation satisfying T(1) =2x^2 + 7 , T(x) = -2x + 1, T(x^2) = -2x^2 + x - 2. Find the image of an arbitrary quadratic polynomial ax^2 + bx + c . T(ax^2 + bx + c) =___

Answers

The image of the given arbitrary quadratic polynomial is T([tex]ax^2 + bx + c[/tex]) = [tex](-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex].

Find the image of the arbitrary quadratic polynomial?

To find the image of the arbitrary quadratic polynomial [tex]ax^2 + bx + c[/tex] under the linear transformation T, we can express the polynomial in terms of the standard basis of P3, which is {[tex]1, x, x^2[/tex]}.

The polynomial [tex]ax^2 + bx + c[/tex] can be written as a linear combination of the basis vectors:

[tex]ax^2 + bx + c = a(x^2) + b(x) + c(1)[/tex]

Since we know the values of T(1), T(x), and T([tex]x^2[/tex]), we can substitute them into the expression:

[tex]T(ax^2 + bx + c) = aT(x^2) + bT(x) + cT(1)[/tex]

Substituting the given values:

[tex]T(ax^2 + bx + c) = a(-2x^2 + x - 2) + b(-2x + 1) + c(2x^2 + 7)[/tex]

Simplifying the expression:[tex]T(ax^2 + bx + c) = (-2ax^2 + ax - 2a) + (-2bx + b) + (2cx^2 + 7c)[/tex]

Combining like terms:

[tex]T(ax^2 + bx + c) = (-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex]

Therefore, the image of the arbitrary quadratic polynomial [tex]ax^2 + bx + c[/tex] under the linear transformation T is [tex](-2a + 2c)x^2 + (-2b + a)x + (-2a + b + 7c)[/tex].

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What is 12x3 – 9x2 – 4x + 3 in factored form?

(
x2 –
)(
x –
)

Answers

Answer:

(√3·x - 1)(√3·x + 1)(4x - 3)

Step-by-step explanation:

Note that the last two coefficients are -4 and +3, and the associated factor is (4x - 3).

The first two terms are

12x^3 - 9x^2, which become 3x(4x^2 - 3x) through factoring and then 3x^2(4x - 3).  

Therefore, 12x3 – 9x2 – 4x + 3 can be rewritten as:

                   (4x - 3)(3x^2 - 1).  

It's possible to factor 3x^2 - 1, even though 3 is not a perfect square.  Write 3x^2 - 1 as (√3·x - 1)(√3·x + 1)    

Then 12x3 – 9x2 – 4x + 3 = (√3·x - 1)(√3·x + 1)(4x - 3)

Answer:

( 3 x2 –  1 )( 1  ⇒ 4x –  3 )

Step-by-step explanation:

I did it lol

Some trapezoid has an area of 213.86 yd2 and a height of 18 yd. If one of the bases measures 5 yd, then the other base must measure ___ yd.

Answers

Answer:

The other base measure 18.76 yd.

Step-by-step explanation:

A = h ((a+b) / 2)

213.86 = 18 ((5 + b) /2)

(5 + b) /2 = 11.88

5 + b = 23.76

b = 18.76 yd

Which number line shows 1.5 graphed?

Answers

Answer:

The third one down

Step-by-step explanation:

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 7. Using the empirical rule, what percentage of males in the town have a systolic blood pressure between 98 and 112?

Answers

Answer:

Answer:

68%

Step-by-step explanation:

The percentage of males in the town who have systolic blood pressure between 98 and 112 is 68%.

What is a normal distribution?

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

For males in a certain town, the systolic blood pressure is normally distributed with a mean of 105 and a standard deviation of 7.

68 percent of the data is within one standard deviation of the mean, i.e. between μ - σ and μ + σ.

μ - σ = 105 - 7 = 98

μ + σ = 105 + 7 = 112

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2 7/9 × 1 1/5 ÷ 2 1/2

Answers

Answer

5/36 ([tex]\frac{5}{36}[/tex])

Answer:

22/35

Step-by-step explanation:

27/9 = 3

3 × 11/5 ×2/21

=22/35

List the measurements with units of kilometers, centimeters, and
millimeters that are equal to 4 meters.

Answers

Answer:

0.004 km; 400 cm; 4000 mm

Step-by-step explanation:

1 km = 1000 m

1 = (1 km)/(1000 m)

4 m * (1 km)/(1000 m) = 4/1000 km = 0.004 km

1 m = 100 cm

1 = (100 cm)/(1 m)

4 m * (100 cm)/(1 m) = 400 cm

1 m = 1000 mm

1 = (1000 mm)/(1 m)

4 m * (1000 mm)/(1 m) = 4000 mm

Answer: 0.004 km; 400 cm; 4000 mm

Will mark brain list

Answers

it’s either 65 or 70
I think the answer is 70

Use cylindrical coordinates to evaluate

∫∫∫ xyzdv

where E is the solid in the first octant that lies under the paraboloid. z= 4-z² - y².

Answers

To evaluate the triple integral ∫∫∫ xyzdv using cylindrical coordinates, we need to express the integral in terms of the cylindrical coordinates (ρ, φ, z).

The given solid E lies under the paraboloid z = 4 - z² - y². In cylindrical coordinates, this paraboloid equation becomes z = 4 - ρ² - y².

To set up the triple integral, we need to determine the limits of integration for each variable.

Since the solid lies in the first octant, the limits of integration are as follows:

ρ: from 0 to some value ρ₁

φ: from 0 to π/2

z: from 0 to the upper limit of the paraboloid, which is given by the equation z = 4 - ρ² - y².

Now we can set up the triple integral:

∫∫∫ xyzdv = ∫₀^(π/2) ∫₀^ρ₁ ∫₀^(4-ρ²-y²) (ρcosφ)(ρsinφ)z dz dρ dφ

Simplifying the integrand and integrating, we can evaluate the triple integral to obtain the final result.

Note: The specific value of ρ₁ and the complexity of the integration depend on the precise shape of the solid E, which is not provided in the given information. Therefore, the final evaluation of the integral requires additional information about the solid E.

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A bakery sells glazed donuts for $1.09 each. Cinnamon bagels and onion bagels are $1.59 each. Max buys x donuts, y cinnamon bagels, and z onion bagels. Which expression represents the total amount Max spent at the bakery?
A.
1.09x + 1.59yz
B.
1.09x + 1.59y + 1.59z
C.
1.09x + 3.18(y + z)
D.
(1.09 + 1.59)(x + y + z)

Answers

Answer:

The answer is B.

Step-by-step explanation:

Answer:

B.

1.09x + 1.59y + 1.59z

I hope this helps

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XS Exponential growth and decay: word problems UKO
If a city with a population of 100,000 doubles in size every 28 years, what will the population
be 56 years from now?

Answers

Answer:

400,000

Step-by-step explanation:

Calculate the doubling time period-

Doubling time period(t)=

doubling time period(t)= 2

Calculate the new population using the doubling time formula below where t is the number of doubling periods:

Population = Initial Population * [tex]2^{t}[/tex]

Population = 100000 * [tex]2^{2}[/tex]

Population = 100000 * 4

Angel's Ice Cream Shop sold 235 scoops of marshmallow ice cream yesterday, and they sold 265 scoops of all the other flavors combined. What percentage of the ice cream they sold yesterday was marshmallow ice cream?

Choices:
A: 53%
B: 11%
C: 89%
D: 47%

(Please help, 20 points!)

Answers

Answer:

C : 89%

Step-by-step explanation:

If they sold 235 scoops of marshmallow ice cream and in total of all day they sold a total of 265 scoops of ice cream. 265 - 235 = 30

My answer is C : 89%

1.in an electrical circuit the current,I amperes, is directly proportional to the square root of the power,p watts.
I=4 when p=100
A) find an equation connecting I and P.
B) calculate I when P= 144

Answers

Answer:

A for ever I  P=25

b. 5.76

Step-by-step explanation:

Details Adults in various age groups were asked if they voted in a recent election. The results were as indicated below. Age Voted? Under 30 30 - 50 Over 50 Yes 35 64 25 56 19 1 No A test is conducted at the a = 0.100 significance level to determine whether age and voting behavior are independent Fill in the expected"table for this independence test. Age Voted? Under 30 30 - 50 Over 50 Yes 88 No Find the value of the chi-square statistic for this independence test.

Answers

The value of the chi-square statistic for this independence test is approximately 82.23.

To calculate the expected values for the independence test, we need to determine the expected number of individuals in each category if age and voting behavior were independent. We can calculate the expected values using the formula:

Expected value = (Row total * Column total) / Total number of observations

Let's calculate the expected values for each category:

Age Voted?         Under 30    30 - 50    Over 50    Total

Yes                       35                  64               25               124

No                        56                  19                 1                 76

Total                     91                  83               26               200

Expected value for "Yes" under "Under 30" category:

Expected value = (91 * 124) / 200 = 56.57 (approximately 57)

Expected value for "No" under "Under 30" category:

Expected value = (91 * 76) / 200 = 34.82 (approximately 35)

Similarly, calculate the expected values for the other categories:

Expected values for "Yes" in the "30 - 50" and "Over 50" categories:

30 - 50: 83 * 124 / 200 ≈ 51.77 (approximately 52)

Over 50: 26 * 124 / 200 ≈ 16.12 (approximately 16)

Expected values for "No" in the "30 - 50" and "Over 50" categories:

30 - 50: 83 * 76 / 200 ≈ 31.63 (approximately 32)

Over 50: 26 * 76 / 200 ≈ 9.88 (approximately 10)

The expected table for the independence test is as follows:

Age Voted?         Under 30    30 - 50    Over 50      Total

Yes                       57                  52               16               124

No                        35                  32               10                76

Total                     91                  83               26               200

To find the chi-square statistic for this independence test, we use the formula:

χ² = Σ [(Observed value - Expected value)² / Expected value]

Now, let's calculate the chi-square statistic by summing the values for each category:

χ² = [(35 - 57)² / 57] + [(64 - 52)² / 52] + [(25 - 16)² / 16] + [(56 - 35)² / 35] + [(19 - 32)² / 32] + [(1 - 10)² / 10]

χ² = 23.09 + 2.46 + 5.06 + 40.69 + 4.53 + 6.4

χ² ≈ 82.23

Therefore, the value of the chi-square statistic for this independence test is approximately 82.23.

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ANSWER ASAP
5. A square has a 40-cm diagonal. How long is each side of the square? Round your answer to the nearest tenth of a centimeter.
Hint - draw a picture.
O 27.1 cm
O 28.3 cm
O O O
O 29.5 cm
O 30.7 cm

Answers

Answer:30.7 mybe i am not 100%

Step-by-step explanation:first you would devide 40 by 4 and then you would round

X squared minus 3x minus 10 equals 0

Answers

Answer:

The image below explains read for the steps Your Welcome :)

Find integers s, t, u, v such that 1485s +952t = 690u + 539v. b 211, 307, 401, 503 are four primes. Find integers a, b, c, d such that 211a + 307b + 401c + 503d = 0 c Find integers a, b, c such that

Answers

One possible values of the integers is: a = 8020k, b = -10025k, and c = 401k where k is an arbitrary integer.

To find integers s, t, u, v such that 1485s + 952t = 690u + 539v, we can use the Extended Euclidean Algorithm. First, we compute the greatest common divisor of 1485 and 952:

gcd(1485, 952) = gcd(952, 533) = gcd(533, 419) = gcd(419, 114) = gcd(114, 91) = gcd(91, 23) = 23

Using the algorithm, we can write 23 as a linear combination of 1485 and 952:

23 = (-17) * 1485 + (27) * 952

Multiplying both sides by (30), we get:

690 = (-510) * 1485 + (810) * 952

and

539 = (357) * 1485 + (-567) * 952

Therefore,

s = -510u + 357v

t = 810u -567v

where u and v are arbitrary integers.

For the second part of the question, we need to find integers a, b, c, d such that:

211a + 307b +401c +503d =0

One possible way is:

a = -262

b = -169

c = 122

d = 97

To check that this, we substitute these values into the equation:

211(-262) +307(-169) +401(122) +503(97) = -55682 -52083 +51122 +50691 =0

Therefore, this is a valid solution.

Finally, for the third part of the question, we need to find integers a, b, c such that:

690a +539b=401c

Using the Extended Euclidean Algorithm, we can write:

gcd(690, 539) = gcd(539, 151) = gcd(151, 86) = gcd(86, 65) = gcd(65, 21) = gcd(21, 2) = 1

and

1 = (20) * 690 + (-25) * 539

Multiplying both sides by 401, we get:

401 = (8020) * 690 + (-10025) * 539

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plzz help meeee



thank you smmmmm

Answers

Answer:A

Step-by-step explanation:

the y-intercept is when x-axis is 0 and that means that hours of jogging is 0 and the y-axis is 1 minunte

Answer:

The first option.

Step-by-step explanation:

The y-intercept is where the line crosses through the y-axis, which, in this case, would be at point (0, 1). The labeling on the left side shows what each number on the y-axis represents, and it would be minutes stretching when not jogging.

hope this helped! :)

To stream Netflix without major interruptions, the desired internet speed should be 75 Mbps. However, network traffic can affect the internet speed. The speed varies by 2 Mbps.Create an absolute value equations that can determine the maximum and minimum internet speeds.What are the maximum and minimum internet speeds?

Answers

Answer:

See, this is what i do not get. equations like this. People now in days would just by faster internet speed. Why would we need to know this if  we will never ever get to use this in our life. Also you could just call the internet cable person. This makes absolutely no since at all. Also who even uses Netflix anymore?

Step-by-step explanation

PLEASE HELP I DON'T UNDERSTAND!!!!!! I WILL MARK!!!

Answers

Answer:

the first one.

Step-by-step explanation:

The answer to the problem is the first answer choice


PLS PLS HELP PLS PLS PLS HELP PLS HELP PLS BOTH OF THEM PLS

Answers

Answer:

16. Right isosceles

17. D

Step-by-step explanation:

The triangle has a right angle this makes it a right trangle. Also all parallelograms are not squares, all rectangles aren't squares and all parallelograms aren't rhombuses.

16. right isosceles

17. C: all rectangles are squares

Construct a formal proof of validity for each of the following arguments.

51) ⁓ A

Conclusion: A ⸧ B

52) C

Conclusion: D ⸧ C

53) E ⸧ (F ⸧ G)

Conclusion: F ⸧ (E ⸧G)

Answers

The conclusion F ⸧ (E ⸧ G) is valid

To construct a formal proof of validity for each of the given arguments, we will use logical inference rules.

⁓ A

Conclusion: A ⸧ B

⁓ A (Premise)

A ⸧ ⁓ A (Conjunction, from 1)

A (Simplification, from 2)

B (Modus ponens, from 3)

Therefore, the conclusion A ⸧ B is valid.

C

Conclusion: D ⸧ C

C (Premise)

D ⸧ C (Implication, from 1)

Therefore, the conclusion D ⸧ C is valid.

E ⸧ (F ⸧ G)

Conclusion: F ⸧ (E ⸧ G)

E ⸧ (F ⸧ G) (Premise)

F ⸧ G (Simplification, from 1)

G ⸧ F (Commutation, from 2)

E ⸧ G (Simplification, from 1)

E ⸧ F (Transposition, from 4)

F ⸧ (E ⸧ G) (Implication, from 5)

Therefore, the conclusion F ⸧ (E ⸧ G) is valid.

In all three arguments, we have successfully constructed formal proofs of validity using logical inference rules, demonstrating that the conclusions are logically valid based on the given premises.

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!
A store is selling electronics
and mark up all the prices by
30%. If the store's cost for a
printer is $25, what is the
customer's cost?
בדד
תחזרי

Answers

Answer:

im guessing 32.5$ but i honestly dont know lol

Step-by-step explanation:

which expression is equivalent to 18 * 12 A) 12 * 18) B) 10*8*12) C) (10+8) * (10+12). Please hurry ​

Answers

Answer:

12*18

Step-by-step explanation:

18*12 is the same as 12*18 and they both equal 216

Verify the equation: (sin x + cos x)(tan x + cot x) = sec x csc x

Answers

Answer:

The equation (sin(x) + cos(x))(tan(x) + cot(x)) = sec(x)csc(x) is not solvable because the two sides are not equal.

A researcher believes that a new training program will increase test scores. Previous research shows that test scores increase 8 points between the first and second administration of the test being used. This researcher believes his training program will cause a significant increase, beyond the expected 8 points. If a paired-samples t test is used by this researcher, what value would he expect to be at the center of the comparison distribution, a distribution of mean differences

Answers

Answer:

value = 8

Step-by-step explanation:

when a paired-samples t test is used by this researcher we will write out the hypothesis as follows

H0: μd ≤ 8  ( null )

Ha: μd >  8 ( alternate )

Given the above Hypothesis

If a paired-sample T test is used by the researcher  the value that would be at the center of the comparison will be 8

5^2 + 4^3 - 21=

Need answer immediately please.​

Answers

Answer:

68

Step-by-step explanation:

Answer: 5^2 + 4^3 - 21= 68

Let X₁, X₂, X₃, ... be i.i.d. variables taking values between +1 and +[infinity] with probability density given by:
f(x) = (λ - 1)/x^λ
for every x ≥ 1 where λ > 1 is an unknown parameter. For x < 1, we assume the probability density to be 0. Estimate λ using maximum likelihood, given X₁ = 3, X₂ = 4, X₃ = 5

Answers

To estimate the unknown parameter λ using maximum likelihood, given X₁ = 3, X₂ = 4, X₃ = 5, we need to find the value of λ that maximizes the likelihood function based on the observed data. The likelihood function represents the probability of observing the given data for different values of λ.

The likelihood function L(λ) is defined as the product of the probability density function evaluated at each observed data point. In this case, we have L(λ) = f(3) * f(4) * f(5), where f(x) is the given probability density function.
Substituting the values into the likelihood function, we have L(λ) = ((λ - 1)/3^λ) * ((λ - 1)/4^λ) * ((λ - 1)/5^λ).
To find the maximum likelihood estimate of λ, we need to maximize the likelihood function. Taking the natural logarithm of the likelihood function (ln L(λ)), we can simplify the problem to finding the value of λ that maximizes ln L(λ).
Taking the derivative of ln L(λ) with respect to λ and setting it to zero, we can solve for the maximum likelihood estimate of λ.
By solving the equation, we can obtain the estimate for λ based on the observed data X₁ = 3, X₂ = 4, X₃ = 5.

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Write an expression to show the following:“Fourteen more than the product of nine and a number”

Answers

14(9•x) X would be the variable, aka the number.
Other Questions
How do the random assignment and multiple regression methodsdiffer in identifying causal effects? Is Game of Thrones based on history or hollywood? Identify and describe the contributions of the Gupta. What did the Gupta build, invent, or create? Annette is a high school student who reads at the level of a typical third grader. She wants to get her driver's license, but is unable to read the driver's manual or the questions on the driving test. For purposes of driver training, annette would be considered to have Which of the following was responsible for successfully carrying out the Boston Tea Party? A. The Sons of Liberty B. Loyalists C. The Whig Party a system does 566 kj of work and loses 246 kj of heat to the surroundings. what is the change in internal energy, , of the system? note that internal energy is symbolized as in some sources. An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 9:00 A.M. will have assembled f(x)=x3+12x2+15x units x hours later. a) Derive a formula for the rate at which the worker will be assembling units after x hours. r(x)=_______. b) At what rate will the worker be assembling units at 10:00 A.M.? The worker will be assembling ______ units per hour. c) How many units will the worker actually assemble between 10:00 A.M. and 11:00 A.M. ? The worker will assemble _________ units. Water flows through plants in the following sequence: a) transpiration from the leaves b) absorption from the soil by root hairs c) movement from roots to stem d) flow upwards in the stem *A. c, a, b, dB. b, c, d, aC. a, b, c, dD. c, d, b, a 3. Find the values of x, y, and z. *125 pls help asap will give brainliest You and your friends went to UNO's for dinner (way back in 2019). Together the total bill for your meals was $40. You have a 15%-off coupon for the meal! Then, after the discount, a 7% sales tax is applied. What is the final price, after the discount and the tax, that you are your friends have to pay for the meal? here is the problemAssuming the relevant range is 20,000-50,000 units, total fixed costs at 45,000 units would be O $176,000. O $25,000. unknown. O $135,000.30.000 units 45,000 units Variable Costs $135,000 ??? Fixed which bond does water atom share Which situation is most clearly ironic?O A. A contest between two chess grand mastersB. A series of quick exchanges between two palsO C. A sweater sale on the hottest day of the yearOD. A gazebo on a lonely hilltop during a huge storm Suppose you buy four 900-stike puts and sell two 1000-strike calls that will expire in 3 months. Premium for 900 strike put is of $10 while 1000-strike call has a premium of $15. Annual Effective interest rate is 10 percent. | a. Write the profit function for this strategy. b. Draw the Profit graph of this strategy c. Find the profits for the following spot prices: $800 and $1100. If $972,000 of 6% bonds are issued at 102 1/2, what is the amount of cash received from the sale? Select the correct answer. $729,000 $1,030,320 $972,000 $996,300 The quastion is on graph theory, matching.Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B.Consider taking |E| =aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B.6) Show that taking |E| = 3/N, the expected number of matchings goes to 0 as N [infinity]. (5 points)7) Show that taking |E| = 4.V, the expected number of matchings goes to infinity as N [infinity]. (5 points) Apple stock prices provided realized returns of 10%, -5%, 23%, and 14% over four consecutive quarters. What was the annual realized return for Apple stock for the year? ulric neisser asked participants to watch a video of men passing a basketball. the participants were so diligent that most of them did not notice a partially transparent woman walking across the basketball court. this finding illustrates: Which of the following statements is true about both mysteries? A Each mystery has to do with homework assignments. B Something unexpected is discovered in an unlikely place. c Wwather makes the main character's problem worse. D Talking to a distant family member finally solves the mystery.