You have an ace, king, queen, and jack from a deck of cards. After shuffling the cards, you draw one card. Then you replace the card, shuffle again, and again draw a card. What is the probability that you will draw a king and a queen in either order? An ace, king, queen, and jack playing card. CLEARCHECK The total number of possible outcomes is x . The probability of drawing a king and a queen in either order is x

Answers

Answer 1

Answer:

[tex]\dfrac{2}{169}[/tex]

Step-by-step explanation:

A standard 52-card deck comprises 4 suits (Spades, Hearts, Diamonds, and Clubs).  

Each suit comprises 10 numerical cards (numbered 2 through 10, plus an "ace") and 3 "court" cards (jack, queen and king).

Therefore:

The total number of possible outcomes is 52.There are 4 kings and 4 queens in a standard deck of cards.

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

[tex]\implies \sf P(Queen)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]

[tex]\implies \sf P(King)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]

Therefore, the probability of drawing a king, replacing the card, and drawing a queen is:

[tex]\implies \sf P(King)\;and\;P(Queen)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]

Similarly, the probability of drawing a queen, replacing the card, and drawing a king is:

[tex]\implies \sf P(Queen)\;and\;P(King)=\dfrac{1}{13}\times \dfrac{1}{13}=\dfrac{1}{169}[/tex]

Therefore, the probability of drawing a king then a queen, or a queen then a king is:

[tex]\implies \sf P(King\;and\;Queen)\;or\;P(Queen\;and\;King)=\dfrac{1}{169}+\dfrac{1}{169}=\dfrac{2}{169}[/tex]


Related Questions

Solve for x. Leave your answer in simplest radical form.

Answers

Answer:

√122

Step-by-step explanation:

first we have to find the missing side with x on the 5 and 9 triangle by using the theorem


a^2+b^2=c^2

9^2+5^2=c^2

81+25=c^2

106=c^2

√106=c


and now we can use this as a side to find x

4^2+√106^2=x^2

16+106=x^2

122=x^2

√122=x

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The temperature T°C of a cup a tea t minutes after being poured is modelled by the exponential decay function:
T=18+68e^-t/8, t>/= 0

a) What is the initial temperature of the tea the moment it was poured?

b) When will the temperature of the tea reach 35°C?

c) Explain why the tea will never reach an ambient temperature of 15°C.

Answers

Using the exponential function T = 18 + 68e^(-t/8), the initial temperature is 86°C, the time the temperature will reach 35°C is 11.1 minutes

Exponential Function

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form f(x) = aˣ

In the question given, the exponential function given shows an exponential decay

T = 18 + 68e^(-t/8)

a) The initial temperature when the tea was poured would be (t = 0)

T = 18 + 68e^(-0/8)

T = 16 + 68 = 86°C

b) The temperature of the tea at 35°C

35 = 18 + 68e^(-t / 8)

T = 11.1

c) The reason why the the tea will never reach 15°C is because there's no solution for the expression.

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order the fraction to least to greatest 2/3 3/7 4/8

Answers

2/3, 4/8, and 3/7. :P

Apply the distributive property to simplify the expression


8(12x – 20)

Answers

I believe the answer must be 96x-160

Because we have to multiply 8x12 which is 96. and there is x next to it. so keep the x as it is.

and next to it is minus ( - ) sign so keep it as it is.

now we have to multiply 8x20 which is 160.

so if we write it together it will be:

so if we write it together it will be:96x - 160.

Thank you

The function f(x) = 2x3 + 3x2 + 2x – 1 is divided by (x – 1) .

Answers

Step-by-step explanation:

here is your answer hope it helps you plaz mark me as brainlist

Find the probability of exactly three
successes in six trials of a binomial
experiment in which the probability of
success is 50%.

Answers

The probability exactly three successes in six trials is 31.30%

What is Binomial Distribution?

A binomial distribution can be defined as the probability of a success or failure outcome in an experiment or survey that is repeated multiple times.

The probability distribution of a binomial distribution is given by :

P(x = k) = n! /k!(n - k)! P^x(1 - P)^(n - k)

In our case :

n = 6

P = 50/100 = 0.5

Now we want the probability that:

x = 3

This is because the question states that we want the probability that the number of successes are exactly 3.

We do the substitution in the probability distribution function as follows :

P(x = 3) = 6!/3!(6 - 3)! × 0.5³ × (1 - 0.5)³

= 0.3125

= 31.25%

= 31.30%

Hence, the probability of exactly three successes in six trials of a binomial experiment in which the probability of success is 50 is 31.30%

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HELP PLEASE I NEED IT

Answers

Answer:=

Step-by-step explanation:

2 = x
3 26
How do i solve this equation

Answers

Answer:

do the butterfly method if you don't know how to do that comment and I'll show you a screenshot

m/3 - 6 = 4

solve for m

Answers

Answer:

m=10

Step-by-step explanation:

m/3-6=4

30/3=10

10-6=4

If 41 and 42 are complementary angles and if the measure of 41 is 50° more than the measure of 42, determine the measures of 41 and 42

Answers

Answer:

m∠1 = 70

m∠2 = 20

Step-by-step explanation:

41 and 42 are complementary angles:  m∠1 + m∠2 = 90

measure of 41 is 50° more than the measure of 42:  m∠1 = m∠2 + 50

substitute: (m∠2 + 50) + m∠2 = 90

simplify and solve:  2(m∠2) + 50 = 90

                                2(m∠2) = 40

                                m∠2 = 20

Find the area of a shaded portion 10 km 20 km 20km

Answers

The area of the shaded region will be 150 square kilometers.

What is Parallelogram? What is triangle?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a 2- D figure as shown in the image.

The area of the shaded region will be -

A[shaded] = A [square] - {A [Δ1] + A [Δ2] + A [Δ3]}

A[shaded] = (20 X 20) - [{1/2 x 10 x 10} + {1/2 x 10 x 20} + {1/2 x 10 x 20}]

A[shaded] = 400 - [50 + 100 + 100]

A[shaded] = 400 - 250

A[shaded] = 150 square kilometers

Therefore, the area of the shaded region will be 150 square kilometers.

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What is the equation of the line that passes through the point (2,-6) and has a slope of -3?

Answers

Answer is y = -3x

Step by step

We can use point slope form to solve

y - y1 = m (x - x1)
Substitute your x and y and slope

y - -6 = -3 (x - 2)
Distribute

y + 6 = -3x + 6
Subtract 6 from both sides


y +6 -6 = -3x + 6 - 6
Combine

y = -3x is your answer


Using division, what is the quotient (2x3 - 2x - 12) ÷ (x - 2)?
2x² + 4x-6 +
2x² - 4x + 6
1
X 2)

Answers

Answer: 2x²+4x+6

Step-by-step explanation:

[tex]\displaystyle\\\frac{2x^3-2x-12}{x-2} =\\\\\frac{2(x^3-x-6)}{x-2}=\\\\ \frac{2(x^2-8+8-x-6)}{x-2} =\\\\\frac{2(x^3-2^3-x+2)}{x-2} =\\\\\frac{2((x^3-2^3)-(x-2))}{x-2}=\\\\\frac{2((x-2)(x^2+2x+2^2)-(x-2))}{x-2} =\\\\\frac{2(x-2)(x^2+2x+4-1)}{x-2}=\\\\2(x^2+2x+3)=\\\\2x^2+4x+6[/tex]

using a slope formula find the slope pf the line theough the points (0,0) and (2,6)

Answers

Step-by-step explanation:

slope formula: (y2-y1)/(x2-x1)

at the point (0,0), it is known that x=0 and y=0.at the point (2,6), it is known that x=2 and y=6.

slope: (6-0)/(2-0) =6/2 =3

Evie just had her birthday. she got a $30 gift card for dunkin donuts and she can’t spend more than $30. the small coffees cost $2 and the large cost $4. she wants to buy at least 10 coffees. how many coffees can she buy using only her gift card?

Answers

Answer:

Step-by-step explanation:

30 dollars to spend she wants to buy at least ten which mean's since 2 times 5 is 10 and 4 times 5 is 20 and 10 plus 20 equals thirty which means she can buy 5 small coffee's and 5 large coffee's

Find the smallest length that can be divided exactly into equal sections of length 5m,8m and 12m

Answers

As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.

What is an LCM example?

The acronym LCM stands for the least common multiple or factor of any two or more specified integers. The least common multiple for the numbers 16 and 20 is 80, hence the LCM of those two numbers will be, for instance, 2 x 2 x 2 x 2 x 5 = 80.

What is the LCM of 4 and 8?

8 is the LCM of 4 and 8. The LCM is the number that can be divided by the provided numbers equally. You can discover the least common multiple of 4 and 8 by looking at the common multiples. 4 is a multiple of 8, 12, 16, 20, 24, etc.

finding prime factors of the given numbers by repeated division method in order to find the LCM;

2 | 5,8,12

5 | 5,4,6

2 | 1,4,6

2 | 1,2,3

3 | 1,1,3

0 | 1,1,1

so we get 2x5x3x2=60

As the LCM of 5, 8, and 12, which is 60 so it is the smallest length that can be divided exactly into equal sections of length 5 m, 8 m, and 12 m.

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The shortest length which can be split into equal segments of length 5 meters, 8 meters, or 12 meters is 120.

What does "section" signify in terms of forms and purposes?

Your form may be divided into sections with the help of sections, as the name suggests. This enables your users to input responses that might be categorized. The fact that sections divide your form into distinct screens is another significant benefit. For instance, a first screen shows section 1. When concealed lines in external views cannot adequately represent a part's inner design, sections are employed. The internal components can be viewed more clearly by imagining cutting through the thing and removing a section of it.

Briefing:

Finding the LCM by repeatedly dividing the supplied integers to get their prime components:

2 | 5,8,12

2 | 5,4,6

2 | 5,2,3

3 | 5,1,3

5 | 5,1,1

1 | 1,1,1

So we get 2*2*2*3*5*1 = 120

The lowest length that could be divided into precisely equal segments in lengths 5 m, 8 m, and 12 m is 120, which equals the LCM of 5, 8, & 12.

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6,370 x 30 find the products
How do I show my thinking or ideas
Example
637•3 6370•30
=1911 =(6370•3)• (10•10)

Answers

Answer:

Product: 191,100

Step-by-step explanation:

Show your work:

(It should look something like this)

6370                                                                                                                              x   30

First: 0 x 0 = 0 (so you put):

6370                                                                                                                              x   30

      0

(everything else times 0 just equals 0 so you'd get this):

6370                                                                                                                              x   30

0000

Next: 3 x 0 = (so you put):

6370                                                                                                                              x   30

0000

    0

Next: 3 x 7 = 21 (so you put):

6370                                                                                                                              x   30

0000

  10

(carry the 2)

Next: 3 x 3 = 9 (so you put):

 2

6370                                                                                                                              x   30

0000

 1 10

(add the number you carried to 9: giving you 11 so you also have to carry a 1 again)

(the first number: 0 of 110 goes under the third 0 of 0000)

(the spacing is just to make sure that the placement is correct: the first 1: of 110 goes under the first 0 of 0000)

Next: 3 x 6 = 18 (so you put):

1 2

6370                                                                                                                              x   30

  0000

191 10

(you add the 1 that you carried to 18 to give you 19)

(again: I only moved the zeros over so that the placement is correct)

Next: Now you add(this is why the placement of the numbers is important):

1 2

6370                                                                                                                              x   30

     0000

+ 191 10

  191,100

(you will put imaginary zeros over 19 because you know that there is already nothing there. You will also add an imaginary zero under the last zero that is hanging there because you know there is nothing there either.)

(Hope this helps! I know its really confusing, if you have any further questions or if the way I explained confused you please tell me or ask me those questions.) :)

Find the Maclaurin series of the following functions. Step by Step Please

Answers

The Maclaurin series of xcos(-x) up to n = 3 is

[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

The function is given in the question as

m(x) = xcos(-x)

Taylor (Maclaurin) series of xcos(x) up to n=5

A Maclaurin series is given by  f(x),

[tex]f\left(x\right)=f\left(a\right)+\frac{f^'\left(a\right)}{1!}\left(x-a\right)+\frac{f^{''}\left(a\right)}{2!}\left(x-a\right)^2+\frac{f^{'''}\left(a\right)}{3!}\left(x-a\right)^3+\ldots[/tex]

[tex]f\left(x\right)=f\left(0\right)+\frac{f^'\left(0\right)}{1!}\left(x\right)+\frac{f^{''}\left(0\right)}{2!}\left(x\right)^2+\frac{f^{'''}\left(0\right)}{3!}\left(x\right)^3+\ldots[/tex]

We need to do to get the desired polynomial is to calculate the derivatives, evaluate them at the given point, and plug the results into the given formula.

f⁽⁰⁾(x) = f(x) = xcos(x)

Evaluate the function at the point: f(0)=0

1st derivative: f(1)(x)=(f(0)(x))′=(xcos(x))′=−xsin(x)+cos(x)

1st derivative at the given point: (f(0))′=1

2nd derivative: f(2)(x)=(f(1)(x))′=(−xsin(x)+cos(x))′=−xcos(x)−2sin(x)

Evaluate the 2nd derivative at the given point: (f(0))′′=0

3rd derivative: f(3)(x)=(f(2)(x))′=(−xcos(x)−2sin(x))′=xsin(x)−3cos(x)

Evaluate the 3rd derivative at the given point: (f(0))′′′=−3

Now, use the calculated values to get a polynomial:

[tex]m(x)=0+\frac{1}{1!}x+\frac{0}{2!}x^2+\frac{-3}{3!}x^3+.....[/tex]

[tex]m(x)=x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

Thus, the Maclaurin series of xcos(-x) up to n = 3 is

[tex]m(x)= xcos(-x)= x-\frac{1}{2}x^3+\frac{1}{24}x^5-\frac{1}{720}x^7+\frac{1}{40320}x^9+\ldots \:[/tex]

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There are approximately 123,000 people on the waiting list to get season tickets for the Green Bay Packers. This is about 14 times as many as are waiting for Bears tickets and 12 times the number of people waiting on lion's tickets. About how many people are waiting for chicago bears season tickets?

Answers

Answer:

8786

Step-by-step explanation:

123,000/14 = 8786  Since it is about, I rounded to the nearest whole number.

"How do we transform System A into System B?
Equation [A1] → Equation [B1]
Equation [A2]→ Equation [B2]
Equation [A1]+Equation [A 2] → Equation [B 2]
Equation [A2]+ Equation [A 1] → Equation [B 1]"

Answers

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform system A into System B ?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step by step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

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Given m || n, find the value of x.

Answers

Answer:

x=11°

Step-by-step explanation:

Because line t is 180°, (9x-5)°+(6x+20)°=180°

Simplify:

(9x-5)°+(6x+20)°=180°

9x-5+6x+20=180

15x-5+20=180

15x+15=180

15x=165

x=11

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Which of the following choices is equivalent to the equation?

3(x−1) = 27


x – 1 = 9

x – 1 = 3

x – 1 = -3

Answers

Answer:

just finished a challenge

Step-by-step explanation:

10 less than the product of 8 and b

Answers

Step-by-step explanation:

8b-10

hope it helps. please mark brainliest

Answer:  The correct answer is (8*b) - 10

Step-by-step explanation:

When translating word problems into equations, the term "product" denotes multiplication, and "less than" denotes subtraction.

This wording "10 less than the product of 8 and b" tells us to multiply 8 and b, then subtract 10:

(8*b) - 10

4 7/8 + (2 1/6). It’s fractions by the way.

Answers

Answer:

7 and 1/24

Step-by-step explanation:

4 7/8 + 2 1/6

First when adding fractions, we want to have a common denominator. To do that, we must multiply the fractions until we get a desired denominator. We can find LCM.

The LCM of 6 and 8 is 24, so we must multiply accordingly.

We can put this into improper fraction form:

39/8 + 13/6

Then multiply accordingly. Multiply by 3 on both sides for the first fraction, and multiply by 4 on both sides for the second to get a denominator of 24.

117/24 + 52/24

Now, we can add the fractions.

169/24

Simplify

7 and 1/24

Find the probability of rolling a sum greater than 7 given that you rolled an odd number first.

Answers

Answer:

I think the answer is 1/2. Given the first die was odd, you rolled either a 1,3, or 5. Now on the second roll only a 6,4, or a 2 will give you a sum of 7. Given that is half of the sample space of the second die, it is 1/2?

Step-by-step explanation:

An airplane cruises 1 kilometer in
1
12
of a minute. What is its cruising speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
kilometers per minute

Answers

Answer: It is 12 kilometers per minute

Step-by-step explanation:

in the problem that you'll need to simplify your answer and write it as a proper fraction, mixed number, or whole number so I can confirm this is 100% correct.

Step-by-step explanation:

3) A
a
Square with an area of 25m² and
perimeter of 20 is reflected across line
L, then translated 20m right, and then
rotated 20 degrees clockwise, what is
area and perimeter after these transformations?
the

Answers

Answer:

Area =25m²

Perimeter = 20m

Step-by-step explanation:

None of the transformations described change the size or shape of the original object, only position and orientation are changed

Please help!!!!
Write an equation in point-slope form that passes through the points (2, 4) and (-3, -6).

Answers

Answer:

uh let's see

Step-by-step explanation:

2,4 and -3,-6

y2-y1/

x2-x1

-6-4

-3-2

-10/-5 = 2

slope is 2

u do the rest I'm tired

In a clothing store, 50% of the customers buy a shirt, 30% of the customers
buy a pair of pants, and 15% of the customers buy both a shirt and a pair of
pants.
If a customer is chosen at random, what is the probability that he or she buys
a shirt or a pair of pants?
A. 0.20
B. 0.18
C. 0.65
D. 0.80

Answers

Answer:

.20

Step-by-step explanation:

because customers are always right

A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $22 . Find a linear equation in the form p(n)=mn+b that gives the price p they can charge for n shirts.

Answers

The linear equation in the form p(n) = mn + b that gives the price p they can charge for n shirt is p(n) = - 1 / 250n + 34.

How to linear equation in slope intercept form?

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

m = slopeb = y-intercept

Therefore, the clothing business finds there is a linear relationship between the number of shirts, n,  it can sell and the price, p , it can charge per shirt.  1,000 shirts can be sold at a price of $30 , while 3,000 shirts can be sold at a price of $22 .

Therefore,

using  (1000, 30) and (3000, 22) let's find the slope.

m = 22 - 30 / 3000 - 1000

m = - 8 / 2000

m = - 1 / 250

Hence, let's find the y-intercept using (1000, 30)

p(n) = mn + b

where

p = pricen = number of shirt

Therefore,

30 = - 1 / 250 (1000) + b

30 = - 4 + b

b = 30 + 4

b = 34

Hence, the linear equation is p(n) = - 1 / 250n + 34

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a right triangle has a hypotenuse of length 3 units and one side of length 2 units. what is the area of the triangle? The following tabulated data were gathered from a series of Charpy impact tests on a tempered 4340 steel alloy. Temperature (C) 0 25 50 75 100 113 125 150 175 200 Impact Energy (J) 105 104 103 97 63 40 34 28 25 24 (a) Plot the data as impact energy versus temperature. (Hint: use engineering paper for the graph) (b) Determine a ductile-to-brittle transition temperature as the temperature corresponding to the average of the maximum and minimum impact energies. (c) Determine a ductile-to-brittle transition temperature as the temperature at which the impact energy is 50J johnny observed a traumatic incident with a schoolmate that has resulted in avoidance of needles for the past 12 years. what brain structure is most clearly implicated in this phobic response? while working on a project, a developer spent a few weeks modeling the intended data schema before writing any code. this person was most likely working with a document database. On January 1, 2021, Twister Enterprises, a manufacturer of a variety of transportable spin rides, issues $430,000 of 6% bonds, due in 20 years, with interest payable semiannually on June 30 and December 31 each year.3. If the market interest rate is 5%, the bonds will issue at $483,971. Record the bond issue on January 1, 2021, and the first two semiannual interest payments on June 30, 2021, and December 31, 2021. (If no entry is required for a particular transaction/event, select "No Journal Entry Required" in the first account field. Round your answers to the nearest dollar amount.) Nor Ram does his work. into positive what fraction is exactly between 4/7 and 3/5 the amplitude of the measurable nmr signal is reduced from 2 mvpeak-peak to 1 mvpeak- peak. how many discrete signal levels become useless when the adc has 10 bits? (use the same gain of the amplifier that is calculated in 1b). why would a marketer identify and analyze the target audience before defining the advertising objectives when developing an advertising campaign? what factors could cause a firm to invest more or less at any given level of the interest ratre? that is, what could cause the investment demand curve to shift (increase or decrease)? while studying classical conditioning of eyeblink response in rabbits investigators suppress the activity of the redf nucleus what results will occur by 1872, many republican leaders had come to believe that which group offered the best hope for honesty, order, and prosperity in the south? what may the white bull in the painting represent? group of answer choices a sacrificial victim the spanish dictator franco the country of spain masculine brutality identify all resonance structures for the following radical. there may be more than one correct anwserTo receive credit, make sure to select all that apply. What is the duty of good government, according to Jonathan mayhew? x-mart uses the periodic inventory system to account for its merchandise. on may 1, it sold $400 of merchandise on account with terms of 2/15, n/40. on may 3, its customer returned $50 of merchandise due to defect. on may 11, its customer paid the remaining balance due. demonstrate the required journal entry to record the receipt of payment by selecting all of the correct actions below. what pressure would it take to compress 250. l of helium gas initially at 1.00 atm into a 2.00 l tank at constant temperature?express your answer with the appropriate units. The relationship between the prices of the underlying stock, a call option, a put option, and a riskless asset is referred to as the _____ relationship.A. put-call parityB. covered callC. protective putD. straddleE. strangleA. put-call parity Unit 5 relationships with triangle homework3 publicity is information about a company, a product, or an event transmitted by the general mass media to attract public attention. true or false