suppose 3 balls are distributed completely at random into 3 cells. let x be the number of cells that remain empty and let y be the number of balls in cell number 1. find the joint pmf of x and y

5xy - 4x

Step-by-step explanation:

6xy-xy= 5by

-5x+ x= -4x

Hey there!

6xy - xy - 5x + x

= 6xy - 1xy - 5x + 1x

COMBINE the LIKE TERMS

= (6xy - 1xy) - (5x + 1x)

= 6xy - 1xy - 5x + 1x

= 6xy - xy - 5x + x

= 5xy - 4x

Therefore, the answer should be:

5xy - 4x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Yoink:

hey imma yoink your points  and not answer the question ok?

Jk:

jk, number 1 is b

number 2 is a

number 3 is d

and number 4 is c

The number of arrangements of the letters in "FULFILLED" that satisfy all the given properties simultaneously is 144.

To find the number of arrangements that satisfy the given properties, we can break down the problem into smaller steps:

Step 1: Consider the three L's as a single unit. This reduces the problem to arranging the letters F, U, L, F, I, L, L, E, D. We can represent this as FULFILL(E)(D), where (E) represents the unit of three L's.

Step 2: Arrange the remaining letters: F, U, F, I, E, D. The vowels E, I, U must be in alphabetical order, so the only possible arrangement is E, F, I, U. This gives us the arrangement FULFILLED.

Step 3: Now, we need to arrange the (E) unit. Since the three L's must be next to each other, we treat (E) as a single unit. This leaves us with the arrangement FULFILLED(E).

Step 4: Finally, we consider the three F's as a single unit. This reduces the problem to arranging the letters U, L, L, I, E, D, (E), F. Again, the vowels E, I, and U must be in alphabetical order, so the only possible arrangement is E, F, I, U. This gives us the final arrangement of FULFILLED(E)F.

Step 5: Calculate the number of arrangements of the remaining letters: U, L, L, I, E, D. Since there are six distinct letters, there are 6! = 720 possible arrangements.

Step 6: However, the three L's within the (E) unit can be arranged among themselves in 3! = 6 ways.

Step 7: The three F's can also be arranged among themselves in 3! = 6 ways.

Step 8: Combining the arrangements from Step 5, Step 6, and Step 7, we have a total of 720 / (6 * 6) = 20 arrangements.

Step 9: Finally, since the three F's can be placed in three different positions within the arrangement FULFILLED(E)F, we multiply the number of arrangements from Step 8 by 3, resulting in 20 * 3 = 60 arrangements.

Therefore, the number of arrangements of the letters in "FULFILLED" that satisfy all the given properties simultaneously is 60.

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if the average time to serve a customer is 3 minutes, then the service rate is 3 per hour. group of answer choices is False.

If the average time to serve a customer is 3 minutes, then the service rate is actually 20 customers per hour, not 3 per hour. This is because there are 60 minutes in an hour, so in one hour, there are 60/3 = 20 sets of 3 minutes, each of which can serve one customer.

what is  average time?

Average time refers to the sum of all the times divided by the total number of observations or events. It is a measure of central tendency that provides information about the typical or representative time for a certain process or event.

For example, if the times to complete a task are 2 seconds, 4 seconds, 6 seconds, and 8 seconds, the average time would be:

(2 + 4 + 6 + 8) / 4 = 5 seconds

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Answer:

m = -9/4

Step-by-step explanation:

Hope this helps!

The minimum degree of the polynomial is 2.

Given the polynomial has zeros of 7, 6 means it has total of 2 zeroes. So it has only two factors possible \((x-7) and (x-6)\) and on multiplying these factors we finally had a polynomial of degree 2 like\((ax^{2} +bx+c)\).

So the given polynomial be a quadratic polynomial which has degree of 2.

Hence the minimum degree of the polynomial is 2.

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Thus, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

The equation of exchange is an economic equation that relates the money supply (M) with the price level (P), the velocity of money (V), and the real output of the economy (Q). The equation is M x V = P x Q.

Using the given values of M = $1.5 trillion, V = 7, and P = 1.05, we can solve for Q by rearranging the equation as Q = M x V / P.

Plugging in the numbers, we get:

Q = ($1.5 trillion x 7) / 1.05 = $10 trillion

Therefore, if M = $1.5 trillion, V = 7, and P = 1.05, the real output of the economy (Q) is $10 trillion.

It's worth noting that the equation of exchange is a theoretical model and may not reflect actual economic conditions. In practice, changes in any one of the variables (M, V, P, or Q) can affect the others, and there may be other factors at play that influence the economy.

Nonetheless, the equation of exchange provides a useful framework for thinking about the relationship between the money supply, prices, and economic activity.

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Complete question

in the equation of exchange, if m = $1.5 trillion, v = 7, and p = 1.05, then:

Find real output.

Answer:

child buffet = $16, adult buffet =$23

Step-by-step explanation:

lets assume that child buffets costs, $x

and adult buffets costs $y

2x+4y= $124 .............this is our first equation

x+4y =$108 ................our second equation

2x + 4y = 124

2x = 124 - 4y

x = 62 - 2y ....from first equation

---------------------------------------------------------------------------------------------------

x+4y =$108

x = 108 -4y ... from second equation

---------------------------------------------------------------------------------------------------

now we will solve it through simultaneous equations

62 - 2y = 108 -4y

2y = 46

y = $23

if y =$23

then x = 108 - 4(23)

x = $16

Answer:

Step-by-step explanation:

An isosceles triangle is a one that has two of its sides equal. Hence option (c) is correct because here two sides have length of 11.9.

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Answer: The original price is $17.98

Step-by-step explanation:

a. Since the series \(1/n^3\) is convergent, the given series ∑ₙ₌₁ \((1/n^{(3n+1)})\) is also convergent.

b. The given series ∑ₙ₌₁ \((-1)^n ln(n)\) diverges.

c. The given series ∑ₙ₌₁ (3 + 2/3n) / (2 + 3/2n) is divergent.

d. The given series ∑ₙ₌₂ \(n / (ln(n))^n\) is convergent.

e. The given series ∑ₙ₌₁ \((1/n^(ln(n)^n))\) is also divergent.

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To determine whether the given series are convergent or divergent, let's analyze each series using different tests:

a) ∑ₙ₌₁ \((1/n^{(3n+1)})\)

To analyze this series, we can use the Comparison Test. Since \(1/n^{(3n+1)\) is a decreasing function, let's compare it to the series \(1/n^3\). Taking the limit as n approaches infinity, we have:

\(lim (1/n^{(3n+1)}) / (1/n^3) = lim n^3 / n^{(3n+1)} = lim 1 / n^{(3n-2)\)

As n approaches infinity, the limit becomes 0. Therefore, since the series \(1/n^3\) is convergent, the given series ∑ₙ₌₁ \((1/n^{(3n+1)})\) is also convergent.

b) ∑ₙ₌₁ \((-1)^n ln(n)\)

To analyze this series, we can use the Alternating Series Test. The series \((-1)^n\) ln(n) satisfies the alternating sign condition, and the absolute value of ln(n) decreases as n increases. Additionally, lim ln(n) as n approaches infinity is infinity. Therefore, the given series ∑ₙ₌₁ \((-1)^n ln(n)\) diverges.

c) ∑ₙ₌₁ (3 + 2/3n) / (2 + 3/2n)

To analyze this series, we can use the Limit Comparison Test. Let's compare it to the series 1/n. Taking the limit as n approaches infinity, we have:

lim [(3 + 2/3n) / (2 + 3/2n)] / (1/n) = lim (3n + 2) / (2n + 3)

As n approaches infinity, the limit is 3/2. Since the series 1/n is divergent, and the limit of the given series is finite and non-zero, we can conclude that the given series ∑ₙ₌₁ (3 + 2/3n) / (2 + 3/2n) is divergent.

d) ∑ₙ₌₂ \(n / (ln(n))^n\)

To analyze this series, we can use the Integral Test. Let's consider the function \(f(x) = x / (ln(x))^x\). Taking the integral of f(x) from 2 to infinity, we have:

∫₂∞ x \(/ (ln(x))^x dx\)

Using the substitution u = ln(x), the integral becomes:

∫_∞ \(e^u / u^e du\)

This integral converges since \(e^u\) grows faster than \(u^e\) as u approaches infinity. Therefore, by the Integral Test, the given series ∑ₙ₌₂ \(n / (ln(n))^n\) is convergent.

e) ∑ₙ₌₁ \((1/n^{(ln(n)^n)})\)

To analyze this series, we can use the Comparison Test. Let's compare it to the series 1/n. Taking the limit as n approaches infinity, we have:

\(lim (1/n^{(ln(n)^n)}) / (1/n) = lim n / (ln(n))^n\)

As n approaches infinity, the limit is infinity. Therefore, since the series 1/n is divergent, the given series ∑ₙ₌₁ \((1/n^(ln(n)^n))\) is also divergent.

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Answer:

yes

Step-by-step explanation:

Answer:

1  7/8 or 15/8

Step-by-step explanation:

Keep change flip

Answer:

b) ¿Qué edad tiene cada uno?

Step-by-step explanation:

Answer:

12. 6= 68°

15. 4= 52°

Step-by-step explanation:

12.

since 5= 22°

5+6= 90° since it Is a right angle

6= 90-22

therefore 6 is 68°

15.

since 3 is 38°

and 3+4= 90° since it is a right angle

4= 90-38

therefore 4 is 52°

The formula used to simulate values of V is given by v = u - α.

It is a horizontal transformation. As it shifts α units left, this transformation is not monotone or one-to-one since it takes values of U that are greater than α and assigns them to the same value of V.

The CDF of V can be calculated as follows:FV(v) = P(V ≤ v)FV(v) = P(U − α ≤ v)FV(v) = P(U ≤ v + α)FV(v) = ∫_0^(v+α) 1 duFV(v) = v + α, for 0 < v < 1 - α.

Hence, the possible values of v are 0 < v < 1 - α.c) Using the Inverse CDF Method, let U be a uniform random variable on (0, 1). To generate the simulated values of V, we take the transformation V = U - α. We know the CDF of V to be FV(v) = v + α, for 0 < v < 1 - α. We solve this equation for v to get:v = FV^(-1)(u) - αWe substitute the value of FV^(-1)(u) = u - α for v to get:v = u - α

Transformation GraphIt is a horizontal transformation. As it shifts α units left, this transformation is not monotone or one-to-one since it takes values of U that are greater than α and assigns them to the same value of V.The CDF of V can be calculated as follows:FV(v) = P(V ≤ v)FV(v) = P(U − α ≤ v)FV(v) = P(U ≤ v + α)FV(v) = ∫_0^(v+α) 1 duFV(v) = v + α, for 0 < v < 1 - α.

Hence, the possible values of v are 0 < v < 1 - α.

Using the Inverse CDF Method, let U be a uniform random variable on (0, 1). To generate the simulated values of V, we take the transformation V = U - α. We know the CDF of V to be FV(v) = v + α, for 0 < v < 1 - α. We solve this equation for v to get:v = FV^(-1)(u) - αWe substitute the value of FV^(-1)(u) = u - α for v to get:v = u - α.

Therefore, the formula used to simulate values of V is given by v = u - α.

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Answer:

y = 1

Step-by-step explanation:

the equation of a horizontal line parallel to the x- axis is

y = c

where c is the value of the y- coordinates the line passes through

the line passes through (- 8, 1 ) and (7, 1 )

both with y- coordinates of 1 , then

y = 1 ← is the equation of the line

Answer:

7

Step-by-step explanation:

The length of MN is 61.6 feet

The given statement is, In ΔMNO, the measure of ∠O=90°, the measure of ∠M=64°, and NO = 70 feet. Find the length of MN to the nearest tenth of a foot.

The length of MN using trigonometry, we can use the Sine Ratio which is expressed as,

Sine Ratio = Opposite side/Hypotenuse

Let's draw a figure for the given question and label the given information of the triangle in the figure below:

\(\Delta MNO\) [asy] size(80); pair M,N,O; O=(0,0); N=(70,0); M=(70,37); draw(M--N--O--M); label("$M$",M,NW); label("$N$",N,SE); label("$O$",O,SW); label("$x$",(M+O)/2,SE); label("$70$",(N+O)/2,SW); label("$64^\circ$",(.25,.12)); label("$26^\circ$",(.1,-.35));  draw(rightanglemark(M,O,N,20)); [/asy]

Using trigonometry, we have;

sin(64) = MN/OHypotenuse = ON = 70 feet

sin(64) = MN/70

Multiply by 70 on both sides to find the value of MN,

MN = 70 sin(64)MN ≈ 61.6 feet

Therefore, the length of MN is 61.6 feet (rounded to the nearest tenth of a foot).

Hence, the required answer is 61.6 feet (rounded to the nearest tenth of a foot).

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Answer:

The surface area of given cuboid is: 148 square centimeters

Step-by-step explanation:

Let

l = 5

w = 4

h = 6

The cuboid has 6 rectangular surfaces.

The surface area of a cuboid with height h, length l and width w is given by:

\(TSA = 2 ( lw+wh+hl )\)

Putting the values

\(TSA = 2(5*4 + 4*6 + 6*5)\\= 2(20+24+30)\\=2(74)\\=148\ cm^2\)

Hence,

The surface area of given cuboid is: 148 square centimeters

Answer:

n = 17

Step-by-step explanation:

The difference between the 5th and 6th terms is 13 - 11 = 2

Therefore, the next term can be found by adding 2 each time.

If we continue with this sequence, we get:

5 = 11

6 = 13

7 = 13 + 2 = 15

8 = 15 + 2 = 17

9 = 17 + 2 = 19

10 = 19 + 2 = 21

So n = 17

-------------------------------------------------------------------------------------

Arithmetic sequence

General form of an arithmetic sequence: \(a_n=a+(n-1)d\)

where:

Given terms of the sequence:

\(a_5=11\\a_6=13\\a_8=n\\a_{10}=21\)

The common difference can be found by subtracting one term from the next term:

\(d=13-11=2\)

To find a, substitute the found value of d into the equation for one of the given terms:

\(\begin{aligned}a_5 =a+(5-1)2 & =11\\ a+8 & =11\\ a & = 3\end{aligned}\)

Therefore, the formula to find the nth term is:

\(\implies a_n=3+(n-1)2\)

\(\implies a_n=2n+1\)

So, the 8th term is:

\(\implies a_8=2(8)+1=17\)

Lets form a equation

Slope:-

Equation:-

So

Put x=8

Coffee shops per capita in city is 7235.294118

What is per capita?

The Latin phrase "per capita" means "by head." In statistics, the term "per capita" is sometimes used in place of "per person" to denote the average per person.

Main Body:

total population of city = 246000

Total coffee shops = 34

Per capita shops for population can be calculated by dividing total population by total shops.

calculatiing,

Per capita shops = total population/ total shops

                            = 246000/34

                            = 7235.294118

Hence number of coffee shops per capita is 7235.294118

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Answer:

n=11/2 or 5 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distribute:

2n-12-15=-6n+18-1

Combine like terms:

2n-27=-6n+17

Put -27 on other side and -6n on other side:

8n=44

Divide:

n=5.5

Evin is walking home from the museum. She starts 38 blocks from home and walks 2 blocks each minute. Evin's distance from home is a function of the number of minutes she has been walking.

(a) which variable is independent and which variable is dependent in this scenario?

(b) Fill  in the table below for a variety of time values.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks  

Answer:

Step-by-step explanation:

From the given information:

(a) which variable is independent and which variable is dependent in this scenario?

An independent variable is a variable that when two variable occurs in a particular event, one variable does not in any way affect the event of the other variable.

A dependent variable is a variable where on variable is dependent on the other variable.

From the question given;

time (t) in minutes is the independent variable

Distance D from home is the dependent variable

(b) Fill  in the table below for a variety of time values.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks      

We are being told that Evin starts 38 blocks from home,

Then she is just starting, i.e from rest

Then; at time t = 0 , she is 38 block distance from home

However, if she walks 2 blocks each minute,

then after 1 minute , that will be 38 blocks - 2 blocks = 36 blocks distance from home.

If she walks for 5  minutes,

then she will be (38 - 2(5) ) blocks away from home

= 38 - 10

= 28 blocks away from home

If she walks for 10 minutes,

then she will be (38 -2(10)blocks away from home

= 38 - 20

= 18 blocks away from home.

Time, t, in minutes                                0               1            5          10

Distance from home, D, in blocks      38              36         28        18

b) φ^(-1)(0.5) = 4 and it tells us that at t = 4 nanoseconds, there will be 0.5 nanograms of extract A remaining. This represents the inverse relationship between the amount of extract A remaining and time.

(c) False. Based on the given facts, there is no specific time mentioned when the amount of extract A remaining is exactly 4 nanograms. The known data points do not include φ(t) = 4.

(d) To calculate φ(φ^(-1)(1)), we substitute φ^(-1)(1) into the function φ. Since φ^(-1)(1) = 3, we evaluate φ(3). The result is φ(3) = 1, which means that at t = 3 nanoseconds, there will be 1 nanogram of extract A remaining.

(e) To calculate φ^(-1)(φ(6)), we substitute φ(6) into the inverse function φ^(-1). Since φ(6) = 0, we evaluate φ^(-1)(0). The result is φ^(-1)(0) = 10, indicating that at t = 10 nanoseconds, there will be 0 nanograms (or none) of extract A remaining.

(f) The domain of the function φ is the set of possible values for time t, which can range from 0 to a positive value, based on the experiment's time frame. The range of the function φ is the set of possible values for the amount of extract A remaining, which can range from 0 to 6 nanograms, based on the given facts.

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According to the given information, the absolute value is |x - 7/6| = 5/6.

What is an algebraic expression?

A mathematical expression known as an algebraic expression can include variables, integers, and mathematical operations including addition, subtraction, multiplication, and division.

When expressing quantities or values that might change depending on the values given to the expression's variables, algebraic expressions are utilised. Expressions in algebra can include one or more variables and be simple or complex.

Two solutions x=1/2, x=-1/3

|x - 7/6| = 5/6.

We know that the absolute value of (1/2 - 7/6) equals the absolute value of (-1/3 - 7/6) because they are opposites and have the same absolute value. So we need an expression that equals 5/6 when either 1/2 - 7/6 or -1/3 - 7/6 is plugged in for x.

To get an expression that equals 5/6 when 1/2 - 7/6 is plugged in for x, we can subtract 7/6 from 1/2 and take the absolute value of the result:

|1/2 - 7/6| = |-1/6| = 1/6.

To get an expression that equals 5/6 when -1/3 - 7/6 is plugged in for x, we can subtract 7/6 from -1/3 and take the absolute value of the result:

|-1/3 - 7/6| = |-9/6| = 3/2.

Since both expressions have the same absolute value of 5/6, we can use either one as the absolute value expression in the equation. Thus,

|x - 7/6| = 5/6.

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Answer:

I'm sorry, because I can only answer questions number 5

For f'(x) = 2x + 4, the corresponding integration formula is given by; ∫ (2x + 4) dx = x² + 4x + C, where C is the constant of integration.

The given function is; f(x) = x² + 4x + 4

Find the derivative of the function and state the corresponding integration formula as follows:

To find the derivative of the given function, we apply the power rule of differentiation.

The power rule of differentiation states that for any real number

n; d/dx [xn] = n*x^(n-1).

Therefore, we can differentiate each term in the given function as follows:

f'(x) = d/dx[x²] + d/dx[4x] + d/dx[4] = 2x + 4 + 0 = 2x + 4

Therefore, the derivative of the given function is f'(x) = 2x + 4.

The corresponding integration formula for this derivative is the reverse of the power rule of differentiation.

Therefore, for f'(x) = 2x + 4, the corresponding integration formula is given by;

∫ (2x + 4) dx = x² + 4x + C, where C is the constant of integration.

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Step-by-step explanation:

thats the answer i think