in how many ways can the nine us supreme court justices be seated for a photo-session so that none of the three women justices sit side by side?
Answers
There are 367416 ways to seat the nine justices for the photo-session such that none of the three women justices sit side by side.
We can approach this problem using the principle of inclusion-exclusion. First, we find the total number of ways to seat 9 justices in a row, which is simply 9! = 362880.
Next, we count the number of ways in which all three women justices sit together. We can treat these three women as a block and arrange the block and the remaining 6 justices in a row. This can be done in 7! * 3! = 15120 ways (where the factor of 3! represents the number of ways to arrange the women within their block).
However, we have overcounted the cases where two of the women justices sit together, and we need to subtract these cases from our count. There are 3 ways to choose which two women sit together, and we can treat these two women as a block and arrange the block and the remaining 7 justices in a row. This can be done in 8! * 2! = 80640 ways (where the factor of 2! represents the number of ways to arrange the women within their block).
Finally, we need to add back the cases where all three women justices sit together in order to get our final answer. There is only one such case, so we add back 7! * 3! = 15120.
Therefore, the total number of ways to seat the nine justices for the photo-session such that none of the three women justices sit side by side is:
9! - 7! * 3! + 3 * 8! * 2! + 7! * 3! = 362880 - 15120 + 80640 + 15120 = 367416.
Thus, there are 367416 ways to seat the nine justices for the photo-session such that none of the three women justices sit side by side.
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Related Questions
He quickly ate 1/4 of it. He gave 1/2 of what was left to Karen. Select all of the following that shows how much Karen received.
Answers
Answer:
the answer is 3/8 or 0.375
Step-by-step explanation:
Which property is used in the following: (2.3).5=2.(3.5) ?
Answers
Answer:
Associative property
Step-by-step explanation:
you can group factors in any order and the answer will be the same
I took a pic I hope that's fine
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Answer:
20/35
Step-by-step explanation:
The framed wall art Modern is 20 and the total is 35 so unless you have to simplify this should be the answer
Which of the following does not represent
function of x?
Answers
Answer:
F
Step-by-step explanation:
The x and y do not match up
Answer:
It is F.
Step-by-step explanation:
It is F because all the x's are the same as that cannot happen.
In a binomial situation, n=18 and π=0.60. Determine the standard
deviation*
Answers
Answer:
Use colon method
Step-by-step explanation:
So it is more easy
Tell whether the rates are equivalent. 7 1/2 miles for every 3/4 hour 1/2 mile for every 3 minutes justify your answer
Answers
A local supermarket has sodas on sale this week. If you buy fewer than three packs of soda, then each pack costs $3.99. If you buy 3 or more packs of soda, then each pack is $2.50. Which function represents this sale? Question 7 options:
Answers
Answer:
$5.95 is the answer I think
PLEASE HELP ME 15 POINTS
1- Which vehicle has the better gas mileage? Explain your reasoning using a line graph comparing the number of gallons to the number of miles covered.
2- Describe the graph:
Answers
You have to add the background info for us to answer this
A fruit company recently released a new applesauce. By the end of its first year, profits on this product amounted to $37,000. The anticipated profit for the end of the fourth year is $68,200. After the first year, the ratio of change in time to change in profit is constant. Let x be years and P be profit in dollars. a. Write a linear function P(x) that expresses profit as a function of time. P(x)=
Answers
Answer:
P(x) = 35,900 + 2,800(x-1)
Step-by-step explanation:
P(x)
P(1) = $35,900
P(4) = $44,300
Difference in profits
P(4) - P(1)
= P(3)
= $44,300 - $35,900
= $8,400
Rate of change per year = $8,400 / 3
= $2,800 per year
The linear equation
P(x) = 35,900 + 2,800(x-1)
Where
x = number of years
Which pair of lines are perpendicular lines?
A.
y = 4x - 6
y = 4x + 11
B.
y = -4x - 6
y = 4x + 11
Ос. у.
y=**-6
y = 4x + 11
OD, y=-**-6
y = 4x + 11
Answers
explanation: m1=-4 m2=4 so yes that’s perpendicular.
The answer is b. I know cuz I took the test!
What current density would produce the vector potential, A = k Î¦Ë (where k is a constant), in cylindrical coordinates?
Answers
The current density vector Jz that would produce the given vector potential A in cylindrical coordinates is Jz = -k/c r sin(θ).
The current density required to produce the given vector potential A = kΦ is J_φ = k (∂Φ/∂ρ), where Φ is the magnetic flux.
First, let's define the cylindrical coordinates:
r = r(theta, z)
θ = θ(theta, z)
z = z
Now, we need to find the vector potential A = k Φ. Using the right-hand rule, we can determine the direction of the vector potential as the direction of the positive z-axis.
The curl of A in cylindrical coordinates is given by:
curl(A) = (1/r)(∂/∂r)(rA) + (1/rsin(θ))(∂/∂θ)(Asin(θ)) + (1/sin(θ))(∂/∂z)(Acos(θ))
Since we want A = k Φ, we have kA = -1/r(∂A/∂r) - 1/rsin(θ)(∂A/∂θ) - 1/sin(θ)(∂A/∂z).
Substituting the expression for A, we get:
k(1/r)(∂A/∂r) - 1/rsin(θ)(∂A/∂θ) - 1/sin(θ)(∂A/∂z) = -1
Now, we need to find the divergence of the magnetic field B, which is given by:
div(B) = (1/r)(∂B/∂r) + (1/rsin(θ))(∂B/∂θ) + (1/sin(θ))(∂B/∂z)
Using the Biot-Savart law, we can find the magnetic field B in cylindrical coordinates. The magnetic field is given by:
B = (1/4π)∫(J(r',θ',z') x r') x r dA'
where J(r',θ',z') is the current density vector.
We can substitute the expression for J in cylindrical coordinates and simplify the integral to obtain:
B = (1/4π)∫[(-1/r)(∫z' J(r',θ') dθ')r') - (1/sin(θ'))(∫z' J(r',θ') dz')] x r dA'
Now, we need to find the current density vector J. Using the Maxwell-Ampere law, we can find the curl of the electric field E in vacuum, which is given by:
curl(E) = -∂B/∂t
Substituting the expression for E in cylindrical coordinates, we get:
curl(E) = -∂B/∂t = (1/c) ∂(Jz)/∂t
where c is the speed of light in vacuum.
Now, we can substitute these expressions for B and curl(E) into the equation for the magnetic field and simplify to obtain:
k(1/r)(∂A/∂r) - 1/rsin(θ)(∂A/∂θ) - 1/sin(θ)(∂A/∂z) = -1
(1/c)(∂(Jz)/∂t) - 1/rsin(θ)(∂A/∂θ) - 1/sin(θ)(∂A/∂z) = -1
Solving these two equations simultaneously, we can find the constants k and Jz. Once we have these values, we can substitute them into the expression for the vector potential A to obtain:
A = k r sin(θ) + Jz/c
Therefore, the current density vector Jz that would produce the given vector potential A in cylindrical coordinates is Jz = -k/c r sin(θ).
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Given parallelogram A B C D below, DE = 31 If EB = x-7, solve for x.
Answers
The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.
Given parallelogram A B C D below, DE = 31 If EB = x - 7.
By the definition, then the equation is given as,
EB = DE
x - 7 = 31
Simplify the equation, then we have
x - 7 = 31
x = 31 + 7
x = 38
The value of the variable 'x' is 38.
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Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
Answers
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Solve the following systems system.
A) 2y = x + 1
-2x – y = 7
B) 3x - 2y = 8
2x - 2y = 5
C) 6x - 4y = 54
-9x + 2y = -69
Answers
Which of the following is an equivalent expression to the expression
a4
A
a12
B
C
7
Q12
2
HELP.
Answers
Answer:
D is the correct option.
All the best!
a pumpkin farmer collects 20 pumpkins randomly sampled from his pumpkin patch and weighs them. the mean weight of the pumpkins is 26 lb. he wonders whether the weight of his pumpkins follows a normal distribution. which answers are clear signs that the pumpkin weights are not normally distributed?
Answers
Outliers or extreme skewness in the distribution of pumpkin weights would be clear signs that they are not normally distributed.
There are several signs that can indicate the pumpkin weights are not normally distributed based on the farmer's sample of 20 pumpkins with a mean weight of 26 lb.
Skewed Distribution: If the distribution of pumpkin weights is noticeably skewed, it suggests a departure from normality. Positive skewness occurs when the tail of the distribution is stretched towards higher values, indicating a higher number of lighter pumpkins.
Negative skewness is the opposite, with a tail stretched towards lower values, suggesting a higher number of heavier pumpkins.
Outliers: The presence of extreme values that deviate significantly from the majority of the data can be a clear sign of non-normality. If there are a few pumpkins with exceptionally high or low weights compared to the rest, it indicates the presence of outliers and a potential departure from a normal distribution.
Bimodal or Multimodal Distribution: If the pumpkin weights exhibit multiple peaks or modes instead of a single bell-shaped curve, it suggests a non-normal distribution. This could indicate the presence of distinct subpopulations of pumpkins with different weight ranges.
Non-linear Patterns: If there is a distinct non-linear pattern or trend in the data, it deviates from a normal distribution. For example, if there is a systematic increase or decrease in weights as the pumpkin size increases, it suggests a departure from normality.
Departure from the 68-95-99.7 Rule: In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. If the sample data significantly deviates from these percentages, it indicates a departure from normality.
It is important to note that these signs alone do not definitively prove that the pumpkin weights are not normally distributed. Further statistical tests such as the Shapiro-Wilk test, Anderson-Darling test, or visual inspections of a histogram, Q-Q plot, or kernel density plot can provide more evidence to assess the distributional assumption.
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HELP QUICKLY PLEASE!!
Answers
Answer:
D
Step-by-step explanation:
Because the first equation is equivalent to 1, and d is equivalent to 1, the rest are incorrect
kimberly is making a wall hanging. she has graphed the wall hanging as polygon are A(1,5),B(1,9),C(7,9),D(7,5),E(5,3), and F(3,3). graph the polygon on the coordinate plane. Waht is the area of Kimberly's wall hanging.
Answers
The area of Kimberly's wall hanging will be 32 square units.
Given that:
Points, A(1, 5), B(1, 9), C(7, 9), D(7, 5), E(5, 3), and F(3, 3)
The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.
The polygon is shown in the graph below.
The area of the polygon is given as,
A = Area of rectangle + Area of trapezium
A = 4 x 6 + 1/2 x (6 + 2) x 2
A = 24 + 8
A = 32 square units
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Find the equation of the line.
Use exact numbers.
y =
Answers
Y intercept is 4
Points hit 2 up 3 over
y = mx+b
y = 2/3x + 4
PLEASE HELP. !!!!!!!!!!
Answers
Answer:
25.13
Step-by-step explanation:
by using formula
3.14 × radius²× height
Solve.
4 + x/7 = 2
A) -14
B) 10
C) 12
D) 42
Answers
Answer:
the answer is A
-14
Step-by-step explanation:
subtract 4 in both sides
Answer:
X= -14
Step-by-step explanation:
SUBTRACT 4 FROM BOTH SIDES OF THE EQUATION.
SIMPLIFY
Multiply all terms by the same value to eliminate fraction denominators
Cancel multiplied terms that are in the denominator
Multiply the numbers
THEN AFTER YOU DO THESE STEPS YOU WILL GET THE SOLUTION ABOVE.
Find l.
l
l= [?] in
115 in.
12 in.
please help me i’m desperate
![Find l.ll= [?] in115 in.12 in.please help me im desperate](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/KJQE1zytiwHuVgACr8GJUv1hJ7DD3F7L.png)
Answers
…………………..
…………
Using Pythagorus
15*2 + 6*2 = l * 2
225+36= 261 = l*2
Under root 261 = L
A scientist who studies teenage behavior was interested in determining if teenagers spend more time playing computer games then they did in the 1990s. In 1990s, the average amount of time spent playing computer games was 10. 2 hours per week. Is the amount of time greater than that for this year? twenty students were surveyed and asked how many hours they spent playing video games. The test statistics is equal to 1. 39. What is the p-value?.
Answers
0.3317 is the p-value .
What is the P value?
The likelihood, for a particular statistical model, that the statistical summary would be equal to or more extreme than the actual observed findings when the null hypothesis is true is known as the P value.The test hypothesis should be rejected if the result is statistically significant (P 0.05), which indicates that the test hypothesis is false. There was no effect, according to a P value greater than 0.05.H0 : Mu = 10.2
H1 : Mu > 10.2
Test statistic
t=0.45 (since n is small)
P value = 0.3317
Hence P is greater than 0.10
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If the value of X - 5 = y and x² - y² = 15 then how much is x+ y =?
Answers
Answer:
x + y = 4 - 1 = 3.
Step-by-step explanation:
First, in order to solve for the sum of x and y, we should substitute (x - 5 = y) into our given equation of x² - y² = 15.
Given:
x - 5 = yx² - y² = 15Substitute:
x² - (x - 5)² = 15.
Use the FOIL Method:
x² - x² + 10x - 25 = 15.
Simplify:
10x - 25 = 15
10x = 40
x = 4.
Solve for y by substitution:
4 - 5 = -1 (y)
x = 4.
y = -1.
Therefore,
x + y = 4 - 1 = 3.
someone pls help me t-t
Answers
Answer:
35+62 = 97
50 - 97 = -47
you are 47 dollars in debt
What is equivalent to the product (x-4) (x+9)
Answers
Answer:
x^2+5x-36
Step-by-step explanation:
x^2+9x-4x-36
Answer:
x²+ 5x - 36
Step-by-step explanation:
Given
(x - 4)(x + 9)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 9) - 4(x + 9) ← distribute both parenthesis
= x² + 9x - 4x - 36 ← collect like terms
= x² + 5x - 36
What are the 3 shortcuts to prove triangles are similar?
Answers
In order to prove the triangles are similar, you have to use SAS, SSS and AA rule.
In triangle, the similarity theorem states that if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Here we have to find the 3 shortcuts to prove the triangles are similar.
According to the similarity theorem, here we have triangle that is similar to other if two pairs of angles are congruent (AA) or if two pairs of sides are proportional and the included angles are congruent whereas if three pairs of sides are proportional (SSS).
Here we must know that the term similarity and congruent are similar terms.
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What is the value of expression of x=5
What is the coefficient of 6x-3
Answers
Answer:
27
Step-by-step explanation
6x - 3
6(5) - 3 || replace the x with its value
30 - 3 || multiply (also known as simplify)
27 || subtract 3 from 30
someone please help me I’m struggling with these questions
Answers
Briefly describe the criterion used to obtain the ordinary least square estimator.
Answers
The criterion used to obtain the ordinary least square (OLS) estimator is to minimize the sum of the squared differences between the observed values and the predicted values.
In OLS, the goal is to find the line that best fits the given data points. The estimator minimizes the sum of the squared residuals, which are the differences between the observed values and the predicted values. The squared residuals are used to ensure that both positive and negative differences contribute to the overall error measure.
The OLS estimator achieves this by calculating the coefficients of the linear regression model that minimize the sum of the squared residuals. It finds the intercept and slope of the line that minimizes the total squared distance between the data points and the regression line. This minimization process is based on the principle of least squares, which aims to find the best-fitting line by minimizing the overall error.
By minimizing the sum of the squared residuals, the OLS estimator provides a measure of how well the regression line represents the data points. It allows for the determination of the line's slope and intercept, which can be used for predicting values and understanding the relationship between the variables.
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