The four families consisting of 12 distinct individuals can be seated in 12! (479,001,600) ways. There are no seating restrictions, so each person can occupy any of the twelve seats.
Explanation:The subject of this question is combinatorics, a branch of mathematics. In this problem, you have four families, each consisting of 1 male and 2 females, and you want to know in how many ways they can be seated in a row of twelve seats.
Given there is no restriction about the seating pattern, each member can occupy any seat. So, consider each family member as a distinct person; you then have 12 people to be seated in 12 different ways. This can be done in 12 factorial (12!) ways. Factorial implies the product of all positive integers up to that number. A simple way to calculate 12 factorial is: 12*11*10*9*8*7*6*5*4*3*2*1, which equals 479,001,600.
So, the four families can be seated in a row of twelve seats in 479,001,600 ways. This principle of arrangements is a key part of combinatorics and discrete mathematics.
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Considering each family as a single unit, the total number of ways they can be seated in a row of twelve seats is given by the formula: 12! divided by (2!) to the power of 4.
Explanation:This is actually a problem that is solved using the principles of permutations and combinations in mathematics. Given we have 4 families each with 1 male and 2 females, we have a total of 12 people. Now, if we are to arrange these 12 people in a row of twelve seats, we have 12! (factorial) ways to do it. However, each family group is to be considered as a single unit and within each unit, arrangements don't count, so we must divide by the number of ways to arrange the 2 females within each family of 4, which is 2!. Hence, the total number of ways to seat the group is given by (12! / (2!)^4).
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The mean water temperature downstream from a discharge pipe at a power plant cooling tower should be no more than 100°f. past experience has indicated that the (population) standard deviation of temperature is 2°f. the water temperature is measured on nine randomly chosen days, and the average temperature is found to be 98°f. if you were to do a hypothesis test using the data from this problem to test the hypothesis that the population mean temperature is 97 degrees f, which test statistic would you need to use?
Actually in this case we will make use of the z test statistic. In which we calculate for the z score and then use the standard normal distribution tables to find for the P value at the calculate z score.
z = (x – u) / s
z = (97 – 98) / 2
z = -0.5
The z value should be greater than 1.65 to for the null hypothesis to be accepted. Hence rejected.
A multivitamin tablet contains 0.16g of vitamin C. How much vitamin C does a bottle of 60 tablets contain?
2/5 of the students in your class are in band. Of these, 1/4 play the saxophone. What fraction of your class plays the saxophone?
The planet Mercury has a diameter of 4,878 km whereas the Moon has a radius of 1736.5 km. Which object is larger and why?
The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.
Here,
Given that;
The planet Mercury has a diameter of 4,878 km.
And, The Moon has a radius of 1736.5 km.
We have to find the larger planet.
What is the relation between radius and diameter?
The radius is half or the diameter of the object.
Now,
The planet Mercury has a diameter of 4,878 km.
Hence, The radius of Mercury = 4,878/2 = 2,439 km
And, The radius of the Moon = 1736.5 km
Clearly, 2,439 > 1,736.5
So, The planet Mercury is larger than the Moon, because the radius of Mercury is greater than the Moon.
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At Travis's Hats, 60% of the 25 hats are baseball caps. How many baseball caps are there?
Help for C if anyone knows, thanks
What number is the solution to n over 3 is negative 12
A -36
B -4
C 4
D 36
you have n/3 = -12
to solve for n, multiply both sides by 3
n = -12 * 3 = -36
answer is A. -36
3/4x+5/6=5x-125/3 solve for x
Final answer:
To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. Multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. Combine like terms and solve for x.
Explanation:
To solve the equation 3/4x + 5/6 = 5x - 125/3 for x, you can start by getting rid of the fractions. To do this, multiply every term in the equation by the least common multiple (LCM) of the denominators, which in this case is 12. This gives you:
9x + 10 = 60x - 500
Next, combine like terms by subtracting 9x from both sides of the equation:
10 = 51x - 500
Then, add 500 to both sides of the equation:
510 = 51x
Finally, divide both sides of the equation by 51 to solve for x:
x = 10
In model trains, O scale means the models are made using a 1:48 scale. In the U.S., real train tracks have rails that are 4 ft 8 in apart.
a. If miniature train track was made using O scale, how far apart should the rails be? Round to the nearest hundredth of an inch.
b. The word gauge refers to how far apart the model rails are. For some reason, O gauge track does not exactly use O scale, and O gauge rails are 1.25 inches apart. Find the relative difference of the rail spacing on O gauge track compared to what it should be if it followed O scale. Round to the nearest tenth of a percent.
Final answer:
The correct O scale model train track spacing should be 1.17 inches. However, the actual O gauge spacing is 1.25 inches. The relative difference in the rail spacing is approximately 6.8%.
Explanation:
To solve for the correct O scale model train track spacing:
Convert the real train track gauge to inches: 4 feet x 12 inches/foot + 8 inches = 56 inches.
Divide the real gauge by the scale factor of 48 to find the model gauge: 56 inches / 48 = 1.1667 inches.
Round the result to the nearest hundredth of an inch: 1.17 inches.
Now to calculate the relative difference between O scale and the actual O gauge:
Determine the actual O gauge spacing: 1.25 inches.
Calculate the difference in spacing: 1.25 inches - 1.17 inches = 0.08 inches.
Find the relative difference by dividing the spacing difference by the O scale spacing and then multiply by 100 to get the percentage: (0.08 inches / 1.17 inches) x 100 = 6.8%.
Round the result to the nearest tenth of a percent: 6.8%.
Find the laplace transform of f(t)={0,(t−4),0≤t<4t≥4
The Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
Sure, let's find the Laplace transform of the piecewise function [tex]\( f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} \).[/tex]
Define the function for all ( t ):
[tex]\[ f(t) = \begin{cases} 0, & 0 \leq t < 4 \\ t - 4, & t \geq 4 \end{cases} = (t - 4)u(t-4) \][/tex]
where u(t) is the unit step function.
Use the definition of the Laplace transform:
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^\infty f(t)e^{-st} dt \][/tex]
Break the integral into two parts based on the piecewise definition of f(t) :
[tex]\[ \mathcal{L}\{f(t)\} = \int_0^4 0 \cdot e^{-st} dt + \int_4^\infty (t - 4)e^{-st} dt \][/tex]
Solve each integral separately:
[tex]\[ \int_0^4 0 \cdot e^{-st} dt = 0 \][/tex]
[tex]\[ \int_4^\infty (t - 4)e^{-st} dt = \int_4^\infty te^{-st} dt - 4\int_4^\infty e^{-st} dt \][/tex]
Integrate:
[tex]\[ = \left[ -\frac{1}{s}te^{-st} \right]_4^\infty - \left[ -\frac{4}{s}e^{-st} \right]_4^\infty \][/tex]
[tex]\[ = \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) - \left(0 - \left(-\frac{4}{s}e^{-4s}\right)\right) \][/tex]
[tex]\[ = \frac{4}{s}e^{-4s} \][/tex]
Combine the results:
[tex]\[ \mathcal{L}\{f(t)\} = \frac{4}{s}e^{-4s} \][/tex]
So, the Laplace transform of f(t) is [tex]\( \frac{4}{s}e^{-4s} \)[/tex].
The Laplace transform of the given piecewise function f(t) is found using the Heaviside step function and shifting theorem, yielding[tex]\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
To find the Laplace transform of the function f(t), we'll break it down into two parts: one for t < 4 and another for [tex]\( t \geq 4 \).[/tex]
For t < 4 , f(t) = 0 , so its Laplace transform is simply 0.
For [tex]\( t \geq 4 \), \( f(t) = (t - 4)^3 \)[/tex]. We'll use the property of the Laplace transform that states [tex]\( \mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}} \). So, for \( f(t) = (t - 4)^3 \)[/tex], we get:
[tex]\[ \mathcal{L}\{(t - 4)^3\} = \frac{3!}{s^{3+1}} \\\[ = \frac{6}{s^4} \][/tex]
Now, we can combine both parts:
[tex]\[ \mathcal{L}\{f(t)\} = 0 \quad \text{for } t < 4 \\\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \quad \text{for } t \geq 4 \\\text{Therefore, the Laplace transform of}\; \( f(t) \) is:\[ \mathcal{L}\{f(t)\} = \frac{6}{s^4} \][/tex]
the difference between two integers is 13 and their sum is 87. What are the two integers
it would be 50 and 37
For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. the relationship can be represented by ŷ = 63.80 + 0.61x where y represents height (in centimeters) and x represents age (in months). joseph is 23.5 months old and is 80 centimeters tall. what is joseph's residual?
a.78.135
b.112.600
c.5.865
d.1.865
e.-32.600 f) none of the above
Answer: Joseph's residual is 1.86 (option d).
Step-by-step explanation:
Hi, to answer this question we have to replace the variable "x" for Joseph’s age (23.5 months) in the equation given:
y = 63.80 + 0.61x.
y = 63.80 + 0.61 (23.5)
y = 63.80 + 14.335 = 78.135
Now, we subtract the amount obtained to Joseph's height ( 80 centimeters).
Mathematically speaking:
80 - 78.135 = 1.865
So, Joseph’s residual is 1.86 (option d).
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what value of x makes the equation true? 9x - 15 - 2x = -60 + 9x
Thr profits in December were 5 times the profits in June. If Decembers profit were $3455 how much were thw profits in June?
Identify the binomial A. x2 −4x + 2 B. x2 C. x2 − 4 D. 2x2 + 3x −1 + y
The number 272 is a palindrome because it reads the same forward or backward How many numbers from 10 to 1000 are palindromes
how to slove multistep equation 2/5(x-2)=-3
PLEASE HELP NO ONE WILL HELP ME! I NEED PROS! TYSM! For f(x) = 3 x 5 − 5 x 3 + 3 . Determine the interval(s) on which f(x) is concave up and on which f(x) is concave down AND indicate where f(x) has inflection point(s). (If there are none, please tell me). Also, indicate where f(x) has local maximum and local minimum points. Also, can you please help me determine the interval(s) on which f(x) is increasing and on which f(x) is decreasing.
In six test runs, a truck operated 8, 10, 15, 7, 9, and 11 miles with one gallon of gasoline. at the 95% level of confidence, is this sufficient evidence to show that the truck is operating at a mean rate of about 13.1 miles per gallon (confidence interval)
Towing charge 30$ plus $3 per mile if I paid $117 how far was the car towed
What is a normal distribution with a mean of 0 and a standard deviation of 1 called?
A normal distribution with a mean of 0 and a standard deviation of 1 called The Standard normal distribution or z - distribution.
What is Standard normal distribution?A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.
Given that a normal distribution with a mean of 0 and a standard deviation of 1
In the given condition, the normal distribution is called Standard normal distribution or z - distribution or Gaussian distribution.
Hence, the normal distribution with a mean of 0 and a standard deviation of 1 called Standard normal distribution or z - distribution or Gaussian distribution.
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What is Kaycie's net income?
Answer:
Net income of Kaycie is $1,195
Step-by-step explanation:
We are given a monthly Income statement of September 2013.
First we count total income of Kaycie's
Income = Wages
Total Income = $2,700
Now we calculate total expenses
Kaycie's expenses are on food, rent clothing, transportation, medical and Insurance.
Expenses = Food+Rent+Clothing+Transportation+Medical+Insurance
Expenses=210+975+90+120+60+50
Total Expenses = $1,505
Net Income = Total Income - Total Expenses
Net Income = 2700 - 1505
Net Income = $1,195
Thus, Net income of Kaycie is $1,195.
Answer:
In so many words its "1,195"
Step-by-step explanation:
an office has an area 120 square meters and a width of 12 meters write an equation to represent the area
Ben is 8 years older than Sarah 10 years ago Ben was twice as old as Sarah how old are Ben and Sarah today
If you bike for 60km at 30km/h and return at 20km/h what is your average speed for the whole trip
What is the selling price if the actual cost is $720 and 43% markup on selling price
two pumps of different sizes, working together, can empty a fuel tank in 3 hours. the larger pump can empty the tank in 4 hours less than the smaller one. if the larger pump is not working, how long will it take the smaller pump to do the job alone?
To find the time it takes for the smaller pump to empty the tank alone, we need to first determine the rate of the smaller pump and solve an equation involving the rates of both pumps.
Explanation:Let's denote the rate at which the smaller pump can empty the tank as x gallons per hour. Since the larger pump can empty the tank in 4 hours less than the smaller pump, its rate would be x+4 gallons per hour.
Working together, the total rate at which they can empty the tank is the sum of their individual rates:
x + (x+4) = 1/3 gallons per hour.
Solving this equation will give us the rate of the smaller pump (x), and we can then calculate how long it would take the smaller pump to empty the tank alone.
Final answer:
To find the time it takes for the smaller pump to empty the tank alone, we calculate the combined rate of both pumps and set up an equation based on their separate rates. After solving, we find that it takes the smaller pump 6 hours to empty the tank by itself.
Explanation:
To solve this problem, we can set up a system of equations based on the rates at which the pumps work. Let's denote the time it takes the smaller pump to empty the tank alone as x hours. According to the problem, the larger pump can do this in x - 4 hours. When working together, they can empty the tank in 3 hours.
If the smaller pump's rate is 1/x tanks per hour and the larger pump's rate is 1/(x-4) tanks per hour, the combined rate when they work together is the sum of their individual rates, which is 1/3 tanks per hour.
We can set up the equation as follows:
1/x + 1/(x-4) = 1/3
To solve for x, find a common denominator and combine terms:
(x-4 + x)/(x(x-4)) = 1/3
Multiply all terms by the common denominator x(x-4) to clear the fractions:
2x - 4 = x(x-4)/3
Multiply both sides by 3 to get rid of the fraction:
6x - 12 = x2 - 4x
Rearrange the equation to set it to zero and solve for x:
x² - 10x + 12 = 0
By factoring, we find that x equals 6 or 2. However, since x - 4 must be greater than zero (a pump can't empty a tank in negative time), we discard the solution x = 2 and keep x = 6 hours as the correct answer.
Therefore, the smaller pump will take 6 hours to empty the tank alone.
A company’s profits (P) are related to increases in a worker’s average pay (x) by a linear equation. If the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, what is the slope of the graph of the equation?
Since the company’s profits drop by $1,500 per month for every increase of $450 per year in the worker’s average pay, the slope of the graph of the equation is -40.
In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
[tex]Slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]
Based on the information provided, we can logically deduce that the rise and run are as follows;
Rise = 12 × -1500 = 18,000 units (its negative because the profit drops)
Run = 450 units.
By substituting the given data into the formula for the slope of a line, we have the following:
Slope (m) = rise/run
Slope (m) = -18000/450
Slope (m) = -40.
A european outlet supplies 220 v (rms) at 50 hz. how many times per second is the magnitude of the voltage equal to 220 v
Explains how many times per second the magnitude of the voltage equals 220 V in a European outlet at 50 Hz frequency.
Explanation:The frequency at which the magnitude of the voltage is equal to 220 V is:
Convert the given 220 V (rms) to peak voltage: 220 V x √2 = 311.13 VSince the voltage alternates sinusoidally, it will reach 311.13 V twice per cycle (positive and negative peaks).For a 50 Hz frequency, the number of times the magnitude of the voltage equals 220 V will be 2 x 50 = 100 times per second.in the diagram below,point O is the center of the given circle.
Love them or hate them, they do be spitting straight facts