Since 3 members want to sit together, we'll calculate total ways for it and then for remaining seats in each of its case, we'll see in how many ways can those rest of 5 people wants to sit.
The total number of ways those 8 people can sit is 3,991,680 ways.
Given that:Total 14 seats are there in a row in a doctor's waiting room.8 people are waiting to be seated.3 people are of same family and want to sit together.To find:In how many ways can those people sit?
Number of ways in which 3 family members can sit:Since 3 people wants to sit together, then suppose seats are numbered 1,2,3,...,14.
Then those 3 people can choose seats as:
1,2,3
2,3,4
...
...
12,13,14
Total 12 ways.
In each way, those three can sit on those 3 chairs in any order. The number of ways 3 people will arrange themselves is 3! = 6 ways.
Thus:
Total ways those 3 people can sit in = 12 times 6 = 72 ways.
( i did multiplication since for each of 3 seat chosen they were sitting in 6 ways, and this repeated 12 times would end up on 12 times 6 = 72 ways).
Number of ways those remaining 5 people can sit on remaining 11 seats:On remaining seats (14-3 = 11), we have 5 people to sit.
Those people can choose any seat they want to sit on.
Total ways(combinations) they together choose 5 seats is given by: [tex]^11C_5 = 462 [/tex]
For each of those choice of seats, they can arrange themselves in 5! = 120 ways.
Thus, those 5 people can sit in 120 times 464 = 55440 ways.
Since on each choice of those 3 family members , we have 55440 ways of 5 people sitting on remaining 11 seats, thus in total we have:
55440 times 72 = 3,991,680 ways.
Thus, in total, those 8 people can sit in 3,991,680 number of ways in that row of the doctor's waiting room.
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Foston is between library and West Quan and is 4 inch away from the library on the map how far is Boston from West qual
Boston is 4 inches away from West Quan.
Explanation:Foston, positioned between the Library and West Quan on the map, is noted as being 4 inches away from the Library. Given that Library and West Quan lie on the same line, it can be inferred that Foston and West Quan share the same 4-inch separation. Consequently, the distance from Boston to West Quan is deduced to be 4 inches. This deduction is based on the assumption that the spatial relationship between Foston, Library, and West Quan forms a straight line. Therefore, the proximity of Foston to the Library serves as a reference for determining the distance between Foston and West Quan, establishing it at 4 inches.
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The gasoline tank of a minivan holds 18 gallons. How many quarts can the tank hold?
To convert 18 gallons to quarts, multiply by the conversion factor of 4 quarts per gallon, giving a result of 72 quarts.
The gasoline tank of a minivan holds 18 gallons. To determine how many quarts it can hold, we need to use the conversion factor that 1 gallon is equivalent to 4 quarts. Since we are converting from a larger unit to a smaller unit, we will multiply the number of gallons by 4.
18 gallons x 4 quarts/gallon = 72 quarts
Therefore, the minivan's gasoline tank can hold 72 quarts of gasoline.
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. 1)A deer is 10 miles per hour faster than a bison. 2)A bison is 10 miles per hour faster than a deer. 3)A deer is 0.66 miles per hour faster than a bison. 4)A bison is 0.66 miles per hour faster than a deer.
A coin is tossed 5 times. let x count the number of heads tossed. determine x hhtht ( ).
how do I set up 37 and 43
Suppose another sample of 41 students is to be randomly selected from this population. find the probability that the mean of this sample is greater than 110.
What is 225 percent as a decimal or fraction in simpilist form
Clay is playing darts. his dartboard contains ten equal-sized zones with point values from 1 to 10. write code that simulates his total score after 1000 dart tosses. make sure to use a for loop.
Answer:
Given parameters
Point values = 1 to 10 = 1,2,3...10
Dart tosses = 1000
Required:
Simulate total scores using a for loop
#This program is written using Python Programming Language
# Comments are used for explanatory purpose
#Program starts here
# The next line declares and initialize point_value as an array
point_value = make_array(1,2,3,4,5,6,7,8,9,10)
# The next line initializes total_score to 1
total_score =make_array(0)
# Initialise number of toss
tosses = 1000
# Simulate using for loop iteration
for i in np.arange(tosses)
result = np.random.choice(point_value)
# get score after playing each toss
total_score=np.append(total_score, result)
#calculate totalscores after 1000 games
totalscore=sum(total_score)
#Output result
print("The total score after simulation of 1000 tosses is ")
print(totalscore)
#End of program
Which expression is equivalent to −4.6+(−0.4)+(−7.2) ?
−(4.6−0.4)+(−7.2)
(4.6+0.4+7.2)
−4.6−(0.4+7.2)
(4.6+0.4)+(−7.2)
I took the test it's −4.6−(0.4+7.2)
The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 )
Here,
The given expression is −4.6+(−0.4)+(−7.2)
We have to find expression equivalent to −4.6+(−0.4)+(−7.2)
What is Number system?
A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
Now,
The given expression is,
−4.6+(−0.4)+(−7.2) = -4.6 - 0.4 - 7.2
= -4.6 - (0.4 + 7.2) ( we take common negative sign )
Hence,
The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 ).
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How many five digit zip codes are possible if digits cannot be repeated?
1st digit - 0-9 = 10 numbers
2nd digit = 9 numbers
3rd digit = 8 numbers
4th digit = 7 numbers
5th digit = 6 numbers
10 * 9 * 8 * 7 * 6 = 30,240 zip codes
A total of 428 tickets sold for the school play. They were either adults tickets or student tickets. The number of students tickets sold was three times the number of adult tickets sold. How many adults tickets were sold.
107 adult tickets were sold for the school play.
Explanation:Let's denote the number of adult tickets sold as x. According to the given information, the number of student tickets sold is three times the number of adult tickets sold. So, the number of student tickets sold would be 3x. The total number of tickets sold is 428, so we can set up the equation:
x + 3x = 428
Combining like terms, we have:
4x = 428
Dividing both sides of the equation by 4, we find:
x = 107
Therefore, 107 adult tickets were sold.
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An implicit equation for the plane passing through the point (-1,-4,5) that is perpendicular to the line l(t) = <1+2t,1+t,5+3t> is
Final answer:
The implicit equation of the plane is 2x + y + 3z - 14 = 0, found using the direction vector of the line as the normal vector for the plane and the given point to determine the specific plane equation.
Explanation:
To find an implicit equation for the plane passing through the given point (-1,-4,5) and perpendicular to the given line, we need to determine the direction vector of the line which will also serve as the normal vector to the plane. The equation of the line is given as l(t) = <1+2t, 1+t, 5+3t>, which suggests that the directional vector of the line (and thus the normal vector of the plane) is <2, 1, 3>.
Now, the general equation of a plane in 3D space can be given by Ax + By + Cz + D = 0, where <A, B, C> is the normal vector to the plane. Thus, substituting the normal vector and the given point into this equation will allow us to find the value of D and hence the implicit equation of the plane. In this case, the equation is given by:
2(x + 1) + 1(y + 4) + 3(z - 5) = 0, simplifying this gives:
2x + y + 3z - 14 = 0,
which is the implicit equation of the desired plane.
Final answer:
The implicit equation of the plane passing through the point (-1, -4, 5) and perpendicular to the line ℒ(t) is 2x + y + 3z - 9 = 0.
Explanation:
To find an implicit equation for a plane that is perpendicular to a given line, we first need the direction vector of the line. The line ℒ(t) = <1+2t, 1+t, 5+3t> has a direction vector of <2, 1, 3>, which also serves as the normal vector of the plane. The normal vector (A, B, C) and a point (x0, y0, z0) on the plane can provide an equation via the dot product: A(x - x0) + B(y - y0) + C(z - z0) = 0.
For the given point (-1, -4, 5), the equation becomes 2(x + 1) + 1(y + 4) + 3(z - 5) = 0. Simplifying, we get:
2x + 2 + y + 4 + 3z - 15 = 0
2x + y + 3z - 9 = 0
This is the implicit equation of the plane that passes through the point (-1, -4, 5) and is perpendicular to the given line.
The price of stamps just increased by $0.03. Beth wants to send out 30 party invitations. Write a formula that will help her determine how much it will cost. Let’s let p=old price per stamp
t=total cost for stamps
Find an equation in standard form for the hyperbola with vertices at (0, ±10) and asymptotes at y = ± five divided by six times x.. (2 points)
How do transformations affect the logarithmic graph?
Your great aunt sally loans you $5000 for three years and asks that you repay it with annually compounding interest at the rate of 8% per year. how much do you repay her after three years?
Prove that for any positive integer n a field f can have at most a finite number of elements of multiplicative order at most n
{$7.04,$7.04,$7.05,$11.99,$12.50,$12.99,$9.98,$9.99,$8.51,$11.95}
What is the mode?
What is the median?
What is the mean?
What is the IQR?
The mode of the given data set is $7.04, the median is $9.99, the mean is $9.634, and the IQR is $3.48.
Explanation:The mode of the given set is $7.04, as it occurs the most number of times.
The median is $9.99, which is the middle value when the data is arranged in ascending order.
The mean can be calculated by finding the sum of all the values and dividing it by the total number of values. In this case, the mean is $9.634.
The IQR (Interquartile range) is the difference between the third quartile and the first quartile. To find the IQR, we need to first calculate the quartiles. First, we arrange the data in ascending order: $7.04, $7.04, $7.05, $8.51, $9.98, $9.99, $11.95, $11.99, $12.50, $12.99. The first quartile is the average of the 3rd and 4th values, which is $8.51. The third quartile is the average of the 8th and 9th values, which is $11.99. Therefore, the IQR is $11.99 - $8.51 = $3.48.
Which equation has no solution? 4(x + 3) + 2x = 6(x + 2) 5 + 2(3 + 2x) = x + 3(x + 1) 5(x + 3) + x = 4(x + 3) + 3 4 + 6(2 + x) = 2(3x + 8)
Answer:
the answer is 5+2(3+2x)=x +3 (x+1)
Step-by-step explanation:
The equation second 5+2(3+2x)=x +3 (x+1) has no solution.
We have given that,
4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)
We have determine which equation has no solution.
When equation has no solution?The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
Therefore the equation second has no solution
[tex]5+2\left(3+2x\right)=x+3\left(x+1\right)[/tex]
[tex]4x+11=x+3x+3[/tex]
[tex]4x+11=4x+3[/tex]
[tex]4x+11-11=4x+3-11[/tex]
[tex]0=-8[/tex]
[tex]\mathrm{The\:sides\:are\:not\:equal}[/tex]
Therefore the second equation has no solution.
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A student expressed a sum of two whole numbers as 3 x (2 + 5). What were the two whole numbers?
Compute the maximal area obtainable if we assume that the farmer builds a field in the shape of an isosceles triangle, where the two equal sides are the fenced sides, and the third side is the river.
The maximal area of an isosceles triangle-shaped field by the river is achieved when the triangle is also a right triangle. The area can be maximized by using the derivative of the area expression, considering the sides of the triangle and the fixed perimeter.
Explanation:The question is asking to find the maximal area of an isosceles triangle-shaped field with two equal sides and the third side being the river.
To maximize the area of an isosceles triangle, the height of the triangle should be as large as possible, which occurs when the triangle is also a right triangle. The side opposite the right angle, which lies along the river, will be the base of the triangle.
By applying the Pythagorean theorem, if we have a fixed perimeter and the two equal sides are 'a' and 'a', and the base 'b' is along the river, we can express the area 'A' as A = (b/2) × √(a² - (b/2)²).
The area is maximized when the derivative of this area expression with respect to 'b' equals zero.
what is 75% of 400? Write an evaluate an expression to find the answer. Then explain how to use the model to justify the answer
Answer:
Step-by-step explanation: love your self
HELP ASA AND EXPLAIN!!
there is 2 attachments btw pppllzzz explain both of them
Solve the equation. 6^2x-4=14701 to 4 decimal places. (Doing Logs)
Evaluate the integral by interpreting it in terms of areas. 0 4 + 36 − x2 dx −6
To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. This represents the area between the curve and the x-axis.
Explanation:To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. Since the function is given as 36 - x^2, it represents the area between the curve and the x-axis. The integral from 0 to 4 represents the area between the curve and the x-axis above the x-axis, while the integral from 0 to -6 represents the area between the curve and the x-axis below the x-axis.
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Find the general solution of the given differential equation. x2y' + x(x + 2)y = ex
What is 0.003 of 1/10 as much as
How many solutions does the following equation have?
|3x + 12| = 18 (5 points)
No solution
One solution
Two solutions
Infinitely many solutions
Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) > 0, cos (t) < 0.
For the past 7 years, George and Sue have deposited $10,000 in a retirement account with a simple interest rate of 4%. They plan to continue to make annual deposits for the next 15 years. Explain how their money will grow over time. Note: You do not need to extend their entire savings for 22 years in your explanation. Focus on the earning for the first several years and explain how their money will grow.
Answer:
George and Sue's money will grow due to both to their contributions and the simple interest that they accrue. Simple interest means that the interest they receive will be applied to the principle, but not the interest that has been accrued. This means that for every $10,000 they put in, they will receive $400 dollars in interest every year, and this number will not change with time.
Right now, they've deposited 10,000 every 7 years for a total of 70,000 dollars. Their annual interest therefore is 400 * 7 = 2800. With every 10,000 dollars they deposit, the yearly interest will grow by $400. This is different from compounding interest, in which annual interest will grow by more than $400 dollars every year since the rate will be applied to principle and all accrued interest.
Step-by-step explanation: