The Volume of the solid obtained by rotating the region bounded by the curves is 5 cm³.
Volume of a solid plain:
The volume of a solid is a measure of the space occupied by an object. It is measured by the number of unit cubes required to fill the solid.
Given in the question:
y = 2 - 1/2x
y = 0 , x = 1 and x = 2
As we know that:
[tex]\int\limits^2_1 {\pi (2 - \frac{1}{2}x - 0 })^2 \, dx[/tex] ------------------------------ (1)
Simplifying,
[tex]\pi \int\limits^2_1 {(2 - \frac{x}{2} )}^2 \, dx[/tex][tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi \int\limits^2_1 {(4 - 2x + \frac{x^2}{4} )\, dx[/tex]
⇒ [tex]\pi [ 4x - x^2 + \frac{x^3}{12}]_1^2[/tex]
⇒ [tex]\pi [(8 - 4+ \frac{8}{12} ) - ( 4 - 1 + \frac{1}{12} )[/tex]
⇒ [tex]\pi (1 + \frac{7}{12})[/tex]
⇒ [tex]\frac{19\pi }{12}[/tex]
We can write 19π / 12 as
(19× 22/7 )÷ 12
= 209/ 42
= 4.97 ≈ 5 cm³
Therefore, the volume is 5 cm³
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9y+4=7y+20
Please explain step by step to get marked as brainliest
Answer:
y=8
Step-by-step explanation:
9y-7y=20-4
2y=16
y=16/2
y=8
Fetzer Company declared a $0.55 per share cash dividend. The company has 480,000 shares authorized, 456,000 shares issued, and 19,200 shares in treasury stock. The journal entry to record the payment of the dividend is:
Debit Common Dividends Payable $ 234,850 ; credit Cash $ 234,850.
What is arithmetic?
Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addi - tion, subtraction, multiplication, division, exponents, and root extraction. The Peano axioms, developed by the Italian mathematician Giuseppe Peano in the 19th century and still vital to the modern study of mathematical logic, formalised arithmetic. There are only a few ancient artefacts that can be used to date the invention of addition and subtraction. The best-known of these is the disputedly interpreted Ishango bone from africa, which dates to between 20,000 and 18,000 BC.
Main Body:
Debit Common Dividends Payable $100,100; credit Cash $100,100.
= $0.55 * (456,000 shares - 19,000 shares)
= $0.55 *427,000 shares
= $ 234,850
Hence ,debit Common Dividends Payable $ 234,850 ; credit Cash
$ 234,850.
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The formula F = (9/5)C + 32 can be used to convert between degrees Celsius (C) and degrees Fahrenheit (F). What number of degrees Fahrenheit corresponds to 30° Celsius?
Group of answer choices
A) 86
B) 13
C) 62
D) 22
The required number of degrees is 86° Fahrenheit corresponds to 30° Celsius.
The formula is given in the question following as:
F = (9/5)C + 32 ....(i)
It can be used to convert between degrees Celsius (C) and degrees Fahrenheit (F).
We have to number of degrees Fahrenheit corresponds to 30° Celsius
As per the given question, we have
F = (9/5)C + 32
Substitute the value of C = 30 in the given formula, and solve for F
F = (9/5)(30) + 32
F = (270)/(5) + 32
F = 54 + 32
F = 86
Thus, the required number of degrees is 86° Fahrenheit corresponds to 30° Celsius.
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Answer: the answer is 86
Step-by-step explanation: I have my ways ;>
What is 13(2x+5)-11x
Which of the following is an identity?
A. csc²x + cot²x = 1
B. (cscx + cotx)2 = 1
C. sin²x-cos²x = 1
D. sin²x sec²x + 1 = tan²x csc²x
Answer:
Step-by-step explanation:
it is D as
L.H.S.=sin²x sec²x+1
[tex]\frac{sin^2x}{cos^2x} +1\\=\frac{sin^2x+cos^2x}{cos^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
again
[tex]R.H.S.=tan^2x csc^2x\\=\frac{sin^2x}{cos^2x} \times \frac{1}{sin^2x} \\=\frac{1}{cos^2x} \\=sec^2x[/tex]
L.H.S.=R.H.S.
A rectangle is 4 feet longer than it is wide. If the area of the rectangle must be less than or equal to 672 square feet, find the possible values for the width .
The possible values for the width of rectangle are 24 and -28.
What is area of rectangle?
The area of a rectangle formula. Area of a Rectangle is A = l × b. Once the length and width of a rectangle are known, the area can be calculated. The area of the rectangle is calculated as a square unit by multiplying the length and width.
Let x is the width of rectangle.
As given a rectangle length is 4 feet longer than it is wide.
⇒ l = 4 + x
Since,
Area of rectangle = length x width
672 = (4 + x) x x
672 = 4x + x^2
x^2 + 4x - 627 = 0
To find the value of x we can use the quadratic formula.
Here a = 1, b = 4, c = -672
[tex]x = \frac{-b +-\sqrt{b^2-4ac} }{2a} \\x = \frac{-4+-\sqrt{4^2-4(1)(-672)} }{2(1)} \\x = \frac{-4+-\sqrt{2704} }{2} \\x = \frac{-4+-52}{2} \\x = -2+-26[/tex]
⇒ x = -2 + 26, x = -2 - 26
⇒ x = 24, x = -28
Hence, the possible values for the width of rectangle are 24 and -28.
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8.22. Let S be the set of all polynomials of degree at most 3. An element s(x) of S can then be expressed as
s(x) = ax3 + bx2 + cx + d, where a, b, c, d ? R. A relation R is defined on S by p(x) R q(x) if p(x) and
q(x) have a real root in common. (For example, p = (x ? 1)^2 and q = x^2 ? 1 have the root 1 in common so
that p R q.) Determine which of the properties reflexive, symmetric, and transitive are possessed by R.
R possess Symmetric property.
Let S be the set of all polynomials of degree at most 3.
s(x) = ax³ + bx² + cx + d
we know that polynomial is a mathematical expression of one or more algebraic terms each of which consist of a constant multiplied by one or more variables raised to a non negative power.
The reflexive property states that every element of the set is related to itself.
The symmetric property is defined as if one element in a set is related to the other, then we can say that the second element is also related to the first element.
The transitive property states that if a, b, c are three quantities, and if a is related to b and b is related to c then a and c are related to each other.
So here we observe that R will posses symmetric property.
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for which equation is 0 not a solution x 5 4 6 x 4 4 3 x 0 x 9 9
On solving the provided question we can say that the answer is third one , that equation is 3 x = 0.
What is quadratic equation?Any equation that can be written in standard form, with x denoting an unknown value and a, b, and c denoting known integers, is referred to as a quadratic equation in algebra. In general, it is assumed that a > 0; equations with a = 0 are thought to be degenerate since they become linear or even more basic.
Here,
thus ,the given equation :
x - 5 = 4
6 x + 4 = 4
3 x = 0
x + 9 = 9
Thus , the given equation 3 x = 0 have 0 as its solution.
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suppose the measurement of the side of a square is found to be 30 cm with an error of cm. use differentials to estimate the propogated error in computing the area of the square.
The propagated error in computing the area of the square is 6.01 cm
According to the question,
It is given that Length of side of square was found = 30cm
The possible error in measurement = 0.1cm
So, the length will be 30 + 0.1cm or 30 - 0.1cm
As we know that
Area of the square : A = x²
Where x is side of square
The differential of this equation =
=> dA/dx = 2x --------(1)
If dx is the error of the side length of the square
dA = 2(30)(0.1)
=> dA = 6
Therefore , The propagated Error = ΔA = (x + Δx)² - x²
=> (30 + 0.1)² - (30)²
=> 906.01 - 900
=> 6.01
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on a field trip, there are `3` chaperones for every `20` students. there are `92` total people on the trip.
There are 12 chaperones in total.
In molecular biology, molecular chaperones are proteins that help big proteins or macromolecular protein complexes fold or unfold conformationally. There are different groups of molecular chaperones, all of which have the same purpose: to help big proteins fold properly during or after synthesis as well as following partial denaturation. Protein translocation for proteolysis involves chaperones as well.
The first molecular chaperones to be identified are an assembly-type of chaperones that help nucleosomes form from folded histones and DNA.
Since heat stress increases the propensity for protein aggregation, one of the main roles of molecular chaperones is to prevent the accumulation of misfolded proteins. As a result, many chaperone proteins are categorized as heat shock proteins.
Chaperones and students combined: 3 + 20 = 23
by the number of individuals in total:
92 / 23 = 4
Divide that sum by the proportional number of chaperones:
4 x 3 = 12
There are 12 chaperones in total.
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et p be prime. determine the number of polynomials of the form x2 ax b which are [15 pts] irreducible over zp.
We observe that there are p² polynomials of the form x² + ax + b in Zp.
Since there are p choices for each of a and b.
Now a polynomial which is reducible over Zp may be rewritten in the form
(x - c)(x - d)
where c and d are roots.
So there are p choices if c = d
and if c ≠ d then there are [tex]\frac{p(p-1)}{2}[/tex] choices, the division of 2 eliminates repeated pairs.
Therefore there are p² - ( p + [tex]\frac{p(p-1)}{2}[/tex]) polynomials irreducible over Zp.
A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. The property of irreducibly depends on the field or ring to which the coefficients are considered to belong. Irreducible polynomials appear naturally in polynomial factorization and algebraic field extension.
A polynomial expressible as the product of two or more polynomials of lower degree is known as Reducible polynomial.
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what is the slope of a line parallel to the line whose equation calculator; what is the slope of a line parallel to the line whose equation is y; what is the slope of a line parallel to the line y=โ3/2x+3?; what is the slope of a line perpendicular to the line whose equation; what is the slope perpendicular to the line โ2x+y=โ7?; simplest form fractions
The slope of a line parallel to the line y=3/2x+3 is 3/2 and the slope of the line perpendicular to the line 2x+y=7 is 1/2
In this question we need to find the slope of line.
a)
We need to find the slope of a line parallel to the line y=3/2x+3
The slope of line y=3/2x+3 is 3/2
We know that the slope of parallel lines is equal.
So, the slope of a line parallel to the line y=3/2x+3 is 3/2
b)
We need to find the slope of the line perpendicular to the line 2x+y=7
We can write above equation of line in slope-intercept form of equation of line.
y = -2x + 7
This line has slope -2
We know that the product of slopes of perpendicular lines is -1.
Let m be the slope of required line.
So, m * (-2) = -1
m = 1/2
So, the slope of the line perpendicular to the line 2x+y=7 is 1/2
Therefore, a) the slope of a line parallel to the line y=3/2x+3 is 3/2
b) the slope of the line perpendicular to the line 2x+y=7 is 1/2
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what is the answer? i need it graphed out for me
The graph of the piece-wise function in this problem is given by the image shown at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, based on which interval the input value of the function belongs to.
In this problem, the function has three definitions, given as follows:
Zero -> to the left of -1, with -1 inclusive.y = -x - 1, to the right of -1 and to the left of 2, inclusive at 2.y = -1, to the right of 2.Hence the graph is defined as follows:
Horizontal line at y = 0 to the left of -1, with a closed circle at point (-1,0).Decaying line between points (-1,0) and (2,-3), with a closed circle at (2,3).Constant line at y = -2 from x = 2 and until infinity.More can be learned about piece-wise functions at https//brainly.com/question/19358926
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a deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.
40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.
Given fill-in-the-blank;
A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.
The answer for this case is Intermediate.
A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.
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On January 1, Year 1, the Platte Corporation issues a 5-year note payable for $5,000. The interest rate is 5% and the annual payment of $1,156, due each December 31, includes both interest and principal. Which of the following correctly shows the effect of the issuance of the note on Platte's financial statements?
The correct effect of the note issuance on Platte's financial statements is A. Cash and Notes Payable increased by $5,000 on the balance sheet and an increase in Financing Activity on the Cash Flows Statement.
What is the journal entry to record the issuance?The journal entry to record the issuance of the 5-year note payable for $5,000 by Platte Corporation on January 1, Year 1 includes:
Debit to Cash
Credit to Notes Payable.
This entry increases the Cash account, an asset that appears on the balance sheet.
It also increases the Notes Payable, a liability on the balance sheet.
On the Cash Flow Statement, the issuance is a financing activity as cash inflow is increased by the amount.
January 1, Year 1:
Note payable = $5,000
Note period = 5 years
Interest rate = 5%
Annual payment = $1,156
Thus, the note issuance does not affect the Income Statement and will not have an effect on the Equity, but Option A is correct.
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Question Completion:Answer Options are attached.
A study found that 50 pedestrians gave more money to a street beggar if the beggar had a cute and hungry-looking dog with them compared to if they were alone. The gender of the pedestrians was also noted. Which of the following sentences describes a simple effects analysis on these data? A The effect on donations, of having a dog compared to not calculated separately for male and female pedestrians B The difference in donations when the beggar had a dog compared to not C Using a graph to do a simple inspection of the mean donations from male and female pedestrians when the beggar had a dog or was alone D The relative difference between male donations and female donations when the beggar had a dog compared to not
The effect on donations, of having a dog compared to not calculated separately for male and female pedestrians is a simple effects analysis on these given data. So the option A is correct.
There are two degrees of gender representation when comparing women and men. Each independent variable in an experiment comparing the effects of a drug to a control group receiving no treatment can have two or more levels.
Street beggars and panhandlers collectively carry a lot of stigma. This study is based on an ethnographic street survey of local panhandlers who are homeless. These frequent exchanges between certain street people and certain.
A simple effect analysis is "The difference in donations between having a dog and not, measured individually for male and female pedestrians."
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El coche de juan viaja 20 m/s y el coche de pedro recorre 150 metros en 5 segundos. Si ambos tienen rapidez constante ¿ cuantas veces es mas rapido el coche de pedro que el coche de juan?
Therefore , the Pedro's car speed is 2 times the Juan car speed.
Define the speed.Speed is a measure of how fast something or an individual is moving. It is possible to determine an object's average speed if you are aware of how far it has come and how the time it took to get there. Speed is determined by the formula: speed = distance * time.
Here,
Juan car travels 15 m/s
Where as Pedro's car travels 150 meters in 5 seconds.
Thus,
Pedro car speed is
=> 150/5
=>30 m/s
thus , pedro car speed is 30 m/s
Therefore , the pedro car speed is 2 times the Juan car speed.
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. A cartographer creates a map using the function
d = 250n where n is the number of inches on the
map and d is the actual distance between the
locations in miles. If the actual distance between
two cities is 1,125 miles, how far apart on the ma
should the cities be?
(A) 0.5 inches
(B) 1.5 inches
(C) 2.5 inches
(D) 4.5 inches
To find the distance between two cities on the map, we can use the formula provided in the question:
d = 250n
where d is the actual distance between the cities in miles, and n is the number of inches on the map. Since we are given that the actual distance between the two cities is 1,125 miles, we can substitute this value for d in the formula above to find the number of inches on the map:
1,125 = 250n
Solving for n, we get:
n = 1,125 / 250 = 4.5 inches
This means that the distance between the two cities on the map should be 4.5 inches, so the correct answer is (D) 4.5 inches.
The T distribution :
A) assumes the population is normally distributed
B) approaches the normal distribution as sample size increase
C) has more area in the tails than normal distribution
D) all the above
According to the T distribution, the correct option is (d) All the above
T distribution:
In statistics, t-distribution is used in all forms of t-tests. Where the T-tests are all classified as inferential statistical tests and will follow all of the same steps required to complete the process of null hypothesis significance testing. And it defines the exact shape of the t-distribution is governed by the degrees of freedom. And the t-distribution is associated with a degrees of freedom equal to the sample size minus a value of 1.
Given,
Here we need to find the correct option according to the T distribution.
As per the given options, the correct answer is best represented by option D. All of the above are correct.
Because, the t-distribution, along with the normal distribution, both assume data is normally distributed in the population.
When the sample size increases towards 30, the t-distribution will resemble the normal distribution, provided the data in the population is normally distributed.
If it is correct to state that the tails of the t-distribution are thicker compared to the normal distribution.
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The adjusted R^2: is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model
True False
True , The adjusted R^2: is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model .
Given :
The adjusted R^2: is used primarily to monitor whether extra explanatory variables really belong in a multiple regression model .
If the regression equation includes anything other than a constant plus the sum of products of constants and variables, the model will not be linear.
Adjusted R^2 is a corrected goodness - of - fit ( model accuracy ) measure for linear models. It identifies the percentage of variance in the target field that is explained by the input or inputs.
So the above statement is true.
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what was the mistake that was made?
Answer:In step 1 the equation should be 1/4r=8
Step-by-step explanation:
1/4r+2=10
-2 -2
1/4r=8
r=32
The error was instead of subtracting 2 from each side Yusuf added 2 to the ten. The correct way would be.
1/4r + 2 = 10
- 2 - 2
1/4r = 8
÷1/4 ÷1/4
r = 32
what is the remainder in the synthetic division below
The Remainder in the Synthetic division is three, for given problem
1 |__1___2__-3__3 is 3.
So, the correct option is option(c).
The Synthetic Division:
It is defined as the method of dividing the polynomial by the binomial is known as the synthetic division. It stands for polynomial division. Here, the division principle is performing in the coefficient of the polynomial.
We have given that the synthetic division is
1 |__1___2__-3__3
We find out the remainder in the synthetic division :
Multiply the carry-down value (i.e 1) by the test zero on the left, and carry the result(i.1×1 = 1) up into the next column inside:
1 | 1 2 -3 3
|______________
1
Add down the column( 2+1 = 3) :
1 | 1 2 -3 3
|____1_________
1 3
Multiply the previous carry-down value (i.e 3) by the test zero, and carry the new result up into the last column:
1 | 1 2 -3 3
|____1____3____
1 3 0
1 | 1 2 -3 3
|____1____3___0_
1 3 0 3
three, last carry-down value is the remainder.
Therefore, the remainder is 3. The option c is correct.
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Complete question:
What is the remainder in the synthetic division problem below?
a. 6
b. 4
c. 3
d. 5
You bought a car 3 years ago, taking out a $14,000.00 loan at a 5.8% interest rate for 4 years.
Your monthly payments are $327.51.
A. How much will still be owed after making payments for 3 years?
I will still owe ________
after making payments for 3 years.
B. If the car's value is now $7,500.00 then how much equity do you have after making payments for 3
years?
I will have ______ in equity after making payments for 3 years.
Enter the given values.
N: =
0
Number of Compounding Periods
1:%=
0
Annual Interest Rate as a Percent
PV: =
0
Present Value
PMT: = 0
Payment
FV: =
Future Value
P/Y:
Payments per Year
C/Y:
0
12 :
Solve
Solve
12 :
Compounding Periods per Year
PMT: = END Payments are made at the end of the period
Answer:
To answer these questions, we need to first calculate the total number of payments you have made over the past 3 years. We can do this by multiplying the number of payments per year (12) by the number of years (3). This gives us a total of 36 payments.
Next, we can use a financial calculator or spreadsheet program to solve for the remaining balance on your loan after making 36 payments of $327.51 each. In a financial calculator, we can enter the following values:
N: 36
I: 5.8
PV: -14000
PMT: 327.51
FV: 0
Solving for PV gives us a remaining balance of $4,819.56. Therefore, the answer to part A is $4,819.56.
To find your equity in the car, we can subtract the remaining balance on the loan from the value of the car. In this case, your equity would be $7,500.00 - $4,819.56 = $2,680.44. Therefore, the answer to part B is $2,680.44.
Step-by-step explanation:
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a one sided confidence interval bounding the high side is desired for the true average stray-load loss (in watts) for a certain induction motor when the line current is held at 10 amps for a speed of 1500 rpm. assume that the stray-load loss population is normally distributed with standard deviation = 2. Compute a one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71. Give your answer accurate to three decimal pointsPlease show steps with out excel or calculators I use tables only
using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
The standard normal distribution table is used to calculate the critical value for this problem.
The critical value at 99% confidence level is 2.576.
The formula for the one-sided confidence interval is given by:
Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n))Therefore, the one-sided 99% Confidence Interval for mu when n = 86, and X_Bar =71 is:
Upper Bound = 71 + (2.576 * 2/sqrt(86))
Upper Bound = 71 + (1.41)
Upper Bound = 72.41
The one-sided 99% Confidence Interval for mu when n = 86 and X_Bar =71 is calculated by using the standard normal distribution table to find the critical value of 2.576, and then using the formula Upper Bound = X_Bar + (critical value * standard deviation/sqrt(n)) to calculate the upper bound of the interval. The result is an upper bound of 72.41.
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Evaluate for d = 10, u = 7, e = 3. 2 de
i think its 28 but im not sure
Answer:
32
Step-by-step explanation:
Just plug in the numbers for [ d times e ]
The equation is then [ 10 x 3.2 = ? ]
The answer is 32
6. Solve 8(12-4x) ≥ 82 and graph the solution set.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
The solution set is x ≤ 0.4.
The graph of the solution is
<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>
<------------------o
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
8(12 - 4x) ≥ 82
96 - 32x ≥ 82
96 - 82 ≥ 32x
14 ≥ 32x
x ≤ 14/32
x ≤ 7/16
x ≤ 0.4
This can be graphed using a number line.
<-----__-1.5__-1__-0.5__0__0.5__1__1.5------>
<------------------o
Thus,
The solution set is x ≤ 0.4.
The graph of the solution is given above.
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A baker has 1 1/4 cups of sprinkles, and he buys another 1/2 cup of sprinkles. He plans to use them to spread on cupcakes. Each cupcake needs 1/8 cup of sprinkles. How many cupcakes can the baker sprinkle?
Answer:
i think it 5/
orry if i wrong
Step-by-step explanation:
Jangles Co. earned $1.80 per share. Assuming a closing price of $40, the PE ratio is: (Round to the nearest whole number.)
Multiple Choice
7
22
72
20
The PE ratio will be equal to $22. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jangles Co. earned $1.80 per share. Assuming a closing price of $40. The PE ratio will be calculated as,
Earning per share = $1.80
The price of the share = $40
PE ratio = Price of the share ÷ Earning per share
PE ratio = $40/$1.8-
PE ratio = $22.
Therefore, the PE ratio will be equal to $22. The correct option is B.
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a popular online video game can be played on multiple platforms: video game consoles, personal computers, and mobile devices. the game offers 333 gameplay modes: solo, duo, and squad. lee and avery regularly play matches as teammates in duo mode on a video game console. they are curious how their average scores per match compare to other players. they use the game's website to take a large random sample of duo mode players on any platform. the sample has a mean of 585585585 points per match.
Choose 1 answer: a. Only the players in the sample b. Only duo mode players who also play on a video game console c. Players of any mode who play on a video game console d. only Only duo mode players who play on any platform e. Players of any mode on any platform
Only duo mode players who play on any platform .
The correct answer will be Option D.
Given, Popular online video game .
As they have taken the random sample from the population of duo mode players from any of the three platform, in this regard, 558 points will be the legitimate estimate of the mean from that population only as this sample is a part of that population.
In general, we can say 558 points is the point estimate of the mean of the population that play duo mode in any platform.
Hence option D is correct .
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There are 8 people participating in a focus group for a new software product related to the health system, 3 of them are software engineers, 2 of them are nurses, 1 of them is a doctor, and the remanining 2 people are technicians. In how many ways they can be seated in a row so that no two software engineers are together? Show all your work to get credit
In 480 ways people can be seated in a row so that no two software engineers are together.
We have given that there are 8 people participating in a focus group, 3 of them are software engineers, 2 of them are nurses, 1 is doctor and 2 are technicians.
So the 3 software engineers can sit in 3! ways,
2 nurses can sit in 2! ways,
doctor can sit in 1! way and
2 technicians can sit in 2! ways.
We have to find that how many ways they can sit such that no two software can sit together.
So we first place 5 people in a row and software engineers has to sit between them so no two software engineers are to be sited together.
We get that in 6 places they can sit in 6C3 ways
i.e 6C3 = 20 (by formula of combination)
Therefore total ways are,
6 × 2 × 1 ×2 × 20 = 480.
Hence in 480 ways people can be seated in a row so that no two engineers are together.
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