Answers
Answer:
D
Step-by-step explanation:
The augmented matrix for the system of three equaitons is
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\5&2&-2&|&11\\5&-4&4&|&-7\end{array}\right)[/tex]
Multiply the first row by 5, the second row by -3 and add these two rows:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\5&-4&4&|&-7\end{array}\right)[/tex]
Subtract the third row from the second:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&6&-6&|&18\end{array}\right)[/tex]
Divide the third row by 6:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&1&-1&|&3\end{array}\right)[/tex]
Now multiply the third equation by 26 and add it to the second row:
[tex]\left(\begin{array}{ccccc} 3&-4&-5&|&-27\\0&-26&-19&|&-168\\0&0&-45&|&-90\end{array}\right)[/tex]
You get the system of three equations:
[tex]\left\{\begin{array}{r}3x-4y-5z=-27\\-26y-19z=-168\\-45z=-90\end{array}\right.[/tex]
From the third equation
[tex]z=\dfrac{90}{45}=2.[/tex]
Substitute z=2 into the second equation:
[tex]-26y-19\cdot 2=-168\\ \\-26y-38=-168\\ \\-26y=-168+38=-130\\ \\y=\dfrac{130}{26}=5.[/tex]
Now substitute z=2 and y=5 into the first equation:
[tex]3x-4\cdot 5-5\cdot 2=-27\\ \\3x-20-10=-27\\ \\3x-30=-27\\ \\3x=-27+30=3\\ \\x=1.[/tex]
The solution is (1,5,2)
The correct answer is option d (1, 5, 2).
To solve the system of equations, let's write the augmented matrix and perform row operations to get it into reduced row-echelon form (RREF). The system of equations is as follows:
3x−4y+5z (1)
5x+2y−2z (2)
5x−4y+4z (3)
The augmented matrix for this system is:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\5&2&-2&|11\\5&-4&4&|7\end{array}\right][/tex]
Now, let's perform row operations to get the reduced row-echelon form:
Subtract 5 times the first row from the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\5&-4&4&|7\end{array}\right][/tex]
Subtract 5 times the first row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&22&-27&|-134\\0&16&-21&|-118\end{array}\right][/tex]
Multiply the second row by 8/11:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&16&-21&|-118\end{array}\right][/tex]
Subtract 16 times the second row from the third row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&5/11&|10/11\end{array}\right][/tex]
Multiply the third row by 11/5:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&-8/11&|-67/11\\0&0&1&|2\end{array}\right][/tex]
Add 4/11 times the third row to the second row:
[tex]\left[\begin{array}{ccc}3&-4&5&|27\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the third row to the first row:
[tex]\left[\begin{array}{ccc}3&-4&0&|35\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Add 4 times the second row to the first row:
[tex]\left[\begin{array}{ccc}3&0&0&|39\\0&1&0&|1\\0&0&1&|2\end{array}\right][/tex]
Now, we can read off the solutions:
3x=39⇒x=13
y=1
z=2
So, the correct answer is (d) (1,5,2).
Related Questions
NEED HELP ASAP!!
20 POINTS and please explain if you can.
Answers
Answer:
x = 12 or A
Step-by-step explanation:
Tangents from an exterior point to the circumference of a circle are equal
Since one of the tangents = 17, the other one must as well
x + 5 = 17 Subtract 5 from both sides.
x + 5-5 = 17-5
x = 12
The answer is A
dwight is 3 years older than twice his sisters age . how old is dwight (write the expression)
Answers
Answer:
Step-by-step explanation:
let dwight represent x nd his sister represent y
y+3x2=x
Answer:
I did not know that Dwight Schrute has a sisterrrrr
Step-by-step explanation:
Um just the other dude brainliest
An elevator in a hotel moves at 20 feet per second. leaving from the ground floor, its height in feet after t seconds is given by the formula h(t)=20t. A bolt comes loose in the elevator shaft above, and its height in feet after falling for t seconds is given by h(t)=-16t^2+200. At what time and at what height does the bolt hit the elevator?
Answers
Answer:
After 7.5 seconds and a height of 0
Step-by-step explanation:
The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.
Given that the elevator height is h(t)=20t while the bolt height is given by h(t)=-16t² + 200.
At the point when the bolt hit the elevator, they would be at the same height, hence:
-16t² + 200 = 20t
16t² + 20t - 200 = 0
t = -4.2 or t = 3
Therefore the time taken for the bolt to hit the elevator is 3 seconds, the height is:
h(3) = 20(3) = 60 feet
The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.
Find out more at: https://brainly.com/question/11600459
g(r)=−(r+11)(r+14)
1) What are the zeros of the function?
Write the smaller r first, and the larger r second.
smaller r____
larger r_____
2) What is the vertex of the parabola
(___,____)
Answers
1) What are the zeros of the function?
smaller r: -11, larger r: -14
2) What is the vertex of the parabola
Vertex: (-12.5, 3)
1. Zeros:
The zeros of the function occur when G(r) = 0. So we need to solve the equation:
-(r + 11)(r + 14) = 0
Since the product of two factors is zero when one or both factors are zero, we can set each factor equal to zero and solve for r:
r + 11 = 0 --> r = -11 (smaller r)
r + 14 = 0 --> r = -14 (larger r)
2. Vertex:
The function is given in factored form, which makes finding the vertex a bit easier. The vertex of a parabola in factored form is exactly between the two zeros.
Therefore, the x-coordinate of the vertex is:
(smaller r + larger r) / 2 = (-11 - 14) / 2 = -12.5
To find the y-coordinate (i.e., the function's value at the vertex), we can plug the x-coordinate of the vertex back into the function (G(r)). However, since the function is multiplied by -1, it might be easier to use one of the original zeros (say, r = -11).
G(-11) = -(-11 + 11)(-11 + 14) = 3 (notice how the negative sign cancels out)
Percent Increase
Example 1: Ann works in a supermarket for $10.00 per hour. If her pay is increased to $12.00, then what is her percent increase in pay?
Analysis: When finding the percent increase, we take the absolute value of the difference and divide it by the original value. The resulting decimal is then converted to a percent.
Answers
Answer:
20% increase
Step-by-step explanation:
Percent increase = (difference) / original *100 percent
= (12-10)/10 * 100percent
= 2/10 *100 percent
= 1/5 * 100 percent
=.2 * 100 percent
= 20%
Find the area of the rhombus.
Please help ASAP
Answers
Answer:
The area of rhombus = 195 yd²
Step-by-step explanation:
Points to remember
Area of rhombus = d₁d₂/2
Where d₁ and d₂ are the diagonals of the rhombus
To find the area of given rhombus
Here diagonals of rhombus are given
From the figure we get,
d₁ = 13 + 13 = 26 yd and
d₂ = 7.5 + 7.5 = 15 yd
Area = d₁d₂/2 = (26 * 15 )/2 = 13 * 15 = 195 yd²
Therefore the area of rhombus = 195 yd²
Find the mean for each set of data. Round to the nearest tenth if necessary.
5, 10, 10, 20, 20, 5, 20, 20, 15, 15
Answers
Answer:
14
Step-by-step explanation:
Mean = (5+10+10+20+20+5+20+20+15+15)÷10
= 140÷10
= 14
Distance formula: Does the point (2, rt sqr. 6 ) lie on the circle shown? Explain.
Answers
Answer:
Thus, the fourth answer choice is the correct one
Step-by-step explanation:
Let's check this, using the Pythagorean Theorem:
"Yes, the distance from (0, 0) to (2, square root 6 ) is 3 units."
Does 2² + (√6)² = 3²?
Does 4 + 6 = 9? NO. .
Given: Ray BC bisects angle ABD.
Which pair of angles must be congruent?
A) ∠ABD & ∠EBD
B) ∠ABC & ∠DBE
C) ∠ABC & ∠DBC
D) ∠ABD & ∠CBDill mark brainliest if correct and give 50 pts.
Answers
Congruent is the same size and same shape. When a ray bisects an angle, the two newly created angles will be congruent, since the ray went right in the middle of the first angle (so in this case, ABC and DBC will be congruent)
Answer: C) ∠ABC & ∠DBC
Step-by-step explanation:
When a ray bisect an angle , then it divided the original angle into two congruent angles.
We are given that Ray BC bisects angle ABD.
Then, Ray BC divides ∠ABD into two congruent angles.
From the picture, The angle formed by it : ∠ABC & ∠DBC
So ∠ABC & ∠DBC must be congruent.
Hence, the pair of angles must be congruent : ∠ABC & ∠DBC
Type the correct answer in each box. Use pi= 22/7, and round your answers to the nearest interger. The perimeter of the largest cross section of a sphere is 88 centimeters. The radius is 14 cm. The volume of the sphere is __ cm^3
Answers
Answer:
11,499 cm^3
Step-by-step explanation:
The volume of a sphere is given by the formula [tex]V=\frac{4}{3}\pi r^3[/tex]
The radius is given as 14, we plug it into the formula and find the volume:
[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}(\frac{22}{7}) (14)^3\\V=11498.66[/tex]
rounded to nearest integer, the volume is 11,499
Answer:
r=14 cm
V=11499 cubic cm
Step-by-step explanation:
If the radius of the sphere is r cm, then the perimeter of the largest cross section is the circumference of the circle qith radius r. Thus,
[tex]88=2\pi r,\\ \\r=\dfrac{88}{2\pi}=\dfrac{44}{\pi}=\dfrac{44}{\frac{22}{7}}=\dfrac{44}{1}\cdot \dfrac{7}{22}=14\ cm.[/tex]
Thvolume of the sphere can be calculated using formula
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Since r=14 cm, we get
[tex]V=\dfrac{4}{3}\cdot \dfrac{22}{7}\cdot 14^3=\dfrac{4\cdot 22\cdot 2\cdot 14^2}{3}=\dfrac{34496}{3}\approx 11499\ cm^3.[/tex]
How is that equal to 10.17378? How do you write that on a calculator? Sorry, haven’t learnt logarithms.
Answers
Answer:
Step-by-step explanation:
The log is basically saying: 13/5 to what exponent gives you 50 000/3.
and the exponent is approximated at 10.17378.
Help needed !!! Use synthetic division to find the quotient and remainder!!!
Answers
For this case we must build a quotient that multiplied by the divisor, is eliminating the terms of the dividend until you reach the remainder of the division. It must be fulfilled that:
Dividend = Quotient * Divider + Remainder
Answer:
See attached image
Option D
Select all of the values that are solutions to this inequality.
Answers
Answer:
12, 18.
Step-by-step explanation:
2x-5 < 33
2x < 38
x < 38/2
x < 19
Mary spends 2 2/3 hours on math homework every week. She also spends 3 1/3 hours on art homework every week. How much time does Mary spend in total on math and art over 4 weeks?
Answers
Answer:
2 2/3+ 3 1/3 = 6. Multiply 6 by 4 weeks. 24 as your whole number.
Step-by-step explanation:
Final answer:
Mary spends a total of 24 hours on math and art homework combined over a period of 4 weeks.
Explanation:
Mary spends 2 2/3 hours on math homework and 3 1/3 hours on art homework each week.
To find out how much time she spends on both subjects over 4 weeks, first, we add the weekly hours:
2 2/3 + 3 1/3 = 6 hours per week.
Next, we multiply this weekly total by 4 to determine the monthly total: 6 hours/week × 4 weeks = 24 hours.
Therefore, Mary spends a total of 24 hours on math and art homework over 4 weeks.
Which statements are true about finding the volume of the soup cans? Check all that apply.
A) The diameter is squared to find the area of the base of a cylinder.
B) The volume is the area of the base times the height.
C) Given the radius or the diameter, you can calculate the area of the base of a cylinder.
D) The height of a cylinder is the distance between the 2 parallel bases.
E) The radius is half the distance of the height.
Answers
Answer:
the answers are B, C, and D.
The given item soup can is a cylinder.
The volume of the cylinder is given as :
[tex]V=\pi r^{2} h[/tex]
Here 'h' is the height and 'r' is the radius.
So, the true statements are:
B) The volume is the area of the base times the height - The base of the cylinder is circular and the area of the circle is [tex]\pi r^{2}[/tex], so the volume is the area of base multiplied by height.
C) Given the radius or the diameter, you can calculate the area of the base of a cylinder - Yes as the area is [tex]\pi r^{2}[/tex] where 'r' is the radius.
D) The height of a cylinder is the distance between the 2 parallel bases. Yes this is right.
Is (1, 2) a solution of the system y > 2x and x+y<3?
Select one:
a. Yes, because (1, 2) is a solution to both inequalities.
b. Yes, because (1, 2) is the point of intersection of the two boundary lines of
this system.
c. No, because (1, 2) is a solution to only one of these inequalities.
d. No, because (1, 2) is not a solution to either inequality.
Answers
Answer:
d
Step-by-step explanation:
To determine if (1, 2) is a solution to the system
Substitute x = 1, y = 2 into the inequalities and check their validity.
y > 2x → 2 > 2 ← incorrect statement
x + y < 3
1 + 2 < 3 → 3 < 3 ← incorrect statement
(1, 2) is not a solution to either inequality → d
Jennifer's bill for 6 cans of grape juice and 4 cans of apple juice was $13.10. When she got home she found out that she should have bought 4 cans of grape juice and 6 cans of apple juice. Although she mixed up the order, she did save 60 cents. What is the cost per can of apple and grape juice
Solve the system using substitution and elimination.
Convert your equations to slope intercept form and identify the variables for your x and y axes. Then graph.
SHOW ALL WORK
Answers
Answer:
Part 1) The system is solved using elimination
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) The system is solved using substitution
The cost per can of grape juice is [tex]\$1.19[/tex] and the cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) The system is solved by graphing
The graph in the attached figure
Step-by-step explanation:
Part 1) Solve the system by elimination
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex] -----> equation B
Solve the system by elimination
Multiply the equation A by -6 both sides
[tex]-36x-24y=-78.6[/tex] -------> equation C
Multiply the equation B by 4 both sides
[tex]16x+24y=54.8[/tex] -------> equation D
Adds equation C and equation D
[tex]-36x-24y=-78.6\\16x+24y=54.8\\----------\\-36x+16x=-78.6+54.5\\-20x=-23.8\\x=1.19[/tex]
Substitute the value of x in the equation A
[tex]6(1.19)+4y=13.10[/tex]
[tex]4y=5.96[/tex]
[tex]y=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 2) Solve the system by substitution
Let
x----> the cost per can of grape juice
y----> the cost per can of apple juice
we know that
[tex]6x+4y=13.10[/tex]
[tex]4y=-6x+13.10[/tex]
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]4x+6y=13.10+0.60[/tex]
[tex]4x+6y=13.70[/tex]
[tex]6y=-4x+13.70[/tex]
[tex]y=-(4/6)x+13.70/6[/tex]
[tex]y=--0.67x+2.28[/tex] -----> equation B
Substitute equation B in equation A and solve for x
[tex]-0.67x+2.28=-1.5x+3.275[/tex]
[tex]1.5x-0.67x=3.275-2.28[/tex]
[tex]0.83x=0.995[/tex]
[tex]x=1.19[/tex]
Find the value of y
Substitute the value of x in the equation A
[tex]y=-1.5(1.19)+3.275=1.49[/tex]
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Part 3) Solve the system by graphing
we have
[tex]y=-1.5x+3.275[/tex] -----> equation A
[tex]y=-(4/6)x+13.70/6[/tex] -----> equation B
Remember that
The solution of the system of equations is equal to the intersection point both lines
The solution is the point [tex](1.19,1.49)[/tex]
see the attached figure
therefore
The cost per can of grape juice is [tex]\$1.19[/tex]
The cost per can of apple juice is [tex]\$1.49[/tex]
Convert 67,000 pounds to tons. Choose the words and numbers to complete the statements.
Answers
Answer: 33.5 tons
Direct conversion formula: 1 Tons (metric) / 2204.5855379189 = 1 Pounds
Opposite conversion: 67000 Pounds to Tons (metric)
The lions little league team drinks a gallon of Gatorade each game. Every player gets a cup as a serving. 1 cup =1/16 gallon. The last game, The lions only used 1/2 gallon of Gatorade. How many cups of Gatorade were served to the players during the last game?
Answers
Answer:
8 cups
Step-by-step explanation:
8/16 equals 1/2 gallonThe number of cups of Gatorade served to the players during the last game was 8 cups.
To solve the problem, we need to determine how many cups are in half a gallon, given that 1 cup is equal to 1/16 of a gallon.
First, we establish the conversion factor between cups and gallons:
1 cup = 1/16 gallon
Now, we need to find out how many cups are in 1/2 gallon. To do this, we multiply the amount of Gatorade used in the last game by the conversion factor:
Cups served = (1/2 gallon) * (16 cups / 1 gallon)
Performing the multiplication:
Cups served = 1/2 * 16
Cups served = 8 cups
Therefore, 8 cups of Gatorade were served to the players during the last game.
16x to the 3rd / y * 5 y to the second / xy
Answers
Answer:
Final answer is [tex]80x^2[/tex].
Step-by-step explanation:
Given expression is [tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex].
Now we need to simplify this expression as shown below:
[tex]\frac{16x^3}{y}\cdot\frac{5y^2}{xy}[/tex]
[tex]=\frac{80x^3\cdot y^2}{y\cdot xy}[/tex]
[tex]=\frac{80x^3\cdot y^2}{xy^2}[/tex]
[tex]=\frac{80x^3}{x}[/tex]
[tex]=80x^2[/tex]
Hence final answer is [tex]80x^2[/tex].
Use the given information to write an equation of the circle.
center at (-7,-3), radius 2
Answers
The equation of a circle is written as (x-h)^2 +(y-k)^2 = r^2
h and K are the center points of the circle and r is the radius.
replace the letters with the provided center and radius:
(x- (-7))^2 + (y- (-3))^2 = 2^2
Simplify:
(x+7)^2 + (y+3)^2 = 4
Segments Ra and Ny are best described as which of the following
Answers
Answer:
B
Step-by-step explanation:
B). RA and NY are perpendicular segments
Answer:
The correct answer option is B. Perpendicular segments.
Step-by-step explanation:
We are given two segments RA and NY and we are to determine whether which of the given answer options describe them the best.
Since the angles ∠RDA and ∠NDY are perpendicular angles and they lines RA and NY intersect each other at point D so the formed segments are also perpendicular.
Therefore, the option which best describes this is B. Perpendicular segments.
The numbers 4 through 14 are placed in a
bowel and drawn at random then replaced
after being drawn. What is the probability of
drawing the number 14 and then a number
less than 12?
Answers
The probability of drawing the number 14 is 1/10 (because there are 10 different numbers to pick from). The probability of drawing a number less than 12 is 8/10 (or 4/5 simplified). Multiply the fractions: 1/10 *4/5 = 4/50. Simplify to 2/25. The probability of drawing 14 and then a number less than 12 is 2/25.
Drag the values to order them from least to greatest, with the least at the top.
Answers
Answer:
√143 = 11.958
√79+√63 = 16.825
4π = 12.66
Im pretty sure this is correct since I used a calculator. Hope it helps
Each person in the vale family drinks 481/2 ounces of water a day how much water will each person drink in 7 days
Answers
Each person in the Vale family will drink a total of 339.5 ounces of water over the course of 7 days.
The student is asking how much water in ounces each person in the Vale family will drink over the span of 7 days if each person drinks 48.5 ounces of water daily.
To find the total amount of water consumed by one person in 7 days, we multiply the daily intake by the number of days:
48.5 ounces/day imes 7 days = 339.5 ounces
So, each person will drink a total of 339.5 ounces of water in 7 days.
Please help!!!
Use the equation below to find y, if m=8,x=4, and b=6
Equation: y=mx-b
Answers
Answer:
y=26
Step-by-step explanation:
We just subsitiute.
y=8(4)-6
8*4=32
y=32-6
y=26
15. Divide the polynomial x^3 + x^2 - 2x + 3 by (x - 1).
Answers
Answer:
x² + 2x + [3\x - 1]
Step-by-step explanation:
Since the divisor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:
1| 1 1 -2 3
↓ 1 2 0
------------------
1 2 0 3 → x² + 2x + [3\x - 1]
You start by placing the c in the top left corner, then list all the coefficients of your dividend [x² + 5x - 36]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder, which in this case is a 3, so what you is set the divisor underneath the remainder of 3. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², 2 becomes 2x, and the remainder of 3 is set over the divisor, giving you the other factor of x² + 2x + [3\x - 1].
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
Find the volume of the prism.
Answers
Answer:
[tex]V=120\ units^3[/tex]
Step-by-step explanation:
we know that
The volume of a prism is equal to
[tex]V=BL[/tex]
where
B is the area of the base of the prism (triangular base in this problem)
L is the length of the prism (perpendicular distance between the top and the bottom)
Find the area of the triangular base B
[tex]B=\frac{1}{2}(3)(4)=6\ units^2[/tex] ---> area of a triangle
we have
[tex]L=20\ units[/tex]
substitute in the formula of volume
[tex]V=6(20)=120\ units^3[/tex]
Note The problem does not specify whether the measurements are in centimeters or in units, so I assume they are in units.
A bag contains an orange tile, a yellow tile, and a purple tile. Two tiles are drawn randomly without replacement. If the first tile is yellow, find the probability of drawing a second tile that is orange.
PLEASE HELP ASAP IM TRYING TO GO TO RECESS LOL
Answers
Answer:
It's a 50% chance
Step-by-step explanation:
Answer:
1/3 most likely
Step-by-step explanation:
because you take out one tile and it only has one of each color so there are only three left so 1/3
tents hold 2, 3, 5, 6, or 12 people. how many combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.
Answers
there would be 12 combinations
Answer:
12
Step-by-step explanation:
We are given that tent hold 2,3,5,6 or 12 people.
We have to find the combinations of tents are possible to sleep 32 all tents are fully occupied and exactly one 12 person tent is used.
If one 12 person tents is used then remaining people=32-12=20
Therefore, 20 people that must be in other tents.
To place 20 persons in combination of 2,3,5 and 6.
20=5+5+5+5
20=5+5+5+2+3
20=6+6+6+2
20=2(10)=2+2+....+2(10 times)
20=5+5+2(5)(5 times add 2)
20=6+6+2(4) (4 times add 2)
20=3+3+3+3+3+3+2
20=3+3+3+3+3+5
20=3+2+6+5+2+2
20=3+3+3+3+6+2
20=3+3+5+5+2+2
20=6+6+3+5
Hence, there are 12 possible combination of tents to sleep 32 all tents are fully occupied and exactly one 12 person tents is used.