All three parts of the given problem regarding trails, paths and walks have been solved below.
A path is defined as a way in which we can traverse the graph such that neither vertices nor the edges are repeated. In the given graph we can see that for going from a to c there are 4 ways that satisfy the condition of a path. A Trail is an open walk in which no edge is repeated but the vertex can be repeated. So, in the given graph we can see that there are 3!(4) ways in which we can go from a to b and then c and 4 paths in which we can go directly from a to c.
The walk is a sequence of vertices and edges of a graph that can be closed if we come to the same point after traversing the graph or open if we go from one point to another. In the given graph since we go from a point to c point the walk is open but the length of edges of the walk is not defined so if we take the no. of edge length to be 4
there can be 44 ways
so,
number of paths from a to c = 4
number of trails from a to c = 4+3!(4)= 28
number of paths from a to c = 4+3!(4)+2!(6)+1!(4)= 44
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if no chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is not present in the flock? show how you found your answer.
The probability that the veterinarian will conclude that the h6n2 virus is not present in the flock is 0.988
Since there are only two possible outcomes for this problem—that the bird is infected or not—the probability of a binomial distribution is involved.
Let's now assume that in this case, x represents a random variable that represents the number of afflicted chickens.
P(false positive test)=0.05, suggests that.
False positive tests indicate that the bird is not infected but the veterinarian still reports that it is. P(false negative test)=0.10 where.
False negative results indicate that the bird is infected even though the veterinarian says it is not.
Then, P(bird tested false positive) = 1-0.05=0.95 and P(bird is not infected) = 1.
Similar to that, P(bird tested false negative) = 1 - P(bird tested positive) 1- 0.10=0.90
Now, according to the question, the flock is considered contaminated if at least three out of every ten chickens are infected.
Therefore, i, if the veterinarian does not declare the birds as infected, it merely signifies that less than 3 birds are infected.
P(vet declares uninfected) then equals P(x=0) + P(x=1) + P(x=2)
P= (0.05)⁰ (0.95¹⁰) + (0.05)¹ (0.95)⁹ +(0.05)² (0.95)⁸ = 0.988
This is calculated, and the result is 0.988.
your question is incomplete but most probably your full question was
suppose a veterinarian applies the procedure to a flock of 100,000 chickens at a commercial egg production farm. the elisa test is known to have probability 0.05 of producing a false positive result and probability 0.10 of producing a false negative result for a single chicken. if no chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is not present in the flock? show how you found your answer.
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the image is the question
The number of 2-button special moves possible with the controller is 42 combinations.
Define the term combination of the numbers?Combination is still a mathematical method for counting the number of potential configurations in a set of elements where the orientation of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination would be a selection of the whole or a portion of a group of items, regardless of the sequence in which the items are chosen.For the given query:
The number of total buttons : 4 + 3 = 7
Number of digits two be formed 2-button special moves.
So,
First place cane be filled with all 7 numbers.
Second place can be filled with remaining 6 numbers.
Thus,
= 7 x 6
= 42 combinations.
Thus, the number of 2-button special moves possible with the controller is 42 combinations.
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Ians car can go 296 miles on 8 gallons of gas. During a drive last weekend, ians used 7 gallons of gas. How far did he drive?
Answer:
259 miles
Step-by-step explanation:
To find this, we need to multiply his 8 gallons by [tex]\frac{7}{8}[/tex] since he only uses 7 gallons of gas. In turn, we also need to multiply 296 by [tex]\frac{7}{8}[/tex]. We get:
[tex]296 * \frac{7}{8} = 37 * 7 = 259[/tex]
So, Ian drove 259 miles last weekend.
Hope this helped!
D) 3-2 (s-1) = 13+6s
Answer: -1
E) 2 (n+9) = -6 (2n-5) +8
Answer: 10/7
F) 5 (4k-3) -5k = 10+2 (3k+1)
Answer: 3
The solution for the variable of each expression is given as follows:
D) 3 - 2(s - 1) = 13 + 6s: s = -1.
E) 2(n + 9) = -6(2n - 5) + 8: n = 10/7.
F) 5(4k - 3) - 5k = 10 + 2(3k + 1): k = 3.
How to solve the expressions?The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.
The expression for item d is given as follows:
3 - 2(s - 1) = 13 + 6s
Hence:
3 - 2s + 2 = 13 + 6s -> Distributive property.
8s = 5 - 13 -> Combine the like terms.
8s = -8
s = -8/8
s = -1.
The expression for item e is given as follows:
2(n + 9) = -6(2n - 5) + 8
2n + 18 = -12n + 30 + 8 -> Distributive property.
14n = 20 -> Combine the like terms.
n = 20/14
n = 10/7.
The expression for item f is given as follows:
5(4k - 3) - 5k = 10 + 2(3k + 1)
20k - 15 - 5k = 10 + 6k + 2
15k - 15 = 12 + 6k
9k = 27
k = 27/9
k = 3.
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[WILL GIVE BRAINLIEST!]
Determine the value of x.
Answer:
8.1
Step-by-step explanation:
12/x = tan56
12/x =1.48
so x = 12/1.48 =8.1
For every pound a company spends on advertising, it spends £0.24 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answer:
25:6
Step-by-step explanation:
1/0.24
100/24
50/12
25/6
Solve the system of linear equations by elimination.
3x+4y=-1
-2x-5y=10
Answer:
x = 5
y = -4
Step-by-step explanation:
3x+4y = -1
-2x-5y = 10
We time the first equation by 2 and the second equation by 3
6x + 8y = -2
-6x -15y = 30
-7y = 28
y = -4
Now put -4 back in for y and solve for x
3x+4(-4) = -1
3x - 16 = -1
3x = 15
x = 5
Let's check
3(5) + 4(-4) = -1
15 - 16 = -1
-1 = -1
So, x = 5 & y = -4 is the correct answer.
Find the value of X and Y
==========================================================
Explanation:
Let z be adjacent to angle y, and angle z is inside the triangle on the right.
Adding up the inside angles of any triangle always gets us to 180 degrees.
We'll use this fact to find z.
z+30+50 = 180
z+80 = 180
z = 180-80
z = 100
Angle y and angle z are supplementary angles. They form a straight line of 180 degrees.
So,
y+z = 180
y+100 = 180
y = 180-100
y = 80
--------------
We can follow the same steps as in the previous section to determine that angle x is 110 degrees.
A shortcut is to use the Remote Interior Angle Theorem.
This theorem says that adding two interior angles will get us the exterior angle that isn't adjacent to either interior angle mentioned.
Notice for instance that angle x is not adjacent to the bottom-left 30 degree angle nor is it adjacent to angle y.
Furthermore, you could use the Remote Interior Angle Theorem to determine the measure of angle y. Note how y = 30+50 = 80. This time the "30" we focus on here is inside the triangle on the right.
Round each angle to the nearest degree and round each Side to the nearest hundredth. Do not use rounded answers in your calculations to find missing measures.
Length of AB = c = 7.12
Measures of angles:
A = 56°
B = 34°
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
AB² = AC² + BC²
Given in the figure,
AC = 3.96
BC = 5.96
AB = ?
A = ?
B = ?
By Pythagoras theorem
AB² = AC² + BC²
AB² = 3.96² + 5.96²
AB² = 15.6816 + 35.5216
AB² = 51.2032
AB = √51.2032
AB = 7.1156
Rounded to nearest hundredth
AB = 7.12
Now, tan B = AC/BC
tan B = 3.96/5.96
tan B = 0.6644
B = tan⁻¹ (0.6644)
B = 33.6°
Sum of Interior angles of a triangle = 180°
A + B + C = 180°
A + 33.6° + 90° = 180°
A + 123.6° = 180°
A = 180° - 123.6°
A = 56.4°
Rounded to nearest degree,
A = 56°
B = 34°
Hence, 7.12 is the measure of AB, 56° and 34° are the measures of angles A and B respectively.
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Simon decided to develop his own board game and sell it from home, advertising on a social media platform.
His biggest decision is what price to sell the game at. He studies similar games to determine he can use the
function P(z) = -125 (17)2 +25000, where P is total profit and is the retail price, to determine
what price to sell his game.
Answer: Simon can use the function P(z) = -125z^2 + 25000 to determine the total profit he will make at different retail prices for his board game. The function shows that his profit will be maximum at 25000 dollars and it will decrease as the price increases or decreases from that point. Simon can use this function to determine the optimal price to sell his game at in order to maximize his profit.
Step-by-step explanation:
3. A regular hexagon has six congruent sides. If the
length of each side is represented by the
expression 7x + 4 which expression is equivalent to
the perimeter of the figure?
A. 13x + 24
B. 13x+10
C. 42x + 24
D. 42x + 10
The equivalent expression of the perimeter of the regular hexagon is,
⇒ 42x + 24
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
We have to given that;
A regular hexagon has six congruent sides.
And, The length of each side is represented by the expression (7x + 4).
Now, We know that;
The sum of all sides of a regular hexagon is called its perimeter.
Hence, We get;
Here, The length of each side is represented by the expression 7x + 4.
So, We get;
The perimeter of Hexagon = 6 × (7x + 4)
= 42x + 24
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(a−2b)3 when a=−3 and b=−12
help plsss
(the three is an exponent)
Answer:
9261
Step-by-step explanation:
[tex](-3-2(-12))^3=(-3+24)^3=21^3=441(21)=9261[/tex]
Find the value of x. Round your answer to the nearest tenths.
In a trapezium, the sum of the outer angles is always equal to 360 degrees because, in any convex quadrilateral, the sum of the four angles is consistently 360 degrees. As a trapezium is a type of convex quadrilateral, the sum of its four angles is 360 degrees, regardless of its shape or size.
Solve for xWe can simplify this equation by combining like terms on one side and isolating the variable on the other.
First, combine like terms: x + 5 + 3x - 8 + 5x + 10 + x + 10 = 360
(x + x) + (5 + 10 + 10) + (3x + 5x) = 360
10x + 17 = 360
Then, subtract 17 from both sides to isolate the variable on one side:
10x = 343
Finally, divide both sides by 10 to solve for x:
x = 34.3
So the solution to the equation is x = 34.3
Find Z and X in each diagram below using the given area under the curve
The values of Z and X, considering the normal curve, are given as follows:
Z = -1.175.X = 115.3.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution, which is the area to the left under the normal curve.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 120, \sigma = 4[/tex]
The p-value is of 0.12, hence the z-score is given as follows:
-1.175.
Then the value of X is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
-1.175 = (X - 120)/4
X - 120 = -1.175 x 4
X = 115.3.
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Need help 30 points....
in triangle abc, the measure of the largest angle is 32 less than 3 times the smallest angle. the measure of the middle angle is 8 more than half the measure of the largest angle. what is the measure of the middle angle? _______ degrees
The measure of the middle angle of triangle abc is 52°
Let the largest angle of triangle be x, the smallest angle be z, and the third angle be y.
Given that the measure of the largest angle is 32 less than 3 times the smallest angle.
So, we get an equation,
x = 3z - 32 ............(1)
Also, the measure of the middle angle is 8 more than half the measure of the largest angle.
So, we get an equation,
y = 8 + (x/2) .......(2)
From equation (1),
z = (x + 32)/3 ..........(3)
We know that the sum of all angles of triangle is 180 degrees.
x + y + z = 180
Substitute the values of y and z in above equation.
x + 8 + (x/2) + (x + 32)/3 = 180
6x + 48 + 3x + 2(x + 32) = 1080
9x + 48 + 2x + 64 = 1080
11x + 112 = 1080
11x = 1080 - 112
11x = 968
x = 88
Substituting above value of x in equation (2)
y = 8 + (88/2)
y = 8 + 44
y = 52 degrees
Therefore, the middle angle of triangle measures 52 degrees.
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Lamonte has a bag that contains apple chews, strawberry chews, and lime chews. He performs an experiment. Lamonte randomly removes a chew from the bag, records the result, and returns the chew to the bag. Lamonte performs the experiment 34 times. The results are shown below:
An apple chew was selected 13 times.
A strawberry chew was selected 6 times.
A lime chew was selected 15 times.
Based on these results, express the probability that the next chew Lamonte removes from the bag will be apple chew as a percent to the nearest whole number.
The probability that the next chew Lamonte removes from the bag will be apple chew will be 38%
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur
In this case, Lamonte has a bag that contains apple chews, strawberry chews, and lime chews. He performs an experiment and then randomly removes a chew from the bag, records the result, and returns the chew to the bag.
Since Lamonte performs the experiment 34 times, the probability that the next chew Lamonte removes from the bag will be apple chew will be:
= 13 / 34
= 38%
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Explain how to solve 5x − 2 = 8 using the change of base formula . include the solution for x in your answer.
The solution to the given exponential equation is 0.791.
What is a logarithm?
The logarithm is the inverse function of exponentiation in mathematics. That is, the exponent to which b must be raised to produce x is the logarithm of a number x to the base b.
Given exponential function is
5x⁻² = 8
Divide both sides by 5:
x⁻² = 8/5
x⁻² = 1.6
Taking logarithm of base x:
[tex]log_x(x^{-2})=log_x1.6[/tex]
-2 [tex]=log_x(1.6)[/tex]
Now applying the logarithm of change of base formula:
-2 = log 1.6/log x
Divide both sides by -2:
1 = log 1.6/( -2log x)
Multiply both sides by log x:
log x = log 1.6/-2
log x = -0.1021
Now applying the formula [tex]log_xa = b[/tex] implies [tex]a = x^b[/tex]:
x = 10^(-0.1021)
x = 0.7905
x = 0.791
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you find a wood fragment during a village excavation in tibet. your analysis shows that c-14 has been reduced to 25% of the amount the tree had when it was alive. how old is the wood fragment?
The wood fragment is 11,460 years old by C-14 dating if only 25% of the amount the tree had when it was alive is left.
The process of carbon-14 dating can be used to determine the age of an organic material such as wood. Carbon-14 is a radioactive isotope of carbon that is present in all living organisms. When an organism dies, the carbon-14 begins to decay at a known rate, and the amount of carbon-14 in the material decreases over time. By measuring the amount of carbon-14 remaining in a sample, it is possible to determine how long ago the organism died.
If the analysis shows that the C-14 has been reduced to 25% of the amount the tree had when it was alive, it means that 75% of C-14 has decayed, and the material is therefore 75% of its way through its radioactive decay.
Carbon-14 has a half-life of 5,730 years, which means that after 5,730 years, half of the carbon-14 in a sample will have decayed. To find the age of the wood fragment, you would need to multiply the sample's decay percentage (75%) by the material's half-life (5730 years) to get the number of years that have passed.
[tex]t = \frac{5730\ ln(0.25)}{-ln2}[/tex]
Where t is the number of years to decay to 25%.
t = 5730 × ( ln(4)/ ln(2))
t = 5730 × 2
t = 11,460
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Find the sum of 8/9 and 3/4. Enter the numerator followed by the denominator separated by a comma.
After finding the LCM, the sum of 8/9 and 3/4 is 59/36
In the given question, we have to find the sum of 8/9 and 3/4.
The given numbers are 8/9 and 3/4
Sum = 8/9 + 3/4
The denominator of the both number are different. So to find the sum we find the LCM of the both number 9 and 4.
So the LCM of 9 and 4 is 36.
Multiply 4 on the number 8/9 and 9 on the number 3/4. So
Sum = [tex]\frac{8}{9}\times\frac{4}{4}+\frac{3}{4}\times\frac{9}{9}[/tex]
Sum = 32/36 + 27/36
Now the denominator is same. So now we add them.
Sum = (32+27)/36
Sum = 59/36
Hence, the sum of 8/9 and 3/4 is 59/36.
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An earthworm was in the soil 9 inches below the surface. To find moister soil, it moved down 7 inches.
What is the position of the earthworm now relative to the surface?
inches
Using the addition operation, the position of the earthworm relative to the surface is 16 inches below the surface.
What is the addition operation?One of the four basic mathematical operations, including subtraction, division, and multiplication, is the addition operation.
Using the addition operation involves adding two or more addends to determine the sum. It also involves using the addition operand (+) and the equal symbol (=).
The initial position of the earthworm below the surface = 9 inches
The depth it moved down to find moister soil = 7 inches
The current position = 16 inches (9 + 7) below the surface.
Thus, based on the addition operation, the earthworm is 16 inches below the surface in its endless search for moister soil.
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The aquarium has 10 more red fish than blue fish. 60% of the fish are red. How many blue fish are in the aquarium? Show your work.
Answer:
20 blue fish
Step-by-step explanation:
r=red fish, b=blue fish. r = 10+b. 60%r=r+b. (10+b)= 0.6(r+b); 10+b = 0.6(2b+10); 10+b=1.2b+6; 4=0.2b; b=20.
f(x)=\left\{\begin{array}{ll}x+4&\quad-4\le x < 3\\2x-1&\quad3\le x < 6\end{array}\right.
This is a piecewise defined function. For input values of x between -4 and 3 (exclusive), the function is defined as f(x) = x + 4. For input values of x between 3 and 6 (exclusive), the function is defined as f(x) = 2x - 1.
HELP Someone please help me ASAP
Answer: 67 degrees
Step-by-step explanation: If you add two angles together, this is actually equal to the second angle because it has to be if you pay attention to the complementary angles.
consider the following normal-form game: 2 l c r 1 u 4, 11 3, 5 6, 12 m 2, 4 1, 8 5, 6 d 3, 10 4, 7 3, 8 a. is there a strictly dominant strategy for some player? b. are there strictly dominated strategies for some player? find them all. c. find the set of outcomes that survive the process of iterative elimination of strictly dominated strategies. is the game solvable?
The probability game is solvable, and Player 1 has a strictly dominant strategy of Left (L), while Player 2 has four strictly dominated strategies. The surviving outcomes are (L, U), (L, M), (L, D), and (L, R).
This normal-form game is solvable, with Player 1 having a strictly dominant strategy of Left (L). Player 1's left strategy is strictly dominant because it will always yield a higher payoff than any other strategy for Player 1, regardless of what Player 2 does. Player 2, on the other hand, has four strictly dominated strategies: Up (U), Middle (M), Down (D), and Right (R). These strategies are strictly dominated because they will always yield a lower payoff than any other strategy for Player 2, regardless of what Player 1 does. The set of outcomes that survive the process of iterative elimination of strictly dominated strategies is (L, U), (L, M), (L, D), and (L, R). In other words, Player 1 will always choose left, and Player 2 will choose either Up, Middle, Down, or Right.
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Can someone answer this question with an actual answer, I’ll give you brainliest.
Answer:
A.) Angle A Congruent to Angle D
C.) The scale factor of DE/AB is 2
Step-by-step explanation:
Image shows and supports those.
27 g^7 k^3 z^4 - 9 g^2 K^5 z
The subtraction of the expression 27 g^7 k^3 z^4 - 9 g^2 K^5 z is 18(g⁷k³z⁴ - g²k⁵z)
What are algebraic expressions?Algebraic expressions are described as expressions that are known to consist of terms, coefficients, constants, variables and factors.
They are also described as expressions composed of arithmetic operations, such as;
DivisionBracketParenthesesAdditionMultiplicationSubtractionIt is also important to note that index forms are mathematical representation of variables or values too large or small in more convenient forms.
From the information given, we have the expression;
27 g^7 k^3 z^4 - 9 g^2 K^5 z
Subtract the coefficient
18(g⁷k³z⁴ - g²k⁵z)
Hence, the value is 18(g⁷k³z⁴ - g²k⁵z)
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steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 7 am, and walks steadily at 3 miles per hour. elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 10 am. when will the distance between them be 35 miles? (round your answer to the nearest minute.)
At 2.57 hours distance between them is 35 miles
(2t)2 + (2.5(t - 2))2 = 302
4t2 + (2.5t - 5)2 = 900
4t2 + 6.25t2 - 25t + 25 = 900
2.25t2 - 25t - 875 = 0
Let t (hours) be the amount of time Elsie needs to travel in order to reach a distance of 35 miles. Steve travels t + 2 miles to the north in the time it takes him since he is 2 hours early.
Solve for t, then add to 7:00 for your time.
which will give you 2.57 hours.
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The correct question will be
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 3 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 9 AM.
When will the distance between them be 35 miles?
Find the volume of this shape
Answer:
Step-by-step explanation:
The volume on the shape on top is 10x3x8=240
The volume of the shape is 3x5x6=90
The bottom shape is 8x5x2=80
the total volume is 240+90+80=410
Solve the word problem below using the steps given in the lesson above. Show your equation and each step you take to solve it. Neil and Tom love to collect baseball cards. Neil has 83 more baseball cards than Tom. Neil has 517 baseball cards. How many baseball cards does Tom have
In linear equation , the number of baseball cards Tom has is 434.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
We need to find the amount of cards Tom has.
The number of cards Tom has is 434.
Let the number of baseball cards Tom has be X .
Neil has 83 more baseball cards than Tom so
X + 83 is the number of baseball cards that Neil has.
The number of baseball cards Neil has is 517
So,
x + 83 = 517
x = 517 - 83
x = 434
Hence, the number of baseball cards Tom has is 434.
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Find the vector, not with determinants, but by using properties of cross products, (j - k) times (k - i) Use the given vectors to answer the following questions. a = <1, 3, 3>, b = <-3, 3, 0>, c = <0, 0, -3> Find a times (b times c). a times (b times c) = < > Find (a times b) times c. (a times b) times c = < >
According to the claim, cross product properties rather than determinants are used to define the vector i + j + k. By usig the supplied vectors a * (b *c) is < 27, -27, 18> and (a * b) * c is < 27, -27, 0>
What is a vector, exactly?A vector is a quantity or phenomenon with independent properties both to and direction. The scientific or geometrical depiction of a quantity is another meaning of the word. Among the components of vectors seen in nature are force, weight, electric interfering, and movement.
1). (j-k) * (k-i)
= (j*k) - (j*i) - (k*k) + (k*i)
= I - (-k) - (0) + (j) (j)
= i + j + k
(2). (a). (b*c)
[tex]\left|\begin{array}{ccc}j & j & k \\-3 & 3 & 0 \\0 & 0 & -3\end{array}\right|[/tex]
= i(-9-0)-j(9-0)+k(0-0)
= -9i - 9j + 0k
= < -9, -9, 0>
Then, a*(b*c)
[tex]\left|\begin{array}{ccc}i & j & k \\1 & 3 & 3 \\-9 & -9 & 0\end{array}\right|[/tex]
i (0+27) - j (0+27) + k(-9 + 27)
= 27i -27j + 18k
= < 27, -27, 18>
(b). (a*b)
[tex]\left|\begin{array}{rrr}i & j & k \\1 & 3 & 3 \\-3 & 3 & 0\end{array}\right|[/tex]
= i(0-9) - j(0+9) + k (3+9)
= -9i - 9j + 12k
= < -9, -9, 12>
(a*b)*c
[tex]\left|\begin{array}{ccc}4 & j & k \\-9 & -9 & 12 \\0 & 0 & -3\end{array}\right|[/tex]
= i(27-0) - j(27-0) + k (0-0)
= 27i - 27j + 0k
= < 27, -27, 0>
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