Answer:55%
Step-by-step explanation:So, first find the total number of tickets sold 374+306=680. Now, divide the number of discount tickets by the total number and multiply the result by 100% to express the result as a percentage. Percentage of discount tickets=(374/680)100%=55%. So, 55% percent of the tickets sold at the amusement park were discounted.
The area of a rectangle is 65 m2 and the length of the rectangle is 3 m less than twice the width. Find the dimensions
The dimensions of the rectangle are:
Length = 10 m
Width = 6.5 m
How to Find the Dimensions of a Rectangle?Recall that the area of aa rectangle is given as, length × width.
Given the following:
Area of the rectangle = 65 m²
Let the width of the rectangle be represented as w.
Length of the rectangle = 2w - 3 m
Therefore:
(2w - 3)(w) = 65
Expand:]
2w² - 3w = 65
2w² - 3w - 65 = 0
Factorize:
w = 6.5 or w = -5
The width cannot be negative, therefore, the width = 6.5 m.
Length of the rectangle = 2w - 3 = 2(6.5) - 3 = 10 m
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what was the mistake that was made?
Answer: No mistake
It seems that there are not any problems with these steps.
a nonprofit organization sells chances for a $50,000 classic mustang at $100 per ticket. it sells 1500 tickets and offers four prizes, summarized in the table. what are the expected winnings (or loss) for each ticket? (round your answer to the nearest cent.)
The nonprofit company charges $100 each ticket for the opportunity to win a $50,000 vintage Mustang. With four prizes and 1500 tickets sold, he expects to lose $54.53 on each one.
The chance of winning is multiplied by the bet multiplier to determine the mathematical anticipated value. Typically, expected value is estimated for a bet of one unit. To determine the predicted profit, multiply the win chance by the stake amount.
Chances of getting first prize = 1/1500
Chances of getting second prize = 1/1500
Chances of getting third prize = 1/1500
Chances of getting Fourth prize = 1/1500
Cost of one ticket = $100
Expected winning = -100 +1/1500 (56000 + 6600 + 4300 + 1300)
= -100 + 68200/1500
= - 54.53 dollars
There is an expected loss of $54.53.
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>) Solve:
1) 7 millions
thousands
hundred
Answer:
70
Step-by-step explanation:
1 million = 10 hundred thousands because 100,000 x 10 = 1,000,000
Given A(1,4), B(-2,5)and C(3, 4), which coordinate pair will make AB perpendicular to CD ?
The coordinate pair of D that will make AB perpendicular to CD is ( 4,7)
How are lines perpendicular in a coordinate?The slopes of perpendicular lines are opposite reciprocals of each other. Their product is -1.
The slope of a line is given as ( y1-y2)/(x1-x2)
for AB and CD to be perpendicular
( y2-y1)/(x2-x1) × ( y4-y3)/(x4-x3) = -1
therefore (5-4)/-2-1 = ( y4-y3)/(x4-x3)
1/-3 ×(y4-4)/(x4-3) = -1
(y4-4)/(x4-3) = 3/1
therefore 3= y4-4 and 1 = x4-3
therefore y4 = 3+4= 7
and x4 = 1+3= 4
therefore the coordinate of D = (x4,y4) for AB perpendicular to CD = (4,7)
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multiply the polynomial (x 2y)(x2 - 2xy 4y2). write your answer in descending order. please use the palette below to enter your answer.
The descending order of the polynomial is (x³ + 8y³)
The term polynomial in algebra is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division
Here we have given that (x+2y)(x²−2xy+4y²)
And we have to multiply the polynomial and write your answer in descending order.
Here we have the polynomial (x+2y)(x²−2xy+4y²).
Now, we have to use the identity
=> a³ + b³ = ( a² − ab + b² ) ( a + b ) ,
Now, we have to apply these identity one the given polynomial, then we get,
=> ( x + 2y ) ( x² − 2xy + 4y² )
=> (x³ + ( 2 y )³) = (x³ + 8 y³) .
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The white wood material used for the roof of an ancient temple is imported from a certain country. The wooden roof must withstand as much as 100 centimeters of snow in the winter. Architects at a university conducted a study to estimate the mean bending strength of the white wood roof. A sample of 25 pieces of the imported wood were tested and yielded the statistics x-75.2 and s 8.6 on breaking strength (MPa). Estimate the true mean breaking strength of the white wood with a 95% confidence interval. Interpret the result. Find the 95% confidence interval for the true mean breaking strength of the white wood (Round to two decimal places as needed.) Interpret this confidence interval. Choose the correct answer below 0 A. The architects can be 5% confident that the mean breaking strength of the white wood is 75.2 O B. The architects can be 95% confident that the mean breaking strength of the white wood is within this interval 0 C. The architects are confident that 95% of the white wood is described by this interval 0 D. The architects can be 97.5% confident that the mean breaking strength of the white wood is outside this interval 0 E. The architects can be 5% confident that the mean breaking strength of the white wood is within this interval
95% confidence interval for the true mean breaking strength of the white wood is (71.66 MPA, 78.74 MPA)
The result above means that the lower limit of the true mean breaking strength of the white wood is 69.89 MPA and the upper limit is 81.51 MPA.
Confidence Interval:
The definition says, "A confidence interval is a range of values derived from a sample statistic that likely includes the value of an unknown population parameter."
To calculate the confidence interval, we need to know three parameters of the sample: the mean (average value) μ, the standard deviation σ, and the sample size n (number of measurements). Then you can calculate standard error and tolerance using the following formulas:
standard error = σ/√n
Given in the question:
Confidence interval = mean + or - Error margin (E)
Mean = 75.2 MPA
Standard deviation = 8.6 MPA
Sample size, n = 25
Now,
Degree of freedom = n - 1 = 25 - 1 = 24
Confidence level (C) = 95% = 0.95
Significance level = 1 - C
= 1 - 0.95
= 0.05 = 5%
Therefore, t-value corresponding to 24 degrees of freedom and 5% significance level is 2.06
Again,
E = t × sd/√n
= 2.06 × 8.6/√25
= 2.06 × 1.72
= 3.54 MPA
Lower limit = Mean - E
= 75.7 - 5.81
= 69.89 MPA
Upper limit = Mean + E
= 75.7 + 5.8
= 81.51 MPA
95% confidence interval is (69.89 MPA, 81.51 MPA)
The result means that the true mean breaking strength of the white wood is between 69.89 and 81.51 MPA.
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Write a take from word problem that fits naturally with the equation 25- ?= 13
The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
Let the missing number be 'x'. Then the equation is given as,
25 - x = 13
Simplify the equation, then the value of the variable 'x' will be given as,
25 - x = 13
x = 25 - 13
x = 13
The word form of equation 25 - x = 13 will be the difference between 25 and the number 'x' is 13. And its solution is 12.
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Tamia's curtain company is making curtains for a local hotel. She wants each curtain to be 24 inches long. At the fabric store, fabric is sold by the foot. If Tamia's curtain company wants to make 83 curtains, how many feet of fabric will she need?
1 inch =
1
12
foot
Tamia will need 166 feet of fabric
How to determine how many feet of fabric she will need?
Given that:
Tamia wants each curtain to be 24 inches long
At the fabric store, fabric is sold by the foot
Tamia's curtain company wants to make 83 curtains
1 curtain = 24 inches
83 curtains = 24×83 = 1992 inches
To convert inches to feet multiply by 1/12:
1992 inches = 1992 × 1/12 feet = 166 feet
Thus, she will need 166 feet
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Writing equations of lines
Write the equation of each line with the given information
through: (-5, -3), perp. to y = -5/7x -5
Answer:
y = [tex]\frac{7}{5}[/tex] x + 4
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals.
So the slope is 7/5
Us the slope and the point to find the y intercept
m = 7/5
x = -5
y = -3
y= mx + b
-3 = (7/5)(-5) + b
-3 = -7 + b Add 7 to both sides
4 = b
y = mx + b
y = 7/5 x + 4
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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Roberta took two tests. She scored 10 points more on the second test. Her average score for the two tests was 75 points. If x= her score on the first test, and y= her score on the second test, then the average is given by the formula x+y2. What did she score on the second test? She scored points on the second test. The solution is
If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.
How to find the number of score?Average score = (x+y)/2
he scored 10 points less on the second test than he did on the first.
y = x - 10
Replace y with x-10
(x + x - 10) / 2
(2x-10)/2
Average score on both tests is 75
(2x-10)/2 = 75
Multiply both sides of this equation by 2
2x-10 = 150
Add 10 to both sides
2x = 160
Divide both sides by 2x
x = 160/2
x = 80 (She got 80 on the first test)
He got 80 - 10 = 70 (She got 70 on the second test)
(80+ 70) / 2 = 150/2 = 75 (She got average of 75 on both tests)
Therefore she scored 70 on the second test is your solution.
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Select the correct answer. What are the solutions to this equation? 16x2 + 9 = 25 A. x = -4 and x = 4 B. x = 0 and x = 4 C. x = 0 and x = 1 D. x = -1 and x = 1
Answer:
Step-by-step explanation:16x^2+9=25
16x^2=16
x^2=1
x=1 or -1
D
which expotential function has a y-intercept of (0, -4)?
HELP WILL MARK BRAINLIEST
Answer:
[tex]y=2^x-5[/tex]
Step-by-step explanation:
The y-intercept occurs when x = 0.
Therefore, substitute x = 0 into each equation to find its y-intercept.
[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]
Therefore, the exponential function that has a y-intercept of (0, -4) is:
[tex]\large\boxed{y=2^x-5}[/tex]
estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.
The area under the given curve is 77/60. SO the option B is correct.
In the given question we have to estimate the area under the curve given the following fuction, interval, and number of subintervals using the right endpoint method.
The given function is
F(x) = 1/x; [1,5]; n=4
The given options are:
A≈77/240
A≈77/60
A≈77/15
A≈25/3
A≈25/12
Since, f(x) =1/x
∆x = (b-a)/n
∆x = (5-1)/4
∆x =4/4
∆x = 1
Now the table is
x 1 2 3 4 5
f(x) 1 1/2 1/3 1/4 1/5
R(4) = [f(2)+f(3)+f(4)+f(5)]∆x
R(4) = [1/2+1/3+1/4+1/5]1
R(4) = (30+20+15+12)/60
R(4) = 77/60
Hence, the area under the given curve is 77/60. SO the option B is correct.
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The right question is given below:
If 60% of the population supports massive federal budget cuts, what is the probability in that a survey of 250 people ,at most 155 people support such cuts
Probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given:
If 60% of the population supports massive federal budget cuts.
We have to find the probability in that a survey of 250 people, at most 155 people support such cuts.
So, the probability is, 155 / 250 = 0.62
Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.
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Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
x = 13
x = 1
Step-by-step explanation:
The (x – 7)2 = 36 gives the value of x as 25.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
(x – 7)2 = 36
Now, dividing both side by 2
(x – 7)2/2 = 36 /2
(x – 7) = 18
Now, add 7 both side
x- 7+ 7= 18 + 7
x = 25
Hence, the value of x is 25.
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+6y= -18
Answer: [tex]y=-\frac{1}{2} x-3[/tex]
Step-by-step explanation:
[tex]3x+6y=-18[/tex]
[tex]-3x[/tex] [tex]-3x[/tex]
[tex]6y=-3x-18[/tex]
[tex]\frac{6y}{6} =\frac{-3x}{6} -\frac{18}{6}[/tex]
[tex]y=-\frac{1}{2 } x-3[/tex]
Your sorority is preselling tickets for an end of year formal. You will save 22% off the door price by prepay
$56.40 per ticket now.
How much will you pay if you wait to purchase tickets at the door?
You will pay a price of $72.31 if you wait to purchase tickets at the door
How to calculate the amount you will pay?Discount is defined as a deduction from the usual cost of something. You will save 22% off the door price by prepay $56.40 per ticket now.
Let P represent the original price. We can write that:
P - 22% of P = $56.40. It should be noted that this can be rewritten as:
P - (22% × P) = 56.40
P - 0.22P = 56.40
Subtract
0.78P = 56.40
Divide through by 0.78
P = 56.40/0.78
P = $72.31
Therefore the price is $72.31.
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John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio. If profits are $70,000, Sally’s share would be;
Multiple Choice
$10,000
$20,000
$30,000
$70,000
The amount Sally’s share would be;
⇒ $30,000
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
Given that;
John, Sally and Jane form a partnership. They agree to distribute profits using a 2:3:2 ratio.
And, The profits are $70,000.
Now,
Since, The profits are $70,000.
Hence, We get;
⇒ 2x + 3x + 2x = $70,000
⇒ 7x = $70,000
⇒ x = $10,000
So, The amount of Sally’s share would be;
⇒ 3x = 3 × 10,000
= $30,000
Thus, The amount Sally’s share would be;
⇒ $30,000
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Determine if the statement below is true or false.
If BCA, then AUB=A.
Is the statement true or false?
O False
O True
The statement If B ⊂ A, then A U B = A is true.
How to determine the truth value of the statement?From the question, we have the following parameters that can be used in our computation:
If BCA, then AUB=A.
When the above statement is represented properly, we have the following representation
If B ⊂ A, then A U B = A
The statement If B ⊂ A means that
The set B is a subset of the set A
In other words, the whole of set B is in set A
If this is true, then the union of both sets represented by A U B is set A
Hence, it is true that If B ⊂ A, then A U B = A
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A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 114 inches (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.)
X= ??????
Y= ???????
The dimensions of the rectangular package with the condition of maximum volume is equal to x = 19inches and y = 38inches.
As given in the question,
Let us consider length of the cross section which is square be x
Perimeter of the cross section is 4x
And y be the length of the rectangular package
Maximum combined ( length + perimeter of the cross section ) = 114
y + 4x = 114
⇒ y = 114 -4x
Volume of the package 'V' = x²y
⇒V = x²(114 -4x)
⇒V = 114x² -4x³
Differentiate both the side of the equation with respect to x,
dV/dx = 228x - 12x²
For maximum Volume
dV/dx =0
228x -12x² = 0
⇒12x( 19 -x ) =0
⇒12x = 0 or 19 - x =0
⇒x =0 or x =19
x =0 is not possible
⇒x =19inches
y = 114 - 4(19)
= 38inches
Therefore, the dimensions of the rectangular package with the given condition of volume is equal to x = 19inches and y = 38inches.
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A scatter plot containing the point (4,9) has the regression equation y=5x+2 what is the residual e when x=4?
Answer:
the observed value of 9 is 13 units lower than the predicted value of 22.
Step-by-step explanation:
A residual is the difference between the observed value of a data point and the predicted value of that data point based on a given model. In a regression analysis, the residual is calculated using the formula e = y - y', where y is the observed value, y' is the predicted value, and e is the residual.
In this case, we are given the point (4,9) and the regression equation y = 5x + 2. Plugging in the value x = 4 into the regression equation, we get:
y' = 5(4) + 2 = 22
Since we are also given that the observed value of the point (4,9) is 9, we can plug these values into the formula for the residual to calculate the residual:
e = 9 - 22 = -13
Therefore, the residual e when x = 4 is -13. This means that the observed value of 9 is 13 units lower than the predicted value of 22.
Show the solution and answer
(3x + 5)(x - 9)
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Both the inequalities (- 3 > 1 - 3 = 3) and (1 < 3 - 3 < 1) are false.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following integers -
- 3, 1 and 3.
The given inequality are -
- 3 > 1 - 3 = 3
1 < 3 - 3 < 1
- 3 > 1 - 3 = 3
- 3 > - 2 = 3
Which is false.
1 < 3 - 3 < 1
1 < 0 < 1
Which is false.
Therefore, both the inequalities (- 3 > 1 - 3 = 3) and (1 < 3 - 3 < 1) are false.
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Suppose the life time (in hours) of a battery brand is normally distributed. A random sample of 16 batteries results in a sample variance of
3.25
hours
2
. We want to test if there is significant/sufficient evidence in the sample data to claim that the variance of the battery life population is different than 4 hours
2
at significance level of
0.05
. Which of the following is INCORRECT? A.
H 0
:σ 2
=4 vs H 1
:σ 2
=4
B. The test statistic is found to be
12.1875
C. We should reject the null hypothesis and there is sufficient evidence to claim that the variance of battery life is different than 4 hours
2
at significance level of
0.05
. D. None of the above.
there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
answer is D. None of the above.
To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:
X2 = (n-1)*(s2/σ2)
where n is the sample size, s2 is the sample variance and σ2 is the population variance.
In this case, n = 16, s2 = 3.25 and σ2 = 4
X2 = (16-1)*(3.25/4) = 12.1875
The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
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The display shows musicians' ages in a community orchestra.
1 7 9
2 0 4 4 6
3 2 3 5 5 7
4 2 4 8 9
5 1 2
6 5
Key 1 7 = 17
Which of the following describes this data set?
Answer:
I think Numerical and univariate
Step-by-step explanation:
Answer:
Step-by-step explanation:
This would be numerical and univariate because the information shown represents a stem and leaf plot.
Hope this helps! :)
The graph of the function f(x) = (x + 2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
the interval, the function returns zero (-6,-2) –6 < x < –2
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The given f(x) = (x + 2)(x + 6)
In this function, a quadratic equation is represented (vertical parabola open upward)
The vertex stands for a minimum.
the use of a graphing tool
view the attached image
x=-6 and x=-2 are the x-intercepts.
Point: the y-intercept
The point is called the vertex.
The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)
The range is in the range [-4,].
x -6 or x > -2 make the function positive.
For the interval, the function returns zero (-6,-2) –6 < x < –2
Hence, the interval, the function returns zero (-6,-2) –6 < x < –2
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John spends $2.75 on donuts for his office employees every weekday. On Sunday mornings he takes his wife and kids to the donut shop and spends $12.99. How much money does John spend on donuts throughout the week?
Answer:
26.74
Step-by-step explanation:
add the money John spends on the week days(13.75) to 12.99 and you get your answer
Suppose we have the triangle with vertices P(9, 0, 0), Q(0, 18, 0), and R(0, 0, 27). Answer the following questions. Find a non-zero vector orthogonal to the plane through the points P, Q, and R. Answer: Find the area of the triangle delta PQR. Area:
The non-zero orthogonal vector to the plane is 486i + 243j + 162j and the area of the triangle is 4374 unit squares.
The vertices of the triangle are P(9, 0, 0), Q(0, 18, 0), and R(0, 0, 27).
So, firstly we should find the vector PQ and PR,
Now,
PR = (0)i + (-18)j + (27)k
PR = -18j + 27j
And PQ,
PQ = (-9)i + (18)j + (0)k
PQ = -9i + 18j
Now, the normal vector which is also a non-zero orthogonal vector,
n = PQ x PR
n = 486i + 243j + 162j
Now, the area of the ΔPQR will be,
Ar(PQR) = [tex]\left[\begin{array}{ccc}9&0&0\\0&18&0\\0&0&27\end{array}\right][/tex]
Solving further,
Ar(PQR) = 4374 unit square.
So, the area of the triangle is 4374 unit square.
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