Confidence interval for 68% confidence level = (0.548, 0.572)
Confidence interval for 95% confidence level = (0.536, 0.584)
Confidence interval for 99.99% confidence level = (0.523, 0.598)
The mean of this sample distribution is
Mean = μₓ = np = 0.61 × 1600 = 976
But the sample mean according to the population mean should have been
Sample mean = population mean = nP
= 0.56 × 1600 = 896.
To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.
We will be doing the calculations in sample proportions,
We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).
Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.
Confidence interval = (Sample mean) ± (Margin of error)
Sample Mean = population mean = 0.56
The margin of Error = (critical value) × (standard deviation of the distribution of sample means)
Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =
[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124
The critical value for 68% confidence interval = 0.999 (from the z-tables)
The critical value for 95% confidence interval = 1.960 (also from the z-tables)
Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)
Confidence interval for 68% confidence level
= 0.56 ± (0.999 × 0.0124)
= 0.56 ± 0.0124
= (0.5476, 0.5724)
Confidence interval for 95% confidence level
= 0.56 ± (1.960 × 0.0124)
= 0.56 ± 0.0243
= (0.5357, 0.5843)
Confidence interval for 99.7% confidence level
= 0.56 ± (3.000 × 0.0124)
= 0.56 ± 0.0372
= (0.5228, 0.5972)
Therefore,
Confidence interval for 68% confidence level = (0.548, 0.572)
Confidence interval for 95% confidence level = (0.536, 0.584)
Confidence interval for 99.99% confidence level = (0.523, 0.598)
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- is slightly variable - and follows a nearly normal distribution - with a mean of 25 square feet - and a standard deviation of 3 square feet. (a) what is the probability that - the area covered by a can of spray paint - is more than 27 square feet?
The probability that the area covered by a can of spray paint is 0.251
The variable of interest is:
X: are objects that can be painted with a single can of spray paint.
This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.
Symbolically:
P(X≥27)
To calculate the probability, use the standard normal distribution, so first standardize the value of X using:
Z= (X-μ)/σ
P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)
Now, because the Z-table contains cumulative probability information:
P(Zα≤Z₀)=1-α
you must perform the following conversion to calculate the requested probability:
1 - P(Z<0.67)= 1 - 0.749= 0.251
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a random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. the balances of all checking accounts at the bank are normally distributed. develop a 95% confidence interval estimate for the mean of the population.
The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x (SD / √n)
where CI = confidence interval
μ = sample mean
z = found by using a z-score table
SD = sample standard deviation
n = sample size
At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.
(100 - 95) / 2 = 2.5
100 - 2.5 = 97.5
Find 0.975 in the z-table to get the value of z.
At p = 0.95, z = 1.96
Plug in the values and solve for the confidence interval.
CI = μ ± z x (SD / √n)
CI = 300 ± 1.96 x (45 / √26)
CI = 300 ± 17.30
CI = [$282.70, $317.30]
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Consider the quadratic equation.
X^2 -5x=6
If a student wants to factor this equation by the method of completing the square, why term should the student add to both sides as the first steps?
In completing the square method, considering the equation X^2 - 5x = 6 the student should add 25 / 4 to both sides of the equation
How to know term should the student add to both sidesThe quadratic equation is an equation of the form
ax^2 + bx + c
The completing the square method is on of the methods of solving equations of the form above
The factor to be added on the both sides of the equation while using the completing the square method is
(b / 2a)^2
compared to the equation in the problem X^2 - 5x = 6 it is
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1. Name a plane parallel to plane WXT
2. Name two segments parallel to VU.
3. Name two segments parallel to SW.
4. Name two segments skew to XY.
5. Name two segments skew to VZ.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
What are parallel lines ?Lines that are always the same distance apart in a plane are said to be parallel. Lines that are parallel never cross. Lines that cross at a straight angle (90 degrees) are said to be perpendicular.
Given : The quadrilateral prism
Parallel lines means lines which does not interact and run parallel meaning they have equal distance between them.
The plane which is parallel to the line WXT is UVZW
two segments parallel to VU is ST and WX
two segments skew to XY is UT
two segments skew to VZ is YU and TX
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There are 1,459 children registered for camp. There is enough room for 18 campers to sleep in
each cabin. What is the least number of cabins needed for all the registered campers?
Answer:
82 rooms
Step-by-step explanation:
1459/18=81.05
so 82 rooms
Please mark as brainliest
Answer:
82
Step-by-step explanation:
1459/18
[tex]1459 \div 18[/tex]
for each cabin there 18 And there are 1459
81.05 \times 48=159
since you can't have a half a cabinet the answer is 82
Find the measure of the angle indicated by 11x + 1.
10x+10
11x +1
The measure of angle 11x+1 is 100°.
According to the question,
We have the following information:
We have a figure where two parallel lines are divided by a line. We know that the vertically opposite angles are equal. And when two parallel lines are cut by another line then the alternate interior opposite angles are equal.
Now, we have 10x+10 as the alternate opposite interior angle to 11x+1.
So, we have the following expression:
10x+10 = 11x+1
11x-10x = 10-1
x = 9
Putting the value of x in 11x+1:
11*9+1
99+1
100°
Hence, the measure of angle 11x+1 is 100°.
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Phil lives in a state where his tax rate does not change when his income changes. This is an example of a(n) ____ ?
Phil lives in a state where his tax rate does not change when his income changes. This is an example of a proportional or flat tax.
What is tax?Tax is defined as the official way individuals contribute to their state revenue through the compulsory deduction of some amount of money from their monthly income.
There are two types of tax which include the following:
Regressive tax,Progressive tax, andProportional or flat tax.Proportional or flat tax: This is defined as the type of tax that is being paid by individuals from different class in the society whereby all are expected to pay tax with the same rate irrespective of the income.
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Decide whether each equation is true for all, one, or no values of x.
Answer:
For the first equation, it is "True for one value of x."
For the second equation, it is "True for no value of x."
For the third equation, it is "True for all values of x."
Step-by-step explanation:
Just solve the equation and check the numbers:
If both numbers are the same, it is "true for all values of x"
If there is a variable and a number, it is "true for one value of x"
If there are two numbers and they are different, it is "true for no values of x"
Hope this helps!
Please give brainliest
We need to check whether the given equations are true for all values of [tex]x[/tex] , one value of [tex]x[/tex] , or no values of [tex]x[/tex] .
The equations are ,
[tex]3x +9 = -4.5x +20[/tex]solve this equation for x ,
[tex]\longrightarrow 3x +9=-4.5x+20\\[/tex]
[tex]\longrightarrow 3x+4.5x =20-9\\[/tex]
[tex]\longrightarrow 7.5x =11\\[/tex]
[tex]\longrightarrow \underline{\underline{x =\dfrac{11}{7.5}}}[/tex]
Hence the equation is true for one value of x .
[tex] 9(x+3)=9x+12[/tex]solve out for x ,
[tex]\longrightarrow 9x +27=9x-12\\ [/tex]
[tex]\longrightarrow 9x -9x =-27-12\\ [/tex]
[tex]\longrightarrow 0 = -39[/tex]
This can never to true , so the equation is true for no values of x .
[tex]4(2x+3)=12+8x[/tex]solve out for x ,
[tex]\longrightarrow 8x+12=12+8x \\[/tex]
[tex]\longrightarrow 12-12=8x-8x\\[/tex]
[tex]\longrightarrow 0=0 [/tex]
Hence this equation is true for all values of x .
And we are done!
TEXT ANSWER
Jason provided the following work when asked to convert 0.105 to its simplest fraction
form.
1. Why did Jason get the problem wrong?
2. Provide the work for properly writing the decimal in its simplest fraction form.
Jason's Work:
0.105=
105
21
1000 200
Answer:
See below
Step-by-step explanation:
.105 is 105 THOUSANDTHS or 105/1000
Divide top and bottom by '5'
to get 21/100
The equation 2x(x + 8) = 110 represents the area of a rectangle.
Solve the equation. What are the approximate dimensions of the rectangle? Express your answers as decimals rounded to the nearest tenth.
The rectangle has its dimensions to be 8.8 units by 12.4 units
How to determine the dimensions of the rectangle?From the question, the equation is given as
2x(x + 8) = 110
This equation represents the area of the rectangle
So, we have
2x(x + 8) = 110
Divide by 2
x(x + 8) = 55
Open the brackets
This gives
x² + 8x = 55
Rewrite as
x² + 8x - 55 = 0
Using a graphing calculator, we have the solutions to be
x = -12.4 and x = 4.4
The variable x cannot be negative
So, we have
x = 4.4
In 2x(x + 8) = 110, we have
Length = 2x
Width = x + 8
So, we have
Length = 2 x 4.4
Width = 4.4 + 8
Evaluate
Length = 8.8
Width = 12.4
Hence, the dimensions of the rectangle are 8.8 units by 12.4 units
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Which equation represents the sentence, "The sum of twenty-four and p minus fifteen is q"?
A. 24 + p + 15 = q
B. 24 + p – 15 = q
C. p + q – 15 = 24
D. 15 + p = q – 24
Answer:
B is correct: also if u add C and D together there both different and if u added B and A correctly u would have got B as your answer.
Step-by-step explanation:
Can anyone state the vertex of the graph?
There is no vertex in the graph and the transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
In this case, there is no maximum or minimum in the graph
This means that that there is no vertex in the graph
The transformationHere, we have:
We can see that:
The graph is 4 units to the left of the origin and 2 units below the origin
This means that the function has been shifted down and shifted to the left
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A rectangular book measures 3*5. What is the length of its diagonal to the nearest tenth?
The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
Area of rectangle = length × width.
The angle between any two consecutive sides will be 90 degrees.
As per the given rectangle with dimensions 3 × 5.
The rectangle has been attached below,
The length of the diagonal using Pythagoras' theorem is,
x = √(3² + 5²)
x = √34 = 5.8
Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".
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it is claimed that the mean age of bus drivers in chicago is 50.2 years. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
The null hypothesis is a statement which describe the claim of 'no difference'.
Let μ be the population mean.
Given claim : The mean age of bus drivers in Chicago is 50.2 years.
i.e. μ = 50.2
Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.
Then, the null hypothesis for the given situation is
Ηο : μ = 50.2
If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.
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48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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3. Suppose that your calculator does not have a square root key. How could you still use your calculator to determine √144?
Answer
12
Step-by-step explanation:
click on square root
click on 144
then your answer will pop out below your equation
Graph the equation by using the slope intercept method
For the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
As given in the question,
Given equation is equal to :
4x + 3y = 21
To get the slope intercept form of the given equation we have,
Subtract 4x from both the sides of the given equation we have,
4x + 3y - 4x = 21 - 4x
⇒ 3y = 21 - 4x
Now divide by 3 on both the sides of the equation we get,
3y / 3 = (-4/3)x + (21/3)
⇒ y = (-4/3) x + 7
Graph of the given equation in slope intercept form y = (-4/3) x + 7 is attached.
When x = 0 ⇒ y = 7
y= 0 ⇒ x = 21 /4
Therefore, for the given equation 4x + 3y =21 the slope intercept form is given by y = (-4/3)x + 7.
Graph is attached.
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Which equation represents a line which is perpendicular to the line y=2x-5y?
A.2x-y=-42x−y=−4
B.2y−x=4
C.x+2y=−6
D.2x+y=−2
Answer:
C) x + 2y = - 6Step-by-step explanation:
We know that perpendicular lines have opposite-reciprocal slopes.
Given line:
y = 2x - 5Its slope is 2 and the perpendicular line has a slope of - 1/2.
Let's find the line with the slope of - 1/2:
A) 2x - y = - 4y = 2x + 4, the slope is 2, the answer is NOB) 2y - x = 42y = x + 4y = 1/2 x + 2, the slope is 1/2, the answer is NOC) x + 2y = - 62y = - x - 6y = - 1/2 x - 6, the slope is - 1/2, the answer is YESD) 2x + y = - 2y = - 2x - 2, the slope is - 2, the answer is NOAnswer:
c
Step-by-step explanation:
Let's find
11
6
- Im
First, write the addition so the fractions have denominator 6.
Then add.
1 1
6
1
3 6
0 0
6
The required addition of the given fraction is given as 7/6.
Given that, a mixed fraction is given 1 1 /6 we have to determine the simplified fraction.
Fraction is defined as the number of compositions that constitutes the Whole.
Here,
Given fraction = 1 1 /6
This fraction is written as 1 + 1/6
Simplifying the fraction by multiplying the one with 6 and adding the product to the 1 in the numerator,
= [1×6 + 1]/6
= 7/6
Thus, the required addition of the given fraction is given as 7/6.
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Question 3(Multiple Choice Worth 6 points)
(02.07 MC)
What are the solutions of 2x² + 3x= -8?
The solutions to the equation [tex]2x^{2} +3x=-8\\[/tex] are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex] respectively.
What is a quadratic equation?
A second-degree algebraic equation is a quadratic equation in x.
[tex]ax^{2} +bx+c=0[/tex] is the quadratic equation in standard form, where a and b are the coefficients, x is the variable, and c is the constant term.
To find the root value of x, [tex]x= \frac{-b}{2a}[/tex] ± [tex]\frac{\sqrt{b^{2} -4ac} }{2a}[/tex]
Given, [tex]2x^{2} +3x=-8\\[/tex]
or, [tex]2x^{2} +3x+8=0[/tex]
Comparing the equation [tex]2x^{2} +3x+8=0[/tex] with the equation [tex]ax^{2} +bx+c=0[/tex] , we get
[tex]a=2, b=3, c=8[/tex]
Then, [tex]x= \frac{-3}{2*2}[/tex] ± [tex]\frac{\sqrt{3^{2} -4*2*8} }{2*2}[/tex]
or, [tex]x= \frac{-3}{4}[/tex] ± [tex]\frac{i\sqrt{55} }{4}[/tex]
Taking '+' sign, we get [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex]
Therefore, the solutions of the given equation are [tex]x=\frac{-3+i\sqrt{55} }{4}[/tex] and [tex]x=\frac{-3-i\sqrt{55} }{4}[/tex].
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The mass of 1cm³. of copper is 8.5 grams. Correct to 1.d.p. Complete statement about total mass, T, grams of 12cm³. of copper.
There are 102 grams of copper in 12 cm³ of copper.
What are unit rate?A unit rate means a rate for one of something.
Given that 1 cm³ of copper have mass of 8.5 grams
Therefore, 12 cm³ = 12*8.5 = 102 grams
Hence, There are 102 grams of copper in 12 cm³ of copper.
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What would the final cost be
for a trick or treat bucket that
originally costs $3.00 if you
have a coupon for 10% off and
you have to pay tax of 7.5%?
Answer:
4.73
Step-by-step explanation:
10% is 10
so, you have to multiple 3×.10=.30
3-.30=2.70
2.70×.75 because 7.5% is .75
that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73
Hope that works
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The vertex of the graph is (-2, 2), the axis of symmetry of parabola is -2 and the parabola opens downwards.
In the given question we have to find the vertex, axis of symmetry and whether the parabola opens upwards and downwards.
Firstly we find ing the vertex of the graph.
As we know that vertex is the highest and lowest point of the graph.
From the graph the highest point is (-2, 2).
So the vertex of the graph is (-2, 2).
As we know that the axis of symmetry always passes through the vertex of parabola. The x coordinate of the vertex of parabola is the axis of symmetry of parabola.
So the axis of symmetry of parabola is -2.
As we can see that the parabola opens downwards.
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john wanted a pressure washer for a flat fee of $50 plus $9 per hour how many hours did he rent the pressure washer if the total bill was $86?
He rented the pressure washer for 4 hours, given that the total bill was $86.
An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.
Let x = total number of hours he rented the pressure washer
The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.
Hence, the equation will be 50 + 9x = 86.
Solve for x.
50 + 9x = 86
9x = 86 - 50
9x = 36
x = 4
total number of hours he rented the pressure washer = 4
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A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold. How many textbooks of each type were sold?
Taking into account the definition of a system of linear equations, the textbook store sold 141 math textbooks and 282 psychology textbooks.
System of linear equationsA system of linear equations is a set of linear equations (that is, a system of equations in which each equation is of the first degree) in which more than one unknown appears.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"p" is the number of psychology textbooks sold."m" is the number of math textbooks sold.You know:
A textbook store sold a combined total of 423 psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold.The system of equations to be solved is
p + m= 423
p=2m
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first one you get:
2m + m= 423
3m=423
m= 141
Substituting this value in the second equation you get:
p= 2m
p= 2×141
p= 282
Finally, 141 math textbooks and 282 psychology textbooks were sold by the textbook store.
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Find the slope and the y-Intercept of the line.
-5x + 4y = -3
Write
your answers in simplest form.
Answer:
slope=5/4 y intercept=-3/4
Step-by-step explanation:
put it into slope intercept form y=5/4x-3/4
pull out 5/4 as slope and -3/4 as y intercept
Write an equivalent ratio for each ratio
Answer:2/5=4/10 and 1/4=2/8
Step-by-step explanation: you can simplify 4/10 to get 2/5 and same with 2/8. You would divide the fraction by two.
Which of the following sets is equal to {1, 2, 3, ...}?
The set which is equivalent and equal to the given set; {1, 2, 3, ...} is; Z+.
Which set is equivalent to the given set?It follows from the task content that the set which is equivalent to the given set; {1, 2, 3, ...} is to be determined.
Since the numbers in the set are all integers and which happen to be positive integers.
Hence, the best representation of a set which is equivalent to the given set as given in the task content is; Z+.
The set of positive integers is represented as Z+. It implies all the integers greater than 0.
Hence, the set which is equivalent to the given set; {1, 2, 3, ...} is; Z+.
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A cat’s heart beats approximately 45 times in 15 seconds. At this rate how many times does the cat′s heart beat per second?
Work Shown:
45 beats = 15 seconds
45/15 beats = 15/15 seconds
3 beats = 1 second
To convert to beats per minute (bpm), multiply by 60.
Two complementary angles have measures of x and y. If y is 9 less than twice x, write a system of linear equations that can be used to determine the measure of each angle. Find the measure of each angle.
Using system of linear equation, the complementary angles (x, y) are 27 and 63 degrees respectively.
Complementary AnglesWhen the sum of two angles is equal to 90 degrees, they are called complementary angles. For example, 30 degrees and 60 degrees are complementary angles. However, when the sum of the two angles is equal to 180 degrees, the angles are supplementary angles
In this case, we have two angles x, y which are complimentary to one another.
We can represent this with system of equations;
x + y = 90 ...eq(i)y - 9 = 2x ... eq(ii)solving equation (i) and (ii)
The value of x and y are 27 and 63
The complementary angles are 27 and 63
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