Determine whether the following statement is true or false. Sample evidence can prove that a null hypothesis is true. Choose the correct answer below O True O False
False, sample evidence cannot prove that a null hypothesis is true.
Sample evidence can be used to infer whether a null hypothesis is true or not, but it cannot prove it to be true. The null hypothesis is a statement of no effect or no difference, and it is typically used as a starting point for statistical hypothesis testing. When sample data is collected, it is used to calculate a test statistic, which is then used to make a decision about the null hypothesis.
If the test statistic falls within the acceptance region, meaning that it is not unlikely to occur if the null hypothesis is true, then the null hypothesis is not rejected. However, if the test statistic falls in the rejection region, meaning that it is unlikely to occur if the null hypothesis is true, then the null hypothesis is rejected. The conclusion is that the sample evidence provides a probability that the null hypothesis is true or not, but it cannot prove it to be true.
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Karl spent $30 decorating for the annual holiday party. Each, x, table cover cost $2
and each, y, center piece cost $6. Karl bought 7 items total.
what are the first and second equation?
The two pair of linear equations are 2x+6y=30 and x+y=7.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Each, x, table cover cost $2 and each, y, center piece cost $6.
Karl spent $30 decorating for the annual holiday party.
So, the equation is 2x+6y=30 --------(I)
Karl bought 7 items total.
Now, x+y=7 --------(II)
From equation (II), x=7-y
Substitute, x=7-y in equation (I), we get
2(7-y)+6y=30
14-2y+6y=30
14+4y=30
4y=16
y=4
Substitute y=4 in equation (II), we get
x=3
Therefore, the two pair of linear equations are 2x+6y=30 and x+y=7.
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A scenic train ride has one price for adults and once price for children. One family of two adults and two children pays $62 for the train ride. Another family of one adult and four children pays $70. Which system of linear equations can you use to find the price x for an adult and the price y for a child? please help i will mark you brainliest.
The system of linear equations with our defined variables are 2x + 2y = 62 ...eq(i) and x + 4y = 70 ...eq(ii)
What is System of Linear EquationA system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of a system of linear equations is the set of values for the variables that make all of the equations in the system true.
In this problem, let's define our variables as;
x = adultsy = childrenThe equations can be written as;
2x + 2y = 62 ...eq(i)
x + 4y = 70 ...eq(ii)
Which is synonymous to option D in the question
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The table represents the relationship between the number of employees scheduled per estimated customer at a clothing store.
The graph represents the relationship between the number of employees scheduled per estimated customer at a coffee shop.
At the clothing store, how many customers can one employee help?
At the coffee shop, how many customers can one employee help?
The clothing store's rate of customers per employee is less than the coffee shop's rate.
For the table, we have that the rate between the output and the input is given as follows:
12/3 = 16/4 = 28/7 = 32/8 = 4.
Meaning that this is a proportional relationship, and that one employee can help 4 customers, which is the constant of proportionality.
The graph has a constant slope and an intercept of zero, meaning that it also represents a proportional relationship, with the rate given as follows:
k = 8/1 = 8.
Missing InformationThe data is given by the image presented at the end of the answer.
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What shape has 69 sides?
The polygonal shape of the hexacontakaienneagon has 69 sides.
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge. Polygons include shapes like triangles, hexagons, pentagons, and quadrilaterals.
The hexacontakaienneagon shape's number of sides is indicated by the name. For instance, a triangle has three sides, whereas a quadrilateral has four. A two-dimensional closed figure with three or more straight sides is called a polygon. A polygon is any shape with straight edges, such as a triangle or rectangle. Figures with open sides or any curved sides are not considered to be polygons.
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SOMEONE PLEASE HELP PLS SOLVE ALL 4
Answer:
(4.) 4(3 + 9)
(5.) 5(n + 7)
(6.) 7(11 + 3)
(7.) 8(5+n)
Step-by-step explanation:
(4.) The area of a rectangle is length * width. Because there are two rectangles, the areas must be combined in order to find the total area.
The area of the first rectangle is 4*3 and the area of the second is 9*4 so the total area would be 4*3 + 4*9. We can factor out the 4 and simply add the 9 and 3 to get area = 4(3 + 9).
(5.) The total area before using the distributive property is 5 * n + 5 * 7. We factor out the 5 and add the n and 7 to get area = 5(n + 7)
(6.) We need two numbers whose product is 77 and two numbers whose product is 21. Also, one of the numbers must be the same (namely the width, since the width of both rectangles is equal and doesn't change).
We can use 7*11 for the first rectangle and 7*3 for the second rectangle. We factor out the 7 and add the 3 and 11 to get area = 7(3 + 11).
(7.) We need two numbers whose product is 5n and two numbers whose product is 40. Like number 6, the width of both rectangles must be the same. Since we already have 8 for the first rectangle, we can use 8 * n and 8 * 5.
We factor out the 8 and add the 5 and n to get 8(5 + n).
A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10. 50, and tickets cost $32. 50 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park.
Using the idea of inequality and some simple math calculations, the total number of persons who can visit an amusement park is 4.
Given that a group of friends has a maximum of $160 in this question.
$10.50 is the cost of parking.
The price of each ticket is $32.50.
We must address inequality.
So let's attempt to define inequity.
Inequalities in mathematics describe the connection between two non-equal quantities. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal sign (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.
A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">" "<" "≥" "≤".
Let's Suppose we have a total of x number of persons.
then the total cost of tickets is 32.5 * x.
cost of parking is $10.50.
So the total cost to visit an amusement park is = 32.5x+ 10.50
Given that the total cost will be no more than $160.
So according to that
32.5x+ 10.50 ≤ 160.
32.5x ≤ 160-10.50
32.5x ≤ 149.5
x ≤ 149.5/32.5
x ≤ 4.6.
The nearest integer will be 4.
So the number of people who can go to an amusement park is 4.
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The group of friends can have no more than 4 people go to the amusement park.
We can use an inequality to determine the number of people who can go to the amusement park. We know that the group has no more than $160 to spend on parking and admission. We also know that parking is $10.50 and tickets cost $32.50 per person, including tax.
The inequality we can use to determine the number of people who can go to the amusement park is: 10.50 + 32.50x ≤ 160
To solve the inequality, we must first subtract 10.50 from both sides of the equation to isolate variable x. This gives us: 32.50x ≤ 149.50
Next, we must divide both sides of the equation by 32.50 to solve for x. This gives us: x ≤ 4.62
Since x is the number of people who can go to the amusement park, we must round down to the nearest whole number. This gives us: x ≤ 4
Therefore, we can conclude that the group of friends can have no more than 4 people go to the amusement park.
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3. Your friend Juan says the perimeter of the rectangle can be represented by the expression,
8x +4. Determine if the expression you wrote in #2 and the expression Juan wrote are
equivalent. Justify your answer.
Common factor
8x+4
4(2x +1)
∴ Solution is 4 (2x+1)
What is perimeter?In geometry, the perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape. It is measured in linear units of measurement like centimeters, meters, inches, or feet.A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.To learn more about perimeter refer to:
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help please
-17= -3r
Answer:
r=17/3
Step-by-step explanation:
Given -17=-3r
Divide both sides by -3
-17/-3=r=17/3
r=17/3
Hope this helps :)
What is fully factored form of 32a3 12a2?
On factorizing , we get that the fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] can be written as [tex]4a^{2} (8a+3)[/tex] .
The Factorizing is defined as a process of expressing the given number or the algebraic expression as a product of its factors .
the expression is given as : [tex]32a^{3} + 12a^{2}[/tex] ;
the first term of the expression is ⇒ [tex]32a^{3}[/tex] , it can be expressed as [tex]4\times 8 \times a \times a \times a[/tex] ;
the second term of given expression is ⇒ [tex]12a^{2}[/tex] , it can be expressed as [tex]4\times 3 \times a \times a[/tex] ;
we see that in both terms , the common factor is [tex]4\times a \times a = 4a^{2}[/tex] ;
which means that , it is written as : [tex]4a^{2} (8a+3)[/tex] ;
Therefore , the fully factored form is [tex]4a^{2} (8a+3)[/tex] .
The given question is incomplete , the complete question is
What is fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] ?
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Ч.
112:4
SOCIl6
5. Mike buys four equally priced DVD's online. Each DVD costs the same amount. With a $5.98 shipping charge included, the total cost came to $79.94. Write a word equation you could use to find the cost of each DVD.
Answer:
Each DC cost $18.49.
Step-by-step explanation:
[tex](\frac{79.94 - 5.94)}{4}[/tex] Subtract out the shipping cost of 5.98 from the total cost of $79.94 and divide that amount by 4. That will get you 18.49 which is the cost of each DVD.
Find m/ABD and m/DBC.
Check the picture below.
.
Elise wanted to stock up on drinks for an upcoming party. First, she spent $20 on 5 cases of
juice and 5 cases of soda, which is all the store had in stock. A few days later, she returned to
the store and purchased an additional 12 cases of juice and 5 cases of soda, spending a total
of $34. What is the price of each drink?
On solving the provided question, we can say that - by the unitary method price of the each drink will be $4
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here,
she spent $20 = on 5 cases
so of each will be 20/5 = $ 4
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Find the volume of the solid describe below:
The solid lies between the planes perpendicular to the x-axis at x= 0 and x=8 . The cross-sections perpendicular to the axis on the interval 0≤x≤8 are squares whose diagonals run from the parabola y=−√x to the parabola y=√x
Three students practiced
converting values into scientific
notation as shown. In 1-3,
describe the mistake each student
made and correct their work.
(-1,1) and (1,5) write your answer in slope-intercept form
Answer:
Slope (m) = 2
y = 2x
Step-by-step explanation:
Change in y / Change in x
-1 becomes 1 (positive)
1 + 1 = 2
1 - 5 = 4
4/2 = 2
y = 2x
Spencer and Lilly are skiing down the same mountain. Spencer is traveling at a speed of 4/5 mile every 1 and 1/3 minutes, and Lilly is traveling at a speed of 3/4 mile every 1 and 1/8 every minute Who is traveling at a faster speed?
A. spencer 36
B lilly 40
C spencer 50
D lilly 64
Lilly is travelling at a faster speed.
What is Speed?Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.
Speed is a scalar quantity as it only has magnitude and no direction.
Given that,
Distance travelled by Spencer = 4/5 mile
Time taken to travel the distance = 1 1/3 minutes = 4/3 minutes
Speed = Distance / Time = (4/5) / (4/3) = 3/5 = 0.60 mile per minute
Distance travelled by Lilly = 3/4 mile
Time taken to travel the distance = 1 1/8 minute = 9/8 minutes
Speed = (3/4) / (9/8) = 2/3 = 0.67 mile per minute
Hence Lilly is travelling at a greater speed of 0.67 mile per minute.
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Aiden checks out a book from the library. The table below shows the hours Aiden spends reading the rest of the book. If Aiden started at the beginning of the book, how many pages are in the book?
Answer:
270
Step-by-step explanation:
He read 45 pages an hour. If we go back to hour 0, we would add 45 pages to 225
Answer:
270 pages
Step-by-step explanation:
In the attachment, we can see that Aiden read 45 pages per hour. Therefore, since he already read for an hour, we need to add 45 to 225
45+225=270
So, Aiden's book has a total of 270 pages.
Mikaela purchased a paddleboard originally priced at $899. if all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount that mikaela spent on the paddleboard? $385.67 $424.78 $578.51 $604.58
The total amount that Mikaela spent on the paddleboard is $578.506. which is the correct answer would be option (D)
What is the percentage?
The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Mikaela purchased a paddleboard originally priced at $899. If all merchandise was on sale for 40% off and the state tax rate is 7.25%.
Here,
Original cost = $899
Discount = 40% = 0.40
State tax rate = 7.25% = 0.0725
Total amount = Original cost × (1 - Discount) × (1 + State tax)
Total amount = 899×(1 - 40%)×(1 + 7.25%)
Total amount = 899×(1 - 0.40)×(1 + 0.0725)
Total amount = 578.506
Thus, the total amount that Mikaela spent on the paddleboard is $578.506
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The total amount that Mikaela spent on the paddleboard is $578.51. The result is obtained by subtracting the discount from the original price and adding the tax.
How to calculate the total price to pay?When we get a discount of a product, the price will get cheaper. The price is subtracted by the discount. When there is a tax, you have to pay for it.
Mikaela purchased a paddleboard with the original price of $899. She got a discount of 40%. The tax rate is 7.25 %. Find the total amount she paid for the paddleboard!
From the information, we get the discount
= 40% × $899
= 0.4 × $899
= $359.6
The tax would be
= 7.25% × $899
= 0.0725 × $899
= $39.11
The total price is
= original price - discount + tax
= $899 - $359.6 + $39.11
= $578.51
Hence, Mikaela spent $578.51 for the paddleboard.
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Help please I’ll mark brainliest
The logarithm rules and the matching equation is as follows
equation logarithm rule
[tex]log_{3}(\frac{(x-4)}{(x-1)})[/tex] quotient rule
[tex]log_{2}x(x+2})[/tex] product rule
[tex]log(x+2)^{3} x^{3}[/tex] product rule and power rule
[tex]log_{3}(x-4)-log_{3}(x+4)[/tex] quotient rule
3 log (x + 2) - 3 log (x) product rule and power rule
What are the laws of logarithm?The laws of logarithm are generally rules that describes how problems involving logarithm is being solved
The quotient rule refers to when there is a division, the rul when applied changes division to subtraction.
The power rule takes care if exponents and places the number in the exponents to be just before the log sign
The product rule is used to deal with duplication, it changes multiplication to addition
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help everyone help me please
A convex mirror's generated image is always virtual and situated behind the mirror. The picture is erect and situated at the focal point when the item is far from the mirror.
What is the location of the image at the center of the curvature?The radius of curvature is the measurement between the vertex and the center of the curve (represented by R). The sphere from which the mirror was sliced has a radius equal to the radius of curvature. The distance between the vertex of the circle used to create the cylindrical mirror's shape to its center is known as the center of curvature.
In addition, the center of curvature will house the image. The image will be upside-down in this situation. The proportions of the image match those of the object. The image is the same size as the object, actual, and inverted if the object is at the center of the curve. The image is bigger, realer, and inverted if the object lies between the center of curvature and the main focus.
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Find the minimum sample size n needed to estimate μ for the given values of c, o, and E. c= 0.95, σ = 5.7, and E = 1 Assume that a preliminary sample has at least 30 members. n= (Round up to the nearest whole number.)
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
We use the formula
n= (zc/E)2σ2
Where,
n = sample size
zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
E = margin of error
σ = standard deviation
Substituting the given values,
n= [(1.96*0.95)/1]2*5.72
n= 95.29
Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
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What is the projection of (4,4) onto (3,1)? A. 1.3(3,1)
B. 1.3(4,4)
C. 1.6(4,4)
D. 1.6(3,1)
Answer: D
Step-by-step explanation:
what is the soultion 3-4y=19
Answer: y = -4
Step-by-step explanation:
In a reflection the orientation of a figure changes. (The direction of the shape changes.)
TRUE OR FALSE
Answer:
True.
Step-by-step explanation:
In a reflection, the orientation of a figure changes. This means that the direction of the shape is reversed, as if it were being viewed in a mirror. For example, if a figure is facing to the right, it will appear to be facing to the left after it has been reflected. The shape itself is not altered by the reflection, only its orientation.
Factoring trinomials
y^2x - y^x - 20
After factoring the value of y^x = 5 or -4.
What is algebraic expression ?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators (such as +, -, x, ÷). These expressions can be evaluated to determine their numerical value, but they can also be simplified, factored, and manipulated using the rules of algebra. Examples of algebraic expressions include 2x + 3, x^2 - 4, and (x + y)^2.
Given expression,
y^2x - y^x - 20 = 0
Let y^x = t .
t^2 - t - 20
t^2-5t+4t-20 = 0
t (t-5) + 4 (t-5) = 0
(t-5) (t+4) = 0
so, t-5 = 0
we get , t = -4
and t+4 = 0
so we get , t = 5
Hence, the value of y^x = 5 or -4.
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A dealer shuffles a deck of 52 cards then deals out 5. let x = 5 the number of suits represented in the five-card hand.
The total number of possible combinations would be 2,598,960.
The sample space for this experiment would be all possible combinations of 5 cards from a deck of 52 cards. This would include all possible combinations of 5 cards of the same suit (e.g. 5 spades, 5 hearts, etc.), all possible combinations of 4 cards of one suit and 1 card of another suit (e.g. 4 spades and 1 heart, 4 hearts and 1 spade, etc.), all possible combinations of 3 cards of one suit and 2 cards of another suit, and so on. The total number of possible combinations would be 2,598,960.
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The probability mass function (pmf) of x is:
= 0.0020 for x = 1
= 0.1459 for x = 2
P(X = x) { = 0.8825 for x = 3
= 0.5883 for x = 4
= 0 otherwise
In this question we have been given that after shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.
We need to find the pmf of x.
here, sample space n = 52,
and x = 5.
Let x = the number of suits represented in the five - card hand.
So, all possible outcomes for above event would be,
N = 52C5
N = 2598960
For x = 1 (all are spades)
Then the number of ways to get 5 spades would be 13C5 = 1287
so there are 1287 hands of 5S.
Since there are 4 suits, we multiply 1287 by 4C1
Then P(x = 1) = (4 * 1287)/2598960
= 0.0020
For x = 2 (only spades and hearts with at least one of each suit)
Then we can have 4S and 1H; 3S and 2H; 2S and 3H; or 1S and 4H.
And the number of possible outcomes would be,
(13C4 * 13C1) + (13C3 * 13C2) + (13C2 * 13C3) + (13C1 * 13C4)
= 2[(13C4 * 13C1) + (13C3 * 13C2)]
= 2(715 * 13 + 286 * 78)
= 63206
We're choosing 2 suits from the 4, so we multiply this by 4C2 = 6
Then P(x = 2) = (6 * 63206)/2598960
= 0.1459
For x = 3 (a hand with S, H, and clubs (C))
Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.
Using combination formula,
3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]
= 3 [(286 * 13 * 13) + (78 * 78 * 13)]
= 382278
We're choosing 3 suits from the 4, so we multiply this by 4C3 = 6
Then P(x = 3) = (6 * 382278)/2598960
= 0.8825
For x = 4 (2 spades ∩ one of each other suit)
For this case the possible outcomes would be,
13C2 * 13C1 * 13C1 * 13C1
= 78 * 13 * 13 * 13
= 171366
Then we can have 3S, 1H, and 1C; 1S, 3H, and 1C; 1S, 1H, and 3C; 2S, 2H, and 1C; 2S, 1H, and 2C; or 1S, 2H, and 2C.
Using combination formula,
3[(13C3 * 13C1 * 13C1) + (13C2 * 13C2 * 13C1)]
= 3 [(286 * 13 * 13) + (78 * 78 * 13)]
= 382278
Then P(x = 4) = (4 * 382278)/2598960
= 0.5883
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The complete question is:
After shuffling a deck of 52 cards, a dealer deals out 5. let x = the number of suits represented in the five-card hand.
(a) find the pmf of x.
[hint: p(1) = 4p(all are spades), p(2) = 6p(only spades and hearts with at least one of each suit), and p(4) = 4p(2 spades ∩ one of each other suit)](round your answers to five decimal places.)
Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
A. how much will be in the account after 4 years?
B. How much will be in the account after 16 years?
C. How many years will it take for the account to contain $2500?
D. How many years will it take for the account to contain $3000?
Step-by-step explanation:
The account starts at 2000$
2000$×0.06(same as 6%)= 120$
The account gains 120$ yearly
A. After 4yrs that would be 480$ interest
120$×4= 480$
2000$+480$= 2480$ after 4yrs
B. Aftee 16yrs that would be 1920$ interest
120$×16= 1920$
1920$+2000$= 3920$
C. 2500$-2000$= 500$
500$÷120$= 4.16yrs
It will take about 4.2 years for the account to reach 2500$
D. 3000$-2000$= 1000$
1000$÷120$= 8.33yrs
It will take about 8.3yrs for the account to reach 3000$
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 95% confidence interval with a maximum error of 0.19 reproductions per hour. Assuming that the mean is 12.6 reproductions and the variance is known to be 3.61 what is the minimum sample size required for the estimate? Round your answer up to the next integer.
Answer:
the minimum sample size required is 139
Step-by-step explanation:
To construct a 95% confidence interval with a maximum error of 0.19 reproductions per hour, we need to use the t-distribution. The t-distribution is used when the population variance is unknown and the sample size is small.
To find the minimum sample size required, we need to use the following formula:
n = (t_(α/2,df) * s / E)^2
where:
n is the minimum sample size
t_(α/2,df) is the critical value of the t-distribution for a confidence level of 95% (α = 0.05) and df is the degrees of freedom
s is the standard deviation of the population
E is the maximum error allowed
We are given that the mean is 12.6 reproductions and the variance is 3.61. The standard deviation is the square root of the variance, so the standard deviation is 1.9.
To find the critical value of the t-distribution, we need to know the degrees of freedom. The degrees of freedom is equal to the sample size minus 1. Since we don't know the sample size yet, we will use a symbol (let's use "df") to represent the degrees of freedom in the formula.
Plugging the values into the formula, we get:
n = (t_(0.025,df) * 1.9 / 0.19)^2
To find the critical value of the t-distribution, we need to use a t-table or a computer program. Looking up the critical value in a t-table or using a computer program, we find that the critical value for a 95% confidence level and df = 9 is 2.262.
Plugging this value into the formula, we get:
n = (2.262 * 1.9 / 0.19)^2
Simplifying the expression, we get:
n = (11.868)^2
n = 138.7
The minimum sample size required is 138.7. Since we can't have a fractional number of samples, we need to round up to the next integer, which is 139.
Therefore, the minimum sample size required is 139.
Lines A, B, C, D and E intersect as shown. Lines A and B are parallel. Work out the size of angle x.
The value of angle x is 73⁰
What is an angle?You should be aware that a point where two or three straight lines intersect forms an angles.
The parameters that will help us to determine the value of x are
Line B is a straight line. then the sum of angles on a straight line is 180.
⇒110 + b = 180
Making b the subject we have
b = 180 - 110
This means that b = 70°
Also, a = 52° (Opposite angles)
The sum of all interior angles of a triangle is 180.
This means that a + b + c = 180
substitute for a and b to get c
52 + 70 + c = 180
122 + c = 180
Making c the subject of the relation
c = 180 - 122
⇒c = 58°
On the other hand c + d + e = 180
Substitute for c and d to have 58 + 49 + e = 180
107 + e = 180
Making e the subject of the relation we have
e = 180 - 107
e = 73°
But x = e (opposite angles)
There the value of x is 73⁰
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