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Answer:

∠8 = 139°

Step-by-step explanation:

Before we start solving, let's identify the figure to understand the problem.

We are given two parallel lines that are cut by a transversal.

Two lines are parallel if they have the same arrow head marking.

If two parallel lines are cut by a transversal, the following angles are created:

I have attached an image of the different types of angles to this response.

Thus, we can use the types of angles to solve for ∠8.

∠3 and ∠5 are corresponding angles. Therefore, they have the same measure.

Set up the equation to solve for x:

∠3 = ∠5

9x + 14 = 14x - 1 . . . . . . substitute the values

14 = 5x - 1 . . . . . . . . subtract 9x from the LHS and RHS

15 = 5x . . . . . . . . . . add 1  to the LHS and RHS

∴ 3 = x . . . . . . . . . . . . divide the LHS and RHS by 5 to isolate x

Now that we know what x is, we can substitute it into the value of ∠3.

∠3 = 9x + 14

∠3 = 9(3) + 14 . . . . substitute the values

∠3 = 27 + 14 . . . . . compute

∴ ∠3 = 41

∠3 and ∠8 are adjacent angles. Therefore, they add up to 180°.

Set up the equation to solve for ∠8:

∠8 + ∠3 = 180

∠8 + 41 = 180 . . . . substitute the known values

∴ ∠8 = 139° . . . . . subtract 41 from the LHS and RHS to isolate ∠8

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Answer:

Step-by-step explanation:

180-54=139 so 8 equals 139

Answer:

The price of a table is rs1720

Step-by-step explanation:

Let C and T be the individual prices of the tables and chairs.

We know that 3C + 4T = rs7540

We are then told that C = rs220, so we can enter that into the equation to find T:

3C + 4T = rs7540  

3(220) + 4T = rs7540  [for C = rs220]

660 + 4T = 7540

4T = rs6880

T = rs1720

Check:

Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?

Chairs:   rs660

Tables:  rs6880

Total = rs7540  YES

Answer:

13/15

For this question, you could type it into the calculator.

Hence, this question is too trivial, and your question might get deleted as a result. Since this is your first question, I will help you out but subsequently, do use a calculator to solve this kind of questions.

Step-by-step explanation:

4 1/3 can be converted to 13/3 as an improper fraction.

Next, evaluate 13/3 divided by 5

(13/3) / 5 = (13/3) x (1/5)

               = 13/15

Answer:

Step-by-step explanation:

There are a number of ways to do this.  I am going to take a little longer, but I am hoping that it will make sense to you.

4[tex]\frac{1}{3}[/tex] ÷ 5  

Another name for 1 is [tex]\frac{3}{3}[/tex]  I am going to rewrite 4[tex]\frac{1}{3}[/tex] knowing this.

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]

Another way to write 5 is [tex]\frac{5}{1}[/tex].

I want both of my fraction to have the same denominator so I will multiple

[tex]\frac{5}{1}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{15}{3}[/tex]  I am now ready to divide by fractions

[tex]\frac{13}{3}[/tex] ÷ [tex]\frac{15}{3}[/tex]  Divide across

[tex]\frac{\frac{13}{15} }{\frac{3}{3} }[/tex] = [tex]\frac{\frac{13}{15} }{1}[/tex] = [tex]\frac{13}{15}[/tex]

We get the number of bananas as 8 and the number of mangoes as 4.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.

We can write the system of equations as -

x = 2y               .....  (1)

(1/2)x + 2y = 12   ..... (2)

We can write equation (2) as -

(1/2) x 2y + 2y = 12

3y = 12

y = 4

then -

x = 8

Therefore, we get the number of bananas as 8 and the number of mangoes as 4.

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Answer: x= 96 degrees

Step-by-step explanation:

It we figure out the rest of the angles they would be (the outside ans inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444 96 degrees

The measure of an angle x will be equal to 96°.

A Pentagon is a two-dimensional geometric shape that consists of five straight sides and five angles. It is a type of polygon, which is a closed shape with three or more sides.

The Pentagon is often used to represent the shape of buildings, monuments, and symbols in architecture and design.

If we figure out the rest of the angles they would be (the outside and inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444= 96°

Therefore, the measure of an angle x will be equal to 96°.

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Answer:

The bases are congruent

Step-by-step explanation:

From the question, we understand that the top base and the bottom base are directly opposite one another.

When such a scenario arise, it means that the bases have the same shape, they have the same dimension (i.e. size).

With the above analysis, we can conclude that the bases are congruent.

However, the given information can not be used to determine the shape and congruence of the lateral faces.

Lastly, for the bases to be congruent, they must have the same shape (and not any shape).

Hence, only option (b) is correct

Only Erica's equation (y = -0.5x) is proportional

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the Erica equation:

y = -0.5x

The slope is -0.5, hence it is a negative slope and the intercept is at 0, hence it passes through the origin and is proportional

Given the Aliyah equation:

y = 2.5x - 8

The slope is 2.5, hence it is a positive slope and the intercept is at -8, hence it does not pass through the origin and is not proportional

Both equations are linear equations

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Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.

given

DE = DC + CE

44 = 5n – 30 +  6n – 25

44 = 11n - 55

44 + 55 = 11n

n = 9

Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

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Answer:

Step-by-step explanation:

Total surface area:

So

TSA

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).

Here,

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

A statistical data's confidence interval can be expressed as.

=> x+/-zr/√n

=> Knowing that;

Average Sample x = $70.00

$17.50 is the standard deviation.

n = 60 samples were used.

95% confidence interval

95% confidence interval for z = 1.96

substituting our current values;

$70.00+/-1.96($17.50/√60)

$70.00+/-1.96($2.259240285287)

$70.00+/-$4.428110959163

$70.00+/-$4.43

= ( $65.57, $74.43)

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

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Answer:

Its gonna be a 50/50 on the coin and 20/100 chance for the spinner

Answer:

5 outcomes for the spinner and a 50/50 chance for the coin

Step-by-step explanation:

for the spinner, there are five numbers, 1,2,3,4, and 5. so, there is a 1/5 chance or you could also say there is a 20/100 chance.   For the coin, there are two sides and 100 divided by 2 is 50 therefore, there is a 50/50 chance

Hope this helps!!

Step-by-step explanation:

968866j5x4cctyvcyvyvycycc

Step-by-step explanation:

2/3 hours every day for 3 days.

so, for the total hours we need to multiply 2/3 by 3 (3 times 2/3 hours) :

3 × 2/3 = 2 hours

you can get there directly by saying that the factor of 3 and the denominator of 3 are canceling each other out. what is left is 2 in the numerator.

or you can do the full calculation and say

3 × 2/3 = 3×2/3 = 6/3 = 2

999.06ft999.06 in feet is the ladder.

Pythagorean Theorem is a mathematical formula used to calculate the length of the sides of a right triangle. It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, which is known as the hypotenuse. The formula is written as a² + b² = c², where a and b are the two shorter sides, and c is the hypotenuse.

To find the length of the ladder, use the Pythagorean Theorem. The length of the ladder is equal to the square root of the sum of the squares of the side lengths of the right triangle formed by the ladder and the wall.

The two side lengths of the right triangle are 999\,\text{ft}999ft999, start text, f, t, end text and 3\,\text{ft}3ft3, start text, f, t, end text.

Therefore, the length of the ladder is equal to the square root of (999^2+3^2), which is equal to 999.06\,\text{ft}999.06ft999.06,

start text, f, t, end text.

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Answer:January

Step-by-step explanation: if it is asking to explain based on data given, you can show that -11.6<-10.4, but if it is asking based on other information that you recieved, i cant really help other then to tell you to look at the cylces of day and night, because some parts of alaska get no sun for 6 months, so that could be why january is averagly colder

Answer:

d.  15.3%

Step-by-step explanation:

There are a total of 4 + 10 + 7 + 5 = 26 marbles

P(pick a red) = 4/26 = 2/13 = .153 = 15.3%  

Answer:

Vertex is at (4, 2)

Step-by-step explanation:

to find the 'x' value of the vertex, use 'x = -b/2a'

in this problem, a = 1, b = -8, c = 18

x = -(-8)/2(1)

x = 8/2

x = 4

plug 2 in for 'x' in equation and solve for 'y':

y = 4² - 8(4) + 18

y = 16 - 32 + 18

y = -16 + 18

y = 2

Vertex is at (4, 2)

Answer:

D. Each segment of the electorate provides significant support to Mr Quintana

Step-by-step explanation:

From the question, we have the following logic statement;

If those segment that provide significant support to Ms Puerto also provide support to Mr. Quintana then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez

Counter to the If Then Logic structure

At least one segment of the lectorate provides significant support to Mr. Quintana and Mr. Ramirez

Therefore, there is at least one segment that provides support to Mr. Quintana but not to Ms. Puerta

The segments that provide support to Ms. Puerta do not provide support to Mr. Ramirez

Mr. Quintana's support includes those from the supporters of Ms. Puerta and those from the supporters of Mr. Ramirez

Therefore, each segment of the electorate provide significant support to Mr. Quintana.

Answer: 56

Step-by-step explanation:

Given

There are 40 bears  in a national park

After a year, Population increased by 40%

An increase in population is

[tex]=40\times 40\%\\=40\times 0.4\\=16[/tex]

So, a new population is the sum of the original and increased population

[tex]\Rightarrow 40+16\\\Rightarrow 56[/tex]

No. the sum of any two lengths of the triangle is greater than the third length.

Option (A) is correct.

A triangle is a polygon with three edges and three vertices. In Euclidean geometry, a triangle is completely determined by the three points that make up its vertices.

Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances are shown to be 7ft and 2ft.

No the sum of any two lengths of the triangle should be greater than the third side.

but 7 + 2 = 9, so the condition for a triangle is false.

Hence, the correct explanation would be "No. the sum of any two lengths of the triangle is greater than the third length."

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Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances shown be 7ft and 2ft? Identify the answer with the correct explanation. Printer Desk Filing Cabinet

O Yes; the sum of any two lengths is greater than the third length.

O No; the sum of any two lengths is not greater than the third length.

O Yes; the sum of any two lengths is equal to the third length.

O No; the sum of any two lengths is greater than the third length

Answer:

No; The sum of any two lengths is NOT greater than the third length

Step-by-step explanation:

It is given that three objects, a desk, a filing cabinet, and a printer, form a triangle.

Use the Triangle Inequality Theorem to determine whether the given distances can be the lengths of the sides of a triangle.

9+7=16>2

9+2=11>7

7+2=9=9

The sum of one pair of lengths is equal to the third length. Therefore, the distances between the desk, the printer, and the desk and the filing cabinet cannot be 7ft and 2ft since 7+2 equals 9.

The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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The triangle LJK is congruent to the triangle RTS.

What do congruent triangles mean?

Triangles that are congruent share the same matching side lengths and angle measurements. The conditions for triangle congruence are: SSS, SAS (Side, Side, Side) (Side-Angle-Side)

According to the given image of triangles,

We can observe that:

∠L=∠R, ∠T=∠J, ∠S=∠K.

We can also observe that TS=JK, LK=RS, RT=LJ.

Therefore according to SSS congruency ΔLJK ≅ ΔRTS.

According to SAS congruency ΔLJK ≅ ΔRTS.

According to ASA congruency ΔLJK ≅ ΔRTS.

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The y-intercept of the line y = 7x -38 is -38. And the x-intercept is 0

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The equation of the line,

y-4=7(x-6)

Simplify,

y -4 = 7x - 42

y = 7x -38

And slope-intercept form:

y = mx + b,

where m is the slope and y is the intercept.

Comparing with the slope intercept form,

we get,

m = 7 and b = -38

And the x-intercept is 0

Therefore3, y-intercept is -38.

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The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.

The Correct option is (B).

The formula to calculate the margin of error  for the true proportion is;

M = √[p(1 - p)/n]

Given:

n= 40

p = 44/70

Now, The general formula for the margin of error would be:

z x √[p (1-p) ÷ n]

where:

z = values for selected confidence level

p = sample proportion

n = sample size

Since the confidence level is not given,

√[p (1-p) ÷ n]  

=√[44/70 (1 - (44/70) ÷ 70]

=√[0.6286 (0.3714)] ÷ 70

=√0.2335 ÷ 70

= √0.0033357

= 0.05775 or 0.058

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Answer:

sorry

Step-by-step explanation:

Answer:

68 square cm

Step-by-step explanation:

the composite is made up of a triangle , rectangle and parallelogram

area of composite = area of triangle + area of rectangle + area of parallelogram

Area of parallelogram = base x height

9 x 2 = 18

area of triangle = 1/ 2 x base x height

1/2 x 6 x 5 = 15

Area of a rectangle = length x width

5 x 7 = 35

15 + 35 + 18 = 68

Answer:

30%

Step-by-step explanation:

18/60 = 0.30

0.30 = 30%

Answer:

m∠8 = m∠2, option G

Step-by-step explanation:

Angles 8 and 2 are alternate interior angles, which means they are equal. Thus, the answer is option G, m∠8 = m∠2