How do you use the sine rule to work out an obtuse angle?

The Length of FD = 26 cm

According to the given information

FE = FC = 12cm

As FE, FC both are radius of circle

The tangent segments to a circle from a external point are equal

Hence

CD = ED

13x - 16 = 4x + 11

13x - 4x = 11 + 16

9x = 27

x = 27/9

x = 3

CD = 13x - 16

     = 13 × 3 - 16

     = 23 cm

ED = 4x + 11

     = 4 × 3 + 11

     = 23 cm

In Triangle FED

FE is perpendicular to ED

According to Pythagoras Theorem

[tex]FD^{2}= FE^{2}+ED^{2}[/tex]

       = [tex]12^{2}+ 23^{2}[/tex]

       = 673

FD = 26 cm approx.

The Length of FD = 26 cm

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Answer:

Step-by-step explanation:

he bought 7.6 ft2 of sheet metal He used 2.3 ft2 7.6x−2.3x= $95.40 simplify 5.3x = $95.40 divide by 5.3 to get x by itself x = 18 so each sheet of metal costs $18.00 per square foot.

For making apple juice for 8 people she needs 2.67 cans of frozen concentration

What is Proportion?

A proportion is a component, share, or quantity compared to the total. A proportion is a comparison of two integers, each representing a piece of a larger whole.

Solution:

Since, Julia needs 1 can of frozen concentration for making apple juice for 3 people

We can say for 6 people she needs 2 cans

Similarly for 8 people she needs 8/3 cans = 2.67 cans

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The number of different choices for nine questions is 384, when at most one of questions 1 and 2 may be included among the nine.

Given, the exam instructions specify that at most one of questions 1 and 2 may be included among the nine.

We have to find the number of different choices for nine questions.

Now, using the concept of Permutation and Combinations we get

There will be three cases,

Case 1 : we include question 1

Case 2 : we include question 2

Case 3 : we neither include question 1 nor question 2

Case 1 :

question 1 is included, so question 2 can not be included and remaining 7 questions have 2 choices.

Case 2 :  

question 2 is included, so question 1 can not be included and remaining 7 questions have 2 choices.

Case 3 :

neither question 1 nor question 2 is included and also remaining 7 questions have 2 choices.

Total choices = 2^7 + 2^7 + 2^7

So, the number of different choices of nine questions are 384.

Hence, the number of different choices of nine questions are 384, when at most one of questions 1 and 2 may be included among the nine.

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Correct option is C and the angle D and F are complementary angles.

∠D+∠E+∠F=180⁰

 ....Angle sum property

∵∠E=90⁰

⇒∠D+∠F=180⁰

−90 ⁰

⇒∠D+∠F=90⁰

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The radius of the cylinder is found to be 6 cm.

A right circular cylinder is a three dimensional figure having its base and top as a circle and the height is perpendicular to circular base. The volume is given as V = πr²h.

Given that,

The height of the cylinder is 17 cm.

And, the volume is 1921.68 cm³.

Suppose the radius be r cm.

Substitute the corresponding values in the expression of volume V = πr²h as follows,

V = πr²h

=> 1921.68 = π × r² × 17

=> π × r² = 1921.68/17

=> r² =  1921.68/17π    

=> r = 6

Hence, the radius of the cylinder is obtained as 6 cm.

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The solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

The relationship between two values that are not equal is described by inequalities. Equal does not necessarily mean unequal. The "not equal symbol" is typically used to denote that two values are not equal.

Given:

1 / 2x < 6

x < 6 × 2

x < 12

Therefore, the solved inequality for 1/2x < 6 is x < 12, and the graph is attached below.

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Answer:

Step-by-step explanation:

When you rotate 270 degrees counterclockwise, (a,b) turns to (b,-a)

So,

A'(-2,-6)

B'(-6,-8)

C'(-8,-4)

:]

Based on this equation, estimate the price of a car that had been driven 56 thousand kilometers.

Step-by-step explanation:

Answer:

Step-by-step explanation:

An octagon is a 2-dimensional shape with 8 sides and the area is the space within the 8 sides of the shape. To calculate the area of the octagon we can use the area of an isosceles triangle. We divide the area of the shape into eight equal isosceles triangles and calculate it accordingly. A regular octagon has the length of the sides equal and the angles between these sides are equal. The measure of each interior angle is 135° and the exterior angles measure 45° each.

Area of Octagon Formula

The formula used to calculate the area of an octagon is:

2s2(1+√2), where s is the length of the side of the octagon.

Answer:

After 8 years working for the company, Amira would make a salary of $59000 + 8 * $3500 = $70500.

After t years working for the company, Amira would make a salary of $59000 + t * $3500.

Step-by-step explanation:

Answer:x=8.47

Step-by-step explanation:

The given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

Given:

AC and BD are diagonals of quadrilateral ABCD.

From diagram we can see that the measure of AO and OC is same which is 4.

Also measure of BO and OD is same which is 6.

That is diagonals bisects each other.

Hence, the given quadrilateral ABCD is a parallelogram because the diagonals bisect each other.

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Answer: 1.11 kg

Step-by-step explanation:

1 kg = 1000 grams

Nickle has a mass of 5 grams = 0.005 kg

Penny has a mass of 2.5 grams = 0.0025 kg

Now take 0.005 times 186 = 0.93 kg for 186 nickles

Next, take 0.0025 times 72 = 0.18 kg for 72 pennies

0.93 kg + 0.18 kg = 1.11 kg

So the bag is 1.11 kg

Modus is a statistical measure that is used to identify the most frequently occurring number in a set of numbers.

To calculate modus, first arrange the numbers in numerical order. Then count the number of times each number occurs in the set. The number that occurs most often is the modus. To calculate modus, first list all the numbers in the set in numerical order. The number that appears most frequently is the modus. For example, if the set of numbers is [1, 2, 3, 3, 3, 4], the modus is 3 because it appears three times, which is more than any other number in the set.

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Yes. The decision of watching a movie on television is a technique of sampling.

Given,

If you decide whether or not you want to see a new movie or television program on the basis of the "coming attractions" or television commercial previews.

We have to find that whether it is using a sampling technique here;

Here,

Yes, this is a sampling technique. This kind of sampling, meanwhile, is typically not of a scientific nature. Instead of being representative of those movies, the parts that are shown are typically the most entertaining. Although a subset of all potential television shows or movie scenes have been observed, they are not chosen at random to make up the sample.

That is,

Yes. The choice to watch a movie on television is a sampling technique.

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The length of the hypotenuse of the triangle is 4.1.

Here we have to find the length of the hypotenuse of the triangle.

Data given:

A right triangle has one side that measures 4 in and the angle opposite that side measures 80°

To determine the length of the hypotenuse of the triangle, the trigonometry function can be used.

sinФ = perpendicular/ hypotenuse

sin80° = 4/ hypotenuse

0.98 = 4/ hypotenuse

hypotenuse = 4/ 0.98

Hypotenuse = 4.0617 inch.

Therefore the length of the hypotenuse of the triangle to the nearest tenth is 4.1

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By using probability, it can be calculated that

Probability that when two balls are selected at random with no replacement , both are green = 0.357

What is probability?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Number of green balls = 5

Number of red balls = 3

Total number of balls = 5 + 3 = 8

Probability that when two balls are selected at random with no replacement , both are green = [tex]\frac{5}{8} \times \frac{4}{7} = \frac{5}{14} = 0.357[/tex]

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The verbal description of the algebraic expression 3m-8n/13 is;  Three m minus eight n divided by thirteen

Algebraic word problems are defined as questions that need translation of sentences to equations and thereafter solving those equations usually having a single variable. Now, the single variable usually denotes an unknown quantity in a real-life scenario.

To solve an algebraic word problem, the following steps are taken;:

Now, we want to write the verbal description of the algebraic expression given as 3m-8n/13.

This is expressed as Three m minus eight n divided by thirteen

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Complete question is;

Write a verbal expression for 3m-8n/13

Answer:

1. (2x-3)(x^2+3)(x+4)

2. (3x-1)(x+5)(4x^2+1)

Step-by-step explanation:

2x^4+5x^3-6x^2+15x-36

2x^4-3x^3+8x^3-12x^2+6x^2-6x+24-36

x^3(2x-3)+4x^2(2x-3)+3x(2x-3)+12(2x-3)

(2x-3)(x^3+4x^2+3x+12)

(2x-3)[x^2(x+4)+3(x+4)]

(2x-3)(x^2+3)(x+4)

12x^4+56x^3-17x^2+14-5

12x^4-4x^3+60x^3-20x^2+3x^2-x+15x-5

4x^3(3x-1)+20x^2(3x-1)+x(3x-1)+5(3x-1)

(3x-1)(4x^2+20x^2+x+5)

(3x-1)[4x^2(x+5)+x+5]

(3x-1)(x+5)(4x^2+1)

Considering the  car production in Geometric progression (a) about 25th term is 7.00*10¹⁹ cars can be produced in the first 25th week. (b) in the first 6 months, there will be 7.1*10¹⁸ cars. ( c) production in the next 6 months would be 7.1*10¹⁸ cars too

Geometric progression is the type of sequnce in which consecutive terms are gotten by the multiplication of a constant term known as the constant ratio.

the given parameyers are

a=150 cars

r=1.75%

r=1.75/100*150

r= 6.6

Nth term of GP is given as

Nth = [tex]ar^{n-1}[/tex]

a.  The 25th term is given as

25th= [tex]150*6.6^{24}[/tex]

25th term is 7.00*10¹⁹

b.  In a month, there are 4 weeks

in 6 months there are 4*6 = 24 weeks

524th term is 150*6.6²³

7.1*10¹⁸

c.  In a month, there are 4 weeks

in 6 months there are 4*6 = 24 weeks

524th term is 150*6.6²³

7.1*10¹⁸

In conclusion there will be  7.00*10¹⁹ cars , 7.1*10¹⁸  cars and 7.1*10¹⁸ cars for options a, b, and c respectively

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She will serve 640 hors d'oeuvres to 240 people.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Total number of people = 240

Number of hors d'oeuvres per 3 people = 8

Number of hors d'oeuvres to serve 240 people.

= 8 x 240 ÷ 3

= 8 x 240/3

= 8 x 80

= 640

Thus,

The number of hors d'oeuvres to serve is 640

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Perpendicular lines have slopes that are negative reciprocal of each other.

Parallel line have same slope.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

When two lines are perpendicular their slopes are negative reciprocal of each other and they also intersect at a point.

When two lines are parallel they have the same slope and they do not intersect.

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Answer:

112b^2

Step-by-step explanation:

When you multiply two negative numbers, the outcome will always become positive.

7bx16b= 112b^2

Answer:

112b^2

Step-by-step explanation:

Answer:

3 years

Step-by-step explanation:

1600*[tex]1.05^{x}[/tex]=1852.20

1852.20/1600= [tex]1.05^{x}[/tex]

1.157625    = [tex]1.05^{x}[/tex]

[tex]log_{1.05} 1.157625= x[/tex]

x= 3

thus 3 years

Answer:

51/4 - 9f

Step-by-step explanation:

Answer:

  12 3/4 -9f

Step-by-step explanation:

You want the simplified form of the expression 12-3/4(8f-5/3+4f+2/3).

We can simplify inside parentheses first. This consists of combining like terms.

  = 12 -3/4((8+4)f +(-5/3+2/3)) = 12 -3/4(12f -1)

Then the distributive property is applied, and like terms are combined (again).

  = 12 -9f +3/4

  = 12 3/4 -9f

Answer:

c(x) = 5.50 + 21.60x

Step-by-step explanation:

To start, we are told that the service fee of 5.50 is added to the set price per ticket. So we can automatically eliminate B and D

Now, to find how much it costs per ticket, we have to divide 108.00 by 5 since we are told that it costs $108 to buy 5 tickets

108.00/5 = 21.60

This means that it costs $21.60 per baseball ticket

So the third answer choice is correct

The required value of this game in the long run has no value, as game will discarded because both players identical pairs.

A standard 52-card deck contains 13 positions in every one of the four French suits: clubs (♣), precious stones (♦), hearts (♥) and spades (♠). Each suit incorporates three court cards (face cards), Lord, Sovereign and Jack, with reversible (twofold headed) pictures. Each suit additionally incorporates ten numeral cards or pip cards, from one to ten.

After the blended matches are disposed of, there are an equivalent number of dark red still in the deck, so the two players will have similar number of pairs.

So, No one will win the game.

Thus, the game will  discarded.

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The statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups is independent-sample t test.

Given that,

We have to find the statistical test that compares the distribution of mean differences between two groups to the mean difference between two groups.

We know that,

The independent Samples t take a look at analyzes the manner of two separate organizations to see if there's statistical guide that the populace imply values are statistically extensively distinctive. A parametric take a look at is the unbiased Samples t take a look at.

since, the two agencies are independent and we're checking if difference is good sized is independent-samples t test.

consequently, the statistical test that compares the distribution of imply differences between two companies to the imply difference among  corporations is unbiased-pattern t check.

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