In triangle ABC, what is the measure of angle C if A = 120°, a = 25, and b = 20? Round the answer to the nearest hundredth.

Answers

Answer 1

The angle C = 103.85° using the sine rule and rounded to the nearest hundredth.

What is the sine rule?

In trigonometry, the sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Considering the ∆ABC, the sine rule states that;

(a/sinA) = (b/sinB) = (c/sinC)

so

25/sin120° = 20/sinB

sinB = (20 × sin120°)/25 {cross multiplication}

sinB = 0.6928

B = sin^(-1)[0.6928)] {sine inverse}

B = 43. 85°

Sum of interior angles in ∆ABC is 180° so;

C = 180° - (120° + 43.85°)

C = 180° - 76.15°

C = 103.85°

With the application of the sine rule, we can conclude that the value of the angle C is 103.85° rounded to the nearest hundredth.

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Related Questions

in a hypothesis test, we choose a 5% level of significance. which p-value is statistically significant at this level?

Answers

The value of p that is statistically significant at a 5% level of significance refers to a p-value of 0.05 or less.

The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the degree of significance, which is decided by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. The null hypothesis is anticipated to be shown as untrue or rejected if the result is statistically significant.

The symbol indicates the degree of significance (alpha). Therefore, the following definition applies to the level of significance:

Level of Significance = p (type I error) =

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Angie is baking blueberry pies to sell at her bakery. She starts with 3 7/10 cartons of blueberries, of which she uses 1/3 for the first batch of pies. How many cartons of blueberries does Angie use for the first batch of pies?

Answers

Answer:

1 carton

Step-by-step explanation:

3 (7/10)= 21/10

1/3 of 21/10= 7/10

7/10=1 carton

A line passes through the points (–4, –1) and (8, 2). What is its equation in slope-intercept form?

I always get it wrong when I write it out

Answers

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{2 +1}{8 +4} \implies \cfrac{ 3 }{ 12 } \implies \cfrac{1 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y +1 = \cfrac{1 }{ 4 } ( x +4) \\\\\\ y+1=\cfrac{1 }{ 4 }x+1\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 4 }x \end{array}}[/tex]

Find g(x), where g(x) is the translation 1 unit left of f(x)=9x–8.

Answers

Where g(x) is the translation 1 unit left of f ( x ) = 9x – 8 then g(x) is

g (x ) = 9x + 1

What is translation?

Translation refers to a type of transformation that involve a straight line movement.

Movements as seen in translation includes

leftrightupdown

The up and down movements are on the vertical direction controlled by the y coordinate.

The left and right movements are on the horizontal direction controlled by the x coordinate.

When translating a graph, adding units moves the graph to the left and removing units moves the graph to the right.

hence we say

f(x) = 9x – 8

g(x) = f(x + 1)

= 9(x+1) – 8

= 9x + 9 - 8

= 9x + 1

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What is the slope and equation of a line that is perpendicular to the y-axis and passes through the point (3,12)


A. The slope is undefined and the equation of the line is y=12.


B. The slope is zero and the equation of the line is x=3.


C. The dlope is zero and the equation of the line is y=12.


D. The slope is undefined and the equation of the line is x=3.

Answers

Slope equals the change in the vertical (Y value) divided by the change in the horizontal (X value), the slope of a horizontal line is zero and equation of line is Y =12. So option C is correct.

What is equation of line?

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This value c is known as the y-axis intercept.

Here,

Since the Y-axis is vertical, a line perpendicular to it would be horizontal..  The slope of a horizontal line is zero, because slope is the change in the vertical (Y value) divided by the change in the horizontal (X value), and the vertical coordinate does not change from the -3 of the point given.

If we start with the slope-intercept form of an equation of a line

Y = mX + b,

we can write Y = 0X + (12)

Y =12

Slope is the vertical change (Y value) divided by the horizontal change (X value); the slope of a horizontal line is zero, and the equation of the line is Y =12.

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the measure of the middle ordinate of a yaw mark is 6 ft. the radius of the arc is 70 ft. what was the length of the chord used in this situation? round the answer to the nearest tenth of a foot.

Answers

The length of the chord used in this situation is approximately 40.54 ft.

To find the length of the chord used in the situation, we can use the formula for the chord length in a circular arc:

Chord length = 2√(r² - (r - h)²)

where r is the radius of the arc and h is the measure of the middle ordinate.

Given that the radius of the arc is 70 ft and the measure of the middle ordinate is 6 ft, we can substitute these values into the formula:

Chord length = 2√(70² - (70 - 6)²)

Chord length = 2√(4900 - 4489)

Chord length = 2√(411)

Chord length ≈ 2 * 20.27

Chord length ≈ 40.54 ft

Therefore, the length of the chord used in this situation is approximately 40.54 ft.

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The radius of a circle is 15 inches. What is
the circumference of the circle? Write
your answer using T.

Answers

Answer: 30[tex]\pi \\[/tex] or 94.247

Step-by-step explanation:

Circumference=2[tex]\pi[/tex]r

2·[tex]\pi[/tex]·15=30[tex]\pi[/tex]=94.247

Answer:

94.2in.

Step-by-step explanation:

The formula for circumference is 2radius x π

π≈3.14

So we can say:

30in.x3.14=circumference

30x3.14=94.2

94.2in=circumference

(i.e. I don't know what you mean by using T.)

       

Simplify each expression. select the correct answer from the dropâ€""down menu. −6(3i)(−2i) = 2(3 − i)(−2 4i) = 2i(4 − 5i) =

Answers

By simplifying each expression:

−6(3i) (−2i) = -36

2(3 − i)(−2 + 4i) = -4+28i

2i(4 − 5i) = 10+8i

Simplifying each expression step by step:

1. −6(3i)(−2i) =  -6 (-6i²)

= 36 (-1)

= -36

2. 2(3 − i)(−2 + 4i)

= 2 x (-6+12i+2i-4i²)

= -12 +24i +4i - 8i²

= -12 - 8i² +28i

=-12 - 8 (-1) + 28i

= -4+28i

3. 2i(4 − 5i)

= 8i - 10i²

= 8i -10(-1)

= 10+8i

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what is the gcf of 70x^3z and 45y^4z^2

Answers

The GCF of the expressions given as 70x³z and 45y⁴z² is 5z

How to determine the GCF of the expressions?

From the question, we have the following expressions

70x^3z and 45y^4z^2

Rewrite the given expression as follows

This is represented using

70x³z and 45y⁴z²

Factor out z from the expression

So, we have the following representation

70x³ and 45y⁴z => Factored z

Factor out 5 from the expression

So, we have the following representation

14x³ and 9y⁴z => Factored 5z

So, we have

Factored = 5z

This represents the GCF

Hence, the GCF is 5z

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PLEASE EXPLAIN……………………..

Answers

The range of the function is y ≥ -2 so , correct option is option c

What is range of a function ?

Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.

Calculation

The graph of the range of the given function is attached below .

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The PlentyofFish dating site company is designing a marketing campaign with the objective of reducing the purchase risk of its dating service in the customer's mind. PlentyofFish is offering a limited free 30-day trial to test out the site. Which stage has the smallest percentage of prospects associated with the AIDA model is PlentyofFish implementing for its campaign ?

Answers

The stage that has the smallest percentage of prospects associated with the AIDA model is PlentyofFish implementing for its campaign is the action stage.

What is the AIDA Model?

The AIDA Model (Attention, Interest, Desire, and Action) is an advertising effect model that identifies the stages that an individual goes through when purchasing a product or service.

The AIDA model is one of several models known as hierarchy of effects models or hierarchical models, all of which imply that when making a purchase decision, consumers go through a series of steps or stages.

An AIDA model entails the following steps:

Attention: The first step in marketing or advertising is to think about how to get consumers' attention.

Interest: Once a consumer is aware that a product or service exists, the company must work to increase the potential customer's level of interest.

Desire: Once the consumer is interested in the product or service, the goal is to make them want it.

Action: The ultimate goal of a marketing campaign is to motivate the recipient to take action and buy the product or service.

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Identify the kind of sequence shown: 2, 7, 14, 23, 34 ... *
O Arithmetic
O Geometric
ONeither

Answers

An Arithmetic sequence is constant so block that out. And geometric is by a fraction. So neither.

Answer:

  (c)  Neither

Step-by-step explanation:

You want to know the kind of sequence that as terms 2, 7, 14, 23, 34, ....

Differences

The first differences of terms of this sequence are ...

  7 -2 = 5

  14 -7 = 7

  23 -14 = 9

  34 -23 = 11

These difference are not constant, so the sequence is not arithmetic.

These differences do not have a common ratio, so the sequence is not geometric.

Second differences

However, these differences do have a common difference:

  7 -5 = 2

  9 -7 = 2

  11 -9 = 2

The fact that second differences are constant means this is a polynomial sequence of second degree. It is a quadratic sequence, neither arithmetic nor geometric.

__

Additional comment

The sequence is described by the quadratic equation ...

  a(n) = n² +2n -1

a basket contains 13 apples, of which two are rotten. a sample of three apples is selected at random. in how many ways can two rotten apples be chosen? a) 165 b) 11 c) 121 d) 220 e) 9 f) none of the above.

Answers

Answer:

None of the above

Step-by-step explanation:

Find the distance between
(4, 8) and (-2, 2).

Answers

Answer:

[tex]6\sqrt{2}[/tex]

Step-by-step explanation:

Using the distance formula,

[tex]\sqrt{(4-(-2))^2+(8-2)^2} \\ \\ =\sqrt{6^2+6^2} \\ \\ =6\sqrt{2}[/tex]

Answer:

6(sqrt(2))

Step-by-step explanation:

Use the "distance formula" (sqrt((x2-x1)^2 - (y2-y1)^2)), plugging in (4,8) for x1 and y1, and (-2,2) for x2 and y 2

Using subsittuftion, which value of x makes this equation true? z+ ²/² = 1 0z=1/1 0 z=² 10 z=2/20 0 Z=!​

Answers

Answer:

Step-by-step explanation:

Some of the other answers are good examples of solving a system of three equations in three unknowns, which is what this problem is asking. Though the simplest way to solve this problem is actually to notice that, if we sum the three equations, we get:

  X + Y = 10

  X + Z = 20

+  Y + Z = 24

----------------

2X + 2Y + 2Z = 54

Factoring out the 2, we have 2(X + Y + Z) = 54, and dividing both sides by 2 reveals that X + Y + Z = 27.

This won't always work when you're solving three equations in three unknowns, but it's a trick that shows up frequently enough on assignments, standardized tests, etc. that it's worth mentioning.

PR is a chord of a circle Center 0 and radius 20CM - POR = 120° calculate (a) length of the Chord PR (b) length of are PQR ​

Answers

Answer:

i have the similar question just radius is changed frm 12 to 20 cm..

hopefully this will help u ...^⁠_⁠^

can someone help me really quick

Answers

Answer:

100 meters every minute

Step-by-step explanation:

d=100(1)

d=100

Hopes this helps please mark brainliest

Linda had 45 fliers to post around town. Last week, she posted 1/3 of them. This week, she posted 3/5 of the remaining fliers. How many fliers has she still not posted?

Answers

Answer:

Step-by-step explanation:

The number of fliers that he has not posted is 9

What is proportion?

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

• Total number of fliers is 45

• First week, 1/3 of the floors were posted

• This week, 3/5 of the remaining were posted.

To determine the number of fliers remaining, we have that;

Remaining fliers for the First week

= 45 × 1/3

Multiply and find the quotient

= 15 fliers

Fliers remaining after the last week

= 15 × 3/5

Multiply and find the quotient

= 45/5

= 9 fliers

Thus, the number of fliers the he has not posted is 9

Show all of your work and use proper mathematical form and language for full marks.
- A pole 3.8m high casts a shadow 1.3m long. A nearby tree casts a shadow 4.5m long
A. How tall is the tree, correct to one decimal place? Justify your answer.

Answers

The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , [tex]\frac{h}{s}[/tex].

=> [tex]\frac{3.8}{1.3} = \frac{h}{4.5}[/tex]

=> h = [tex]\frac{3.8*4.5}{1.3}[/tex]

=> 13.2 m.

Hence the height of the tree is 13.2 m.

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Which equation represents a line which is parallel to the y-axis?
A.x=−4y
B.x=−8
C.y=x−3
D.y=−7

Answers

The equation that represents a line which is parallel to the y - axis would be B. x = −8.

Which lines are parallel to the y - axis?

When a line is parallel to the y - axis, this means that the line does not cross the y - axis in any way and is both vertical and straight because the y - axis is vertical and straight.

Any line that is parallel to the y - axis will need to be expressed in terms of terms of x because the y axis is expressed in terms of x as x = 0. From the options, the only equation expressed in terms of x is x  = -8. This line is therefore parallel to the y - axis.

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Helppppppppppppp Thxs ‼️

Answers

Answer:

False

Step-by-step explanation:

If is a real number and m and n are positive integers

Solve using method of elimination (full working out step by step)
-4x + 3y = 31
4x- y = -21

Answers

Answer:

answer in the picture step by step

what is the sum of twice a number and five is at least half the difference of six and the same number

Answers

x= 4  is a number and five is at least half the difference of six and the same number.

What is unitary method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

We must first create an equation before solving it.Finding out what the question is asking us will help us get started on this.Let's say our number is x, the value of which we do not yet know. Therefore, two times that amount would be two times, or two.That would be divided by half, or 1/2x. We must now determine what the product of 2x and 1/2x signifies.Since addition is the definition of sum, 2 + 0.5 Equals 2.5. This amount is equivalent to 10, according to the remainder of the question. That implies:
2.5x = 10Our response is: when we divide each side by 2.5.
x = 4

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ethical research methods include multiple choice selecting samples that you know to be biased. always using a census as samples as not reliable. using only convenience sampling to select samples. doing your best to select an unbiased sample.

Answers

Ethical research methods include D. doing your best to select an unbiased sample.

What is research ethics?

In research, ethical considerations are a set of principles that guide your research designs and practices. Active consent, informed consent, anonymity, confidentiality, potential for harm, and results communication are among these principles.

The standards of conduct for scientific researchers are governed by research ethics. To protect the dignity, rights, and welfare of research participants, it is critical to follow ethical principles. Many ethical norms in research, for example, guidelines for authorship, copyright and patenting policies, data sharing policies, and peer review confidentiality rules are intended to protect intellectual property interests while encouraging collaboration.

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help asap please. . . . . ​

Answers

Correct Answer:
The height of the ballon increases 30.5 feet per minute. The ballon starts at the height of 8.7 feet.

In triangle ABC, m∠B = (4x − 15)° and the measure of the exterior angle to ∠B is (14x − 21)°. Find m∠B.

12°
32°
33°
36°

Answers

Applying the definition of exterior angle, the measure of angle B is: c. 33°

What is the Exterior Angle of a Triangle?

When a side of a triangle is extended through an interior angle, the angle formed is called the exterior angle of a triangle.

The angle to the exterior angle of the triangle, when added to the exterior angle will have a sum of 180 degrees, which means their supplementary angles.

Therefore:

4x - 15 + 14x - 21 = 180

4x + 14x - 15 - 21 = 180

18x - 36 = 180

18x = 180 + 36

18x = 216

18x/18 = 216/18

x = 12

m∠B = 4x - 15 = 4(12) - 15 = 33°

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Answer:

its B. 33

Step-by-step explanation:

a bag contains 14 blue, 6 red, 12 green, and 8 purple marbles. 25 marbles are removed from the bag randomly. how many of the removed marbles were green if the chance of drawing a green marble from the bag is now 3/5?

Answers

The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

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y= 3cos 4 0(theta) -1

Answers

The graph of the cosine function y = 3cos(4θ) - 1 is given by the image presented at the end of the answer.

What is a cosine function?

The cosine function is defined by the rule presented as follows:

g(x) = acos(bx+c)+d.

The coefficients have the roles listed as follows:

a is the amplitude of the cosine function.b: The period of the cosine function is of 2π/b.c is the phase shift of the cosine function.d is the vertical shift of the cosine function.

In this problem, the definition of the function is:

y = 3cos(4θ) - 1

Considering the amplitude of 3 and the vertical shift of -1 the function will oscillate between:

-4 and 2.

(Without the vertical shift it would be between -3 and 3).

The period of the function will be as follows:

2π/b = 4

b = 2π/4

b = π/2.

Considering these features, the graph is given at the end of the answer.

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I need what x equals

Answers

Answer: x=143

Step-by-step explanation: the ratio is 1:13 so 11*13=143

Answer: Don't take my word wait until someone else says something.

Step-by-step explanation: i think it is 134 or around that.

Find the discriminant of the following quadratic equation and indicate the nature of the solutions. Then find the solutions to the quadratic equation. Make sure solutions are simplified! 8x² + 15x = 7x - 4 ​

Answers

Answer:

-64

Step-by-step explanation:

Start by moving everything to the left side making the equation equal 0. Then combine like terms.

Other Questions
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