Which of the following equations correctly represents the law of sines?

Answer:

N=3/5

Step-by-step explanation:

(1/5)/N=1/3

N=(1/5)/(1/3)

N=(1/5)(3/1)

N=3/5

Answer:

  (a)   -3/4

  (b)  -0.75

  (c)  -0.75

Step-by-step explanation:

It's a bit hard to tell what constitutes an "iteration" when using the bisection method to approximate a polynomial root. For the purpose here, we'll say one iteration consists of ...

Thus, the result of the iteration consists of a bracketing interval and the choice of one of the interval's ends as the solution approximation.

__

(a) We observe that the graphs intersect in the interval (-1, 0). For the first iteration, we evaluate f(x)-g(x) at x=-1/2. This tells us the solution is in the interval (-1, -1/2). The x-value closest to the root is x=-1/2.

For the second iteration, we evaluate the function f(x)-g(x) at x=-3/4. This tells us the solution is in the interval (-1, -3/4). The x-value closest to the root is x=-3/4.

For the third iteration, we evaluate the function f(x)-g(x) at x=-7/8. This tells us the solution is in the interval (-7/8, -3/4). The x-value closest to the root is x=-3/4.

__

(b) The graph tells us the solution is approximately 0.7549. Rounded to 2 decimal places, the solution is approximately 0.75.

__

(c) The above solution found after 3 iterations rounded to 2 decimal places is exactly 0.75.

__

See the attached table for function values.

_____

Comment on bisection iteration

Since you cut the interval containing the root in half with each iteration, you gain approximately one decimal place for each 3 iterations. When the function value is very nearly zero at one of the interval endpoints, it can take many more iterations to achieve a better result.

Here, it takes 4 more iterations before an x-value becomes closer to the solution (x≈-97/128). And it takes one more iteration to move the end of the interval away from -3/4. After these 5 more iterations (8 total), the solution is known to lie in the interval (-97/128, -193/256). The corresponding solution approximation is -193/256. It is still only correct to 2 decimal places.

Answer:

285 minutes

Step-by-step explanation:

Well first, how many hours form 7 to 11?

11-7 is 4, thus four hours. Since it is 11:45 and not 11, our answer is 4 hours and 45 minutes. We still need to convert 4 hours to minutes though, to do with we multiply 4 by 60.

4*60=240

Now we add 240 and 45

240+45=285

The answer is 285 minutes.

Answer

20.45pi

Step-by-step explanation:

14/2=7

49pi

49pi/2=20.45pi

Answer:

Odds for = Odds against = 1/2

Step-by-step explanation:

In a fair die, we have {1, 2, 3, 4, 5, 6} and [tex]$ n(S) = 6 $[/tex]

{1, 4, 5} and {2, 3, 6} constitute the entire sample space.

So, Probability of getting a 1 or a 4 or a 5

= Probability of getting a 1 +

Probability of getting a 4 +

Probability of getting a 5

= [tex]$ \frac{1}{6} + \frac{1}{6} + \frac{1}{6} $[/tex]

=[tex]$ \frac{3}{6} = \frac{1}{2} $[/tex]

Therefore, Odds for 1 or 4 or 5 = [tex]$ \frac{1}{2} $[/tex].

Since, Probability of getting a number between 1 and 6 is 1 and Probability of getting a number from 2 or 3 or 6 = [tex]$ \frac{1}{2} $[/tex], we have:

Probability of not getting a 1 or 4 or 5 = 1 - [tex]$ \frac{1}{2} $[/tex]

= [tex]$ \frac{1}{2} $[/tex]

Hence, odds for and odds against = [tex]$ \frac{1}{2} $[/tex]

slope = change in y/change in x = (9-6)/(-5-(-3)) = -3/2

answer: -3/2

Answer:

5.

Step-by-step explanation:

3 * 5 = 15

6 * 5 = 30

7*5 = 35

9*5 = 45

So the constant is 5.

Answer:

[tex]r_Y=\frac{3}{\pi}[/tex]

Step-by-step explanation:

Circumference has the formula:

C = 2πr,

Where

C is the circumference

and

r is the radius

Given Circle Y has Circumference of 6, we can find the radius:

C = 2πr

6 = 2πr

r = 6/2π

r = 3/π

So, the radius (r_y) of Circle Y is 3/π, the first choice is right.

Answer:

22%

Step-by-step explanation:

Given: Profit this year= $245000

           Profit last year= $315000

Now, lets find the percentage decrease in profit this year.

Profit percentage= [tex]\frac{\textrm{difference in profit}}{\textrm{last years profit}} \times 100[/tex]

Profit percentage= [tex]\frac{\$ 315000-\$ 245000}{\$ 315000} \times 100[/tex]

⇒ Profit percentage= [tex]\frac{70000}{315000} \times 100[/tex]

⇒ Profit percentage=~[tex]\frac{7000}{315} =  22.22\%[/tex] ≅ 22% (nearest whole percent)

∴ Percent decrease in profit is 22%

Answer:

22%

Step-by-step explanation:

Answer:

The world's population is 23 times larger than the United States population.

Step-by-step explanation:

United States population = 3x10^8=300,000,000 or 300 million

The World's population = 7x 10^9= 7,000,000,000 or 7 billion

7 billion divided by 300 million = 23.33333333

7000000000 / 300000000 = 23.333333333

Answer:

[tex]\$36.25+\$3.89x\le \$58.50[/tex]

Step-by-step explanation:

Let x be the number of folders with paper Jessica buys. If Jessica buys x folders for $3.89 each, then she pays $3.89x for all x folders.

She wants to buy one backpack for $36.25, so her total buying costs

$36.25 + $3.89x

Jessica saved a total of $58.50 to spend on school supplies, then her total buying cannot exceed this sum, so

[tex]\$36.25+\$3.89x\le \$58.50[/tex]

Answer:

0.97

Step-by-step explanation: i used a calculator to divide and then rounded to the nearest hundredth.

Investing $2500 annually for 10 years into an annuity with a 3.4% APR yields approximately $31,790.56, making option B the correct choice.

A recurring-payment variable annuity typically involves regular contributions over time, often with variable returns based on market performance. Option B seems to fit this description best: "An annuity with an APR of 3.4% into which you invest $2500 each year."

To calculate the future value of this annuity, we can use the formula for the future value of an annuity:

FV = Pmt × [(1 + r)^n - 1] / r

Where:

FV = Future value

Pmt = Payment per period ($2500)

r = Interest rate per period (3.4% or 0.034)

n = Number of periods (number of years)

Let's assume we invest for 10 years:

[tex]FV = 2500 * [(1 + 0.034)^10 - 1] / 0.034[/tex]

Calculating this gives us approximately $31,790.56.

Therefore, investing $2500 each year for 10 years into an annuity with an APR of 3.4% would result in a future value of approximately $31,790.56.

Final answer: B. An annuity with an APR of 3.4% into which you invest $2500 each year.

The Correct question is:

Which of these is an example of a recurring-payment variable annuity?

A. An annuity with a minimum APR of 3.4% into which you invest a lump sum of $12,500

B. An annuity with an APR of 3.4% into which you invest $2500 each year C. An annuity with a minimum APR of 3.4% into which you invest $2500 each year

D. An annuity with an APR of 3.4% into which you invest a lump sum of $12,500

Answer:

16 children

Step-by-step explanation:

80% of 20 children comes out to 16 children who are of age 5.

If desired, rewrite "80%" as "0.80" and use that 0.80 as the multiplier of 20:

0.80(20 children) = 16 children.

Final answer:

By setting up a proportion using the percentage 80% as the decimal 0.80, and cross multiplying with the total number of children in the class (20), we find that the number of children age 5 in the class is 16, corresponding to option E.

Explanation:

To determine the number of children age 5 in a kindergarten class when 80% of the class is that age, and the total number of children is 20, we can set up a proportion. Since 80% of the class is age 5, we can express this as 0.80 (the decimal equivalent of 80%). Therefore:

0.80 (the percentage as a decimal) = Number of children age 5 / Total number of children in the class

0.80 = x / 20

Now, we can solve for x, which represents the number of children age 5, by cross multiplying:

0.80 * 20 = x

16 = x

Therefore, the number of children aged 5 is 16, which corresponds to option E.

Answer: C. $3709

Step-by-step explanation:

Using the formula to calculate amount(A) , which is given as :

A = p  [tex](1+r)^{n}[/tex] , where

A = amount

P = principal

r = rate

n = number of years

From the question,

A = ?

P = $3000

r = 3.6%

n = 6

substituting into the formula , we have

A = 3000[tex](1+0.036)^{6}[/tex]

A = 3000 [tex](1.036)^{6}[/tex]

A = 3000 (1.236398679)

A = 3709. 196038

To the nearest dollar

A = $3709

Answer:

C) $3722.

Step-by-step explanation:

Given: Carmen invested $3000 in an account that pays 3.6% annual interest compound monthly. To the nearest whole dollar, what will be the balance in her account after 6 years?

The formula to compound interest is:

I = P(1 + R)^T

Put in the terms:

I = $3000(1 + 3.6%)^6

I = $3000(1 + 0.036)^6

I = $3000 x 1.036^6

I = $3000 x 1.23639868

I = $3709.19604

Rounded, that's C) $3722.

Answer:

8+6n

Step-by-step explanation:

First, distribute the 2 into the parenthesis.

2(6)+2(3n)-4

Then, multiply the numbers.

12+6n-4

Now add(subtract in this case) the common multiples.

12-4= 8

8+6n

Since you can no longer simplify the equation, this is the answer..

8+6n

Answer:

The students who have a cell phone and can use social media are 3.

Step-by-step explanation:

The question is incomplete so the complete question is:

There are 30 students in Mrs. Bailey’s class, and 1/5 of the class has their own cell phone. Of this group of students, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?

Now, as given in question we need to find the number of students have a cell phone and can use social media.

Now, to get the number of students of the class who has their own cell phone:

[tex]\frac{1}{5}\ of\ 30.[/tex]

[tex]=\frac{1}{5} \times 30.[/tex]

[tex]=\frac{30}{5}[/tex]

[tex]=6.[/tex]

Of this group of 6 students, 1/2 of them are  allowed to use social media.

So, to get the number of students who use social media:

[tex]\frac{1}{2}\ of\ 6.[/tex]

[tex]=\frac{1}{2} \times 6[/tex]

[tex]=\frac{6}{2}[/tex]

[tex]=3.[/tex]

Therefore, the students who have a cell phone and can use social media are 3.

Answer:

286 inches

Step-by-step explanation:

26×11=286

Answer:

The interior angle of 12-gon is [tex]150^{\circ}[/tex]  

The exterior angle of 12-gon is [tex]30^{\circ}[/tex]

Step-by-step explanation:

Given as :

A regular 12-gon is a dodecagonal polygon

i.e The number of sides of the polygon = n = 12

Let The exterior angle of 12-gon = x°

And Let The interior angle of 12-gon = y°

Now,

∵ Exterior angle = [tex]\frac{360^{\circ}}{number of sides}[/tex]

So, exterior angle of 12-gon = [tex]\frac{360^{\circ}}{n}[/tex]

Or, x = [tex]\frac{360^{\circ}}{12}[/tex]

∴ x = [tex]30^{\circ}[/tex]

So,The exterior angle of 12-gon = x = [tex]30^{\circ}[/tex]

Again

∵ Interior angle = [tex]180^{\circ}[/tex] - exterior angle

So, interior angle of 12-gon = [tex]180^{\circ}[/tex] - exterior angle

Or, y =  [tex]180^{\circ}[/tex] -  [tex]30^{\circ}[/tex]

∴ y =  [tex]150^{\circ}[/tex]

So,The interior angle of 12-gon = y = [tex]150^{\circ}[/tex]

Hence, The interior angle of 12-gon is [tex]150^{\circ}[/tex] and The exterior angle of 12-gon is [tex]30^{\circ}[/tex] . Answer

Answer:

2 HOURS

Step-by-step explanation:

The 1st hour of Billys moped shop costs $17. While Julios costs $25. But at the second hour mark it Billy's moped shop charges $34 an hour and Julios also charges $34nfor 2 hours of rental.

Answer:

2

Step-by-step explanation:

Billy's Moped Shop charges $17 per hour for a moped + helmet.  Julio's moped shop charges $9 per hour for a moped + $16 upfront for a helmet.

Let x be hours and p be price,  let's set up an equation for each.

Billy's equation is 17x = p

Julio's equation is 9x + 16 = p

After 1 hour,  Billy's would charge $17 and Julio's would have charged $25.  After 2 hours,  Billy's would charge $34 and Julio's would charge $34.  The answer is 2.

Answer:

5/2=2.5, while 1/3= aprox 0.333, therefore 5/2 is not equal to 1/3.

Step-by-step explanation:

Here is the long division table for 5/2

 2. 5 0 0

2 5. 0 0 0

− 4      

 1 0    

− 1 0    

   0 0  

 −   0  

     0 0

   −   0

       0

Here is the long division table 1/3 ( to three decimal places)

0. 3 3 3

3 1. 0 0 0

− 0      

 1 0    

−   9    

   1 0  

 −   9  

     1 0

   −   9

       1

An easier way to do 5/2 is to think of 50/2, which is 25, and then add a decimal point, making it 2.5.

An easier way to do 1/3 is to think of it as one third (of one), or 0.333 repeating.

Answer:

The distance of the object from the base of cliff is 18.24 meters

Step-by-step explanation:

Given as :

The height of the vertical cliff = h = 50 meters

The distance of the object from the base of cliff = x meters

Let The angle of depression of object that level with cliff base = Ф = 70°

Now, from figure

Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

I.e TanФ = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]

Or, TanФ = [tex]\dfrac{\textrm h}{\textrm x}[/tex]

Or, Tan 70° = [tex]\dfrac{\textrm 50 meters}{\textrm x meters}[/tex]

Or, 2.74 = [tex]\dfrac{\textrm 50}{\textrm x}[/tex]

∴ x =  [tex]\dfrac{\textrm 50}{\textrm 2.74}[/tex]

I,e x = 18.24 meters

So, The distance of the object from the base of cliff = x = 18.24 meters

Hence,The distance of the object from the base of cliff is 18.24 meters Answer

We can determine the distance of the object from the base of the cliff using trigonometry. Specifically, we form an equation using the tangent of the given angle and the known height, solve for the distance, and then substitute the known values to obtain the specific distance.

The subject matter of this question falls in the field of trigonometry as it involves calculating distance using a known height and angle of depression. The object is level with the base of the cliff, and therefore forms a right triangle with the cliff and the sight line from the top of the cliff.

We can use the tangent function to solve this problem. In trigonometry, the tangent of an angle in a right triangle is the opposite side (height) over the adjacent side (distance we're looking for). Given the angle of depression (70°) and the height of the cliff (50 m), we can set up the following equation:

tangent(70°) = height/distance

Moving terms around gives:

distance = height / tangent(70°)

Substituting for height and tangent(70°) we get:

distance = 50 m / tan(70°)

Solving the above equation will give us the distance of the object from the base of the cliff.

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Answer: options C and D

Step-by-step explanation:

An Irrational Number is a real number that cannot be written as a simple fraction.

A . 2/3 is a rational number because it is a fraction

B . -[tex]\sqrt{81}[/tex] = -9 which could be written as -9/1 , so it is a rational number

C. 5.76262... is irrational because the decimal has no end point

D. [tex]\sqrt{2}[/tex] is a common example of irrational number , because finding the square root of 2 is also continuous .

Therefore , options C and D are irrational

Answer:

the answer is 1.3 that 8s the answer

The standard form of the given equation is 10y+4x=9.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y = -0.4x + 0.9.

The standard form for linear equations in two variables is Ax+By=C.

Now, y+0.4x=0.9

Multiply by 10 on both the sides of an equation, we get

10y+4x=9

Therefore, the standard form of the given equation is 10y+4x=9.

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Answer:

The answer is 1.25cm/s

Step-by-step explanation:

I took the 10cm and divided by the 8 seconds the get the proportional relationship.

Answer:

req time=2.5 year

Step-by-step explanation:

simple interest=[tex]\frac{P\times R\times T}{100}[/tex]

where P=principle

          R=rate of interest

          T=time

totel amount= principle+simple interest

simple interest=totel amount-principles

simple interest=$575-$500=$75

ac/ques, 75=[tex]\frac{500\times 6\times T}{100}[/tex]

75=[tex]30\timesT[/tex]

T=2.5 year

Answer:

Easiest—divide by 100: The simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100

Move the decimal: Another way to convert a quoted percentage to decimal format is to move the decimal two places to the left. Remember, if you don’t see a decimal, just imagine that it’s at the end, or far right side, of the number. Imagine that the decimal is followed by two zeroes if that helps.

Step-by-step explanation:

Answer:

Converting Percentages to Decimals

Easiest—divide by 100: The simplest way to convert a percentage to a decimal is to divide the number (in percentage format) by 100.

Move the decimal: Another way to convert a quoted percentage to decimal format is to move the decimal two places to the left.

hope this helps

can you help me with this

The war of wall | Why is the wall special to the narrator and Lou?

Answer:

a=-4, b=-4. (-4, -4).

Step-by-step explanation:

-3a+7b=-16

-9a+5b=16

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

-3(-3a+7b)=-3(-16)

-9a+5b=16

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

9a-21b=48

-9a+5b=16

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

-16b=64

b=64/-16

b=-4

-3a+7(-4)=-16

-3a-28=-16

-3a=-16+28

-3a=12

a=12/-3

a=-4

Answer:

They both are equal to -4.

Step-by-step explanation:

Just took the test and got it right hope this helps. :)

Answer:

[tex]f) 120[/tex]

Step-by-step explanation:

1) La règle de simplification des fractions est très simple. Divisez simplement le numérateur et le dénominateur par le même nombre (non nul).

Exemple:

[tex]\frac{6:3}{3:3}=\frac{1}{2}\\[/tex]

2)  Une solution possible à cette question:

[tex]\frac{120}{240}=\frac{120:2=60}{240:2=120}=\frac{60:3=20}{120:3=40}=\frac{20:4=5}{40:4=10}=\frac{5:5=1}{10:5=2}=\frac{1}{2}[/tex]

120 plus petit commun multiple de 2,3,4,5. C'est le principe pour trouver un nombre multiple des nombres 2,3,4 et 5.

Answer: Just by seeing the graph, we can see that the function is decreasing from

x = 1 , to x = 8

(In this section the function has negative slope, its rate of change is negative)

(From x = -5 to x = -2 the function is increasing)

(From x = -2 to x = 1 the function stays the same)