Melissa wants to purchase a digital camera.The listed price of the camera is $195.99.The camera is no sale for 10% off and Melissa has a coupon for 5% off the sales tax is 7%. How much money will the 10% off sale save Melissa

Answer:

The imaginary part is 0

Step-by-step explanation:

The number given is:

[tex]x=(\cos(12)+i\sin(12)+ \cos(48)+ i\sin(48))^6[/tex]

First, we can expand this power using the binomial theorem:

[tex](a+b)^k=\sum_{j=0}^{k}\binom{k}{j}a^{k-j}b^{j}[/tex]

After that, we can apply De Moivre's theorem to expand each summand:[tex](\cos(a)+i\sin(a))^k=\cos(ka)+i\sin(ka)[/tex]

The final step is to find the common factor of i in the last expansion. Now:

[tex]x^6=((\cos(12)+i\sin(12))+(\cos(48)+ i\sin(48)))^6[/tex]

[tex]=\binom{6}{0}(\cos(12)+i\sin(12))^6(\cos(48)+ i\sin(48))^0+\binom{6}{1}(\cos(12)+i\sin(12))^5(\cos(48)+ i\sin(48))^1+\binom{6}{2}(\cos(12)+i\sin(12))^4(\cos(48)+ i\sin(48))^2+\binom{6}{3}(\cos(12)+i\sin(12))^3(\cos(48)+ i\sin(48))^3+\binom{6}{4}(\cos(12)+i\sin(12))^2(\cos(48)+ i\sin(48))^4+\binom{6}{5}(\cos(12)+i\sin(12))^1(\cos(48)+ i\sin(48))^5+\binom{6}{6}(\cos(12)+i\sin(12))^0(\cos(48)+ i\sin(48))^6[/tex]

[tex]=(\cos(72)+i\sin(72))+6(\cos(60)+i\sin(60))(\cos(48)+ i\sin(48))+15(\cos(48)+i\sin(48))(\cos(96)+ i\sin(96))+20(\cos(36)+i\sin(36))(\cos(144)+ i\sin(144))+15(\cos(24)+i\sin(24))(\cos(192)+ i\sin(192))+6(\cos(12)+i\sin(12))(\cos(240)+ i\sin(240))+(\cos(288)+ i\sin(288))[/tex]

The last part is to multiply these factors and extract the imaginary part. This computation gives:

[tex]Re x^6=\cos 72+6cos 60\cos 48-6\sin 60\sin 48+15\cos 96\cos 48-15\sin 96\sin 48+20\cos 36\cos 144-20\sin 36\sin 144+15\cos 24\cos 192-15\sin 24\sin 192+6\cos 12\cos 240-6\sin 12\sin 240+\cos 288[/tex]

[tex]Im x^6=\sin 72+6cos 60\sin 48+6\sin 60\cos 48+15\cos 96\sin 48+15\sin 96\cos 48+20\cos 36\sin 144+20\sin 36\cos 144+15\cos 24\sin 192+15\sin 24\cos 192+6\cos 12\sin 240+6\sin 12\cos 240+\sin 288[/tex]

(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)

A calculator simplifies the imaginary part Im(x⁶) to 0

Answer:

4.4 ft/s

Step-by-step explanation:

Height = 15ft

Rate= 5 ft/s

Distance from the man to the kite= 32ft

dh/dt = 5 ft/s

h = √32^2 - 15^2

h = √ 1025 - 225

h = √800

h = 28.28ft

D = √15^2 + h^2

dD/dt = 1/2(15^2 + h^2)^-1/2 (2h) dh/dt

= h(225 + h^2)^-1/2 dh/dt

= (h / √225 + h^2)5

= (28.28 / √225 + 28.28^2)5

= (28.28 / √1024.7584)5

= (28.28/32)5

= 0.88*5

= 4.4 ft/s

Working together, Maggie and Tom can paint the fence in 5.1 hours

Given that,

Maggie can paint a fence in 9 hours

So in 1 hour maggie paints, [tex]\frac{1}{9}[/tex] of the house

Tom needs 12 hours to paint the same fence

So in 1 hour, tom can paint [tex]\frac{1}{12}[/tex] of the house

To find: time taken to paint the fence if they work together

Let "a" be the time taken to paint the fence if they work together

So working together, in 1 hour, they can paint [tex]\frac{1}{a}[/tex] of the house

We can frame a equation as:

To see how much of the fence they can paint together in one hour, we add these together.

[tex]\frac{1}{9} + \frac{1}{12} = \frac{1}{a}[/tex]

[tex]\frac{1}{a}[/tex] is how much of the fence they can paint together in one hour.  Therefore "a" is the number of hours it will take them both to paint the fence

On solving,

[tex]\frac{12 + 9}{12 \times 9} = \frac{1}{a}\\\\\frac{1}{a} = \frac{21}{108}\\\\a = \frac{108}{21} = 5.1428[/tex]

So working together, Maggie and Tom can paint the fence in 5.1 hours

Answer:

16 green cubes are in the box.

Step-by-step explanation:

No. of red cubes at first (x):

4(x + 12) = 5(2x)

4x + 48 = 10x

6x = 48

x = 8

No. of green cubes:

= 8 * 2

= 16

Answer: 16 green cubes are in the box.

20 red cubes are in the box in the end.

Proof (the ratio in the end is 4:5):

= 16 is to 20

= 16/4 is to 20/4

= 4 is to 5

Answer:

It appears to fly faster than its actual speed.

Step-by-step explanation:

In general, if talking about velocities, the direction of the movement should also be taken into account. For example, if two objects move in opposite directions, a person inside one object observes that the other one moving in the opposite goes faster than its actual speed (because the velocities are summed up). If they are moving in the same direction the opposite phenomenon is true (the velocities are subtracted).

Finally, in this example the planes move in opposite direction, therefore, a plane flying in the opposite direction will appear to fly  faster.

Answer:

whole numbers

Step-by-step explanation:

The domain is the number of people. The smallest number of people you could have would be 0 people so the appropriate domain is whole numbers.

Make me the brainliest

Answer:

whole numbers

Step-by-step explanation:

Answer:

Not possible

Step-by-step explanation:

The only information we are given are the pairs of angles that are congruent which is not enough information to prove that they are congruent

The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The two triangles are congruent if two sides are as well and the angle (angle between any of these two sides) among one triangle is congruent to the comparable two sides as well as the angle of a second triangle.

The triangles cannot be proved congruent by AAA postulates. Then the correct option is D which is not possible.

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Answer:

Step-by-step explanation:

C'(x)=-40+0.08 x

C'(x)=0 gives

-40+0.08 x=0

x=40/0.08=500

C"(x)=0.08>0 at x=500

so C(x) is  minimum if x=500

so 500 cars need to be produced for minimum cost.

or we can solve by completing the squares.

c(x)=12000+0.04(x²-1000 x+250000-250000)

=12000+0.04(x-500)²-0.04×250000

=0.04 (x-500)²+12000-10000

=0.04(x-500)²+2000

c(x) is minimum if x=500

To minimize the cost based on the provided quadratic cost function, 500 cars should be produced.

This a problem of optimization in the arena of Calculus. The cost function C(x) = 12000-40x+0.04x2 is a quadratic function, and the minimum cost occurs at the vertex of the parabola described by this function.  

For any quadratic function f(x)=ax2 +bx + c, minimum or maximum value occurs at x = -b/2a.

In this case, a = 0.04 and b = -40.

So minimum cost occurs when x = -(-40) / 2*0.04 = 500.

So, to incur minimum cost, 500 cars should be produced.

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The equivalent annual cost of the machine, considering a 10% return, is approximately $309,535 per year.

First, accumulate the total cost over the lifespan of the machine which is $750,000 (initial cost) + ($12,000 * 3 years) = $786,000. The equivalent annual cost can be calculated using the formula for the present value of an annuity: PV = PMT [(1 - (1 + r)^-n ) / r], where 'PMT' is the payment per period, 'r' is the rate of return, and 'n' is the number of periods. Rearrange to calculate PMT: PMT = PV * r / (1 - (1 + r)^-n). Substituting in given values gives us, PMT = $786,000 * 0.1 / [1 - (1 + 0.1)^-3] = $309,535/year.

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Answer and explanation :

When we square any number then its gives absolute value for example even when we square the negative numbers it will given positive , that is absolute value

So we can conclude that square of any number is absolute number

And then is we take square root of that absolute number it will always positive and absolute

I don't know.. can you please explain it?

Each person will pay 19.5 dollars.

Step-by-step explanation:

Given

Total bill for dinner = b=$30

First of all we will calculate the 30% of dinner bill to find the amount of tip

So,

[tex]Tip = t = 30\%\ of\ 30\\= 0.30*30\\=9[/tex]

the tip is $9

The total bill including tip will be:

[tex]= 30+9 = \$39[/tex]

Two persons have to divide the tip and dinner equally so,

Each person's share = [tex]\frac{39}{2} = 19.5[/tex]

Hence,

Each person will pay 19.5 dollars.

Keywords: Fractions, division

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Answer:

Step-by-step explanation:

I believe the answer is x² + y² = 9²

Answer: Compound interest is $36.61

Step-by-step explanation:

Initial amount deposited into the account is $500 This means that the principal,

P = 500

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 3.5%. So

r = 3.5/100 = 0.035

It was compounded for 2 years. So

t = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 500 (1+0.035/1)^1×2

A = 500(1.035)^2 = $535.61

Compound interest = 535.6 - 500 = $35.61

Answer:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

Step-by-step explanation:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

We have to find the roots of this given equation.

If a quadratic equation is of the form [tex]ax^{2}+bx +c=0[/tex]

Its roots are [tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

Here the given equation is [tex]2x^{2}-4x-1[/tex] = 0

a = 2

b = -4

c = -1

If the roots are [tex]x_{1} and x_{2}[/tex], then

[tex]x_{1}[/tex] = [tex]\frac{-2+\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}[/tex]

                       = [tex]\frac{4 +\sqrt{24}}{4}[/tex]

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

[tex]x_{2}[/tex] = [tex]\frac{-2-\sqrt{(-4)^{2}-4\times 2\times (-1)}}{2\times 2}[/tex]

                        = [tex]\frac{4 +\sqrt{8}}{4}[/tex]

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

These are the two roots of the equation.

Answer:

P(not yellow or green)=\frac{2}{7}[/tex]

Step-by-step explanation:

a set of cards includes 15 yellow cards, 10 green cards and 10 blue cards

Total cards= 15 yellow + 10 green + 10 blue = 35 cards

Probability of an event = number of outcomes divide by total outcomes

number of outcomes that are not yellow or green are 10 blue cards

So number of outcomes = 10

P(not yellow or green)= [tex]\frac{10}{35} =\frac{2}{7}[/tex]

The probability of choosing a card that is neither yellow nor green from the set is 2/7, as there are 10 blue cards and a total of 35 cards.

The question asks for the probability of choosing a card that is neither yellow nor green from a set containing 15 yellow cards, 10 green cards, and 10 blue cards. To find this probability, we must consider only the blue cards, as they are not yellow or green. The total number of blue cards is 10, and the total number of cards is 35 (since 15 + 10 + 10 = 35).

To calculate the probability, we use the formula:

P(Blue card) = Number of blue cards / Total number of cards = 10 / 35 = 2/7

Thus, the probability of randomly choosing a card that is not yellow or green (i.e., a blue card) is 2/7.

Answer:

[tex]12,600\ ft[/tex]

Step-by-step explanation:

step 1

Find out the number of revolutions in one hour

we know that

The bicycle wheels are making 30 revolutions per minute

One hour are 60 minutes

so

using proportion

[tex]\frac{30}{1}\ \frac{rev}{min}=\frac{x}{60}\ \frac{rev}{min}\\\\x=60(30)\\\\x=1,800\ rev[/tex]

step 2

Find out how many feet the bicycle will travel in one hour

we know that

A bicycle moves approximately 7 feet with each revolution and the number of revolutions in one hour is 1,800

so

Multiply the number of revolutions in one hour (1,800 rev) by 7 feet

[tex](1,800)7=12,600\ ft[/tex]

Answer:

Step-by-step explanation:

They are not similar.  If they were, ∠LMF and ∠GHF would both have the same angle measure and they do not.

Final answer:

Mathematics question on similar triangles; triangles are similar if they have congruent corresponding angles and proportional sides obtained through AA, SSS, or SAS criterion. A similarity statement describes the correspondence of the vertices.

Explanation:

The question provided falls within the subject of Mathematics, specifically within the study of geometry and the concept of similar triangles. To determine if two triangles are similar, we must check if they have the same shape, which implies that their corresponding angles are equal and their corresponding sides are in proportion. In other words, two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional. This can be verified by angle-angle similarity (AA), side-side-side similarity (SSS), or side-angle-side similarity (SAS). The similarity statement provides the order of correspondence of vertices between similar triangles.

When evaluating if triangles BAO and B1A1O are similar, we must compare their corresponding angles and sides. If the given information indicates that at least two angles of one triangle are congruent to two angles of another triangle (AA criterion), or that the sides are proportional (SSS or SAS criterion), then the triangles are similar. For instance, if ∠BAO ≅ ∠B1A1O and ∠BOA ≅ ∠B1O1A1, then by the AA criterion, the triangles are similar, and we could write the similarity statement as triangle BAO ∼ triangle B1A1O.

Answer:

Step-by-step explanation:

You can identify terms and count them before you start factoring. Doing so will identify 3x² as a term in the numerator, and will show you there are 3 terms in the denominator.

When you factor the expression, you get ...

  [tex]\dfrac{3x^2-3}{3x^2+2x-1}=\dfrac{3(x^2-1)}{(3x-1)(x+1)}=\dfrac{3(x-1)(x+1)}{(3x-1)(x+1)}[/tex]

This reveals a common factor of x+1.

So, the above three observations are true of this rational expression.

Final answer:

To find the value of alpha given that alpha and beta are conjugate complex numbers, and alpha/beta^2 is real, we can use the equation |alpha - beta| = 2√3. We can substitute alpha = a + bi and beta = a - bi, and solve for a and b to find the value of alpha.

Explanation:

Let α and β be conjugate complex numbers such that α/β² is a real number and |α - β| = 2√3. We need to find the value of α.

Since α and β are conjugate complex numbers, they have the form α = a + bi and β = a - bi, where a and b are real numbers. Substituting these values into the given equation, we get:

|α - β| = |(a + bi) - (a - bi)| = |2bi| = 2|b| = 2√3

From this, we can conclude that |b| = √3. Since |b| is the absolute value of b, it is always positive. Therefore, we have two options: b = √3 or b = -√3.

If b = √3, then α = a + √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a + √3i)/(a - √3i)² = (a + √3i)/(a² - 2a√3i - 3) = [(a(a² - 3) + √3i(3a - a²)] / (a² - 2a√3i - 3)

This expression is not a real number, so b ≠ √3.

If b = -√3, then α = a - √3i. We can substitute this into the equation α/β² to check whether it is a real number.

α/β² = (a - √3i)/(a + √3i)² = (a - √3i)/(a² + 2a√3i + 3) = [(a(a² + 3) - √3i(3a + a²)] / (a² + 2a√3i + 3)

This expression simplifies to (a(a² + 3) - √3(3a + a²))/ (a² + 3) = a - √3(2a + 1)/ (a² + 3)

For this expression to be a real number, the imaginary term √3(2a + 1) must be equal to 0. So, we have √3(2a + 1) = 0.

Solving this equation, we get 2a + 1 = 0, which implies a = -0.5.

Therefore, the value of α is α = -0.5 - √3i.

Answer: 120 pages

Step-by-step explanation:

42 p on Monday

2/5x on Tuesday

1/4x rest of book

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

42+2/5x+1/4x=x

42*20 +8x+5x=20x

840=20x-8x-5x

840=7x

x=840/7

x=120

The required number of pages in the book is given as 120 pages.

Given that,
Mary read 42 pages of a book on Monday she read 2/5 of the book on Tuesday if she still had 1/4 of the book to read how many pages are there in the book is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
let the number of pages in the book be x,
According to the question,
x - 42 - 2/5x = 1/4x
x - 2/5x - 1/4x = 42
x[1 - 2/5 - 1/4] = 42
x[20 - 8 - 5] / 20 = 42
x [7] / 20 = 42
x = 6 × 20
x = 120 pages

Thus, the required number of pages in the book is given as 120 pages.

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Hello!

To be quick and simple, your answer would be $0.55

The cost of the chocolate bar in the given scenario is $0.55. This was determined by solving a two-variable system of linear equations from the information provided.

This problem is a classic example of a system of linear equations, specifically two-variable linear equations. Here, we need to find the cost of one chocolate bar and one peanut butter bar, and we have two pieces of information that can be translated into equations. The first information is that a peanut butter bar costs $0.07 more than a chocolate bar. The second is that 5 peanut butter bars and 6 chocolate bars total $6.40. We'll use these equations to solve for the variables.

Let's denote the cost of the chocolate bar as x and the cost of the peanut butter bar as y. Then, from the information given, we can form two equations:

Substitute the first equation into the second to solve for x:

So the cost of the chocolate bar is $0.55.

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Answer:  60 years

Step-by-step explanation:

Let x denotes the age of Demochares .

Time he spent as a boy = [tex]\dfrac{x}{4}[/tex]

Time he spent as a youth = [tex]\dfrac{x}{5}[/tex]

Time he spent as a man= [tex]\dfrac{x}{3}[/tex]

Time he spent in dotage= 13 years

As per given , we have the following equation:

[tex]x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13[/tex]

[tex]x=\dfrac{15x+12x+20x}{60}+13[/tex]  [Take LCM]

[tex]x=\dfrac{47x}{60}+13[/tex]

[tex]x-\dfrac{47x}{60}=13[/tex]

[tex]\dfrac{60x-47x}{60}=13[/tex]

[tex]\dfrac{13x}{60}=13[/tex]

[tex]x=13\times\dfrac{60}{13}=60[/tex]

Hence, he is 60 years old.

Answer: the answers b i think

Good evening ,

Answer:

The right answer is B.

Step-by-step explanation:

If we apply the Pythagorean theorem we get

the length of the other leg is :

√(70^2-35^2)

= √(3 675)

= 60,621778264911.

:)

Answer:

Market demand at $5 is 12 pork.

Step-by-step explanation:

In a market, the sum of individual demand for a product from buyers is known as market demand.

It is give that the at the price of $3 a pound of pork, Jason buys 8 pounds of pork and Noelle buys 10 pounds of pork.

So, market demand at $3 is

8 + 10 = 18

When the price rises to $5 a pound, Jason buys 5 pounds of pork and Noelle buys 7 pounds of pork.

So, market demand at $5 is

5 + 7 = 12

Therefore, the market demand at $5 is 12 pork.

Answer:

Number of statues that can be painted are 17

Step-by-step explanation:

Initially Diana has [tex]\frac{7}{8}[/tex] liters of paint remaining.

Every statue requires [tex]\frac{1}{20}[/tex] liters of paint for painting.

We have to find how many statues we will be able to paint with this remaining paint.

To get the number of statues,

Number of statues = [tex]\frac{Paint remaining}{Paint required for 1 statue}[/tex]

number of statues = [tex]\frac{\frac{7}{8} }{\frac{1}{20} }[/tex]

                               = [tex]\frac{35}{2}[/tex] = 17.5

Since the number of statues is not an integer the maximum number of statues that can be painted are 17.

Answer: 35/2

Step-by-step explanation:

Final answer:

To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we expand it by multiplying each term. Simplifying the expression, we get a²*d² + 2a²de + 2abde + b²e².

Explanation:

To complete the statement describing the expression (a+b)(d+e)(a+b)(d+e), we need to expand it. This can be done by multiplying each term in the first factor by each term in the second factor and then multiplying the result by the third factor. So the expression becomes:

(a+b)(d+e)(a+b)(d+e) = (a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e)

We can simplify this further by combining like terms:

(a*d + a*e + b*d + b*e)(a*d + a*e + b*d + b*e) = a²*d² + 2a²de + 2abde + b²e²

its a b and c they all equal 45

Answer:

1 * 45

5 * 9

3 * 15

Hope this helps!

Please,  consider brainliest. I only have 5 left then my rank will go up.

Answer:

a) d = 143,117 ft

b) h = 612.45 ft

Step-by-step explanation:

If height of the mountain = h  

And distance till the surveyor can see = d = 3200.2 SQRT (h)

Refer to attached file for graphical representation

Then;

A) If h=2000 ft

Then d =3200.2 √ (2000)

d = 3200.2 (44.72)

d = 143,117 ft

B) If d = 15 miles

1mile = 5280 ft

15 mile = 15*5280

15 mile = 79,200 ft

Therefore;

d = 79,200 ft

Since,

d =3200.2 √ (h)  

79,200 = 3200.2 √ (h)

79200/3200.2 =√ (h)

√ (h) = 24.75

{√ (h)} ² = (24.75) ²

h = 612.45 ft

Answer:

The Dimension of new garden is [tex]25 \ feet\ \times 10\ feet.[/tex]

Step-by-step explanation:

Given:

Perimeter of new garden = 70 feet.

Let the length of the new garden be 'l'.

Also Let the width of the new garden be 'w'.

We need to find the dimension of new garden.

Now Given:

Length is 5 feet shorter than three times it width.

framing the equation we get;

[tex]l =3w-5 \ \ \ \ equation\ 1[/tex]

Now we know that;

Perimeter of rectangle is equal to twice the sum of length and width.

framing in equation form we get;

[tex]2(l+w)=70[/tex]

Now Diving both side by 2 using Division property of equality we get;

[tex]\frac{2(l+w)}2=\frac{70}{2}\\\\l+w =35[/tex]

Now Substituting equation 1 in above equation we get;

[tex]3w-5+w=35\\\\4w-5=35[/tex]

Adding both side by 5 Using Addition Property of equality we get'

[tex]4w-5+5=35+5\\\\4w=40[/tex]

Now Diving both side by 4 using Division property of equality we get;

[tex]\frac{4w}{4}=\frac{40}{4}\\\\w=10\ ft[/tex]

Now Substituting the value of 'w' in equation 1 we get;

[tex]l =3w-5\\\\l =3\times10-5\\\\l = 30-5\\\\l= 25\ ft[/tex]

Hence The Dimension of new garden is [tex]25 \ feet\ \times 10\ feet.[/tex]