The price of a sweater was reduced from $20 to $12 by what percentage was the price of the sweater reduced

The equation x^2 - y^2 - 2x + 16y = 31 represents a hyperbola.

To determine the conic section represented by the equation, we analyze the coefficients of the variables and the constant term. By completing the square for the x and y terms, we rewrite the equation as (x - 1)^2 - (y - 8)^2 = -32. Since the coefficients of both the x and y terms have opposite signs, the equation represents a hyperbola.

The equation can be rewritten as (x^2 - 2x) - (y^2 - 16y) = 31.

Completing the square for the x and y terms, we get:

(x^2 - 2x + 1) - (y^2 - 16y + 64) = 31 + 1 - 64.

Simplifying further, we have:

(x - 1)^2 - (y - 8)^2 = -32.

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Theorem 4.4.3 is the transitivity of divisibility theorem, which states that for all integers a, b, and c, if a divides b and b divides c, then a divides c. In other words, if a is a factor of b and b is a factor of c, then a is also a factor of c.

To prove this theorem, we can use the definition of divisibility, which states that if a and b are integers, then a divides b if and only if there exists an integer k such that b = ak. Suppose that a divides b and b divides c. Then, we can write b = am and c = bn, where m and n are integers.

Substituting b = am into the expression for c, we get c = anm. Since n and m are integers, their product nm is also an integer, which means that c = a(nm) is a multiple of a. Therefore, a divides c, which proves the transitivity of divisibility theorem.

This theorem is a fundamental property of divisibility and is often used in number theory and other mathematical areas. It allows us to establish relationships between divisors and can be used to simplify calculations involving factors and multiples of integers.

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For the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

To find the ratio of the average flux for e > 45 degrees to the omnidirectional flux in a pancake distribution of sin(a) where a = 0, we need to calculate the directional flux, omnidirectional flux, directional solid angle, and omnidirectional solid angle.

Directional Flux:

The directional flux is the flux within a specific direction or range of angles. In this case, we are interested in e > 45 degrees.

Omnidirectional Flux:

The omnidirectional flux is the total flux in all directions or over the entire solid angle.

Directional Solid Angle:

The directional solid angle is the solid angle subtended by the specified direction or range of angles. In this case, it would be the solid angle corresponding to e > 45 degrees.

Omnidirectional Solid Angle:

The omnidirectional solid angle is the total solid angle subtended by all possible directions or over the entire sphere.

To find the flux per solid angle for both the directional and omnidirectional cases, we can use the formula:

Flux per Solid Angle = Total Flux / Solid Angle

Finally, to find the ratio of the average flux for e > 45 degrees to the omnidirectional flux, we divide the flux per solid angle for the directional case by the flux per solid angle for the omnidirectional case.

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Answer:

-243, 729

Step-by-step explanation:

\(f(x) = {( - 3)}^{x} \)

x = 0, 1, 2, 3, .....

\(f(5) = {( - 3)}^{5} = - 243\)

\(f(6) = {( - 3)}^{6} = 729\)

Answer:

C.

Step-by-step explanation:

cytosine and guanine are 2 of the 4 main chemical bases in DNA

Can I have brainly?

Answer:

Option D is correct.

The margin of error accounts for all of the other listed options in a confidence interval.

Step-by-step explanation:

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

The width around the sample mean provided by the margin of error for the population mean helps to cover a lot of factors that are usually beyond one's control for the population parameter.

All the three options provided, response bias, random chance and small sampling biases all introduce deviations from the sample mean for the population mean. Hence, the width afforded to the possible values of the population mean creates avenue for all of these factors to be incorporated and the range of values becomes more inclusive.

Hence, the width provided by the margin of error about the sample mean accounts for response biases, random chance and small sampling biases.

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Answer:

0=0

1=10

2=15

3=20

Step-by-step explanation:

What I did was I multiplied each number by 5, then added 5.

Step-by-step explanation:

raise 1³ and 4³:

1×1×1 = 1 and 4×4×4 = 64

so the result is 1/64

Answer:

x equals 87

Step-by-step explanation:

37 + 56 = 93

triangles always equal to 180

180 - 93 = 87

the aggregate demand curve is downward-sloping because, other things being equal, With average price reductions, more people purchase goods and services.

This is known as the law of demand, which states that there is an inverse relationship between the price of a good or service and the quantity of that good or service demanded by consumers. When the price of a good or service goes up, consumers tend to demand less of it, and when the price goes down, consumers tend to demand more of it. Therefore, if all other factors affecting demand remain constant, an increase in price will lead to a decrease in the quantity demanded, and a decrease in price will lead to an increase in the quantity demanded. This is why the aggregate demand curve is downward-sloping.

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Compete Question

the aggregate demand curve is downward-sloping because, other things being equal, ____. FILL IN THE BLANKS

A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

To find the area of a sector:

Find the fraction of the circle represented by the sector by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the total area of the circle, which is given by πr².

The result is the area of the sector, which can be expressed as A = ( θ/360)πr².

To find the length of an arc:

Find the fraction of the circle represented by the arc by dividing the central angle  θ by 360 degrees.

Multiply this fraction by the circumference of the circle, which is given by 2πr.

The result is the length of the arc, which can be expressed as L = ( θ/360)2πr.

Hence, A = ( θ/360)πr² is used to find area of sector and L = ( θ/360)2πr used to find  length of the arc.

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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The number of different ways to order 11 different pictures in a photo album is 39,916,800.

To calculate this number, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of items to choose from (in this case, 11 pictures) and r is the number of items to be selected (also 11, since we want to order all the pictures).

Plugging in the values, we get:

11! / (11 - 11)! = 11! / 0! = 11!

We can simplify 11! as:

11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Using a calculator or by hand, we can find that 11! equals 39,916,800.

Therefore, there are 39,916,800 different ways to order 11 different pictures in a photo album.

Hence, the number of ways to order 11 pictures in a photo album can be calculated using the permutation formula, which gives a total of 39,916,800 possible arrangements.

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For the given data, current value of the gold in which Shelby invested is $1548.60 per ounce which is 38.9% more than its original value then the original purchase price is equal to $1114.90 per ounce.

As given in the question,

Current value of the gold is $1548.60 per ounce

Let x be the original purchase price of the gold invested by Shelby

Current value is 38.9% more than the original value of the gold

Required equation to represent the relation between current value and purchase price is given by:

x + (38.9 x/100) = 1548.60

⇒ ( 100x + 38.9x) /100 = 1548.60

⇒ 138.9x /100 = 1548.60

⇒ x = (1548.60 × 100 ) / 138.9

⇒ x = 1114.90 per ounce

Therefore, for the given data, current value of the gold in which Shelby invested is $1548.60 per ounce which is 38.9% more than its original value then the original purchase price is equal to $1114.90 per ounce.

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When multiplying a whole number with a fraction, the first factor will be reduced to a fraction or a decimal, depending on the problem.

In both of the given problems, we are multiplying a whole number with a fraction. When we multiply a whole number with a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator as it is. So, in the first problem, we have 10 multiplied by 1/2. Multiplying 10 with 1 gives us 10, and then we divide it by 2, which gives us 5. Therefore, the first factor, which is 10, will be reduced to 5 in this problem.

In the second problem, we have 15 multiplied by 7/2. Multiplying 15 with 7 gives us 105, and then we divide it by 2, which gives us 52.5. Therefore, the first factor, which is 15, will be reduced to 52.5 in this problem.

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Answer:

Cost of one pack = h+8

Step-by-step explanation:

Given that:

Amount Azil have = RM (h²-64)

Packs of flour Azil wants to buy = h-8

To find the price of a pack of flour, we will divide the total amount by packs of flour.

Unit rate = \(\frac{h^2-64}{h-8}\)

Unit rate = \(\frac{h^2-8h+8h-64}{h-8} = \frac{h(h-8)+8(h-8)}{h-8}\)

Unit rate = \(\frac{(h-8)(h+8)}{(h-8)}\)

Unit rate = h+8

Hence,

Cost of one pack = h+8

A numbered ball was randomly selected from the bowl of numbered balls that are numbered from 1 to 12.:A numbered ball was randomly selected from the bowl of numbered balls that are numbered from 1 to 12.

We are required to find out the probability of the ball selected from the bowl bearing a number that is a multiple of 3.There are a total of 12 balls in the bowl. Therefore, the total number of possible outcomes is 12.

So, the probability of the ball selected from the bowl bearing a number that is a multiple of 3 is 4/12, which can be simplified to 1/3 or 0.333.In conclusion, the probability of the ball selected from the bowl bearing a number that is a multiple.

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The numbered ball was randomly selected from a bowl containing balls numbered from 1 to 12. To determine the probability of selecting a specific number, we need to consider the total number of balls and the number of balls with the desired number. The probability of randomly selecting any specific ball number from a bowl containing balls numbered 1 to 12 is 1/12.

In this case, the total number of balls is 12. Let's say we want to find the probability of selecting ball number 5. We need to determine the number of balls with the number 5, which is 1 in this case.

The probability of selecting ball number 5 can be calculated using the formula:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes).

In this case, the number of favorable outcomes (balls with number 5) is 1, and the total number of possible outcomes (total number of balls) is 12. So, the probability of selecting ball number 5 is 1/12.

To generalize, the probability of selecting any specific ball number from 1 to 12 can be calculated as 1 divided by the total number of balls, which is 12 in this case.

It's important to note that the probability of selecting any particular ball number is the same for all the numbers from 1 to 12 since each ball is equally likely to be chosen.

In summary, the probability of randomly selecting any specific ball number from a bowl containing balls numbered 1 to 12 is 1/12.

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The specific range depends on the material properties and the energy levels involved.

The minimum and maximum frequencies for the acoustic and optic modes depend on the specific system or material under consideration. However, I can provide some general information.

Acoustic Mode:

The acoustic mode refers to the propagation of sound waves or vibrations in a material. In a solid, the acoustic mode can have different types, such as longitudinal and transverse modes.

The minimum frequency for the acoustic mode is typically determined by the size and physical properties of the material. In general, it can be close to zero for macroscopic objects or materials with low elasticity.

The maximum frequency for the acoustic mode depends on factors such as the speed of sound in the material and the characteristic dimensions of the system. It can range from a few kilohertz to several gigahertz.

Optic Mode:

The optic mode is related to the interaction of light with a material. It typically refers to the vibrations of charged particles (such as electrons) in a solid or the oscillations of electric or magnetic fields associated with photons.

The minimum frequency for the optic mode is typically determined by the energy gap between electronic states in the material. For example, in a semiconductor, the minimum frequency is usually in the infrared range.

The maximum frequency for the optic mode is not strictly defined, as it can extend into the terahertz, infrared, visible, ultraviolet, X-ray, and even gamma-ray regions. The specific range depends on the material properties and the energy levels involved.

It's important to note that these frequency ranges are general guidelines and can vary depending on the specific system or material being studied.

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The resultant velocity and acceleration of the skier at t=4.00 sec on the ski jump path are 12.8 m/s and 45.9 m/s², respectively.

To find the resultant velocity, first find the velocity vector components using the parametric equations:

vx = 7.00t, vy = 0.48t³ - 6.00t²/√(t⁴+1)

At t=4.00 s, vx = 28.0 m/s and vy = 10.50 m/s. The resultant velocity is the magnitude of the velocity vector, given by:

|v| = √(vx² + vy²) = 12.8 m/s

To find the acceleration vector components, differentiate the velocity vector components with respect to time:

ax = 7.00 m/s², ay = 1.44t² - 12.00t/√(t⁴+1) - 6.00t³(t⁴+1)^(-3/2)

At t=4.00 s, ax = 7.00 m/s² and ay = 45.9 m/s². The acceleration vector magnitude is:

|a| = √(ax² + ay²) = 46.1 m/s².

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Answer:

h(g(f(x))) = (-8)x^2+(-40)x+(-50).

Step-by-step explanation:

We have:

h(x) = -2x

g(x) = x^2

f(x) = 2x + 5

So, we can replace the respective value:

h(g(f(x)))

first substituting the value of f(x) in x of g(x).

h(g(2x + 5))

second, substituting the value of g(x) in x of h(x).

h((2x + 5)^2)

expanding value using the formula (a+b)^2=a^2+2ab+b^2

h(4x^2+20x+25)

Thirdly, substituting the value of h(x) in x of h(x).

-2(4x^2+20x+25)

opening bracket

-8x^2-40x-50

Therefore, h(g(f(x))) = -8x^2-40x-50.

Answer:

21

Step-by-step explanation:

An isosceles triangle has 2 sides of the same length, those sides being the sides that aren't the base. The perimeter is the total length of all 3 sides of the triangle. We know that the base is 5 inches, and that one side is 8. Because the triangle is isosceles, we know that the others ide is also 8 inches. Therefore, the perimeter is 8+8+5, which is 21.

Answer:

21 in.

Step-by-step explanation:

If the triangle is isosceles, then two of its three sides are of equal length.  We can assume that the side lengths are 5 in., 8 in and 8 in.  Summing these up, we get total length 21 in.  That's the perimeter of the triangle.

Answer:

x= -2

Step-by-step explanation:

Isolate the variable (x) by dividing each side by factors that don't contain the variable (x)

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Answer:

10+10+10

Step-by-step explanation:

if the marginal revenue for a bushel of corn is $3, you should produce 8 bushels of corn to maximize profits.

If the marginal revenue for a bushel of corn is $3, you should produce 8 bushels of corn to maximize profits. Given, The marginal revenue for a bushel of corn is $3. Now, to find out how many bushels of corn should be produced to maximize profits, we need to consider the marginal cost and marginal revenue. Marginal revenue (MR) is the additional revenue earned from selling one additional unit of output. Marginal cost (MC) is the additional cost incurred from producing one additional unit of output. The profit-maximizing output is where marginal revenue equals marginal cost (MR = MC).

Hence, MR = $3 Now, we need to find out the marginal cost to find out the quantity of bushels of corn required to maximize profits. The marginal cost can be obtained from the graph below:

ATC N 1 1500 1400 1200 N 4 16 6 8 10 12 14 Quantity of Bushels (in hundreds) From the graph, we can observe that the marginal cost of producing 8 bushels of corn is $3. Therefore, if the marginal revenue for a bushel of corn is $3, you should produce 8 bushels of corn to maximize profits. To maximize profits, you should produce the quantity of bushels of corn where marginal revenue equals marginal cost.

The given information provides the marginal revenue ($3 per bushel) but does not provide marginal cost. Without knowing the marginal cost, it is not possible to determine the exact number of bushels to produce to maximize profits.

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Answer:

63

Step-by-step explanation:

28/4 = 7 windows per hour

7 × 9 = 63 windows in 9 hours

When one point of the diameter touches the circle at (-3,1) and the other point touches the circle at (3,-7) that is these are endpoints of diameter. Then the radius of this circle is equals to the 5 units.

Radius of a circle is defined as the distance from the center of the circle to any arbitrary point on it's circumference. It is generally represented by symbol 'R' or 'r'. When the diameter of a circle is known, the formula for Radius, R= Diameter/2. We have specified two endpoints, i.e., (-3,1),(3,-7) of a diameter of a circle. Let the radius of circle be 'r '. We have to determine the value of r that is radius of circle. From the above definition we can say that radius is half of length of diameter. So, first we calculate the length of diameter of circle. Using the distance formula, the distance between two points is written as, \(d = \sqrt{(x_2-x_1)²+(y_2-y_1)²}\)

So, the distance between two points (-3,1),(3,-7) is \(d = \sqrt{ ( 3-(-3))²+(-7 -1)²}\)

=> \(d = \sqrt{6²+8²} =\sqrt{ 36 + 64}\)

=> d = 10 units

so, length of diameter of circle is 10 units. Now, by definition of radius, the radius of circle is half of diameter. Thus, the required value of radius, r is 5 units (10/2).

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Answer:

6, 8, and 10 cm

Step-by-step explanation:

3+4+5=12

24/12=2

2*3=6

2*4=8

2*5=10

A chord is a combination of three or more tones (notes) played together.

To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.

In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.

In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.

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