Cos(x)^2 in terms of sin(x)

First, we need to convert 8 yards to inches since the measurement of ribbon needed for one present is given in inches.

1 yard = 36 inches (since 1 yard = 3 feet and 1 foot = 12 inches)

So, 8 yards = 8 x 36 = 288 inches.

To find out how many presents can be wrapped with 288 inches of ribbon, we divide the total length of ribbon by the length needed for one present:

Number of presents = Total length of ribbon ÷ Length of ribbon needed for one present

Number of presents = 288 ÷ 9

Number of presents = 32

Therefore, 32 presents can be wrapped with 8 yards (288 inches) of ribbon.

Hence, the answer is 32 presents.

Answer: c(32

Step-by-step explanation:

The situation in which the quantities combine to make 0 is D.

What is a combination of quantities?

In mathematics, a combination of quantities usually means taking a group of items or values and selecting some of them without regard to their order. A combination is different from a permutation in that order does not matter in a combination, whereas it does matter in a permutation.

For example, if you have three objects labeled A, B, and C, then the possible combinations of two objects are AB, AC, and BC. These combinations are different from the permutations of two objects, which include AB and BA, AC and CA, and BC and CB.

Combinations are often used in probability, statistics, and combinatorics to calculate the number of ways that objects or values can be selected from a set, without regard to their order.

The situation in which the quantities combine to make 0 is:

D. In the morning, the temperature rises 30 degrees. In the evening, it falls by 30 degrees.

In situation D, the temperature rises by 30 degrees in the morning and then falls by 30 degrees in the evening, which means that the overall change in temperature is 0. In situations A, B, and C, the quantities do not combine to make 0. In situation A, the hot air balloon rises a total of 80 feet, which is not 0. In situation B, Kathy has $10 left after giving half to her friend, which is not 0. In situation C, the player earns a total of 8 points, which is not 0.

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Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.

Week New Cases Total Cases So Far Individual at Risk at Start of Week Weekly Incidence Prevalence

1 105 105 920 0.102 0.102

2 180 285 740 0.196 0.278

3 390 675 350 0.527 0.659

4 325 1000 25 0.929 0.976

B) Spring Fever: Incidence and Prevalence per 100

Week Weekly Incidence per 100 Prevalence per 100

1 10.2 per 100 10.2 per 100

2 19.6 per 100 27.8 per 100

3 52.7 per 100 65.9 per 100

4 92.9 per 100 97.6 per 100

C) The 4th-week incidence is much higher, indicating an increase from 0.527 in the 3rd week to 0.929 in the 4th week.

Therefore, teachers should anticipate the greatest increase in spring fever during the 4th week.

Incidence= Number of new cases at particular week/total number of cases in that week

Prevalence= Total number of cases diagnosed/total number of subjects

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The value of cos J rounded to the nearest hundredth is 0.384.

A mathematical function known as the cosine is used in many branches of mathematics, such as geometry and trigonometry. It is described as the proportion between the hypotenuse and the adjacent side of a right triangle. It is represented by the symbol cos-1 or arc cos and is also known as the inverse cosine or arc cosine.

Using Pythagoras theorem lets find IJ

IJ = [tex]\sqrt{13^2 - 12^2}[/tex]

IJ = √25

IJ = 5

Now,

cos θ = Adjacent side/Hypotenuse

cos J = IJ/HJ

= 5/13

= 0.384

Thus, the value of cos J rounded to the nearest hundredth is 0.384.

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Complete question:

Find the value of cos J rounded to the nearest hundredth, if necessary.

Therefore , the solution of the given problem of unitary method comes out to be Mr. Tan makes a total of $30 Plus $18 = $48.

To finish the job using the unitary technique, the equation from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

Let's name the CDs' pre-tax cost "x" for simplicity. The overall cost of the CDs before tax is two times because Lena purchased two of them for the same price. The cost of the Discs, with the addition of the $1.80 sales tax, is:

=> 2x + $1.80

Given that we know the final price, including tax, was $23.40, we can create the following equation:

=> 2x + $1.80 = $23.40

By deducting $1.80 from each half, we arrive at:

=> 2x = $21.60

When you divide both parts by 2, you get:

=> x = $10.80

As a result, each Disc cost $10.80 before taxes.

We can create another equation now that we know his revenues from selling apple juice are $12 higher than his profits from selling lemon juice:

=> 30n - 18n = 12

=> 12n = 12

=> n = 1

As a result, Mr. Tan sells 2n + 5n = 7n = 7 glasses of juice, for a total profit of 30n = $30 from the sale of apple juice and 18n = $18 from the sale of lemon juice.

Therefore, Mr. Tan makes a total of $30 Plus $18 = $48.

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The equation x · 1 = x is true for all real numbers. This is because any number multiplied by 1 is equal to itself.

For example, if x = 2, then 2 · 1 = 2. If x = 5, then 5 · 1 = 5. This is true for any value of x, so the equation is true for all real numbers.

In mathematical terms, 1 is known as the multiplicative identity because it does not change the value of a number when it is multiplied by it. Therefore, the equation x · 1 = x is always true for any real number x.

In conclusion, the equation x · 1 = x is true for all real numbers.

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The doubling time.

A) The exponential function that describes the amount in the account after time t in years is A(t) = 511969*e^(0.052*t), where A(t) is the amount in the account after time t, e is the base of the natural logarithm, and t is the time in years.

B) The balance after 1 year is A(1) = 511969*e^(0.052*1) = 538,926.41
The balance after 2 years is A(2) = 511969*e^(0.052*2) = 567,639.77
The balance after 5 years is A(5) = 511969*e^(0.052*5) = 661,234.83
The balance after 10 years is A(10) = 511969*e^(0.052*10) = 872,032.74

C) The doubling time is the time it takes for the amount in the account to double. We can find this by setting A(t) = 2*511969 and solving for t.
2*511969 = 511969*e^(0.052*t)
2 = e^(0.052*t)
ln(2) = 0.052*t
t = ln(2)/0.052
t = 13.33 years
So the doubling time is 13.33 years.

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To determine how much greater the fractional part of a college student's daily servings that comes from grains than from fruits, we would need to know the specific fractions or percentages of each type of food that the student consumes. Without this information, it is impossible to accurately answer the question.

For example, if the student consumes 1/2 of their daily servings from grains and 1/4 of their daily servings from fruits, then the difference would be 1/2 - 1/4 = 1/4 or 25%. However, without knowing the specific fractions or percentages, we cannot determine the difference.

It is important to remember that a balanced diet should include a variety of food groups, including grains, fruits, vegetables, proteins, and dairy. The specific amounts of each will vary depending on individual dietary needs and preferences.

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if we take 32(origin amount) to be the 100%, what's 7.1 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 32 & 100\\ 7.1& x \end{array} \implies \cfrac{32}{7.1}~~=~~\cfrac{100}{x} \\\\\\ 32x=710\implies x=\cfrac{710}{32}\implies x\approx 22.19[/tex]

Step-by-step explanation:

it is a quadrilateral.

the sum of all angles in a quadrilateral is always 360°.

so,

360 = x + x + 2x + 7 + 2x + 5 = 6x + 12

348 = 6x

x = 348/6 = 58°

that's it.

Answer:

y=2x+3

Step-by-step explanation:

Using the point-slope form of the equation of a line, we can write:

y - 9 = 2(x - 3)

Simplifying, we get:

y - 9 = 2x - 6

y = 2x + 3

Therefore, the equation of the line that is parallel to y=2x+1 and goes through the point (3,9) is y=2x+3.

parallel → the same slope

slope: y = 2x +1 → m = 2

y=2x+3 ⇔ 2(3)+3=6+3=9

y=2x+9 ⇔ 2(3)+9=6+9=15≠9

⇒ answer: y=2x+3

The value of x and y in the line segment are 6 and 6.5 units repsectively.

The lines are three parallel lines cut by two transversal lines. The transversal lines that cut across the parallel lines have same length at intervals .

Using the information in the diagram let's find the value of x and y in the diagram.

Therefore,

2x + 1 = x + 7

2x - x = 7 - 1

x = 6 units

Therefore,

3y - 8 = y + 5

3y - y = 5 + 8

2y = 13

divide both sides by 2

y = 13 / 2

y = 6.5 units

Therefore,

x = 6 units

y = 6.5 units

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Brooklyn has 7 brain teasers and total of 15 brain teasers, then Lincoln has 8 brain teasers.

Linear equations are equations that can be written in the form ax + b = 0, where a and b are constants and x is a variable. Linear equations represent straight lines when graphed on a coordinate plane.

We can solve the Linear equation x + 7 = 15 to determine how many brain teasers Lincoln has.

First, we want to isolate the variable x on one side of the equation. To do this, we can subtract 7 from both sides of the equation:

x + 7 - 7 = 15 - 7

Simplifying the equation gives us:

x = 8

Therefore, Lincoln has 8 brain teasers.

In conclusion, if Brooklyn has 7 brain teasers and together they have 15 brain teasers, then Lincoln has 8 brain teasers.

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Answer:

Let's say that the class has a total of 7x students, where 2x wear glasses and 5x don't.

After 5 of the students who didn't wear glasses now do, the number of students who don't wear glasses becomes 5x - 5.

So, the new ratio of students who wear glasses to those who don't wear glasses is:

2x : (5x - 5)

We can simplify this ratio by dividing both terms by the greatest common factor, which is x:

2 : (5 - 5/x)

We can't simplify this any further, but we can see that the ratio is not fixed and depends on the value of x.

\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]

Let \(T_{1}\) and \(T_{2}\) be linear transformations given by
\[\begin{array}{l}
 T_{1}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 3 x_{1}+6 x_{2} \\ 5 x_{1}-2 x_{2}\end{array}\right] \\
 T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 8 x_{1}+4 x_{2} \\ 5 x_{1}+2 x_{2}\end{array}\right]
\end{array}\]
A linear transformation is a function that takes two input values and returns two output values in a way that preserves the linear structure of the data. It is described by a matrix that determines the output values from the input values. In the case of \(T_{1}\) and \(T_{2}\), the matrix is
\[
 M=\left[\begin{array}{cc}
   3 & 6 \\
   5 & -2
 \end{array}\right]
\]
and
\[
 M=\left[\begin{array}{cc}
   8 & 4 \\
   5 & 2
 \end{array}\right]
\]
respectively. The two linear transformations can be combined using matrix multiplication, which yields the transformation
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=M_{1} M_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)
\]
where
\[
 M_{1}M_{2}=\left[\begin{array}{cc}
   43 & 2 \\
   -10 & 4
 \end{array}\right].
\]
Therefore, the result of applying both transformations to a given input vector is given by
\[
 T_{1} \circ T_{2}\left(\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]\right)=\left[\begin{array}{r} 43 x_{1}+2 x_{2} \\ -10 x_{1}+4 x_{2}\end{array}\right]
\]
This is an example of a linear transformation, where two transformations are combined to produce a single result.

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Answer:

Step-by-step explanation:

When calculating this equation you simply insert the x value into the equation given, in this case (x-2)^2

for example you are given 4 to 4 which is achieved by the method previously described, like this (4-2)^2 = (2)^2 = 4

so the answers would be

6 -> 16 (6 - 2 = 4 and 4^2 is 16)

10 -> 64 (10 - 2 = 8 and 8^2 is 64)

Answer:

66 (at least if that is an answer choice)

Step-by-step explanation:

[tex]\frac{75*88}{100} = 66[/tex]

66 is your answer!

Distance between both factories is 1543 m

In Trigonometry, the law of Cosines, also known as Cosine Rule or Cosine Formula basically relates the length of the triangle to the cosines of one of its angles. It states that, if the length of two sides and the angle between them is known for a triangle, then we can determine the length of the third side. It is given by:

c² = a² + b² – 2ab cosγ

Given,

A man hears the two blasts exactly 6.1 seconds and 2.7 seconds from two factories.

Angle between line of sight γ = 42.4°

Speed of sound = 344m/sec

Distance of factory A from man (a)

6.1 × 344 = 2098.4 m

Distance of factory B from man (b)

2.7 * 344 = 928.8 m

The side opposite the angle between his lines of sight will be the distance between the factories.

Using cosine law

c² = a² + b² – 2ab cos γ, where

c = distance between the factories

c² = 2098.4² + 928.8² – 2(2098.4)(928.8) cos 42.4°

c = √(2098.4² + 928.8² – 2(2098.4)(928.8) cos 42.4°)

c = √(4403282.56 + 862669.44 - 3897987.84(0.74))

c = √(5265952 - 2884511)

c = √2381441

c = 1543.19 m

  ≈ 1543 m

Hence, 1543 m is the distance between both factories.

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To find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.

What are coordinates ?

Coordinates are numerical values that specify the position or location of a point in a given space. In mathematics, coordinates are often expressed as ordered pairs or triplets of numbers, which correspond to the distances of the point from a set of fixed reference points or axes.

Without seeing the figure QRST, it is not possible to give the exact coordinates for point R after the reflection and translation. However, we can use some general knowledge about the effects of reflection and translation on the coordinates of a point.

When a figure is reflected across the x-axis, the x-coordinates of all its points remain the same, but the y-coordinates are negated. That is, if a point has coordinates (x, y) before the reflection, its coordinates after the reflection will be (x, -y).

When a figure is translated down by 3 units, the y-coordinates of all its points are decreased by 3. That is, if a point has coordinates (x, y) before the translation, its coordinates after the translation will be (x, y - 3).

Therefore, to find the coordinates of point R after the reflection and translation, we would need to know its original coordinates in the figure QRST. Then we could apply the above rules to get its new coordinates.

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The volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.

Pyramid is a structure with a polygonal base and triangular sides that meet at a point. Pyramids have been used throughout history as tombs, temples and monuments. Many of the most famous pyramids are located in Egypt, such as the Great Pyramid of Giza.

The volume of a right square pyramid is equal to one-third of the base area multiplied by the height. To find the volume of this pyramid, we first need to calculate the base area.
The base area of a square pyramid is equal to the length of one side (s) squared. Since the length of one side of this pyramid is 6m, the base area is 6m x 6m, which equals 36m².
Now that we know the base area, we can calculate the volume of the pyramid. The volume is equal to one-third of the base area multiplied by the height. In this case, the volume of the pyramid is one-third of 36m² multiplied by 4m, which equals 48m³.
Therefore, the volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.

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Answer:

Step-by-step explanation:

The ball hits the ground when h=0.

[tex]0=154-10t-16t^{2}[/tex]

Solve for t. You can use the quadratic formula.

[tex]t=\frac{-(-10)+-\sqrt{10^{2}(-16\cdot154) } }{2(-16)}[/tex]

[tex]t=\frac{5+-\sqrt{2489} }{16} \\t=-3.43 t=2.81[/tex]

Time cannot be negative.  So, the answer is t=2.81 seconds.

Answer: 28

Step-by-step explanation: Both Of Those Triangles Are Equal. That Means They Both Equal 14. So If We Multiply 14 With 2, We Would Get 28 cm!

Hoped This Helped!

Answer:

28cm

Step-by-step explanation:

its a perfect rectangle so both triangle are Reflexive property so they would be the same size

Comparing the two probabilities, we can see that the probability of any particular letter being called first (1/5) is five times greater than the probability of any particular number being called first (1/75). This is because there are five letters and only one number will be called first.

Viet's description of the probability of each number being called first can be determined as follows. There are 75 numbers in the set, and each number has an equal chance of being called first. Therefore, the probability of any particular number being called first is 1/75.

Quinn's description of the probability of any particular letter being called first can be determined as follows. There are five letters in the set, and each letter has 15 numbers associated with it. Therefore, the probability of any particular letter being called first is 15/75 or 1/5.

Comparing the probabilities, we can see that the probability of any particular letter being called first is greater than the probability of any particular number being called first. This is because there are fewer letters (5) than numbers (75), so the probability of selecting a particular letter is higher than the probability of selecting a particular number.

Therefore, Quinn's probability of any particular letter being called first is greater than Viet's probability of any particular number being called first.

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See transcribed text below

TOPIC

7

MID-TOPIC PERFORMANCE TASK

Viet, Quinn, and Lucy are going to play Bingo, using a standard game set. They make some predictions before the game begins. The table shows how the numbers match with the letters B, I, N, G, and O.

Letter

Numbers

B - 1-15

1 -16-30

N-31-45

G- 46-60

O- 61-75

PART A

Viet describes the probability of each number being called first. Quinn describes the probability of any particular letter being called first. Compare the probabilities.

If the length and width of the pen are both whole numbers the possible perimeters for the pen are 98, 52, 38, 32, and 28.

To find the possible perimeters of the pen, we first need to find all the possible length and width pairs that would give us an area of 48 square feet. Since the length and width are whole numbers, we can start by listing out all the factors of 48:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Each of these factors represents a possible length or width of the pen, and we can find the other dimension by dividing the area (48) by the first dimension. For example, if the first dimension is 1, then the other dimension is 48/1 = 48. However, we need to make sure that the second dimension is also a whole number.

Using this method, we can find all the possible length and width pairs:

1 x 48, 2 x 24, 3 x 16, 4 x 12, 6 x 8

Now we can calculate the perimeter for each of these pairs. The perimeter is the sum of the lengths of all four sides of the pen. Since the length and width are the same for a square pen, we can use the formula:

perimeter = 2(length + width)

For each pair, we can plug in the values for length and width to get the perimeter:

1 x 48: perimeter = 2(1 + 48) = 98

2 x 24: perimeter = 2(2 + 24) = 52

3 x 16: perimeter = 2(3 + 16) = 38

4 x 12: perimeter = 2(4 + 12) = 32

6 x 8: perimeter = 2(6 + 8) = 28

Therefore, the possible perimeters for the pen are 98, 52, 38, 32, and 28.

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To input the given commands and find the Z-scores for the different heights, you will need to use the following steps:

1. Convert the heights from feet and inches to inches. For example, 6'4" would be 76 inches, 5'8" would be 68 inches, and 5'2" would be 62 inches.

2. Use the formula Z = (X - mean) / standard deviation to find the Z-scores for each height. For example, for the height of 6'4", you would use the formula Z = (76 - height.xbar) / height.s.

3. Use the pnorm command to find the percentiles for each Z-score. For example, for the Z-score of the height 6'4", you would use the command pnorm(Z).

4. Use the pnorm command with the lower.tail = FALSE argument to find the portion of people taller than a given height. For example, for the height of 6'4", you would use the command pnorm(Z, lower.tail = FALSE).

5. Use the pnorm command with the lower and upper limits to find the portion of people between two heights. For example, for the heights of 5'2" and 5'8", you would use the command pnorm(upper limit) - pnorm(lower limit).

Using these steps, you can input the given commands and find the Z-scores and percentiles for the different heights. Remember to use the variable names height.xbar and height.s for the mean and standard deviation of the height variable, and to use the number, variable, and height terms in your answer.

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The point that would be included in the region shaded to show the half-plane greater than the line is the point that lies above the line.

In order to determine which point is included in the region shaded to show the half-plane greater than the line, we can use the following steps:
1. Identify the equation of the line.
2. Plug in the x and y values of the point into the equation of the line.
3. If the result is greater than the constant term in the equation of the line, then the point is included in the region shaded to show the half-plane greater than the line.

For example, if the equation of the line is y = 2x + 1, and the point is (2,5), we can plug in the x and y values into the equation:
5 = 2(2) + 1
5 = 5

Since the result is equal to the constant term in the equation of the line, the point (2,5) is included in the region shaded to show the half-plane greater than the line.

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The dimensions of the rectangle is 3.33 by 5.33

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Third side of triangle, w = 12 - 5 - 1/2l

The perimeter of the rectangle is then calculated a

2 * (1/2l + 1/2l + 12 - 5 - 1/2l) = 22

So, we have

(1/2l + 1/2l + 12 - 5 - 1/2l) = 11

Evaluate

1 1/2l + 7 = 11

This gives

3/2l = 5

Evaluate

l = 10/3

The dimension is then represented as

l by 12 - 5 - 1/2l

This gives

10/3 by 12 - 5 - 1/2 * 10/3

Evaluate

3.33 by 5.33

Hence, the dimension is 3.33 by 5.33

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The exponential decay model for this situation is P(t) = 200,000 * (1 - 0.03)^t

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Population in 1992=200000

Time=6years

Rate=3%

To write an exponential decay model to represent this situation, we can use the formula:

P(t) = P * (1 - r)ᵗ

where P(t) is the population after t years, P is the initial population, r is the annual rate of decline as a decimal, and t is the number of years. In this case, the initial population P is 200,000, the annual rate of decline r is 0.03 (since the population declines by 3% each year), and t is the number of years from 1992, so t = 0 corresponds to 1992 and t = 6 corresponds to 1998.

P(t) = 200,000 * (1 - 0.03)^t

where t is the number of years from 1992 to 1998.

Therefore, by the given percent answer will be P(t) = 200,000 x (1 - 0.03)^t

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Answer:$20.40

Step-by-step explanation:

 20% off means that the new price of the skirt will be 80% of the original price:

$30(100%  – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100%  – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40