Unit 4, Lesson 4 Cool-down 4.4 Mis-Steps

Lin solved the equation 8( x - 3 ) + 7 = 2x( 4 - 17 ) incorrectly.
Find the errors in her solution. What should her answer have been?

Lin's solution:

8( x - 3 ) + 7 = 2x( 4 - 17 )

8( x - 3 ) + 7 = 2x(13 )

8x - 24 + 7 = 26x

8x - 17 = 26x

-17 = 34x

-½ = x

Answer:

56

Step-by-step explanation:

75 - 19 = 56

The correct option is A) quantitative data.

The stem-and-leaf plot is used to display the distribution of quantitative data.

Stem-and-leaf plots are very useful graphical techniques to represent data of numeric values. It is a way to represent quantitative data graphically with precision and accuracy, and its detailed structure can show the distribution of data.

Each number in a data set is split into a stem and a leaf, where the stem is all digits of the number except the rightmost, and the leaf is the last digit of the number.

Then the stems are listed vertically, and the leaves of each number are listed in order beside the corresponding stem, allowing you to view the overall shape of the data and identify outliers and patterns.

Thus, stem-and-leaf plot is used to display the distribution of quantitative data.

Therefore, the correct option is A) quantitative data.

The stem-and-leaf plot is used to display the distribution of quantitative data.

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Answer:

this is not propotioinal, because 14 divided by 2 is 7 and 20 divided by 3 is not equal to 7 you need 1 more book in the second box to make it proportional

Step-by-step explanation:

hope this helps      :)

Answer:

210

Step-by-step explanation:

you just need to multiply all numbers

Answer:

366 in^3

Step-by-step explanation:

I believe that would be 1025.4cm³

1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.

2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.

3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.

4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.

5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.

6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.

7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.

1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.

This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.

To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.

However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.

This led to the development of the modern pickup truck, which is now a staple of the American automobile market.

2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.

Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.

3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.

However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.

4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.

In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.

However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.

5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.

6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.

However, they may be necessary for individual companies to remain competitive in the short term.

Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.

7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.

While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.

In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.

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Answer: translation

Step-by-step explanation:

The equation in standard form for the ellipse with its center at the origin, a vertex at (0, 7), and a focus at (0, 3) is x^2/16 + y^2/40 = 1.

The equation in standard form for an ellipse with its center at the origin, a vertex at (0, 7), and a focus at (0, 3) is:

**x^2/16 + y^2/40 = 1

To derive this equation, we can use the standard form of an ellipse equation for an ellipse centered at the origin:

**x^2/a^2 + y^2/b^2 = 1**

Given that the center of the ellipse is at the origin, the coordinates of the center are (0, 0), and we have:

**h = 0** (x-coordinate of the center) and **k = 0** (y-coordinate of the center)

The distance from the center to a vertex is represented by 'a,' so in this case, **a = 7** (distance from the origin to the vertex at (0, 7)).

The distance from the center to a focus is represented by 'c,' so in this case, **c = 3** (distance from the origin to the focus at (0, 3)).

To find 'b,' we can use the relationship between 'a,' 'b,' and 'c' in an ellipse:

**c^2 = a^2 - b^2**

Substituting the given values, we have:

**3^2 = 7^2 - b^2**

**9 = 49 - b^2**

**b^2 = 40**

Plugging the values of 'a' and 'b' into the standard form equation, we get:

**x^2/16 + y^2/40 = 1**

Therefore, the equation in standard form for the ellipse with its center at the origin, a vertex at (0, 7), and a focus at (0, 3) is **x^2/16 + y^2/40 = 1**.

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Answer:

-2

Step-by-step explanation:

2x-6x=8

-4x=8

x=-2

Answer:

x=1

Step-by-step explanation:

AB+BC=AC

2x+6x+8=16

8x+8=16

8x=16-8

8x=8

divide both sides by 8

x=1

a. Bisection Method: To use the bisection method to find the real roots of the equation f(x) = x³ + x² - 10x + 8, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs.

Let's make a preliminary estimate and choose the interval [1, 2] based on observing the sign changes in the equation.

Iteration 1: a = 1, b = 2

c = (a + b) / 2

= (1 + 2) / 2 is 1.5

f(c) = (1.5)³ + (1.5)² - 10(1.5) + 8 ≈ -1.375

ince f(c) has a negative value, the root lies in the interval [1.5, 2].

Iteration 2:

a = 1.5, b = 2

c = (a + b) / 2

= (1.5 + 2) / 2 is 1.75

f(c) = (1.75)³ + (1.75)² - 10(1.75) + 8 ≈ 0.9844

Since f(c) has a positive value, the root lies in the interval [1.5, 1.75].

Iteration 3: a = 1.5, b = 1.75

c = (a + b) / 2

= (1.5 + 1.75) / 2 is 1.625

f(c) = (1.625)³ + (1.625)² - 10(1.625) + 8  is -0.2141

Since f(c) has a negative value, the root lies in the interval [1.625, 1.75].

Iteration 4: a = 1.625, b = 1.75

c = (a + b) / 2

= (1.625 + 1.75) / 2 is 1.6875

f(c) = (1.6875)³ + (1.6875)² - 10(1.6875) + 8 which gives 0.3887.

Since f(c) has a positive value, the root lies in the interval [1.625, 1.6875].

Iteration 5: a = 1.625, b = 1.6875

c = (a + b) / 2

= (1.625 + 1.6875) / 2 is 1.65625

f(c) = (1.65625)³ + (1.65625)² - 10(1.65625) + 8 is 0.0873 .

Since f(c) has a positive value, the root lies in the interval [1.625, 1.65625].

Iteration 6: a = 1.625, b = 1.65625

c = (a + b) / 2

= (1.625 + 1.65625) / 2 which gives 1.640625

f(c) = (1.640625)³ + (1.640625)² - 10(1.640625) + 8 which gives -0.0638.

Since f(c) has a negative value, the root lies in the interval [1.640625, 1.65625].

teration 7: a = 1.640625, b = 1.65625

c = (a + b) / 2

= (1.640625 + 1.65625) / 2 results to 1.6484375

f(c) = (1.6484375)³ + (1.6484375)² - 10(1.6484375) + 8 is 0.0116

Since f(c) has a positive value, the root lies in the interval [1.640625, 1.6484375].

Continuing this process, we can narrow down the interval further until we reach the desired level of accuracy.

b. Newton-Raphson Method: The Newton-Raphson method requires an initial estimate for the root. Let's choose x₀ = 1.5 as our initial estimate.

Iteration 1:

x₁ = x₀ - (f(x₀) / f'(x₀))

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 which gives -1.375.

f'(x₀) = 3(1.5)² + 2(1.5) - 10 which gives -1.25.

x₁ ≈ 1.5 - (-1.375) / (-1.25) which gives 2.6.

Continuing this process, we can iteratively refine our estimate until we reach the desired level of accuracy.

c. Secant Method: The secant method also requires two initial estimates for the root. Let's choose x₀ = 1.5 and x₁ = 2 as our initial estimates.

Iteration 1: x₂ = x₁ - (f(x₁) * (x₁ - x₀)) / (f(x₁) - f(x₀))

f(x₁) = (2)³ + (2)² - 10(2) + 8 gives 4

f(x₀) = (1.5)³ + (1.5)² - 10(1.5) + 8 gives -1.375

x₂ ≈ 2 - (4 * (2 - 1.5)) / (4 - (-1.375)) gives 1.7826

Continuing this process, we can iteratively refine our estimates until we reach the desired level of accuracy.

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9514 1404 393

Answer:

  m = 2k/v

Step-by-step explanation:

Identify the coefficient of m (v/2) and multiply by its inverse (2/v).

  (2/v)k = (2/v)m(v/2) . . . . multiply both sides of the equation by 2/v

  2k/v = m . . . simplify

  m = 2k/v

In table the missing entity are :

1. On June 26, the values are a is 0 ,  b is $ 1300 , c is $1300 , d is $20.8 and e is $ 1320.8

2. On June 27, the values are f is $ 1320.8  , g is 0 , h is $ 1300 , I is $ 41.93 and j is $ 1341.93

3. On June 28, the values are k is $ 1341.93 , l is 0 , m is $ 1300 , n is $ 63.40 and o is $ 1363.40.

What is compound interest ?

The interest on savings that is calculated using both the original principal and the interest accrued over time is called compound interest.

It is given that , the initial deposit is of $1300 on date 26th of June.

The rate of compound interest = 1.6%

We know that the formula to find out the compound interest on a deposit is given by:

CI = P × \([1 + \frac{r}{100}]^{t}\)

Here : P is the principal amount and r is the rate of interest in %.

On June 26 :

Opening balance = 0

Deposit = $ 1300

Principal used = $ 1300

Compound interest will be :

CI = 1300 × \([1 + \frac{1.6}{100}]^{1}\)

CI = $ 1320.8

This is the ending balance.

Interest = 1320.8 - 1300 = $ 20.8

On June 27 :

Opening balance = $ 1320.8

Deposit = 0

Principal used = $ 1300

CI =  1300 × \([1 + \frac{1.6}{100}]^{2}\)

CI = $ 1341.93

This is the ending balance.

Interest = 1341.93- 1300 = $ 41.93

On June 28 :

Opening balance = $ 1341.93

Deposit = 0

Principal used = $ 1300

CI =  1300 × \([1 + \frac{1.6}{100}]^{3}\)

CI = $ 1363.40

This is the ending balance.

Interest = 1363.40 - 1300 = $ 63.40

Therefore , in table the missing entity are :

1. On June 26, the values are a is 0 ,  b is $ 1300 , c is $1300 , d is $20.8 and e is $ 1320.8

2. On June 27, the values are f is $ 1320.8  , g is 0 , h is $ 1300 , I is $ 41.93 and j is $ 1341.93

3. On June 28, the values are k is $ 1341.93 , l is 0 , m is $ 1300 , n is $ 63.40 and o is $ 1363.40.

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In order to know if a triangle is a right triangle on a coordinate plane, you can find the lengths of all three sides of the triangle using the distance formula and apply the Pythagorean theorem.

Find the lengths of the three sides of the triangle using the distance formula.

Once you have the lengths of the sides, check if any of the three sides satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In other words, if a² + b² = c², where c is the longest side, then the triangle is a right triangle.

If one of the sides satisfies the Pythagorean theorem, then the triangle is a right triangle.

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Answer:

it B w=5

Step-by-step explanation:

The employee's yearly salary is calculated as $37,440 using the arithmetic operations.  

The employee earns $18 per hour and works 40 hours per week. To calculate the weekly salary, we multiply the hourly wage by the number of hours worked:

Weekly salary = Hourly wage × Hours worked per week

Weekly salary = $18/hour × 40 hours/week = $720

Next, to calculate the yearly salary, we use the multiplication operation the weekly salary by the number of weeks in a year:

Yearly salary = Weekly salary × Weeks in a year

Yearly salary = $720/week × 52 weeks/year = $37,440

Therefore, the employee's yearly salary is $37,440. This calculation assumes a 40-hour work week and 52 weeks in a year. It's important to note that this calculation does not account for overtime pay or any other additional benefits or deductions that may affect the employee's total annual income.

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Amy is correct, -7.1 is between -7 and -8.  

A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers.

Two students were asked to graph a rational number -7.1.

Amy states that The number is between -8 and -7, but Laura states that the point is between -7 and -6.

In order to be in between -6 and -7, the number would have to be a decimal with a whole number of 6.

But -7.1 has a whole number of 7 then it is in between -7 and -8.

Thus, Amy is correct, -7.1 is between -7 and -8.  

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Answer:

b) 256 inches

Step-by-step explanation:

8x5x2 = 80   (top & bottom)

8x5x2 = 80    (front & back)

8x8x2 = 128    (gross area of 2 sides)

4x4x2 =32      (delete this for side cutouts) Guessing the cutoff dimension on

                                                                       left side is 4m inch.

80+80+128-32 = 256 inches

Answer:

answer B

Step-by-step explanation:

i took test

24 = x+6 is the equation that represents the sentence, "Twenty-four is the sum of a number and six "

Two or more expressions with an equal sign is called Equation.

The given sentence is

Twenty-four is the sum of a number and six ,

Let the other number be x.

By the given sentence, we are clear that we have to get 24 when a number and 6 are added.

Twenty-four is the sum of a number and six , we can write as

24=x+6

Therefore 24=x+6 is the equation that represents sentence "Twenty-four is the sum of a number and six ".

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Answer:

18

Step-by-step explanation:

If she catches 6 pop flies in 5 games, that averages to 1.2 pop flies per game.

So if you multiply 1.2 by 15 you get 18 pop flies per game.

Answer:

18

Step-by-step explanation:

She catches 6 pop flies each 5 games she plays. (5x3=15)

6x3=18

Answer:

x-intercept is 5

y-intercept is -3

Step-by-step explanation:

For the x-intercept:

\(3x - 5(0) = 15\)

\(3x = 15\)

\(x = 5\)

For the y-intercept:

\(3(0) - 5y = 15\)

\( - 5y = 15\)

\(y = - 3\)

Answer:

Y intercept= -3

x-intercept = 5

Step-by-step explanation:

So you would want to get your y alone for it to be in slome intercept form (y=mx+b) so you would:

1. Subtract 3x from both sides to get -5y= -3x+15

2. then you would divide each side by -5 to get y= \(\frac{3}{5}\) x -3

And since in slope intercept form, b= the y-intercept, The y-intercept =-3 and to find the x-intercept you would have to solve for y=0 in your new-found equation.

sorry if this was long

The possible integers the satisfied all the requirements done by Samya are 561, 563, 565, 569, 570, 574, 578, 579, 581, 583 and 587.

In this question we must guess the number that satisfies the following features:

(i) The number is not a multiple of four - Then, the least digit is not 0, 2, 4, 6 or 8 and the .

(ii) It is greater than 560 than 590 and it is not a perfect square - The number must not be 24² = 576.

(iii) The sum of three digits is a primer number - The sum of the digits is equal to 2, 3, 5 or 7. The possible options are 561, 562, 563, 565, 566, 567, 569, 570, 571, 573, 574, 575, 577, 578, 579, 581, 582, 583, 585, 586, 587, 589.

Now we check for each case:

5 + 6 + 1 = 1 + 2 = 3      (YES)

5 + 6 + 2 = 1 + 3 = 4     (NO)

5 + 6 + 3 = 1 + 4 = 5     (YES)

5 + 6 + 5 = 1 + 6 = 7     (YES)

5 + 6 + 6 = 1 + 7 = 8     (NO)

5 + 6 + 7 = 1 + 8 = 9     (NO)

5 + 6 + 9 = 2 + 0 = 0   (YES)

5 + 7 + 0 = 1 + 2 = 3    (YES)

5 + 7 + 1 = 1 + 3 = 4     (NO)

5 + 7 + 3 = 1 + 5 = 6    (NO)

5 + 7 + 4 = 1 + 6 = 7    (YES)

5 + 7 + 5 = 1 + 7 = 8    (NO)

5 + 7 + 7 = 1 + 9 = 1     (NO)

5 + 7 + 8 = 2 + 0 = 2   (YES)

5 + 7 + 9 = 2 + 1 = 3    (YES)

5 + 8 + 1 = 1 + 4 = 5     (YES)

5 + 8 + 2 = 1 + 5 = 6    (NO)

5 + 8 + 3 = 1 + 6 = 7     (YES)

5 + 8 + 5 = 1 + 8 = 9     (NO)

5 + 8 + 6 = 1 + 9 = 1      (NO)

5 + 8 + 7 = 2 + 0 = 2    (YES)

5 + 8 + 9 = 2 + 2 = 4    (NO)

The possible integers thought by Samya are 561, 563, 565, 569, 570, 574, 578, 579, 581, 583 and 587.

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Taring a kitchen scale before weighing an ingredient is essential to obtain accurate measurements by removing the weight of the container, streamlining the process, and ensuring precise and reliable results in culinary preparations.

Taring a kitchen scale before weighing an ingredient is necessary to accurately measure the weight of the ingredient without including the weight of the container or vessel in which it is placed. Taring essentially resets the scale to zero, accounting for the weight of the container so that only the weight of the ingredient being added is measured.

By taring the scale, you eliminate the need to manually subtract the weight of the container from the final measurement. This allows for more precise and efficient measurements in recipes or other culinary applications.

Taring is particularly important when working with small or precise quantities of ingredients, where even a slight variation in weight can significantly impact the final outcome of a dish. It ensures that the weight of the container does not contribute to the measurement, providing accurate and reliable results.

Additionally, taring simplifies the weighing process by eliminating the need to calculate or estimate the weight of the container separately. It saves time and reduces the chances of errors in measurements, promoting consistency and precision in cooking and baking.

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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There are a total of 12870 paths that stay outside or on the boundary of the square.

To go from (-4, -4) to (4, 4) with each step increasing either the x-coordinate or the y-coordinate by 1, you can only move diagonally upwards or diagonally to the right. This means that you can only move in one of two directions at each step.

In order to stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step, you need to make sure that you don't move too far in either direction. Since there are 16 steps in total, you need to choose 8 steps to move in the x-direction and the remaining 8 steps to move in the y-direction.

The number of ways to choose 8 steps out of 16 to move in the x-direction is given by the binomial coefficient "16 choose 8" which can be calculated as C(16, 8) = 12870. Similarly, the number of ways to choose 8 steps out of 16 to move in the y-direction is also 12870.

Therefore, there are a total of 12870 paths that stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step.

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Answer:

B and E

Step-by-step explanation:

I think the choice is wrong. choice B maybe 15a+20b...

5(3a+4b) = 15a+20b (B)

(E) : 10a + 5a + 15b + 5b = 15a+20b

fighting! ✌✌

Answer:

e. 5(3a+4b) = 15a+ 20b = 10a+5a+15b+5b

Bob continues his research because even though there is no linear equation relationship between the number of bedrooms and selling price, there could be another type of relationship.

Bob continues his research because even though the correlation value he calculated between the number of bedrooms and the selling price was only 0.05, this does not necessarily mean that there is no relationship of any kind between these two variables. It simply means that there is no linear relationship between the two. There could still be other types of relationships between the two variables, such as an exponential or quadratic relationship. It is possible that further analysis and exploration of the data set would reveal such a relationship and allow Bob to uncover the relationship between the two variables. Additionally, even if the correlation value is low, it does not necessarily mean that there is no relationship between the two variables. It simply means that the relationship is weak. Therefore, Bob should continue his research in order to uncover any potential relationships between the number of bedrooms and selling price.

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Answer:

.........................

Answer:

Step-by-step explanation:

let's figure out first the value of the angles from 0- 360 degrees

Answer:

4²+b² = 5²

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the length of the missing side.

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.  Algebraically, this is represented as

a²+b² = c²

We have the measure of one leg, 4 in.  We also have the measure of the hypotenuse, 5 in.  This gives us

4²+b² = 5²

I hope this helps <3

Answer:

see below

Step-by-step explanation:

Is there an operator (+, -, x, /) missing between 100 and 15?

Assume the expression is

=b4*10015/3

The order of operations says that multiplications and divisions are done as they occur from left to right.

The number in cell b4 will be multiplied by 10015, then that result will be divided by 3.

If the expression is supposed to be  =b4*100*15/3, then the order is

cell b4 is multiplied by 100, then that is multiplied by 15, then THAT is divided by 3.