A contestant draws a sequence of three cards. one question per card, and tries to answer the three questions. There are five cards with history questions, six cards with literature questions, and seven cards with science questions. Find the probability of each or the following. Round vour answers to four decimal places..
(a) the questions are mistory, hiterature, and science, in that order
(bi all three are literature questions
(c) the first is science, the second is history, and the third is science

The missing polynomial is 40 - 4x - 12x²

The missing polynomial is solved by comparing the polynomials as done below

? - (20 - 4x - 5x²) = 20 - 7x²

? =  20 - 7x² + (20 - 4x - 5x²)

comparing the terms

constant terms: 20 + 20 = 40

x terms : -4x

x² terms : -7x² - 5x² = -12x²

This can be combined as 40 - 4x - 12x²

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You could shade in the faces of the prism or add labels to identify different parts of the drawing.

What is Pentagonal ?

"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.

To draw a pentagonal prism, you'll need to follow these steps:

Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.

Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.

Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.

Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.

Therefore,  You could shade in the faces of the prism or add labels to identify different parts of the drawing.

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Answer: Choice A

Step-by-step explanation:

M= slope

B= y-intercept

1) The cost of both bands would be equal for 100 students. 2) the fixed cost for the caterer is $150 and the rate per student served is $3. 3) Ticket Price = $4.75 4) you can afford a maximum of 3 bouquets of roses.

Let x be the total number of students in Part 1A.

Band A costs $500.

Band B costs $350 plus $1.50 times.

Part B: By graphing the equations, we can determine the location where the price of the two bands is equal.

$500 = $350 + $1.50x \s$150 = $1.50x \sx = 100

As a result, the price for both bands for 100 students would be the same.

Part 2: Let's solve for the fixed cost and rate per student served using the information provided:

50f + 50r = $450

150f + 150r = $1050

When we deduct the first equation from the second, we obtain:

100f + 100r = $600

F plus R equals $6 when we divide by 100.

The result of replacing the value of f in the first equation is:

50($6 - r) + 50r = $450

$300 - 50r + 50r = $450 \sr = $3

As a result, the caterer's fixed fee is $150, and the cost each student served is $3.

Part 3: For 100 pupils, Band A would cost $500, and Band B would cost $350 plus $1.50 (100) for a total of $500.

Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:

Total Price = Band Fee + Caterer Fee

Expense in total is $500 plus ($150 + $3(100)).

Final price: $950

Total Cost / Number of Students x Ticket Price equals $9.50

Band A would cost $500 for 200 pupils, and Band B would cost $350 + $1.50 (200) = $650.

Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:

Total Price = Band Fee + Caterer Fee

Expense in total is $500 plus ($150 + $3(200)).

Final price: $950

Total Cost / Number of Students x Ticket Price is $4.75

Let d be the total number of daisy bouquets and r be the total number of rose bouquets in part 4A.

[tex]25d + 35r \leq $500[/tex]

B. You would have spent $375 if you purchased 15 bouquets of daisies at a cost of 15 ($25).

When we deduct this from the overall budget, we get:

$500 - $375 = $125

The result of dividing by the price of one bunch of roses is: $125/$35 3.57.

Thus, you can buy no more than three rose bouquets.

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The 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.

Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.

The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.

To determine which is a better buy, we need to compare the cost per fl. oz. of detergent for both options.

For the first option, the cost is $3.99 for 25 fl. oz., so the cost per fl. oz. is:

Cost per fl. oz. = $3.99 / 25 fl. oz. ≈ $0.16/fl. oz.

For the second option, the cost is $6.99 for 90 fl. oz., so the cost per fl. oz. is:

Cost per fl. oz. = $6.99 / 90 fl. oz. ≈ $0.08/fl. oz.

Since the cost per fl. oz. is lower for the second option, it is a better buy. Therefore, the 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.

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The complete question is:

It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?

Answer:

the answer is d

Step-by-step explanation:

before the increase the range is three with the lowest number being four and the highest 7

where as after the increase the lowest value is 5 and the highest nine giving us a range of four

four minis three is one therefore the range increases by one mile

Answer: D: The range will increase by 1 mile.

Step-by-step explanation:

The current range is solved by doing the highest number minus the lowest number, so 7-4. The current range would therefore be 3.

The miles on Monday and Tuesday have been increased by 1 mile, from 4 miles to 5 miles.

The miles on Friday, Saturday and Sunday have been increased by 2 miles, from 7 miles to 9 miles.

You subtract the new values: 9 miles - 5 miles = 4 miles

And subtract your new values from your old range: 4 miles - 3 miles = 1 mile

The range would therefore increase by 1 mile.

The value of x for the given triangle is 14 according to the question.

In triangle ABC, right-angled at B, let BM be the altitude from B to AC. Let CM be x.

Using the Pythagorean theorem in triangle ABC of the question:

[tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex]AC^{2}[/tex]

Substituting AB = BM and BC = CM, we get:

[tex]BM^{2}[/tex] + [tex]CM^{2}[/tex] = [tex]AC^{2}[/tex]

Substituting the given values, we get:

[tex](2\sqrt{15}) ^{2}[/tex] +[tex]x^{2}[/tex] =[tex]16^{2}[/tex]

60 + [tex]x^{2}[/tex] = 256

[tex]x^{2}[/tex] = 196

x = 14

A line or segment that forms a straight angle or 90-degree angle with the provided line is said to be perpendicular to it. It is also known as a "orthogonal" or "normal" line.

We must first choose a point on the supplied line in order to determine the perpendicular to it. Then, a line or segment that traverses that point and is perpendicular to the specified line can be created.

The fact that the slopes of perpendicular lines are the negative reciprocals of one another is used to accomplish this. The slope of any line perpendicular to the provided line will be -1/m if the slope of the given line is m.

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-1, -0.10, 0.15, 0.25

So, the answer is the way we do it

-1 , -0.1(or 0.10) , 0.15 , and 0.25

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The confidence interval does not justify the councilman's statement because 45 minutes is greater than the upper bound of the confidence interval.

What is a confidence interval?

A confidence interval is a statistical range that is used to estimate an unknown population parameter based on a sample from that population. It is a measure of the degree of uncertainty or precision associated with the estimated value of the parameter.

The confidence interval of 34.42 ± 8.14 minutes means that we are 95% confident that the true population mean commute time falls between 26.28 minutes (34.42 - 8.14) and 42.56 minutes (34.42 + 8.14). Since the councilman's statement of 45 minutes falls outside of this range, we cannot say that it is justified by the confidence interval.

Additionally, the fact that the mean commute time from the sample of 25 adults was 34.42 minutes does not necessarily mean that the true population mean commute time is also 34.42 minutes. It only provides an estimate, and the confidence interval takes into account the variability of the sample mean.

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Answer:

A. No, because 45 minutes is greater than the upper bound of the confidence interval.

Step-by-step explanation:

Answer:

Since the legs of figure 2 are twice as long as those of figure 1, the scale factor to produce figure 1 from figure 2 would be 1/2. This means that every length in figure 1 is half the length of the corresponding length in figure 2.

Answer:

Option A. 1/2

Step-by-step explanation:

100 on the test!

Answer:

y intercept = +4

slope = +2

domain = (-2,0)

range = (4,0)

Graph is increasing

x intercept = -2

Step-by-step explanation:

Line hits y axis at point 4

Slope is calculated by rise over run (2/1)

Domain is x,y listed

Range is y,x listed

Line is going up

Line hits x axis at -2

Step-by-step explanation:

2 hrs = 7200 seconds

       3 min 59 = 239 s    

    total seconds = 7439 s

42.195 km = 42159 m

42159 m / 7439s = 5.7 m/s

The two skaters might collide at the points (1, 12) and (7, 0).

What are the collide points?

To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.

Setting the two expressions for y equal to each other, we get:

-2x + 14 = -2x² + 14x

Simplifying this equation, we get:

2x² - 16x + 14 = 0

Dividing both sides by 2, we get:

x² - 8x + 7 = 0

This equation can be factored as:

(x - 1)(x - 7) = 0

Therefore, the possible values of x where the skaters might collide are x=1 and x=7.

To find the corresponding values of y, we can substitute each value of x into one of the original equations.

For x=1, we get:

y = -2(1) + 14 = 12

Therefore, one possible point of collision is (1, 12).

For x=7, we get:

y = -2(7)² + 14(7) = 0

Therefore, another possible point of collision is (7, 0).

Therefore, To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.

Setting the two expressions for y equal to each other, we get:

-2x + 14 = -2x² + 14x

Simplifying this equation, we get:

2x² - 16x + 14 = 0

Dividing both sides by 2, we get:

x² - 8x + 7 = 0

This equation can be factored as:

(x - 1)(x - 7) = 0

Therefore, the possible values of x where the skaters might collide are x=1 and x=7.

To find the corresponding values of y, we can substitute each value of x into one of the original equations.

For x=1, we get:

y = -2(1) + 14 = 12

Therefore, one possible point of collision is (1, 12).

For x=7, we get:

y = -2(7)² + 14(7) = 0

Therefore, another possible point of collision is (7, 0).

Therefore, the two skaters might collide at the points (1, 12) and (7, 0).

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By using the P-value method, we conclude that, fewer than half of Americans prefer to watch the news rather than read or listen to it.

What is p-value?

In statistics, the p-value is a probability value that measures the evidence against a null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the actual test statistic, assuming that the null hypothesis is true.

In this problem, we want to test the claim that fewer than half of Americans prefer to watch the news, based on a poll of 1075 Americans where 46.8% of the respondents said they prefer to watch the news.

Let p be the true proportion of Americans who prefer to watch the news. Then the null hypothesis is:

H0: p ≥ 0.5 (more than or equal to half of Americans prefer to watch the news)

The alternative hypothesis is:

Ha: p < 0.5 (fewer than half of Americans prefer to watch the news)

We will use the normal distribution as an approximation to the binomial distribution, since n = 1075 is large and the success-failure condition is satisfied. The expected number of respondents who prefer to watch the news is:

E = np = 1075 × 0.468 = 503.1

The standard deviation of the sampling distribution of p is:

σ = sqrt[(p(1-p))/n] = sqrt[(0.5×0.5)/1075] ≈ 0.015

We can now calculate the z-score for the sample proportion:

z = (x - E) / σ = (1075 × 0.468 - 503.1) / 0.015 ≈ -4.28

where x is the observed number of respondents who prefer to watch the news, which is 1075 × 0.468 ≈ 503.

The P-value for this test is the probability of getting a z-score less than or equal to -4.28 under the standard normal distribution. Using a standard normal table or calculator, we find that this probability is very close to 0. Therefore, the P-value is less than 0.10, the chosen significance level.

Since the P-value is less than the significance level, we reject the null hypothesis. We have sufficient evidence to conclude that fewer than half of Americans prefer to watch the news rather than read or listen to it.

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Step-by-step explanation:

10b = 62 - 12

10b = 50

b = 50/10

b = 5

Answer:

5

Step-by-step explanation:

When trying to find the value of an unknown variable, it is important to take into factors on how to reverse an effect being done to the variable, which is how we can isolate b and figure out the value.

- Addition reverses subtraction

- Multiplication reverses division

We have a simple equation, [tex]10b+12=62[/tex] , and we need to work around the variable b in order to isolate it. By doing this, we are able to find the true value of b.

We can subtract 12 on each side to get the term away from the constant.

[tex]10b+12=62[/tex]

     -   12   -12

[tex]10b=50[/tex]

Then, to isolate the variable from the coefficient, which is 10, we can divide it to negate the multiplication factor on the term.

[tex]\frac{10b}{10} = \frac{50}{10}[/tex]

b=5

Therefore, the variable b=5.

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Answer:2000

Step-by-step explanation:

Dana has 1500 yellow beads when Dana had an equal number of red beads and yellow beads.

Dana had an equal number of red beads and yellow beads, so let's say she had x red beads and x yellow beads.

After using 500 red beads to make necklaces, she was left with x - 500 red beads.

Since she now had 3 times as many yellow beads as red beads, she had a total of 3 * (x - 500) = 3x - 1500 yellow beads.

We know that the total number of yellow beads is x, so we can set the two expressions equal to each other:

x = 3x - 1500

Solving for x, we get:

2x = 1500

x = 750

Therefore, Dana had x = 750 yellow beads.

Since she now has 3 times as many yellow beads as red beads, she has a total of 3 * 750 = 1500 yellow beads.

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The answer of 2nd question Quadrilateral JUMP in a circle is  = Supplementary

What do you mean by Supplementary angle?

Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180 degrees.

Supplementary angles are important in geometry and trigonometry, and they can be used to solve various problems involving angles and their measures. For example, if you know that two angles are supplementary and you know the measure of one of them, you can find the measure of the other by subtracting the measure of the known angle from 180 degrees.

According to question

Quadrilateral JUMP in a circle so opposite angle J and M is supplementary

∴ The sum of opposite angle of a circle Quadrilateral  is supplementary

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Therefore, f(x) = g(x) when function x is approximately 0.235 or 33.765.

A quadratic equation is a polynomial equation of the second degree, which means that the highest power of the variable in the equation is 2. A general quadratic equation can be written in the form:

[tex]ax^2 + bx + c = 0[/tex]

Where 'a', 'b', and 'c' are constants, and 'x' is the variable. The value of 'x' that satisfies the equation is called the root or solution of the equation.

To find where f(x) = g(x), we need to solve the equation:

[tex]\sqrt40x = \sqrt{x} + 3[/tex]

Squaring both sides, we get:

[tex]40x = (x + 3)^2[/tex]

Expanding the right-hand side, we get:

40x = x² + 6x + 9

Bringing all terms to one side, we get:

[tex]x^2- 34x - 9 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

[tex]x = (-b± \sqrt{(b^2 - 4ac))}/2a[/tex]

where a = 1, b = -34, and c = -9.

Plugging in these values, we get:

x = (34 ± √ (34² + 419)) / 2

x = (34 ± √1165) / 2

x ≈ 0.235 or x ≈ 33.765

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The total space that the tiles will cover is 7x, where x is the number of tiles, and each tile has an area of 7 square inches. the maximum number of tiles that Lakita can use is  [tex]20[/tex] .

Since each tile has an area of 7 square inches, the total area that the tiles will cover is 7x, where x is the number of tiles.

Lakita wants to find the maximum number of tiles she can use, so she needs to find the largest integer value of x that satisfies the inequality 7x < y, where y is the total area of the table-top.

To find the value of y, we need to find the area of the rectangle. The rectangle is 10 inches wide and 14 inches long, so its area is:

A = length × width    [tex]= 10 \times 14 = 140[/tex] square inches

Therefore,  [tex], y = 140[/tex] square inches.

To find the maximum number of tiles, we can divide the total area of the table-top by the area of each tile:

[tex]x = y/7 = 140/7 = 20[/tex]

Therefore, the maximum number of tiles that Lakita can use is  [tex]20[/tex] .

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The required value of x is approximately [tex]x = 257.25[/tex] cm.

The volume of cuboid A can be found by multiplying its length, width, and height:

[tex]$V_A = 6\text{ cm} \times 2\text{ cm} \times 5\text{ cm} = 60\text{ cm}^3$[/tex]

To find the volume of cuboid C, we can use the given information that the volume of A multiplied by 343/8 is equal to the volume of C:

[tex]$V_C = V_A \times \frac{343}{8} = 60\text{ cm}^3 \times \frac{343}{8} =2572.5[/tex]

Now, we can use the formula for the volume of a cuboid to find the length of C:

[tex]$V_C = \text{length} \times \text{width} \times \text{height}$[/tex]

[tex]$2572.5}\text{ cm}^3 = x\text{ cm} \times 2\text{ cm} \times 5\text{ cm}$[/tex]

[tex]{2572.5}\text{ cm}^3 = 10x\text{ cm}^3$[/tex]

[tex]x = 257.25[/tex]

Therefore, the value of x is approximately [tex]x = 257.25[/tex] cm.

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The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.

Circumference is the distance around the edge of a closed curve or a circle. It is the length of the boundary of a circular object or shape. In other words, it is the total length of the circular shape.

We can use trigonometry to determine the rotation's angle. The rider's height above the ground is equal to the ferris wheel's radius plus the distance travelled around its circle. Let's call the angle of rotation we're trying to find θ.

The distance traveled along the circumference of the wheel can be calculated as follows:

distance = θ/360 * 2πr

where r is the radius of the wheel. Substituting the given values, we get:

95 = 100 + θ/360 * 2π(100)

Simplifying the equation:

θ/360 = (95-100)/(2π(100))

θ/360 = -0.007957747

θ = -2.8661 degrees or 357.1339 degrees

So there are two possible answers: The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.

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Answer:

they bought 8 candy bars and 8 + 4 = 12 packs of gum.

Step-by-step explanation:

Let's use algebra to solve this problem:

Let x be the number of candy bars they bought.

Then, the number of packs of gum they bought is x + 4.

The total cost of the candy bars is 60x cents.

The total cost of the packs of gum is 85(x + 4) cents.

We know that they spent $15.00, which is 1500 cents, so we can write an equation:

60x + 85(x + 4) = 1500

Simplifying the equation, we get:

145x + 340 = 1500

145x = 1160

x = 8

Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum

Answer: 22

Step-by-step explanation:

The number of the gum is 13 and the number of the candy will be 22.

What is linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.

They spent $26.38 total and bought 35 items total.

Let x be the number of the gum and y be the number of the candy.

Then the equation will be

x + y = 35 ...1

0.54x + 0.88y = 26.38 ...2

By solving the equations 1 and 2, then we have

x = 13 and y = 22

Then the number of the gum is 13 and the number of the candy will be 22.

Answer:

Depreciation at a constant percent is exponential decay:V(t) = V0·(1-rate)tV(t) is the value at year t (we want t = 14 years)V0 is the starting value = $20,700rate is the depreciation rate expressed as a decimal = 0.05t = years = 14V(14) = $20700·(1 - 0.05)14Use your calculator to get the answer.  Round your answer to the nearest cent,  The units are $$.

Step-by-step explanation:

A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice. So, B is the right answer.

The American Society of Home Inspectors is known as ASHI. It is a non-profit company with its main office in Des Plaines, Illinois, and it was established in 1976.

ASHI's major objective is to advance professionalism in the home inspection industry by establishing and upholding high standards for its members. Home inspectors can get education, training, and certification from ASHI. Members are also obliged to abide by the organisation's Code of Ethics and Standards of Practice. The minimal requirements for a house inspection are outlined in the Standards of Practice, along with the inspector's obligations to the client.

A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice.

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Answer: To find the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal, we can divide the cost of an 8-ounce box by the cost of a 16-ounce box:

8 oz: $12

16 oz: $20

The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is:

12/20 = 3/5

So the answer is 3:5.

Step-by-step explanation:

There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.

What is Standard deviation ?

Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.

To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.

We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.

We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:

z = (x - μ) ÷  σ

where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.

For x = 40 kilograms:

z = (40 - 50) ÷  5 = -2

For x = 55 kilograms:

z = (55 - 50) ÷ 5 = 1

Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.

Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.

Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:

0.8186 * 1000 = 818.6 children

Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.

Therefore,  there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.

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Answer:

First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b