What is the slope on this graph

The expression 2m(3/2m + 1) + 3(5/3m - 2) is equivalent to 11m/3 - 3.

To simplify the given expression, let's distribute and combine like terms:

2m(3/2m + 1) + 3(5/3m - 2)

First, distribute 2m to the terms inside the parentheses:

= (2m * 3/2m) + (2m * 1) + (3 * 5/3m) - (3 * 2)

Simplifying each term:

= (3) + (2m) + (5m/3) - 6

Next, combine like terms:

= 2m + (5m/3) - 3

To add the terms 2m and (5m/3), we need a common denominator.

The common denominator is 3:

= (6m/3) + (5m/3) - 3

Combining the terms with the common denominator:

= (6m + 5m)/3 - 3

= 11m/3 - 3

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The expression for their distance apart d at the end of t hours is sqrt[tex](t^2 * [(car's speed)^2 + (truck's speed)^2][/tex]), and the exact value for t can be found using t = sqrt([tex]2500 / [(car's speed)^2 + (truck's speed)^2])[/tex].

To find an expression for the distance apart between the car and the truck at the end of t hours, we can use the concept of distance traveled. Since the car is heading east and the truck is heading south, the distances traveled by each vehicle can be represented as follows:

Distance traveled by the car = (car's speed) * (time) = t * (car's speed)

Distance traveled by the truck = (truck's speed) * (time) = t * (truck's speed)

To visualize the distance between the car and the truck, we can form a right triangle with the car's distance traveled as the horizontal leg and the truck's distance traveled as the vertical leg. The distance between them, represented by d, can be calculated using the Pythagorean theorem:

[tex]d^2 = (car's distance traveled)^2 + (truck's distance traveled)^2[/tex]

Substituting the expressions for the distances traveled:

[tex]d^2 = (t * (car's speed))^2 + (t * (truck's speed))^2[/tex]

Simplifying:

[tex]d^2 = t^2 * [(car's speed)^2 + (truck's speed)^2][/tex]

Taking the square root of both sides to find the distance d:

d = sqrt[tex](t^2 * [(car's speed)^2 + (truck's speed)^2])[/tex]

Therefore, the expression for the distance apart between the car and the truck at the end of t hours is:

d = sqrt[tex](t^2 * [(car's speed)^2 + (truck's speed)^2])[/tex]

Now, if at the end of t hours the two vehicles are 50 miles apart, we can set the expression equal to 50 and solve for t:

50 = sqrt([tex]t^2 * [(car's speed)^2 + (truck's speed)^2])[/tex]

Squaring both sides:

[tex]2500 = t^2 * [(car's speed)^2 + (truck's speed)^2][/tex]

Dividing by [(car's speed)^2 + (truck's speed)^2]:

[tex]t^2 = 2500 / [(car's speed)^2 + (truck's speed)^2][/tex]

Taking the square root:

t = sqrt[tex](2500 / [(car's speed)^2 + (truck's speed)^2])[/tex]

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The expression [tex](m+2z)^2+12tz[/tex] simplifies to [tex]m^2 + 4mz + 4z^2 + 12tz[/tex]

The expression [tex](m+2z)^2+12tz[/tex] represents a mathematical equation involving variables m and z, as well as the constant t.

To simplify the expression, we can expand the square and then combine like terms.

Expanding the square, we have:  

[tex](m+2z)^2 = (m+2z)(m+2z) = m^2 + 4mz + 4z^2[/tex]

Substituting this result back into the original expression, we have:

[tex](m+2z)^2 + 12tz = m^2 + 4mz + 4z^2 + 12tz[/tex]

At this point, we have combined all the terms in the expression, and there are no more like terms to be simplified.

Therefore, the final simplified form of the expression [tex](m+2z)^2+12tz is m^2 + 4mz + 4z^2 + 12tz.[/tex]

It is important to note that this simplified expression is still in terms of the original variables m, z, and t, and no further simplification can be done unless specific values are assigned to these variables.

This equation can be further manipulated or solved depending on the context or purpose it serves within a mathematical problem or equation system.

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The true statement about this function is that: the function is negative for all real values of x, where x < -3 and where x > 1.

A function is a mathematical expression which can be used to define and indicate the relationship existing between two or more variables in a data set.

By critically observing the graph which models the given function (see attachment), we can logically deduce that the true statement about this function is that it's negative for all real values of x, where x is less than -3 and where x is greater than 1.

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To ensure that triangle ABC exists, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's assume that the lengths of the sides of triangle ABC are represented by the variables a, b, and c.

According to the options provided, the inequality that represents the values of x that ensure triangle ABC exists is:

C. 1 < x < 5

This is because if we substitute x with values within this range, the resulting lengths of the sides will satisfy the triangle inequality theorem.

To prove that the inequality 1 < x < 5 ensures the existence of triangle ABC, we need to show that for any value of x within this range, the lengths of the sides of triangle ABC satisfy the triangle inequality theorem.

The triangle inequality theorem states that for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, for triangle ABC, we have:

a + b > c

b + c > a

c + a > b

Let's consider the inequality 1 < x < 5. This means that x is greater than 1 and less than 5.

To prove that triangle ABC exists for this range of x, we need to show that the lengths of the sides a, b, and c satisfy the triangle inequality theorem.

Let's consider the lengths of the sides in terms of x:

Side a = 2x + 4

Side b = x + 18

Side c = 6x

We will check if the inequalities hold for these side lengths:

a + b > c:

(2x + 4) + (x + 18) > 6x

3x + 22 > 6x

22 > 3x

b + c > a:

(x + 18) + 6x > 2x + 4

7x + 18 > 2x + 4

5x > -14

c + a > b:

6x + (2x + 4) > x + 18

8x + 4 > x + 18

7x > 14

From these inequalities, we can see that for any value of x within the range 1 < x < 5, the side lengths satisfy the triangle inequality theorem. Therefore, triangle ABC exists when 1 < x < 5.

This completes the proof that the inequality 1 < x < 5 ensures the existence of triangle ABC.

The expression that is NOT a rational expression is 2x/1.

A rational expression is a ratio of two polynomials. Note that a polynomial has a coefficient a power and a variable. In all of the expressions provided, there are polynomials that contain a coefficient like 2, a variable x, and a power that is either 1, 2, 3, or any other number.

The only exception to this is option 3 which has no polynomial as a denominator.

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Answer:

Circumference = Diameter × π

Circumference = 35 cm × 3.14

Circumference = 109.9 cm

The number of revolutions in 1 minute is given as 100, so the distance covered in 1 minute can be calculated as:

Distance in 1 minute = Circumference × Revolutions

Distance in 1 minute = 109.9 cm × 100

Distance in 1 minute = 10990 cm

To find the distance covered in half an hour, we need to multiply the distance in 1 minute by 30, since there are 30 minutes in half an hour:

Distance in half an hour = Distance in 1 minute × 30

Distance in half an hour = 10990 cm × 30

Distance in half an hour = 329700 cm

To express the answer in km, we need to divide the distance in cm by 100000, since there are 100000 cm in a km:

Distance in km = Distance in cm / 100000

Distance in km = 329700 cm / 100000

Distance in km = 3.297 km

Therefore the distance covered by the wheel in half an hour is 3.297 km.

Answer:

The correct answer is C. No. One output value has more than one input value. A relation is a function if and only if each input value corresponds to exactly one output value. In this case, the output value 14 corresponds to two different input values, 8 and 17, so the relation is not a function.

If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Answer:

B. 2 and 4 es la respuesta correcta

The visual proof demonstrates the Pythagorean Theorem by showing how the areas of squares constructed on the sides of a right triangle relate to each other.

In a visual proof of the Pythagorean Theorem, different geometric figures are used to demonstrate the relationship between the squares of the sides of a right triangle. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

To demonstrate this visually, various transformations and rearrangements of geometric figures are performed. The figures labeled 5 through 9 likely represent different squares or triangles that are used in the proof.

In this visual proof, figure 5 could potentially represent a square constructed on one side of the right triangle, figure 6 could represent a square constructed on the other side of the triangle, and figure 7 could represent a square constructed on the hypotenuse. The lengths of these squares or the areas they cover are related to the original triangle in image one.

The relationship between these figures and the Pythagorean Theorem is that the area of the square constructed on the hypotenuse (figure 7) is equal to the sum of the areas of the squares constructed on the other two sides (figures 5 and 6). This visually represents the mathematical equation a^2 + b^2 = c^2, where 'a' and 'b' are the lengths of the legs of the right triangle, and 'c' is the length of the hypotenuse.

Overall, the visual proof demonstrates the Pythagorean Theorem by showing how the areas of squares constructed on the sides of a right triangle relate to each other. By visually observing the transformations and arrangements of these figures, one can understand and verify the Pythagorean Theorem geometrically.

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Without considering any external factors or influences, the median number of fire hydrants in the neighborhoods overseen by Fire District 9 is 15, as determined by the given data.

To find the median number of fire hydrants in the neighborhoods overseen by Fire District 9, we need to arrange the given numbers in ascending order and determine the middle value.

Here are the numbers sorted in ascending order:

8, 12, 15, 17, 21

Since we have an odd number of values, the median will be the middle number, which in this case is 15.

Therefore, the median number of fire hydrants in the neighborhoods overseen by Fire District 9 is 15.

To explain this concept further, the median is a measure of central tendency that represents the middle value in a set of numbers.

It is calculated by arranging the numbers in ascending or descending order and selecting the middle value.

In cases where there is an even number of values, the median is the average of the two middle numbers.

In this scenario, we have five numbers representing the number of fire hydrants in each neighborhood.

By sorting them in ascending order, we can easily identify the middle value as 15, which serves as the median.

This indicates that half of the neighborhoods have fewer than 15 fire hydrants, while the other half have more than 15 fire hydrants.

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Answer:

We can use the information that 24 families watched 16 hours or less to estimate the sample size. Since the 7th percentile is 16 hours, we know that 7% of the sample watched 16 hours or less. Therefore, we can set up a proportion:

(24 / x) = 0.07

where x is the total number of families in the sample. Solving for x, we get:

x = 24 / 0.07 ≈ 343

Rounding to the nearest integer, we can estimate that there are approximately 343 families in the sample.

The value of the constant k in the probability mass function is 1/4, and P(Z < 3) is equal to 37/64.

To find the value of the constant k in the probability mass function (PMF) and calculate P(Z < 3), we can use the properties of a discrete random variable and the given PMF.

First, we know that the sum of probabilities for all possible values of a discrete random variable must equal 1. Therefore, we can write:

∑ P(Z = z) = 1

Now let's substitute the given PMF into the summation:

∑ k[tex](3/4)^z[/tex] = 1

We can simplify this expression by factoring out the constant k:

k ∑ [tex](3/4)^z[/tex] = 1

Next, we need to evaluate the summation term. The summation represents a geometric series with a common ratio of 3/4. The sum of a geometric series is given by:

∑[tex]r^n[/tex] = 1 / (1 - r), where |r| < 1

In this case, the summation term becomes:

∑ [tex](3/4)^z[/tex] = 1 / (1 - 3/4)

Simplifying further:

∑ [tex](3/4)^z[/tex] = 1 / (1/4) = 4

Now, we can substitute this value back into the previous equation:

k * 4 = 1

Solving for k:

k = 1/4

Therefore, the value of the constant k is 1/4.

Now let's calculate P(Z < 3) using the PMF:

P(Z < 3) = P(Z = 0) + P(Z = 1) + P(Z = 2)

Substituting the given PMF with k = 1/4:

P(Z < 3) = (1/4)(3/4)^0 + (1/4)(3/4)^1 + (1/4)(3/4)^2

        = (1/4)(1) + (1/4)(3/4) + (1/4)(9/16)

        = 1/4 + 3/16 + 9/64

        = 16/64 + 12/64 + 9/64

        = 37/64

Therefore, P(Z < 3) is equal to 37/64.

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The half-life of the radioactive goo is approximately 41.82 minutes. The formula for the amount of goo remaining at time t is G(t) = 296 * (1/2)^(t/41.82). After 38 minutes, there will be approximately 66.5 grams of goo remaining.

To find the half-life of the radioactive goo, we can use the formula for exponential decay:

N(t) = N₀ * (1/2)^(t/h)

where N(t) is the amount of goo remaining at time t, N₀ is the initial amount of goo, t is the time elapsed, and h is the half-life of the goo.

In this case, N₀ = 296 grams, N(t) = 9.25 grams, and t = 135 minutes. We can plug these values into the formula and solve for h:

9.25 = 296 * (1/2)^(135/h)

To solve for h, we can take the logarithm of both sides:

log(9.25) = log(296) + (135/h) * log(1/2)

Simplifying further:

(135/h) = (log(9.25) - log(296)) / log(1/2)

(135/h) ≈ -3.2279

h ≈ 135 / (-3.2279)

h ≈ -41.82

Since the half-life cannot be negative, we take the absolute value:

half-life ≈ 41.82 minutes (rounded to one decimal place)

The formula for the amount of goo remaining at time t (in minutes) can be written as:

G(t) = 296 * (1/2)^(t/41.82)

To find the amount of goo remaining after 38 minutes, we can substitute t = 38 into the formula:

G(38) = 296 * (1/2)^(38/41.82)

G(38) ≈ 66.5 grams (rounded to one decimal place)

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Answer:

Since arc ACD is 326 degrees and arc AD is a semicircle (180 degrees), then arc ACB is:

arc ACB = arc ACD - arc AD

arc ACB = 326 - 180

arc ACB = 146 degrees

Since arc ACB is a central angle, it is equal to twice the inscribed angle BCA:

2 * BCA = arc ACB

BCA = arc ACB / 2

BCA = 146 / 2

BCA = 73 degrees

Therefore, BCA is 73 degrees.

The order of the rotational symmetry of the figure is

Rotational symmetry refers to the property of an object or shape that remains unchanged or appears the same after a rotation of a certain angle around a fixed point called the center of rotation.

The degree  or order of rotational symmetry of an object is determined by the number of distinct positions in which it looks the same during a full rotation of 360 degrees (or 2π radians).

In this case the figure will have only one rotational symmetry

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"What is the measure of ZMOP, given that figure MNOP is a rectangle" is D. 55°.

In a rectangle, all interior angles are 90°.

Therefore, NM is perpendicular to OP.Since NM = 55% of OP, we can construct a right triangle where ON is the hypotenuse and NM is one leg.

Since this is a 45°-45°-90° triangle, the measure of angle ZMO is 45°.

Thus, the measure of angle ZMOP can be found by subtracting 90° (the measure of angle NMO) from 45°.

This gives us 55° as the measure of angle ZMOP.Therefore, the answer is D. 55°.

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With speed of 7.5 mi/hr and 12.5 mi/hr fast he would be going and returning respectively.

To solve this problem, let's denote the speed of Jay's motorcycle on the outbound trip as "x" miles per hour. Since he was able to average 5 mi/hr faster on the return trip, his speed on the return trip would be "x + 5" miles per hour.

We know that the total time for the round trip is 5 hours. The time taken for the outbound trip is the distance divided by the speed, which is 100 / x. The time taken for the return trip is the distance divided by the speed, which is 100 / (x + 5).

According to the problem, the total time for the round trip is 5 hours. Therefore, we can set up the equation:

100 / x + 100 / (x + 5) = 5

To solve this equation, we can multiply through by x(x + 5) to eliminate the denominators:

100(x + 5) + 100x = 5x(x + 5)

Expanding and simplifying the equation, we get:

200x + 500 = 5x^2 + 25x

Bringing all terms to one side and simplifying further, we obtain a quadratic equation:

5x^2 + 25x - 200x - 500 = 0

5x^2 - 175x - 500 = 0

Factoring the equation, we find:

(x - 7.5)(x + 12.5) = 0

So, x = 7.5 or x = -12.5. Since speed cannot be negative, the only valid solution is x = 7.5.

Therefore, Jay traveled at a speed of 7.5 mi/hr on the outbound trip and 7.5 + 5 = 12.5 mi/hr on the return trip.

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Answer:

when y=0

2x=12

we divide by 2 on both sides

x= 6

Area: 11.18 sq units

Perimeter: 26.18 units

To find the area and perimeter of the triangle with vertices A(-6, -1), B(-3, 3), and C(5, -3), follow these steps:

1. Find the lengths of the sides:

  - Side AB: Calculate the distance between points A and B using the distance formula: AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

    Substitute the coordinates: AB = √[(-3 - (-6))² + (3 - (-1))²] = √[3² + 4²] = √(9 + 16) = √25 = 5 units

  - Side BC: Calculate the distance between points B and C using the distance formula: BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

    Substitute the coordinates: BC = √[(5 - (-3))² + (-3 - 3)²] = √[8² + (-6)²] = √(64 + 36) = √100 = 10 units

  - Side CA: Calculate the distance between points C and A using the distance formula: CA = √[(x₂ - x₁)² + (y₂ - y₁)²]

    Substitute the coordinates: CA = √[(-6 - 5)² + (-1 - (-3))²] = √[(-11)² + 2²] = √(121 + 4) = √125 = 11.18 units

2. Calculate the perimeter:

  Perimeter = AB + BC + CA = 5 + 10 + 11.18 = 26.18 units

3. Find the area using the Shoelace Formula:

  Area = 0.5 * |(x₁y₂ + x₂y₃ + x₃y₁) - (x₂y₁ + x₃y₂ + x₁y₃)|

  Substitute the coordinates: Area = 0.5 * |(-6 * 3 + (-3) * (-3) + 5 * (-1)) - (-3 * (-1) + 5 * 3 + (-6) * (-3))|

  Simplify: Area = 0.5 * |(-18 + 9 - 5) - (3 + 15 + 18)|

           = 0.5 * |-14 - 36|

           = 0.5 * |-50|

           = 0.5 * 50

           = 25 sq units

Therefore, the area of the triangle is 25 square units and the perimeter is 26.18 units.

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Answer: p=48.8372093%

Step-by-step explanation:

Step-by-step explanation:

100% = 43

1% = 100%/100 = 43/100 = 0.43

21 is that many % as times 1% fits into 21 :

p = 21 / 0.43 = 48.8372093... %

The volume of the larger boat is 3840 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

Therefore, let's find the volume of the larger boat as follows:

Hence,

(5 / 20)³ = 60 / v

5³ / 20³ = 60 / v

125 / 8000 = 60 / v

cross multiply

125v = 480000

divide both sides by 125

v = 480000 / 125

v = 3840

Therefore,

volume of the larger boat = 3840 cm³

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Answer:

To find the square root of 0.327 up to 2 decimal places, you can use a calculator or mathematical software. The square root of 0.327 is approximately 0.57.

Examining the figure, quadrilateral PQUV is a parallelogram

A parallelogram is a quadrilateral, which is a polygon with four sides. It is a special type of quadrilateral characterized by several distinct properties.

In this case, we assumed that

In addition, the sides as mentioned are parallel to each other

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Answer:

Step-by-step explanation:

50$

At the end of 1 year, the amount in the account is $10,640, and at the end of 2 years, the amount is $11,910.40.

To calculate the amount in the account at the end of each year, we can use the formula for compound interest:

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

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, Boris placed $9500 in an account that pays 12% interest compounded annually.

(a) To find the amount in the account at the end of 1 year, we have:

P = $9500

r = 12% = 0.12

n = 1 (compounded annually)

t = 1 year

Using the formula, we have:

A = 9500(1 + 0.12/1)^(1*1)

A = 9500(1 + 0.12)^1

A = 9500(1.12)

A = $10640

Therefore, the amount in the account at the end of 1 year is $10,640.

(b) To find the amount in the account at the end of 2 years, we have:

P = $9500

r = 12% = 0.12

n = 1 (compounded annually)

t = 2 years

Using the formula, we have:

A = 9500(1 + 0.12/1)^(1*2)

A = 9500(1 + 0.12)^2

A = 9500(1.12)^2

A = $11910.40

Therefore, the amount in the account at the end of 2 years is $11,910.40.

In summary, at the end of 1 year, the amount in the account is $10,640, and at the end of 2 years, the amount is $11,910.40.

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The system of equations given in option 4, y = 2x and 3x + 2y = 21, will have no solution.

2x + y = 9

2x + y = 5

The graph is attached

A system of linear equations will have no solution if the lines represented by the equations are parallel, meaning they have the same slope but different y-intercepts.

Looking at the given options:

y = 12 – 3x

y = 2x – 3

y = x – 1

-5x + y = -5

2x + y = 9

2x + y = 5

y = 2x

3x + 2y = 21

Option 3, 2x + y = 9 and 2x + y = 5, represents parallel lines.

The slopes of the lines are the same (both equations have a coefficient of -2 for x and 1 for y), but the y-intercepts are different

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Step-by-step explanation:

8 x x 2      first x can be  0 - 9   <==== 10 choices

                 second x can also be 0 -9    <====10 choices for each of the FIRST 10 choices

10 x 10 = 100 possible plates.

8 00 2

8012

8022

.

.

.

8 99 2

Answer:

a) see below

b) 100

Step-by-step explanation:

a)

8 _ _ 2

8002

8012

8022

8032

8042

8052

8062

8072

8082

8092

8002

8112

8122

8132

8142

8152

8162

8172

8182

8192

8202

8212

8222

8232

8242

8252

8262

8272

8282

8292

8302

8312

8322

8332

8342

8352

8362

8372

8382

8392

8402

8412

8422

8432

8442

8452

8462

8472

8482

8492

8502

8512

8522

8532

8542

8552

8562

8572

8582

8592

8602

8612

8622

8632

8642

8652

8662

8672

8682

8692

8702

8712

8722

8732

8742

8752

8762

8772

8782

8792

8802

8812

8822

8832

8842

8852

8862

8872

8882

8892

8902

8912

8922

8932

8942

8952

8962

8972

8982

8992

b) There are 100 different license plates.