In Duck Creek, a bicycle license plate consists of one letter followed by one digit; for example, $Q7$ or $J1$. How many different license plates are possible

Answer:

it doesn't have any solutions bc the lines are parallel and don't share any points in common. hope this helps!

Answer: The domain is all values of x that make the expression defined. The range is the set of all valid y values

Step-by-step explanation:

Therefore , the solution of the given problem of function comes out to be Domain: (-∞, ∞) and   Range: (0,∞).

Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.

Here,

Given :  f(x)=[tex]2^{x}[/tex]+1

If a value has not been added, an exponential function's curve normally approaches a horizontal asymptote at y=0 or the x-axis. The curve changes if it has.

The asymptote is unaffected by this function's addition on the exponent because it does not apply to the entire function.

The values of its y-axis remain between 0 and. This is the set of y values, or the range.

However, depending on the leading coefficient, the range of exponentials can vary. If the value is negative, the graph turns inside-out and the range reaches -. It's also lacking in this.

The exponent's addition to 1 moves the function to the left without changing the range.

The x values in exponential functions are often unaffected and all are taken into account in the function. The domain stays the same even while it changes. Its range is (0,∞)

 Range: (0,∞)

Therefore , the solution of the given problem of function comes out to be

Domain: (-∞, ∞) and   Range: (0,∞).

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Bonnie will complete four laps before being passed by Annie because she runs an additional quarter lap for every lap she completes. This indicates that Annie and Bonnie are on an equal footing, and Annie must complete an additional lap to pass Bonnie. Annie will have completed five laps after that.

We can use the unitary method to calculate 100% of an amount. For instance, if 10% of the marbles in a pot are 35, then the total number of marbles in the pot will be 35 x 10%, or 350.

The unitary method can be used to calculate how many kilometres a car will travel on one litre of gas if it travels 44 km on two litres of fuel. In other words, the unitary method is the process by which we determine the value of a single unit and then use that information to determine the values of multiple units.

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1.908 miles Abraham run on Tuesday than on Monday.

Step 1

Monday he run 3.18 miles

Tuesday he run 1.6 times than Monday

how many more miles miles he run?

Step 2

3.18*(1.6-1)

1.6-1 is 1.6 times further than he did on Monday

Step3

3.18*(1.6-1)

=3.18*0.6

=1.908

he run on Tuesday than on Monday is 1.908

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Abraham ran 1.908 more miles on Tuesday than it was on Monday, based on the information provided.

The fundamental ideas in number theory, measurement, and computation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number") (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).

First, he ran 3.18 miles on Monday.

He ran 1.6 times more on Tuesday than on Monday.

how many kilometers did he run in total?

Step 2\s3.18*(1.6-1) (1.6-1)

One and a half times closer than he was on Monday at 1.6-1

Step3\s3.18*(1.6-1)\s=3.18*0.6\s=1.908

He ran 2.908 more on Tuesday than it does on Monday.

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Value of c is determined 61 unit.

What is right-angled triangle?

Triangle that has one angle 90 degree is called right-angled. In case of a right triangle the square of the largest side length is equal of the sum of the square of the other two side length.

SA triangle has three side length 11-unit, 60 unit and 61 unit respectively.

The triangle is verified as a right-angled triangle by Pythagorean theorem.

And as the properties of a Pythagorean theorem the sum of the square of two side length is equal to the square of the largest side length.

if we say, one side length, a = 11 unit

             second side length, b = 60 unit

    the largest side length, c

now we will check,  

√(11²+60²) = c² =√3721 = 61

the value of c = 61 unit.

hence, the SA is right-angled triangle.

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Inverse functions are indicated by the symbol [tex]f^{-1}[/tex] and are functions whose inverse is the function itself (x).

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The inverse function, which also returns the beginning value, returns the result of a function.

The relationship that results from swapping out an independent variable for a variable that depends on a given equation, and which may or may not be a function. Consider the inverse relationship between the functions f and g: f(g(x)) = g(f(x)) = x.

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Answer:

➜ ∠4 = ∠2

➜ ∠2 + ∠3 = 180°

➜ ∠1 = ∠3

Step-by-step explanation:

     We can use vertical angles to prove the first statement true, ∠4 = ∠2.

     Next, ∠2 and ∠3 are supplementary angles, so if you add them together you will get 180 degrees. This statement is also true.

       Then, ∠1 and ∠2 are not complimentary angles. This statement is false.

       Lastly, we can use the same reasoning of the first one to prove this statement true as well. They are vertical angles, ∠1 = ∠3.

The simplified form of expression is, 12x⁶.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ √144 x³⁶

Now, By the property of square root;

⇒ √ ab = √a × √b

We get;

⇒ √144 x³⁶ = √144 × √x³⁶

And, By using the exponent property, we get;

⇒ xᵃᵇ = xᵃ × xᵇ

So, We get;

⇒ √144 x³⁶ = √144 × √x³⁶

                  = √144 × √x⁶ × √x⁶

                  = √12×12 × √x⁶ × √x⁶

                  = 12 × x⁶

                  = 12x⁶

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For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .

The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .

The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;

On differentiating both sides of the curve with respect to "x"  ,

we get ;

the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;

Now for the  x- intercepts , the value [tex]y = 0 ,[/tex]

On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,

we get ;

[tex]x^{2} +x(0)+0^{2} =27[/tex]

On simplifying further ,

we get ;

[tex]x=\pm 3\sqrt{3}[/tex] ;

So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;

to find the slopes , we substitute the values in the slope equation .

On substituting the values in the slope equation ,

we get ;

[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex]  and

[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].

we see that the slope at both the intercepts is same ,

Therefore , the lines tangents of the curve at the x intercepts are parallel .

The given question is incomplete , the complete question is

Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .

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By using the area of circle formula, the solution of the given problem of circle comes out to be 6 + π cm

Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.

Here,

A 9 Pi square centimeter circle's sector has a 60 degree center angle. The sector's exterior border is

Circle area is equal to. πR² = 9π

Circumference =2πR

=> 2π*3 = 6π cm

Arc length equals (60/360)*6 to cm

Arc's perimeter is calculated as follows: Radius + Length of Arc + Radius = π +3 + 3 = 6 +  π cm

Therefore , the solution of the given problem of circle comes out to be

6 + π cm.

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By using the area of circle formula and circumference of a circle formula, the solution of the given problem of circle comes out to be 12π cm

Every location in the plane of a circle is equally separated from the center and is a closed, as double object. Each line tracing the circle contributes to the formation of a line of reflection symmetry. Additionally, each angle has axis of symmetry around the center.

Here,

sector area of circle = 9π

arc measure = 90°

Area of sector  = (arc/360°)*πr²

⇒ 9π = (90°/360°)πr²

⇒ 9π = (1/4)πr²

⇒ 4*9π = πr²

⇒ 36 = r²

⇒ 6² = r²

r = 6

and Circumference of circle = 2πr

=> 2π*6 = 12π cm

Therefore , the solution of the given problem of circle comes out to be

12π cm.

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Answer:

894 mi²

Step-by-step explanation:

the area of parallelogram= base x height= 24mi x 37.25mi = 894 mi²

When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. one-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions

given

a) f(g(1)  

g(1) = 5  and f(g(1)) = 0

b) g(f (2))

f(2) = -3

g(f (2)) = -2

so When f(x) = x - 5 and g(x) = 2x + 3, the value of f(g(1)) is 0 and the value of g(f (2)) is -2.

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The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.

avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.

a)

Hence average value of f(x) on 0≤x≤2

= 1/2 ∫f(x)  with 0 and 2 as intervals

Since integration is basically the area under the curve we get

avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]

Since from 0 to 1, the figure is a triangle and beyond that a straight line we get

1/2[1/2 X 1 X 1 + 0]

= 1/4 sq units

b)

Similarly, the average value of g(x) on 0 ≤ x ≤ 2

1/2[area from 0 to 1 + area from 1 to 2]

= 1/2[0 + 1/2]

= 1/4 sq units

c) here we need to find the average of f(x) . g(x)

Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1

Hence we see that on multiplying the functions, the resultant has to be a 0 function.

Hence its average value will be 0.

d)

Average(f) . Average(g) = 1/4 X 1/4

= 1/16

Average of (f.g) = 0

Hence the statement is false

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Complete Question

The figure attached to the left is a graph of f(x), and below to the right is g(x).

The figure below to the left is a graph of f(x), a

(a) What is the average value of f(x) on 0≤x≤2? avg value = __________

(b) What is the average value of g(x) on 0≤x≤2? avg value = __________

(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________

(d) Is the following statement true?

Average(f) . Average(g)=Average(f.g)

A. Yes

B. No

Answer:

85

Step-by-step explanation:

So you know that there are 26 letters in the alphabet and 3 letters in the license plate, so that would be 26 multiplied by 3 to cover all of those letters.  The first letter can't be I or O, so you subtract 2 from the product.  26 times 3 is 78, minus 2 is 76. There are 10 single digits, but only one in the plate and it can't be 0.  This leaves 9 digits so you add that to the total number.  

76 + 9 = 85

I hope this helps!  :)

Sorry for my previous answer, I misread the question, but this is the correct answer now, hope this helped!

Answer:

129600 license plates

Step-by-step explanation:

This time, we will use an option of solving where we take the number of possibilities for one letter, then multiply it by the next, then multiply it by the next, then multiply it by the number of possibilities for the number. We would have 24 letters to start (not including I or O), then after we pick one, we need to remove it since we can't repeat letters. So just for our letters, we would get:

24 * 25(only the first digit can't have I or O) * 24

Then, we need to multiply that by 9 (since we are not including 0), giving us:

24 * 25 * 25 * 9 = 129600

Meaning, we can have 129600 different license plates.

Hope this helped!

The size of the large tank is 6 liters and the size of the small tank is 3 liters.

The first step is to form a system of equations using the information provided in the question:

3l + 2s = 24 equation 1

2l + 3s = 21 equation 2

Where:

The elimination method would be used to solve the equations:

Multiply equation 1 by 2 and equation 2 by 3:

6l + 4s = 48 equation 3

6l + 9s = 63 equation 4

Subtract equation 3 from equation 4:

5s = 15

Divide both sides of the equation by 5

s = 15 / 5

s = 3 liters

Substitute for s in equation 1 :

3l + 2(3) = 24

3l + 6 = 24

3l = 24 -  6

3l = 18

l = 18 / 3

l = 6

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A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

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The equation point slope is y - y1 = m(x - x1)

we got y - (-16)=3(x-7)

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A three-degree equation is referred to as a cubic equation. The polynomials are referred to as cubic polynomials if they have a degree of three.

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. The polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

given

A three-degree equation is referred to as a cubic equation.

All cubic equations have roots that are either three real roots or one real root and two imaginary roots.

The polynomials are referred to as cubic polynomials if they have a degree of three.

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Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.

Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.

Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.

Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.

For example, the square root of 16 is 4, since 4 x 4 = 16.

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When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg:  factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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Answer:

Step-by-step explanation:

180-120=60

60+50=110

180-110=70

the missing angle is 70 degrees

Answer: $2.45

Step-by-step explanation:

An easy way to find the correct tip is to learn what 20% of 12.25 is

Let's convert the percentage to a decimal by moving the decimal point two spaces to the left. Now we have .2

.2 X 12.25 = 2.45

2.45 is 20% of 12.25

Max mowed the lawns for 6 hours and tutored students for 8 hours.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is that Max has two part-time jobs. He makes $12 per hour mowing lawns and $15 per hour tutoring students. Over the weekend he worked for a total of 14 hours and made a total of $192.

We can write the system of equations as -

x + y = 14

12x + 15y = 192

Refer to the graph attached. On solving the equation graphically, we get-

x = 6, y = 8

Therefore, Max mowed the lawns for 6 hours and tutored students for 8 hours.

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The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.

The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.

What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters

we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,

then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters

the ladder touches the build at 4.53 meters vertical distance from the ground.

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Point p is further from 0 than point q, and to the left of point q.

The correct option is D.

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

Points p and q are negative integers plotted on a number line.

And |p| > |q|.

That means,

The absolute value of p is greater than the absolute value of q.

|p| and |q| are the positive integers.

So, p < q.

So, the q is closer to zero.

And p is left to point q.

Therefore, the q is closer to zero and p is left to point q.

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The decimal form of n/350 terminates after 49 integer values of n between 1 and 349 inclusive.

The technique of expressing all numbers as a product of primes is known as prime factorization. As an example, suppose we have the number 20. We may divide this into two categories. "Well, that's 4 times 5," we may remark. Also, 5 is a prime number. The number four is not a prime number. All numbers are made up of prime numbers. "Factors" are numbers that are multiplied to generate another number. As an example. "Prime factorization" is the process of determining which prime numbers multiply to produce the original number.

Here,

first, find the prime factorization of 350. (2*5^2*7)

then we need to find all multiples of 7 that are between 1 and 350.

the first multiple of 7/350.

The first multiple of 7 between 1 and 350 is 7.

so 7/350=0.02.

Then, drop the two zeros and find out what is 100% (1 whole, ignoring the percent) /2.

Then, we get 49.

49 integer values of n between 1 and 349 inclusive does the decimal representation of n/350 terminate.

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The closing side of the triangle serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.

A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed geometrically, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or phenomenon known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.

given

As stated in the issue, we must determine the resultant vector by adding vectors A and B.

The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.

Option C is the proper response, thus.

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Rotation is the process of turning a figure a specific amount around a point. When we dilate a figure, we increase or decrease its size.

The circular movement of an item about a primary axis is referred to as rotation or spin. A revolving object in two dimensions only has one conceivable central axis and can revolve either clockwise or counterclockwise. There are many conceivable central axes and rotating orientations for a three-dimensional object.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

On a coordinate plane, forms can be rotated and dilated in addition to translated and reflected. When a shape is rotated, the new shape is consistent with the old. When you dilate a shape, the resulting shape is similar to the original.

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