42:29

The function(x) - 3. 25x represents the total amount

collected from cars at one toll booth based on the number of

cars that pass through, x. The mathematical domain for the

function is the set of real numbers,

How does the reasonable domain differ from the

mathematical domain?

The reasonable domain is the set of natural numbers

The reasonable domain is the set of positive real

numbers

The reasonable domain is the set of real numbers greater

than 3. 25

The reasonable domain is the set of whole numbers

greater than 3,25

The expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.

Simplifying an expression means to write it in its simplest form by combining like terms and removing any redundant or unnecessary elements. There are several techniques you can use to simplify expressions, including:

Combining like terms: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms. To simplify an expression, you can add or subtract like terms.

Distributing: Distributing means multiplying a constant or variable by each term within a set of parentheses. For example, if you have the expression 2(x + 3), you can distribute the 2 to each term within the parentheses: 2x + 6.

Factoring: Factoring means finding a common factor among a set of terms and grouping them together. For example, if you have the expression [tex]x^{2}[/tex] + 4x, you can factor out the x: x(x + 4).

Simplifying rational expressions: Rational expressions are expressions that have one fractional term. To simplify a rational expression, you can cancel out common factors in the numerator and denominator.

Let's call the width of the portrait w and the height h. We know that the height of the portrait is 1.5 times its width, so h = 1.5w.

The area of the portrait is the product of its width and height: A = w * h = w * 1.5w =  [tex]1.5w^{2}[/tex].

The width of the frame is 4 inches all along its perimeter, so the total width of the framed portrait is w + 4 + 4 = w + 8.

The total height of the framed portrait is h + 4 + 4 = h + 8 = 1.5w + 8.

The area of the framed portrait is the product of its width and height: A = (w + 8) * (1.5w + 8) = (w + 8) * 1.5w + 8 * (w + 8) = 1.5w^2 + 12w + 64.

So, the expression for the area of the framed portrait in terms of w is: A = [tex]1.5w^{2}[/tex] + 12w + 64.

This expression is already in standard form.

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The augmented matrix for the system of equations 7-6y+8x=0, 6x=-3-2y is:

| 7 -6 8 | 0 |

| 6 0 -2 | 3 |

This matrix represents the system of equations in a matrix form where the coefficients of the variables are on the left and the constant terms are on the right.

An augmented matrix is a rectangular array that is formed by appending the coefficients of variables and the constant terms of a system of linear equations in a single matrix. It is used as a tool in linear algebra to represent a system of linear equations in a compact form.

The augmented matrix is typically written as:

| a11  a12  a13 |  b1  |

| a21  a22  a23 |  b2  |

| a31  a32  a33 |  b3  |

where aij represents the coefficient of the i-th equation for the j-th variable, and bi represents the constant term for the i-th equation.

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There are 17,576,000 possible license plates consisting of 3 letters followed by 4 digits.

Fundamental Counting Principles:

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation.

When something can be done m different ways and n different ways,

there are then [tex]m*n[/tex] ways to accomplish both.

Based on the given information, since the letters and digits may be repeated, there are:

26 ways to fill in the first letter

26 ways to fill in the second letter

26 ways to fill in the third letter

10 ways to fill in the first digit

10 ways to fill in the second digit

10 ways to fill in the third digit and

1 way to fill in the first digit (as the last digit end with 5)

Thus, by Fundamental Principle of Counting, there are 17,576,000 possible license plates.

26 x 26 x 26 x 10 x 10 x 10 x 1  = 17,576,000

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The diagram of the scatter plot is given in the attached image below.

The graph of a linear function is a straight line. The following is the form of a linear function.

a + bx = y = f(x).

One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.

The data are shown in the table below:

x      y

4     1

5.5   2

7.5   3

9     4

11     5

14     6

From the given choices:

the last diagram of the scatter plot is given in the attached image.

Hence, the scatter plot is given below.

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Answer:

see below

Step-by-step explanation:

4x^4 – 20x^2 + 25

= (2x-5)²

so the factor is 2x-5

Answer:

1.8

Step-by-step explanation:

The equation we are given is [tex]\frac{n}{-1.5} = -1.2[/tex]. We can multiply both sides by -1.5 to get n = 1.8.

Answer:

N = 1.8

Step-by-step explanation:

You do cross multiplication

n*1 = -1.5 * -1.2

1n = 1.8

To check it, we plug in 1.8

1.8/-1.5 = -1.2

When solving problems that contain exponents, we must know the value of both elements for the result to be correct. This ability can be improved by knowing how to multiply very well.

An exponent is a mathematical expression that tells us that a value must be multiplied by itself a certain number of times, the most common exponent is the square in which a value must be multiplied by itself once, for example:

To improve in problems with exponents we must know how to multiply very well because this is the basic operation that is most related to solving exponents.

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On solving the provided question, we can say that value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Volume is 704cm3

Total Surface area is 2176

Cylinder volume is calculated as follows: cylinder volume = π * radius² * height.

Length of metallic tube, h = 35 c

Radius (R) =  5.2 cm

inner Radius (r) = 4.7cm

Volume of metal =

3.14*(27.04-22.09)*35

704 cm cubic

Surface area inside

2*22/7*4.7*35

1033 cubic cm

Surface area outside

2*22/7*5.3*35

1143 cubic cm

Value of the total surface area of the outside plus inside of the tube will be (1033+1143) = 2176 cubic cm

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Answer:

1 1/15

Step-by-step explanation:

4 x 4/15 = 4/1 x 4/15 = 16/15 = 1 1/15

The missing angles in the figure are:

∠XVR = 125°

∠RVS = 55°

∠WVS = 125°

∠RST = 110°

∠RSV = 70°

∠VSU = 110°

∠UST = 70°

∠TUS = 39°

Angle geometry is a branch of mathematics that deals with the study of angles and their properties in two-dimensional figures such as circles, triangles, and polygons.

∠XVW + ∠XVR = 180° (sum of angles on a straight line is 180° )

Thus, ∠XVR = 180 - 55 = 125°

∠RVS = 55° (vertically opposite angles are equal)

∠WVS = 125° (vertically opposite angles are equal)

∠RST =  55 + 55 = 110°  (exterior angle of a triangle)

∠RSV = 180-55-55 = 70° (sum of angles in a triangle is 180°)

∠VSU = 110° (vertically opposite angles are equal)

∠UST = 70° (vertically opposite angles are equal)

∠TUS = 180 - 70 -71 = 39° (sum of angles in a triangle is 180°)

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The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.

The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).

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The rational number representation of Micah withdrawing $4.50 from his bank account is -4.5.

A rational number is any fraction with non-zero denominators. A rational number can be written as a fraction with a numerator and denominator that are both integers.

In this case, we can write $-4.50$ as the fraction $\frac{-450}{100}$, where the numerator represents the amount of money withdrawn (in cents) and the denominator represents the unit of currency used (in this case, 100 cents = 1 dollar).

So, the rational number representing the amount of money withdrawn from Micah's bank account is {-450} / {100}$ = -4.5.

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As a result, on a graph of dP/dt vs P, the curve would be concave down for P b/a and concave up for P > b/a. The curve would reach its maximum when P = b/a, with dP/dt equal to zero.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

The equation dP/dt = aP² - bP represents the rate of change of the population P over time t.

When dP/dt is positive, the population is increasing. When dP/dt is negative, the population is decreasing.

To find when dP/dt is positive and negative, we need to find the critical points where dP/dt = 0.

Solving the equation dP/dt = aP² - bP = 0, we get:

aP² - bP = 0

aP(P - b/a) = 0

This equation has two solutions: P = 0 and P = b/a.

For P < b/a, dP/dt is negative (the population is decreasing). For P > b/a, dP/dt is positive (the population is increasing).

So, on a graph of dP/dt against P, the curve would be concave down for P < b/a and concave up for P > b/a. At P = b/a, the curve would have a maximum and dP/dt = 0.

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x and y are not common factors, as they cannot be simplified with themselves.

Common factors in an expression with n terms are the terms that are common to all the terms of an expression.

For example, taking the expression 2 + 4 + 6, we have that 2 is a common factor, as:

For variables to be common factors, we have that they must have the same base, with the same or different exponents.

x and y are different bases, hence they are not common factors.

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Step-by-step explanation:

14 for every 3 would be the same as 14/3

If we make that equal to x/15, what follows...

[tex] \frac{chickens}{geese} = \frac{14}{3} = \frac{x}{15} [/tex]

If we cross multiply

[tex]3x = 14(15)[/tex]

[tex]3x = 210[/tex]

And lastly we divide by 3

[tex]x = 70 \: chickens[/tex]

In 4 hours, and 30 minutes (or 4.5 hours), Wanda will catch up to the hector.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, Hector competing in a 42-mile bicycle race he’s already completed 18 miles of the racing and is traveling at a constant speed of 12 mph.

Let x = the hours needed for Wanda to catch up to Hector.

Hector has already completed 18 miles. Hector travels at 12 miles per hour.

After x more hours, Hector will travel

18 + 12x miles

Wanda travels at 16 miles per hour. In x hours, she travels

16x miles

If Wanda catches up to Hector, then

16x = 18 + 12x

4x = 18

x = 4.5 hours

Therefore, Wanda will catch up to the hector at 4 hours, 30 minutes (or 4.5 hours).

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Complete question:

Answer:

80 percent of people don't like the turkey sandwich because 80 plus 20 equals 100 so think about it as a subtraction equation

Answer: 80% of students don't like turkey sandwiches.

The probability that a randomly chosen patient will be admitted for a reason other than coronary care is equal to one less than the likelihood that they will be admitted for that reason.

The likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 less than the likelihood that they will be admitted for that reason. For instance, if the chance of being admitted for coronary care is 0.25, the chance of being admitted for a different reason is 0.75. This is due to the requirement that the total number of outcomes must equal 1. Accordingly, if one outcome has a 0.25 probability, then the chance of every other outcome must equal 0.75. As a result, the likelihood that a randomly chosen patient will be admitted for a reason other than coronary care is equal to 1 minus the likelihood that they will be admitted for that reason.

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The circumference is 160 feet for a length of 40 feet. The perimeter is 200 feet for a length of 50 feet. The circumference is 240 feet for a length of 60 feet.

A rectangular region with a 1200 square foot area will have a different perimeter depending on how long it is. The perimeter will be 160 feet if the area is 40 feet long. The length of 40 feet is multiplied by four to get a final measurement of 160 feet. In a similar manner, if the area is 50 feet long, the perimeter will be 200 feet.

The length of 50 feet is multiplied by four to get a final result of 200 feet. Finally, the perimeter will be 240 feet if the area is 60 feet long. The length of 60 feet is multiplied by four to get a final measurement of 240 feet. A rectangular region with an area of 1200 square feet will therefore have a different perimeter depending on its length, with a length of 40 feet resulting in a perimeter of 160 feet, a length of 50 feet resulting in a perimeter of 200 feet, and a length of 60 feet resulting in a perimeter of 240 feet.

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Step-by-step explanation:

A line that is parallel to another line has the same slope but a different y-intercept. The slope of the line through the points (1,-2) and (-6,3) can be found using the slope-point formula:

slope = (y2 - y1) / (x2 - x1) = (3 - (-2)) / (-6 - 1) = 5/7

So, a line that is parallel to this line would have the same slope of 5/7. To find an equation for a line with this slope that passes through a different point, we can use the point-slope formula:

y - y1 = m * (x - x1)

Where m is the slope and (x1, y1) is a point on the line. We can choose any point to use in this formula, but a common choice is the origin (0,0). So, plugging in the values we have:

y - 0 = 5/7 * (x - 0)

y = 5/7 * x

This is the equation for a line that is parallel to the line through the points (1,-2) and (-6,3) and passes through the origin.

The area of the shaped portion of the given diagram(circle) would be = 153.86cm²

The formula which is used to calculate the area of a circle = πr²

where π = 3.14

radius = 7 cm

Therefore the area of the shaded part of the circle ;

= 3.14 × 7²

= 3.14 × 49

= 153.86cm²

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The median of the data collected is 1.5. Option B

It is important to note that the median of a given set of data is the middle number or the sum of the pair of numbers arranged in the order from the least to the greatest value.

From the information given, we have the data set;

1/3 2 4 1 7 2/3 4/5 5/2

Arrange the values in an ascending order from the least to the greatest value

1/3, 2/3, 4/5, 1, 2, 5/2, 4, 7

Since the total number is odd, take the two middle number and divide by 2, we get;

1 + 2/2

add the values

3/2

Divide the values

1. 5

Hence, the value is 1.5

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Answer:

40.6428571429

Step-by-step explanation:

To evaluate the expression for the given value of the variable when t = -1/2, we just need to substitute the value of t into the expression:

41 + 5/7 * (-1/2) = 41 - 5/14
41 - 5/14 = 40.6428571429

So the answer is 40.6428571429.

The original price of the bracelet, before tax $0.68

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

Amount = $0.72

Sales tax = 6%

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

Amount = Original amount * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

0.72 = Original amount * (1.06)

So, we have

Original amount = 0.68

Hence, the original amount = 0.68

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This line represents the proportional relationship between x and y, as described by the given equation.

An equation is a physical and mathematical statement the describing physical phenomen or describe the relationship between different physical quantities. It typically consist of two or more variables which are symbol representing physical quantities and an equal sign the variable may be quantities such as force velocity your energy and the question describe how this quantities relate to each other.

To graph this relationship, I first plotted the origin (0,0) on the grid. Then, I made a table of values for x and y, using the given equation. I placed x values from 0 to 10 on the x-axis and the corresponding y values from 0 to 2.5 on the y-axis. Finally, I plotted each point on the graph to create a straight line. This line represents the proportional relationship between x and y, as described by the given equation.

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Answer:

True

Step-by-step explanation:

True. A z-score, also known as a standard score, is a statistical measure that helps to determine how far a particular value is from the mean relative to the data set's standard deviation.

A z-score is a dimensionless quantity that expresses the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean. A positive z-score indicates that the value is above the mean, while a negative z-score indicates that the value is below the mean.

To calculate the z-score for a given value, the formula is: z = (x - μ) / σ where z is the z-score, x is the value being considered, μ is the mean of the data set, and σ is the standard deviation of the data set.

For example, if the mean of a data set is 50 and the standard deviation is 10, and we are interested in finding the z-score for a value of 65, the calculation would be: z = (65 - 50) / 10 = 1.5. This indicates that the value of 65 is 1.5 standard deviations above the mean of the data set.

Z-scores are useful for comparing values across different data sets or for identifying extreme values in a data set. Values with high positive or negative z-scores are typically considered to be outliers, indicating that they are further from the mean than most other values in the data set.

In summary, the statement "z-score helps to determine how far a particular value is from the mean relative to the data set's standard deviation" is true. Z-scores are a statistical measure that help to express the distance between a particular value and the mean of a distribution in terms of the number of standard deviations that the value is from the mean.

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Step-by-step explanation:

I just answered this. how often was that posted ?

the distance of a vertex to its 2 neighboring circle touching points is the same, because tangents emanating from the same point to the same circle must have the same distance to the touching points.

so, AB splits into a (from A to the circle touching point on AB) and b (from the circle touching point on AB to B).

b = AB - a

BC splits into b (from B to the circle touching point on BC) = AB - a, and c (from the circle touching point on BC to C).

c = BC - (AB - a) = BC - AB + a

CD splits into c (from C to the circle touching point on CD) = BC - AB + a, and d (from the circle touching point on CD to D).

d = CD - (BC - AB + a) = CD - BC + AB - a

DA now splits into d (from D to the circle touching point on DA) and ... a (from the circle touching point on DA to A).

a = DA - (CD - BC + AB - a) = DA - CD + BC - AB + a

0 = DA - CD + BC - AB

DA = CD - BC + AB = 8 - 5 + 4 = 7

Answer:

  DA = 7

Step-by-step explanation:

You have quadrilateral ABCD with an inscribed circle and side lengths AB=4, BC=6, CD=8, and you want to know the length of DA.

The tangents from each vertex of the quadrilateral to the inscribed circle are the same length, so we can work our way around the quadrilateral to find the missing length. The attached figure shows the tangent lengths working counterclockwise from vertex A.

The sum of the tangents from A and D is ...

  x + (7 -x) = 7

The length of DA is 7 units.

__

Additional comment

The sum of the lengths of opposite sides is the same in any quadrilateral with an inscribed circle. Here, that sum is 4+8 = 12, so the unknown side is 12-5 = 7.

The value of the exponents will be (x²)³ = x^6 and the value of 7² will be 49.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

The value of (x²)³ will be:

= x^(2 × 3)

= x^6

The value of 7² will be:

7 × 7

= 49

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Miguel buys a dozen (12) bagels for $9.99. How much money did he spend on each bagel?

Answer:.83