to be considered abnormal height a 20 year old must be 2.1 feet below average or 2.1 feet above average. if the average height is 5.8 feet, at what heights (in interval notation) would a 20 year old be considered abnormal?

The horizontal asymptote of function f(x) is y=6.5, which is a straight line, which means that even if time is infinite, the pH of the mouth will not rise above 6.5, which is the normal pH of the mouth.

A function's horizontal asymptote is a horizontal line with which the function's graph appears to coincide but does not actually coincide. The horizontal asymptote is used to determine the behavior of the function.

When either lim x f(x) = k or lim x - f(x) = k, the horizontal asymptote of a function y = f(x) is a line y = k. . It is commonly abbreviated as HA. In this case, k is a real number that the function approaches when x is extremely large or extremely small.However, the maximum number of asymptotes that a function can have is 2.

Given,

[tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex]

The horizontal asymptote of the function f(x) can be determined by

[tex]y=\lim_{x \to \infty} f(x)\\\\=\lim_{x \to \infty}\frac{6.5x^2-89.4x+3734}{x^2+576}\\\\=\lim_{x \to \infty}\frac{x^2(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{x^2(1+\frac{576}{x^2})}\\\\=\lim_{x \to \infty}\frac{(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{(1+\frac{576}{x^2})}\\\\=\frac{(6.5-\frac{89.4}{ \infty}+\frac{3734}{ \infty})}{(1+\frac{576}{ \infty})}\\\\=\frac{6.5-0+0}{1+0}\\\\=\frac{6.5}{1}=6.5[/tex]

Thus, the horizontal asymptote of function f(x) is y=6.5 which is straight line which means even the time reaches infinity the pH of mouth will not increase more than 6.5, which is the normal pH of mouth.

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Your question is incomplete, here is the complete question.

The function [tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex] models the pH level f(x) of a mouth x minutes after eating food containing sugar. The graph of this function is shown.

What is the equation is the horizontal asymptote associated with is function? Describe what this means in terms of mouth's pH level over time.

Answer:

Step-by-step explanation:

1222235567899.99978..88694..6.4.4.6.4.4.5

As the ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. There are 640 adult and 1260 childrens.

Given in the questions:

Ticket price in outdoor Theater = $2.50

For Children = $5.00

Total tickets collected in evening = $6350(collected from 1900 people)

Let p be the adult and

1900 - p be the children's who attained the show.

Now,

   2.5 × (1900- p) +5p = 6350

⇒ 4750 - 2.5p +5p =6350

⇒ 2.5p = 1600

⇒ p = 1600/2.5

⇒ p = 640

Since,

p = 640

Therefore,

   1900 - p = children

⇒ Children = 1900 - 640

⇒ Children = 1260

Therefore, there are total 640 adults and 1260 children's in the theater.

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The given expression as a statement is given by -

1 over z raised to the second power.

Given is the following complex function -

f(z) = (z⁶z⁻⁵)⁻²

We have -

(z⁶z⁻⁵)⁻²

Solving further, we get -

(z⁶⁻⁵)⁻²

z⁻²

1/z²

As a statement, we can write -

1 over z raised to the second power.

Therefore, the given expression is equivalent to -

1 over z raised to the second power.

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The total area of 3 square garden beds = [tex]3s^{2}[/tex] square units

A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width. Many things resemble the square shape when you look around.

A square's area is equal to its side. As a result, the area of a square equals Side2 square units. and the perimeter of a square is equal to four side units.

Given:

She want to bulid = 3 square garden beds

All are for same size,

Therefore total area of three square garden beds = 3 × area of one square garden bed

[tex]area of 3 garden beds = 3 ( s^{2} )\\area of 3 garden beds = 3 s^{2}[/tex]

Therefore, total area of 3 square garden beds = [tex]3s^{2}[/tex] square units

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Answer: a= 16

Step-by-step explanation:

a^2 + 30^2 = 34^2

a^2 + 900 = 1,156

a^2 = 256

a = 16

Answer: Dilations centered at the origin

Step-by-step explanation:

You can dilate figures on the coordinate plane. The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.

For the given right triangle the value of the angle x is 33.7°.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angle.

Given:

PQR is a right angled triangle.

PR= 8cm.

QR= 12cm.

We have to find the value of angle x.

As the triangle is right angle triangle so we use the trigonometric ratio to find the value of x.

[tex]tanx = \frac{Opposite Side}{Adjacent Side} \\tanx = \frac{8}{12} \\tan x = 0.6667\\x = tan^-^1(0.6667)\\x = 33.69^o\\x = 33.7^o[/tex]

Hence, for the given right triangle the value of the angle x is 33.7°.

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A function  y = x² which is nonlinear function. the correct option is A.

In mathematics, linear refer to a proportional behaviour that can be modelled with a line, the functions that model this behaviour are called linear functions, and their graphs are lines.

Now, linear expression refers to an expression which has variables with an exponent equal to 1,

Linear functions are in the form of  y = mx + c and have a constant slope.

But Nonlinear functions have a slope that varies between points.

Also, the linear functions are polynomials with highest exponent equal to 1 and all others are non linear.

Here, the correct option is A. y = x²

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Answer: 3/2

Step-by-step explanation:

Let's start with what we know. For a slope to be perpendicular it is the - reciprocal. So:

-2/3's negative reciprocal is

3/2

Answer:

a = 2b - z

Step-by-step explanation:

2(z+a) = 4b

z + a = 4b/2

z + a = 2b

a = 2b - z

The best interpretation of this result is a. We can not conclude whether earning more money causes more recycling among U.S. adults because this type of study does not allow us to infer causation.

Causation cannot be deduced from the study's design (CORRELATION ≠ CAUSATION). The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number.

However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

The adage "correlation does not imply causation" relates to the difficulty of establishing a cause-and-effect connection between two variables or events based merely on the observation of their association or correlation.

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Using the formula of slope of a line, the slope in the graph is -2/3

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by the formula

m = y₂ - y₁ / x₂ - x₁

Taking two coordinate from the line;

Substituting the values into the formula below

m = y₂ - y₁ / x₂ - x₁

m = 0 - 4 / 6 - 0

m = -4 / 6

m = -2/3

The slope is -2/3

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Answer:

Here are six equivalent expressions to 12x - 6:

6(2x - 1)

3(4x - 2)

2(6x - 3)

1(12x - 6)

4(3x - 1)

(12x - 6) + 0

These expressions are all equivalent to 12x - 6 because they all have the same value, regardless of the value of x. This is because the terms on the right side of the equation cancel out, leaving only the constant value on the left side. For example, in the first expression, 6(2x - 1), the 2x and -1 terms cancel out, leaving only 6. This is the same for the other expressions listed above.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here are six equivalent expressions to the given expression:

Note that in each of the above expressions, the value of 12x - 6 is preserved, but the terms and the order of operations may be different. For example, in the second expression, the subtraction has been expressed as addition with a negative number, and in the fourth and sixth expressions, the subtraction has been expressed as multiplication with a fraction.

Using the linear rate data provided and using simple unitary method, The answer is $150.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

Total balance after 6 months = $750

Rate = $100 per month

Time = 6 months

Balance deposited at the rate in 6 months = 100 * 6

=$600

Initial Balance = $750 -  $600

=$150

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Step-by-step explanation:

Use Pythagorean Theorem,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

C is the hypotenuse

a and b are the legs which is 20 and 48

[tex] {20}^{2} + {48}^{2} = {c}^{2} [/tex]

[tex]400 + 2304 = {c}^{2} [/tex]

[tex]2704 = {c}^{2} [/tex]

[tex]c = 52[/tex]

Answer:

The x-intercept is 40, which represents the number of monthly payments needed to repay the loan

Step-by-step explanation:

We see that the x-intercept is at x=40, and the x-axis is number of monthly payments.

The popcorn box in a shape of a rectangular prism will thus have a length of 0.3 inches in inches.

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism.

A rectangular prism also refers to a cuboid.

A cuboid and a rectangular prism have the same cross-section.

Quadrilaterals make up its faces.

So, a popcorn box's volume is modeled by Gabriel as a right rectangular prism, and a full box can store 74 cubic inches of popcorn.

Its height is 77 in, and its breadth is 3 1/2 in.

Then, the prism's width will be:

W =  3 + 1/2

W = 7/2

Consequently, the popcorn box's length in inches will be:

V = LWH

74 = L * 7/2 * 77

L = 0.2745 = 0.3

Therefore, the popcorn box in a shape of a rectangular prism will thus have a length of 0.3 inches in inches.

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The money that Peter gets paid after 7 hours is 43.75

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

The question given is quite straight forward.

Sinec, we are given with the function y = 6.25x

where x is the hours and y is the pay

To find the pay for 7 hrs

we need to replace x by 7

y = 6.25 * 7

y = 43.75 units

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Answer:

the function y=mx+b all you have to do is fill in what you need. The equation would be y=$12x+$48 the x is how many additional cars there are. The y would be the answer.

Step-by-step explanation:

Answer: $18

Step-by-step explanation:

Answer:

  5/72

Step-by-step explanation:

You want the probability of rolling a 6-sided die 3 times with the sequential outcomes 3, not 3, even number.

The probability of any given sequence of outcomes is the product of the probabilities of the outcomes individually. (We assume independence.)

  P(3) = 1/6

  P(not 3) = 1 -P(3) = 5/6

  P(even) = 1/2

Then the probability of the given sequence is ...

  P(3, 3', even) = (1/6)(5/6)(1/2) = 5/72

The probability of the given sequence is 5/72.

__

Additional comment

The outcomes are independent if the probability of occurrence does not depend on any previous outcome.

The formula used to gain information about an individual data value when the variable is normally distributes is,  Z = (X - μ)/σ.

What is standard normal distribution?

The standard normal distribution, also known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1.

Any normal distribution's values can be transformed into z scores to standardize it.

Z scores indicate the number of standard deviations away from the mean that each value represents.

The Z score is determined by the number of standard deviations above or below the mean for the standard normal distribution.

When a variable (let's say X) is normally distributed, then to get insights from its distribution, we transform it (i.e. X) into standardized variable (which constitutes "Standard" Normal Distribution).

Standardized variable, Z, is given by  (X - μ)/σ

Hence, option B is correct answer.  Z = (X - μ)/σ.

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Complete question:

Complete question is attached below.

The simplified form would be 338√x -72√2y.

If a fraction's top and bottom share only one additional common factor, it is said to be in its simplest form. In other words, the top and bottom cannot be divided further and remain full numbers.

The simplest form is also referred to as "lowest words."

the given expression is :

2(4√16x) - 2(4√2y) + 34√81x - 4(4√32y)

⇒ 8(√16x) - 8(√2y) + 34√81x - 16√32y  

⇒8×4√x - 8√2y + 34×9√x - 16√16×2y     [∵ √16 = 4 and √81 = 9]

⇒32√x - 8√2y + 306√x - 16×4√2y

⇒(32√x + 306√x) - 8√2y  - 16×4√2y      

⇒338√x -72√2y

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Answer:

  A

Step-by-step explanation:

You want to select the scatter plot with strong positive correlation.

Correlation is a measure of how well one variable's values track the values of another variable. Perfectly correlated variables will have a scatter plot that is a straight line. The sign of the correlation (positive, negative) matches the sign of the slope of the line.

The less correlated values are, the more their scatter plot looks like a random placement of points. When there is no correlation at all, knowing the value of one of the variables gives no clue about the value of the other one.

Computed values of correlation range from -1 to +1.

When the plot begins to resemble a line with positive slope, the variables plotted in the scatter plot have strong positive correlation. That is shown in the attached scatter plot.

Answer:  Rule 1: Gerunds can be used as a subject of a sentence. Rule 2: Both gerunds and infinitives can be used as objects of a sentence. Rule 3: Infinitives should be used after many adjectives.

Step-by-step explanation:

The Sum of Interior Angle of a polygon with 33 Sides is 5580°

What are Interior Angles?

The Interior Angle is the smaller of the two angles created when two polygon sides meet/ any of the four angles generated when a third line intersects a pair of parallel lines.

Solution:

The Sum of Interior Angle is given by the formula = (n - 2)*180°

here n is the number of sides

To Find:

Sum of Interior Angle where total sides are 33

Sum of Interior Angle = (33 - 2)*180°

Sum of Interior Angle = 31*180° = 5580°

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The values of unknown measures are m∠C'B'D' = 95°,  CQ = 6 and B'D' = 11

We are given that triangle BCD was dilated using the rule d subscript q, one-half.

Since the sum of the measure of all the angles in a triangle is 180°.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (by dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

[tex]\frac{B C}{B^{\prime} C^{\prime}}=\frac{B D}{B^{\prime} D^{\prime}}=\frac{36}{18}=2[/tex]

[tex]B^{\prime} D^{\prime}=\frac{1}{2} B D[/tex]

= 1/2(22)

=11

The dilated triangles are similar to each other.

Hence,  we can say that ΔC'P'Q ∼ ΔCPQ,

[tex]\frac{C^{\prime} Q}{C Q}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} Q}{P Q}[/tex]

C Q= C'Q x  [tex]\frac{C D}{C^{\prime} D^{\prime}}[/tex]

=C'Q x [tex]\frac{B C}{B^{\prime} C^{\prime}}[/tex]

=2 C'Q

=2(3)

=6

Thus, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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Answer: 95, 6, 11

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

do the reserve to 15

add 5 to get 20 and divide by 2 to get 10

Answer: O 10

Step-by-step explanation:

Yolanda = 2 * Marco - 5 Yolanda = 15 So 15 = 2 * Marco - 5 Add 5 to both sides 20 = 2* Marco