How do you know if a graph is wider or narrower than the parent function?

Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.

Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.

Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.

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In algebra, a symbol is used to denote an unknown numerical value in an equation or algebraic expression.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572[tex]$$x^4[/tex] − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572[tex]$$x^4[/tex] + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

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Number of cars manufactured in 2007 will be equal to 178 or 203 based on quartic model.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572 − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572 + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

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2048 people would fill the stadium to its full capacity

percentage, a relative value indicating hundredth parts of any quantity.

Given that a stadium is filled to 80% capacity

There are  2,560 people are in the stadium

We need to find how many people would fill the stadium to its full capacity.

We have to convert 80% to decimal by dividing 2560 with 100

80/100

0.8

Now multiply 0.8 with 2560

0.8×2560

2048

Hence, 2048 people would fill the stadium to its full capacity

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The time taken by the package to reach the ground will be 5.45 seconds.

The motion of an object is related to the forces acting on it by Newton's laws of motion. According to the first law, unless a force acts on an object, it will not alter its motion. According to the second law, an object's force is determined by multiplying its mass by its acceleration. According to the third law, when two objects interact, they exert equal-sized and opposite-direction forces upon one another.

Solution:-

vo=12m/s

h=80m=yo

Then,

[tex]y-yo= vot-1/2gt^2[/tex]

⇒[tex]0-80m=(12m/s)t - 1/2(9.8m/s^2)t^2[/tex]

⇒[tex](4.9m/s^2)t^2-(12m/s)t-80m=0[/tex]

⇒[tex](4.9m/s^2)t^2-(12m/s)t-80m=0[/tex]

⇒[tex]t=5.45s, t=-3.00s[/tex]

∴[tex]t=5.45s[/tex]

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Answer:

$8.28

Step-by-step explanation:

0.18*46=8.28

Answer:

Step-by-step explanation:

The  5 operations of functions are

1. Input

2. Processing

3. Output

4. Storage

5. Maintenance

Input: When a function is used, it takes in an input value. This input value is used to compute the output. For example, if a function is used to calculate the area of a circle, the input would be the radius of the circle.

Processing: Once the input value is taken, the function will use the input to perform some type of operation on it. For example, if the function is used to calculate the area of a circle, the operation would be to multiply the input by itself and then multiply it by the constant pi.

Output: The output of a function is based on the input. For example, if the function is used to calculate the area of a circle, the output would be the area of the circle.

Storage: Once the output of a function is computed, it can be stored for later use. This allows the same output to be used multiple times without having to recalculate the output.

Maintenance: Functions need to be maintained and updated over time. This can include updating the input, operation, and output, as well as any additional changes that might be needed. This ensures the function is up-to-date and still provides accurate results.

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The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.

To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.

To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length) + 2(width)

Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:

2x + 2y = 60,000

To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:

60,000 - x = 3x + 2y

The total length of the three sides that are not the front is 3x + 2y.

Now we can calculate how much the builder will pay for each type of fence:

Total cost of the fence = $20x + $30x + $20y = $50x + $20y

To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.

However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:

This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.

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The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1

Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]

For n = 21, r = -1 and a1 = 1

[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]

Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1

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Answer: Breadth? Did you mean width? If so, the answer is 128cm

Step-by-step explanation:

Area = Width x Length

8x16=128

The positive value of the distance between the two objects

is [tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, The formula to calculate the gravitational force between two objects

is [tex]F_g = \frac{GM_1M_2}{r^2}[/tex] where r is the distance between the objects M is the individual masses and G is the gravitational constant.

Solving for r would result in two values one positive and one negative and distance can not be negative so we want the positive value.

[tex]F_g = \frac{GM_1M_2}{r^2}[/tex].

[tex]r^2 = \frac{GM_1M_2}{F_g}[/tex].

[tex]r = \pm\sqrt \frac{GM_1M_2}{F_g}[/tex].

[tex]r = +\sqrt \frac{GM_1M_2}{F_g}[/tex].

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Answer:

There are always two possible outcomes H (heads) and T (tails) but the possible combination outcomes are HH, TT, HT, and TH

Step-by-step explanation:

It is just my common sense~

There is 8 possible outcomes.

Step-by-step explanation:

I'm assuming that its 23 to the power x since you said it is an exponential equation.

as for the hint there is no specific base specified so I'll do the best I can with the answer.

Angie can begin solving by applying log to the base 23 on both sides. when this is done, Angie will be left with:

[tex] log_{23}( {23}^{x} ) = log_{23}(6) [/tex]

and as we know the power rule in logarithms allows us to remove the power within the expression.

hence, we'll get:

[tex]x log_{23}(23) = log_{23}(6) [/tex]

furthermore, if we have the same number and base within a logarithmic expression it will simply become 1 giving us the final answer:

[tex]x = log_{23}(6) [/tex]

if the question that I've answered is different to yours please let me know and I'll make sure to fix it.

hope this helps :)

The height of vase b is 34.56 cm.

In mathematics, volume is the space taken by an object.

V=pi*r²*h

Here, given that,

vase A has height 20cm =H

and volume 1500^3. =V

And, A & B similar vases.

Again, vase B has volume 2592cm^3 =v

let, h, the height of vase b.

both radius are equal

so, we get,  V/pi*H = v/pi*h

i.e. 1500/20=2592/h

so, h= 34.56 cm

Hence, the height of vase b is 34.56 cm.

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Geometrically there are 16 different routes from A to B that use each road exactly once.

What is geometry?

The area of mathematics known as geometry is concerned with the dimensions, sizes, forms, and angles of a wide range of everyday objects. Geometry comes from the Ancient Greek terms "geo" and "metron," which both imply "measuring."

Keep in mind that cities C and E can be excluded from the count of paths because there is only one road that can lead out of either city if a path enters it. The geometric diagram is shown below.

Now move on to the casework. It's important to keep in mind that there are two routes from A to D, D to A, B to D, and D to B.

Case 1: A⇒D: If the path from D leads back to A, the subsequent path must go to B⇒D⇒B. The path ADABDB has 2×1×2=4 possible outcomes. The path must continue with either BDAB or BADB if it leads from B to D. There are 8 possibilities as 2×2×2=8. Therefore, there are 4+8=12 potential outcomes in this scenario.

Case 2: A⇒B: BDADB must be the next step on the path. There are 2×2=4 options in this situation.

Combining the two situations results in 12+4=16.

Therefore, there are 16 different routes.

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Answer:

Step-by-step explanation:

m∡IGH = ? m∡FGH = 141 degrees and m∡FGI = 72 degrees

therefore, m∡IGH = m∡FGH - m∡FGI = 141 - 72 =  69 degrees

The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the function:

y = -(x/3) + 2

At x = -3:

y = -((-3)/3) + 2 = 3

At x = 0:

y = -(0/3) + 2 = 2

At x = 3:

y = -(3/3) + 2 = 1

At x = 6:

y = -(6/3) + 2 = 0

The value of y when x = -3 is 3

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Using the number line, the difference between 4 1/2 and 8 will come to -31/2.

A number line is a depiction of a graded straight line that serves as a visual representation of real numbers in primary mathematics. Every point on a number line is presumed to be a real number, and every real number is assumed to be a point.

Subtraction on a number line makes it much easier to subtract smaller values. When subtracting numbers from a number line, we must leap (move) to the left side of the number line.

Thus, moving to the left, 8 times from 4.5 will help us arrive at -3.5. See attached Number line.

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Hello there!

Answer:

[tex]V = 18432\pi[/tex] or approximately 57876.48

Step-by-step explanation:

[tex]V = \frac{4}{3} \pi R^{3}[/tex]

R = 24

[tex]V = \frac{4}{3} \pi *24^{3} = 18432\pi[/tex]

if [tex]\pi =3.14[/tex] then:

[tex]V = 57 876.48[/tex]

On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y = 2x +1

y = 3x - 1

x- 1 = 0

x = 1, y = 2

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Answer:

65 cars

Step-by-step explanation:

The height of Dange who can jump 27.5% of her height is 10.4 inches.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Dange measures and finds that she can do a vertical jump that is 27.5 % of her height f and the distance of the jump is 13.2 inches.

Therefore. (100 + 27.5)% = 127.5% of f is 13.2 inches, This can be numerically expressed as,

(127.5/100)×f = 13.2.

1.275f = 13.2.

f = 13.2/1.27.

f = 10.4 feet.

So, The height of Dange is 10.4 inches.

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Answer:90

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because the account that gets debited depends on the specific transaction

The ratios equivalent to 2:14 are 3:21 and 16:112. Option A &C

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.

2:14 = 2/14

Reducing 2/14 to the lowest terms = 1/7

2:14 is equivalent to 1:7

3:21 = 3/21 = 1/7

Reducing 3/21 to the lowest terms = 1/7

3:21 is equivalent to 1:7

1:2 = 1/2

1:2 is not equivalent to 1:7

16:112 = 16/112 = 1/7

Reducing 16/112 to the lowest terms = 1/7

16:112 is equivalent to 1:7

Hence, 2:14, 3:21 and 16:112 are all equivalent ratios

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Answer:

44.8

Step-by-step explanation:

44.4 - (-0.4) = 44.8

In the given pairs of polygons the scale factor of figure A to figure B is  2:4.

The scale factor is calculated using the following fundamental formula: Scale factor = Dimension of the new shape Dimension of the old shape. The formula for calculating the scale factor is expressed as Scale factor = Larger figure dimensions Smaller figure dimensions in the event that the original figure is magnified.

The ratio of a smaller figure's side to its corresponding side in the bigger figure is the scale factor between the two figures.

As a result, the smaller figure's side length of 4 units and its side length of 10 units are equivalent.

Therefore:

Scale factor = 4:10

i.e. 2:5

Simplify

Scale of the smaller figure to the larger is equal to 2:4.

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Unreasonable Time is the nest option for running the group raffle at an upcoming assembly to give away a prize.

As given that;

Reasonable Time: Algorithms with a polynomial efficiency or lower (constant, linear, square, cube, etc.) are said to run in a reasonable amount of time.

Unreasonable Time: Algorithms with exponential or factorial efficiencies are examples of algorithms that run in an unreasonable amount of time.

Your school is considering running the group raffle at an upcoming assembly to give away a prize.

We have to write a brief explanation of what advice you would give them.

We can use the unreasonable time because  running the group raffle at an upcoming assembly to give away a prize cannot complete their work is the given amount of time.

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Answer:

The equation you have provided is 8 + 9x = 7, where x is the unknown number.

To solve for x, you can first subtract 8 from both sides of the equation to get

9x = -1

Then divide both sides by 9

x = -1/9

So the number x is -1/9, which means that the product of x and 9 is equal to -1.

Keep in mind that this is not a natural number and it is not possible to represent the solution as a whole number.

Step-by-step explanation:

Best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake

Mrs. Campos is making cupcakes for a bake sale. She uses the equation c = 0. 55x to determine the cost, c, for x cupcakes. Which best represents the constant rate at which cupcakes are sold at the bake sale?

55 cupcakes per dollar

$0. 55 per cupcake

$4 per cupcake

c = 0. 55x

to determine the cost, c,

for x cupcakes.

CASE 1

55 cupcakes per dollar

therefor x = 55

c = 0. 55x

c = 0. 55 × 55

 = 30.25

case2

$0. 55 per cupcake

x = 1

c = 0. 55x

c = 0. 55 × 1

   =  0. 55

case 3

$4 per cupcake

x = 1

c = 0. 55x

c = 0. 55 × 1

   =  0. 55

therefor conclusion is best represents the constant rate at which cupcakes are sold at the bake sale $0. 55 per cupcake

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