is the function described by the points in this table linear or nonlinear? x y −3 9 −1 1 0 0 1 1 3 9 responses linear linear nonlinear

To determine if the Mean Value Theorem (MVT) applies to the function f(x) = 4x^(1/7) on the interval [-128, 128), we need to check if the function satisfies the conditions of the MVT.

The Mean Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

In this case, the interval is [-128, 128), which is a closed interval. To check if the MVT applies, we need to ensure that the function is continuous on [-128, 128] and differentiable on (-128, 128).

Continuity: The function f(x) = [tex]4x^(1/7)[/tex] is a power function and is continuous for all x values, including the interval [-128, 128]. Therefore, the function is continuous on the interval.

Differentiability: The function f(x) = [tex]4x^(1/7)[/tex]is differentiable for all x values except at x = 0. Since the interval (-128, 128) does not include x = 0, the function is differentiable on the interval.

Therefore, both conditions for the MVT are satisfied, and we can conclude that the Mean Value Theorem applies to the function f(x) = [tex]4x^(1/7)[/tex] on the interval [-128, 128).

Next, we can find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem.

The Mean Value Theorem guarantees the existence of at least one point c in (-128, 128) such that f'(c) = (f(128) - f(-128))/(128 - (-128)).

Let's calculate the values:

f(128) = [tex]4(128)^(1/7)[/tex]≈ 4.5534

f(-128) = [tex]4(-128)^(1/7)[/tex]≈ -4.5534

f'(c) = (4.5534 - (-4.5534))/(128 - (-128)) = 9.1068/256 ≈ 0.0356

Therefore, by the Mean Value Theorem, there exists at least one point c in the interval (-128, 128) such that f'(c) ≈ 0.0356.

Please note that the specific value of c cannot be determined without further analysis or calculations. The Mean Value Theorem guarantees its existence but does not provide an exact value.

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Only the side lengths 12, 16, and 20 can be used to create a right triangle.(Option-A)

The Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides, must be satisfied for a set of side measurements to create a right triangle.

This theorem allows us to determine which sets of side measurements can create a right triangle. 202 = 400 for the set of measures 12, 16, and 20.

[tex]12^2 + 16^2[/tex] = 144 + 256 = 400

The measurements could result in a right triangle because they meet the Pythagorean theorem.

Measurements 6, 14, and 19 are as follows: 192 = 361 62 + 142 = 36 + 196 = 232 . (Option-A)

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Answer:

12, 16, 20

Step-by-step explanation:

A right triangle is a triangle that has one right angle, which is an angle that measures 90 degrees. The side opposite the right angle is called the hypotenuse. The other two sides are called the legs.

We can use the Pythagorean theorem to determine which set of side measurements. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

So, for each set of side measurements, we can calculate the square of each side and add them together. If the sum is equal to the square of the hypotenuse, then the set of side measurements could be used to form a right triangle.

Set 1: 12, 16, 20

The sum of the squares of the legs is 144 + 256 = 400.

The square of the hypotenuse is also 400.

Therefore, set 1 could be used to form a right triangle.

Set 2: 6, 14, 19

The sum of the squares of the legs is 36 + 196 = 232.

The square of the hypotenuse is 361.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 2 could not be used to form a right triangle.

Set 3: 6, 8, 15

The sum of the squares of the legs is 36 + 64 = 100.

The square of the hypotenuse is 225.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 3 could not be used to form a right triangle.

Set 4: 4, 5, 6

The sum of the squares of the legs is 16 + 25 = 41.

The square of the hypotenuse is 36.

Since the sum of the squares of the legs is not equal to the square of the hypotenuse, set 4 could not be used to form a right triangle.

Therefore, the only set of side measurements that could be used to form a right triangle is set 1.

Answer:

60 and 90

Step-by-step explanation:

150/15 = 10

6 x 10 = 60

9 x 10 = 90

The required number of toys that can be divided among two groups is 60  and 90.

Given that,
To divide 150 toys amongst two groups of children in a ratio of 6:9​.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Ratio = 6 / 9
Total of ratio = 15
Now,
For 1 group toys = 150 [6 / 15] = 60
For group 2 toys = 150 [9 / 15] = 90

Thus, the required number of toys that can be divided among two groups is 60  and 90.

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Answer:

I need a picture of the figure to do it

Answer:

12 - m = 20

Explanation: Less than can also be a subtraction symbol so 12 less than a number, which the number is unknown in this case would be replaced with m then equals to 20. 12 - m =20

The estimated number of kidney stone patients in the Muscat region (N₂) is approximately 447,184, and in the Dhofar region (N₁) is approximately 128,694.

Given,

Estimation of total hospitalization costs for kidney stone patients .

Here,

To obtain the estimates of N and N, the numbers of kidney stone patients expected to be found in the Muscat and Dhofar regions, we can use the stratified sampling formula:

Nᵢ = (nᵢ / n) * N,

where:

- Nᵢ is the estimate of the population size in stratum i.

- nᵢ is the sample size in stratum i.

- n is the total sample size (sum of all stratum sample sizes).

- N is the total population size.

Given the information provided, we have the following data:

For Dhofar region:

- n₁ = 260 (sample size)

- N = 249,729 (population size according to the 2010 census)

For Muscat region:

- n₂ = 150 (sample size)

- N = 775,878 (population size according to the 2010 census)

Using the given formula, we can calculate the estimates for each region:

For Dhofar region:

N₁ = (n₁ / n) * N = (260 / (260 + 150)) * 249,729

For Muscat region:

N₂ = (n₂ / n) * N = (150 / (260 + 150)) * 775,878

To obtain the values, let's calculate them:

For Dhofar region:

N₁ = (260 / (260 + 150)) * 249,729 ≈ 128,694

For Muscat region:

N₂ = (150 / (260 + 150)) * 775,878 ≈ 447,184

Therefore, the estimated number of kidney stone patients in the Muscat region (N₂) is approximately 447,184, and in the Dhofar region (N₁) is approximately 128,694.

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Answer:

The real answer is (-20, 8).

Step-by-step explanation:

I just did the unit test practice or whatever and used the answer above and got it wrong. This is the correct answer.

Answer:5

Step-by-step explanation:

Answer:

5 percent

Step-by-step explanation:

4/80 = 5 percent

Answer:

Step-by-st

Bitly: URL Shortener - Short URLs & Custom Free Link ...bitlep explanation:

Answer:

DE=4

Step-by-step explanation:

got it right on edg

The length of DE is given as: 3 Units. (Option B)
A line that joins two points on a curve is called a Secant Line.

Two secant theorem states that if two secant lines are drawn from a point outside a circle a relationship is formed between the line segments.

Based on the Secant Theorem, from the figure, we know that:

AX * BX = EX * DX

Assuming that the length of DE equals X,:

AX * BX = EX * DX

Equals

(7+2) X (2) = (x + 3) (3)

To solve for x we expand the brackets to state:

9 * 2= 3x + 9

3x = 18-9

3x= 9

x = 9/3

X which is same as DE = 3 Units.

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Bob is exerting a force of 200 N on a 30 kg filing cabinet, but it remains stationary due to the static friction between the cabinet and the floor. The coefficient of static friction is given as 0.80.

The static frictional force acts between two surfaces in contact when there is no relative motion between them. The magnitude of static friction can be determined using the equation F_static = μ_static * N, where μ_static is the coefficient of static friction and N is the normal force.

In this scenario, Bob is applying a force of 200 N to the filing cabinet. In order to overcome the static friction and set the cabinet in motion, the applied force must be greater than or equal to the maximum static frictional force. The maximum static frictional force can be calculated by multiplying the coefficient of static friction with the normal force.

Since the cabinet is stationary, the applied force of 200 N is not sufficient to overcome the maximum static frictional force. The maximum static frictional force can be determined as F_static = μ_static * N = 0.80 * (30 kg * 9.8 m/s^2) = 235.2 N.

As the applied force of 200 N is less than the maximum static frictional force of 235.2 N, the filing cabinet remains stationary. Bob would need to apply a force greater than 235.2 N to overcome the static friction and set the cabinet in motion.

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Answer:

ayuda te solo no eres tonto o si?

Step-by-step explanation:

Answer:

Inequality Form:

x < - 4

Interval Notation:

( − ∞ , − 4 )

Step-by-step explanation:

The probability of making a gain that exceeds one standard deviation from the mean for stock XYZ on any given day is approximately 31.73%.

The probability of making a gain that amounts to more than one standard deviation from the mean on any given day for the stock XYZ can be found using the properties of the normal distribution.

To calculate this probability, we need to find the area under the normal distribution curve beyond one standard deviation from the mean in the positive direction. In this case, the mean (μ) is 20 basis points and the standard deviation (σ) is 40 basis points.

Using the standard normal distribution, we can convert the value one standard deviation above the mean (μ + σ) to a z-score by subtracting the mean and dividing by the standard deviation.

Z = (X - μ) / σ

Z = (μ + σ - μ) / σ

Z = σ / σ

Z = 1

Once we have the z-score, we can look up the corresponding probability using a standard normal distribution table or a statistical calculator.

The area under the normal curve beyond one standard deviation from the mean in the positive direction corresponds to approximately 0.1587 or 15.87%.

Therefore, the probability of making a gain that amounts to more than one standard deviation from the mean on any given day for stock XYZ is approximately 0.1587 or 15.87%.

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Given a linear function f: X -> R that is bounded above on a neighborhood V of the origin, we need to prove that there exists a neighborhood W of the origin such that f(x) < y for all x in W.

To prove this statement, we can use the properties of linear functions and the topology of X. Since f is linear, we know that f(0) = 0.

Let's consider the open ball B(0, y) centered at the origin with radius y. Since f is bounded above on V, there exists a constant M > 0 such that f(x) < M for all x in V.

Now, let's define a neighborhood W = V ∩ f^(-1)(B(0, y/M)). W is the intersection of V and the inverse image of the open ball B(0, y/M) under the function f.

By the properties of inverse images, we know that f(x) < y/M for all x in W.

Therefore, we have found a neighborhood W of the origin such that f(x) < y for all x in W, satisfying the condition we needed to prove.

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Answer:

Step-by-step explanation:

To solve the equation 4cos^2(x)tan(x) - 2tan(x) = 0 on the interval [0°, 360°), we can use algebraic manipulations and trigonometric identities. Let's simplify the equation step by step:

Start with the given equation: 4cos^2(x)tan(x) - 2tan(x) = 0.

Factor out the common term tan(x): tan(x)(4cos^2(x) - 2) = 0.

Set each factor equal to zero and solve separately:

a) tan(x) = 0:

Since tan(x) is zero at x = 0°, 180°, and 360°, we have x = 0°, 180°, 360° as solutions.

b) 4cos^2(x) - 2 = 0:

Add 2 to both sides: 4cos^2(x) = 2.

Divide by 4: cos^2(x) = 1/2.

Take the square root: cos(x) = ±√(1/2).

To find the values of x in the interval [0°, 360°), we need to consider both the positive and negative square root:

cos(x) = √(1/2):

x = 45°, 315° (since cos(45°) = cos(315°) = 1/√2)

cos(x) = -√(1/2):

x = 135°, 225° (since cos(135°) = cos(225°) = -1/√2)

Therefore, the solutions to the equation 4cos^2(x)tan(x) - 2tan(x) = 0 on the interval [0°, 360°) are: x = 0°, 45°, 135°, 180°, 225°, 315°, and 360°.

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1. The given word is "MILLIMICRON". The word has 11 letters in total and consists of 2 M's, 2 I's, 2 L's, 1 C, 1 R, 1 O, and 1 N. So, we can use the formula for finding permutations of n objects of which p are of the same kind, q are of another kind, r are of the third kind, and so on. The formula is `n!/(p!q!r!...)`. Here, we have p = 2, q = 2, r = 2, and so on. So, the number of distinguishable ways that the letters of the word "MILLIMICRON" can be arranged in order is: `11!/(2!2!2!) = 4989600` 2. We are given that the distinguishable orderings of the letters of "MILLIMICRON" begin with "M" and end with "N". We have fixed two letters at the beginning and end.

Now, we have 9 letters left which can be rearranged in the remaining 9 spots. So, the number of distinguishable orderings of the letters of "MILLIMICRON" that begin with "M" and end with "N" is: `9!/(2!2!1!) = 22680`3. We are given that the distinguishable orderings of the letters of "MILLIMICRON" must contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order. We can group "CR" and "ON" together as a single letter. So, we have 9 letters: {M, I, L, L, I, M, C, RON, O}. We need to find all the distinguishable orderings of these letters. Let's consider the group "RON" as a single letter. Now, we have 8 letters: {M, I, L, L, I, M, C, RON}. These 8 letters can be arranged in 8! ways. Within the group "RON", we can arrange the letters "R", "O", and "N" in 3! ways. So, the total number of distinguishable orderings of the letters of "MILLIMICRON" that contain the letters "CR" next to each other in order and also the letters "ON" next to each other in order is: `8!×3! = 20,160`.

Hence, the answers are: 1. 4,989,6002. 22,6803. 20,160

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Answer:

7.6 ounces of silver

Step-by-step explanation:

Hope this helps :)

There ae 3.6 ounces of Gold in the metal bar.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

A metal bar weighs 24 ounces.

And, 15% of the bar is gold.

Now, We can formulate as;

Amount of gold in the bar is,

⇒ 15% of 24

⇒ 15/100 × 24

⇒ 3.6 ounces

Hence, There ae 3.6 ounces of Gold in the bar.

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Answer:

true because you can do that in a amound of the total

Answer:

La temperatura en estos momentos es -2 grados centígrados.

Step-by-step explanation:

Dado que conoces que había una temperatura de 8°C y que a las 22 horas esta ha bajado unos 10 grados, tienes que restar estos 10 grados de la temperatura inicial para saber cuál es la temperatura actual:

8-10=-2

De acuerdo a esto, la respuesta es que la temperatura en estos momentos es -2 grados centígrados.

Answer:

Domain: (-∞,+∞)

Range: (-∞,1)

y-intercept: (0,2)

Asymptote: I am not sure (sorry) I know they can be solved using the equation n(x)=0

Step-by-step explanation:

Domain: the set of all x-values

- this graph has arrows which means the domain is from -∞ to +∞ (-∞,+∞)

Range: the set of all y-values

- the graph extend continuously on the negative side so -∞ and it stops at 1 on the positive side  (-∞,1)

Y-intercept: this point is where the graph crosses the y-axis, this is at (0,2)

Answer:

Division

Step-by-step explanation:

Answer:

31.5 mi/gal

Step-by-step explanation:

[tex]63[/tex]÷[tex]2[/tex][tex]=31.5[/tex]

So, Sophia got 31.5 miles per gallon

Answer: 31.5 I think.

Step-by-step explanation:

Give other person brainliest

The statements that are TRUE with regard to a data set's measures of Central Tendency, Dispersion, and Paired Observations are the following:In a very small set of data, i.e. small n, the Sample Standard Deviation is generally smaller than its Population Standard Deviation.

It is possible for the value of the Correlation between a set of paired observations to be greater than 1.In a set of paired observations of X and Y, if the Correlation is 0.75, then as the values of X increases (decreases), the values of Y also generally increases (decreases) in the same direction.In a very large set of data, i.e. large n, the Standard Deviation is a better measurement than Range.Why these statements are true?In a very small set of data, the Sample Standard Deviation is generally smaller than its Population Standard Deviation because when the sample size is smaller, there is less dispersion and thus the value of the sample standard deviation is generally smaller than that of the population standard deviation.It is possible for the value of the Correlation between a set of paired observations to be greater than 1 because the correlation coefficient r ranges from -1 to 1, inclusive of both endpoints.

However, it is practically impossible to get a value of r outside this range in a real dataset.In a set of paired observations of X and Y, if the Correlation is 0.75, then as the values of X increases (decreases), the values of Y also generally increases (decreases) in the same direction. This is because 0.75 is a strong positive correlation indicating that as the value of one variable increases, the value of the other variable also increases.In a very large set of data, i.e. large n, the Standard Deviation is a better measurement than Range because the standard deviation takes into account all values in the dataset and is less sensitive to outliers as compared to the range. On the other hand, the range only considers the minimum and maximum values of the dataset and thus is less informative.

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