"Find derivatives using Implicit Differentiation and Logarithmic Differentiation." Use Logarithmic Differentiation to help you find the derivative of the Tower Function y = (cot(3x))? Note: Your final answer should be expressed only in terms of x.

To determine if a data point is considered an outlier for a data set, we need to calculate the interquartile range (IQR) and use it to define the outlier boundaries. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). The correct option is (B).

We have that Q1 = 9 and Q3 = 17, we can calculate the IQR as follows:

IQR = Q3 - Q1 = 17 - 9 = 8

To identify outliers, we can use the following rule:

- Any data point that is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR is considered an outlier.

Using this rule, we can evaluate each data point:

A. 27: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

B. 17: This data point is not an outlier because it is equal to the third quartile (Q3).

C. 3: This data point is less than Q1 - 1.5 * IQR = 9 - 1.5 * 8 = -3. It is considered an outlier.

D. 41: This data point is greater than Q3 + 1.5 * IQR = 17 + 1.5 * 8 = 29. It is considered an outlier.

Therefore, the outliers in the data set are A (27) and D (41).

As for when to use the mean, it is generally recommended to use the mean as a measure of central tendency when the data is symmetric and does not have extreme values.

Therefore, the correct option would be B. When the data is symmetric.

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Answer:

x = -3

y = 1

z = -2

Step-by-step explanation:

-2x + 3y + z = 7

-4x - y -2z = 15

x + 2y +3z = -7

|-2 3 1|

|-4 -1 -2|

|1 2 3|

Determinant of this from online determinant calculator is;

D = 21

For Dx, we have;

|7 3 1|

|15 -1 -2|

|-7 2 3|

Determinant of this from online determinant calculator is;

Dx = -63

For Dy, we have;

|-2 7 1|

|-4 15 -2|

|1 -7 3|

Determinant of this from online determinant calculator is;

Dy = 21

For Dz, we have;

|-2 3 7|

|-4 -1 15|

|1 2 -7|

Determinant of this from online determinant calculator is;

Dz = -42

From creamers rule;

x = Dx/D

y = Dy/d

z = Dz/d

Thus;

x = -63/21

x = -3

y = 21/21

y = 1

z = -42/21

z = -2

Thus,

x = -3

y = 1

z = -2

Answer:

A is the answer

Step-by-step explanation:

The correlation would stay the same.

The correlation change if the graduation rate was plotted on the x-axis and tuition plotted one the y-axis is option (A) The correlation would stay the same

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data.

It is a measure of the extent to which two variables are related.

Given,

A graph titled College comparisons has semester tuition (thousands of dollars) on the x-axis, and 4-year graduation rate (percentage) on the y-axis.

The value of the r for the scatterplot = 0.856

Here r is positive value therefore the data lies on a perfectly straight line with a positive slope

Therefore the correlation would stay the same

Hence, The correlation change if the graduation rate was plotted on the x-axis and tuition plotted one the y-axis is option (A) The correlation would stay the same

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we have, |fn(x) - f(x)| < εfor all x in [0, 1] and all n ≥ N = ⌈1/ε⌉, which implies that fn converges uniformly to f.

Given the sequence of functions fn(x) = nx / x+n defined on the interval [0, 1],

Let's first prove that it converges pointwise to a function f(x).

Pointwise convergence means that for each fixed value of x in the interval [0, 1], we find the limit of the sequence fn(x) as n approaches infinity.

So we have to evaluate the limit of fn(x) as n approaches infinity:

lim (n → ∞) fn(x) = lim (n → ∞) nx / x + n= lim (n → ∞) nx / (1 + n/x)= lim (n → ∞) n / (1/x + 1/n)

Since x is fixed in the interval [0, 1], we have 0 ≤ x ≤ 1, which implies that 0 ≤ 1/x ≤ ∞. Also, 0 ≤ 1/n ≤ 1.

Hence, by the squeeze theorem,

lim (n → ∞) n / (1/x + 1/n) = 0

Therefore, the sequence of functions fn(x) = nx / x+n converges pointwise to the zero function f(x) = 0 on the interval [0, 1].

Next, we need to show that fn converges uniformly to f. That is, we need to show that for any ε > 0, there exists an integer N > 0 such that |fn(x) - f(x)| < ε for all x in [0, 1] and all n ≥ N. Let ε > 0 be given. Then we have

|fn(x) - f(x)| = |nx / (x + n) - 0| = nx / (x + n) < nx / n = x for all x in [0, 1] and all n ≥ 1.

Hence, to ensure |fn(x) - f(x)| < ε, it is enough to choose N such that 1/N < ε, or equivalently, N > 1/ε.

Thus, we have

|fn(x) - f(x)| < εfor all x in [0, 1] and all n ≥ N = ⌈1/ε⌉, which implies that fn converges uniformly to f.

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The answer of the given question based on the  sequence of functions is , fn converges uniformly to f on the interval [0, 1].

Given the sequence of functions fn(x) = nx / x+n defined on the interval [0, 1], to prove that it converges pointwise to a function f(x), we will need to find the limit of the sequence of functions as n → ∞.

To find the limit of fn(x), let's fix x in [0, 1].

As n → ∞, we can use L'Hopital's rule to get:
lim (n→∞) nx / x + n

= lim (n→∞) x / 1= x
Therefore, f(x) = x is the pointwise limit of the sequence of functions fn(x).

Now, we will prove that fn converges uniformly to f.

To prove that fn converges uniformly to f, we will show that given ε > 0, there exists a positive integer N such that |fn(x) - f(x)| < ε for all x in [0, 1] and all n > N.

We can write fn(x) - f(x) as:
fn(x) - f(x) = (nx / x + n) - x

= nx / x + n - (x + nx / x + n)

= nx / x + n (1 - x / x + n)
Using the absolute value, we can write:
|fn(x) - f(x)| = |nx / x + n (1 - x / x + n)| ≤ nx / x + n ≤ 1
Since x ≤ 1 for all x in [0, 1] and n > 0, we can write:
|fn(x) - f(x)| ≤ nx / n = x
Therefore, we need to find N such that x < ε for all x in [0, 1] and all n > N.

Let's fix ε > 0.

Then, we can choose N = ⌈1/ε⌉. For any x in [0, 1] and any n > N, we have:
|x| ≤ 1 < ε
|x - 0| ≤ ε
Therefore, fn converges uniformly to f on the interval [0, 1].

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Answer:4

Step-by-step explanation:

18 + 2 + 0 + 0 + 0 = 20

20 /5( number of numbers) = 4

Answer:

B

Step-by-step explanation:

using the rule of radicals

\(\sqrt{\frac{a}{b} }\) × \(\sqrt{\frac{c}{d} }\) = \(\sqrt{\frac{ab}{cd} }\) , then

\(\sqrt{\frac{3x}{2} }\) × \(\sqrt{\frac{x}{6} }\)

= \(\sqrt{\frac{3x^2}{12} }\)

= \(\sqrt{\frac{3x^2}{3(4)} }\)

= \(\sqrt{\frac{x^2}{4} }\)

= \(\frac{\sqrt{x^2} }{\sqrt{4} }\)

= \(\frac{x}{2}\)

Step-by-step explanation:

To compare the distances of 2 miles, 4,800 feet, and 4,400 yards, we need to convert all the distances to the same unit. Let's choose feet as the common unit.

1 mile = 5,280 feet (by definition)

2 miles = 10,560 feet (since 2 miles x 5,280 feet/mile = 10,560 feet)

1 yard = 3 feet (by definition)

4,400 yards = 4,400 x 3 feet/yard = 13,200 feet

Now that we have all distances in feet, we can order them from least to greatest:

2 miles = 10,560 feet

4,400 yards = 13,200 feet

4,800 feet = 4,800 feet

Therefore, the order from least to greatest is: 4,800 feet, 2 miles, 4,400 yards.

Note that it is always important to keep track of the units when comparing or combining quantities.

Answer:

3/10 || 7/10

Step-by-step explanation:

Answer:

30%

70%

Plz mark me brainliest

Step-by-step explanation:

Answer:

Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

solution :

From these we can get is;

119 = n – 66

=> n = 119 + 66

=> n = 185

So option d ) 185 is the correct answer

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Disclaimer: the question was given incomplete on the portal. Here is the Complete Question.

Question: Solve the equation 119 = n - 66 and the options are: a. 53, b.186, c. -185, d. 185

We get that the value of n is option (d) 185 for the equation n - 66 = 119.

We are given an equation:

n - 66 = 119.

An equation is an expression that has an equality sign in between.

For example: 3 x + 3 y = 6 or 7 x + 5 y = 9

We have to solve the equation to find the value of n.

First, we will add 66 to both the sides of the equation.

n - 66 + 66 = 119 + 66 .

Now simplifying the expression, we get that:

n = 119 + 66

Solving the expression to get the value of n:

n = 185

So, option (d) 185 is correct.

Therefore, we get that the value of n is option (d) 185

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Answer:

C.) 35

Step-by-step explanation:

Supplementary angles equal 180, therefore, the opposite side of both the angles 90 and 125, must be 180 minus that value.

180-125=55

180-90=90

Now we know that the two inside angles equal 55 and 90. Together, that's 145.

Since all the angles within a triangle equal 180, we subtract the two other angles to find p.

180-145=35

Answer:

What are the answer choices?

Step-by-step explanation:

Answer:

16 girls

because 4+3=7 when you add the ratios which is the total number of parts in the ratio.

then you divide 28/7=4 which is equal to one part

then you multiply 4x4 because you are trying to find out the number of girls and there are 4 part girls in the ratio. 4x4=16 so therefore there are 16 girls in the class

Answer:

26, 31, 36

Step-by-step explanation:

Add 5 for each term

It will take the faster train 8 hours to catch up to the slower train.

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

In one hour, the slower train travels 40 miles, so after t hours (where t is the time it takes for the faster train to catch up), the slower train will have traveled:
d = 40(t + 1)
The faster train travels at a rate of 45 mph, so in t hours it will have traveled:
d = 45t
We can set these two equations equal to each other, since they both represent the same distance:
40(t + 1) = 45t
Expanding the left side gives:
40t + 40 = 45t
Subtracting 40t from both sides gives:
40 = 5t
Dividing both sides by 5 gives:
t = 8
So it will take the faster train 8 hours to catch up to the slower train.

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Answer:

scale factor = \(\frac{5}{6}\)

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original.

scale factor = \(\frac{C'D'}{CD}\) = \(\frac{25}{30}\) = \(\frac{5}{6}\)

The average rate of change tell you in this context the volume of water in the base as the volume changes from 2.5 cups to 4.25 cups.

The average rate of change is a mathematical concept used to describe how a change in one quantity affects another quantity.

To calculate the average rate of change, we need to know the height of water in the vase at two different volumes. Let's call the height of water at a volume of 2.5 cups "h1" and the height of water at a volume of 3.25 cups "h2". Then, the average rate of change over the interval from 2.5 cups to 3.25 cups is calculated as:

=> (h2 - h1) / (3.25 - 2.5) = (h2 - h1) / 0.75

This average rate of change tells us how much the height of water changes, on average, for every one cup increase in the volume of water in the vase.

In other words, the average rate of change provides us with a measure of the "slope" of the relationship between the height of water and the volume of water in the vase over the interval from 2.5 cups to 3.25 cups.

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Answer: 90 degrees

Step-by-step explanation:

The hypotenuse is opposite the right angle, which is created by the two shortest sides.

The equation to represent the cost of each drink is 3(x + 2.5) + 3x = 25.50. The cost of each drink will be $3.

In the given question, it is stated that the family spent a total of $25.50 and they bought 3 Popcorn and 3 Drinks. Each popcorn costs $2.5 more than the drink. Now, suppose the cost of one drink is 'x' then we get:

Cost of 3 Drinks = 3x

Cost of 3 Popcorn = 3(x + 2.5)

The equation to represent this will be:

=>  3(x + 2.5) + 3x = 25.50

=>  3x + 7.5 + 3x = 25.50

=>  6x = 18

=>  x = 3

We get x = 3, Cost of one drink will be $3

Hence,  equation representing it will be 3(x + 2.5) + 3x = 25.50, and the cost of each drink will be $3

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The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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The original recurrence relation T(n) = T(n - 1) + n into a closed-form expression T(n) = T(n - 1) + n(n + 1)/2.

Recurrence relations are mathematical equations that define a sequence based on its previous terms. Solving recurrence relations is an important topic in computer science and mathematics. One technique used to solve such recurrences is called unrolling. In this explanation, we will use the unrolling technique to solve the given recurrence relation.

To solve the recurrence relation T(n) = T(n - 1) + n, with T(1) = 0, we will apply the unrolling technique. Unrolling involves expanding the recurrence relation by repeatedly substituting the recurrence equation into itself until we reach a base case.

Let's start by expanding the recurrence relation for a few terms:

T(n) = T(n - 1) + n

      = T(n - 2) + (n - 1) + n

      = T(n - 3) + (n - 2) + (n - 1) + n

We can observe a pattern here. Each time we expand the recurrence, we add the next term in the sequence, starting from n and going down to 1.

Continuing this process, we can express T(n) as the sum of all the terms from n to 1:

T(n) = T(n - 1) + T(n - 2) + T(n - 3) + ... + T(2) + T(1) + n + (n - 1) + (n - 2) + ... + 2 + 1

We can simplify this expression by grouping the terms:

T(n) = [T(n - 1) + T(n - 2) + T(n - 3) + ... + T(2) + T(1)] + [n + (n - 1) + (n - 2) + ... + 2 + 1]

The first part in square brackets represents the sum of the previous terms in the recurrence relation, which we denote as S(n-1):

T(n) = S(n - 1) + [n + (n - 1) + (n - 2) + ... + 2 + 1]

The second part in square brackets represents the sum of the integers from 1 to n, which is a well-known formula and can be written as n(n + 1)/2:

T(n) = S(n - 1) + n(n + 1)/2

Now, we need to find a closed-form expression for S(n-1). To do that, we can apply the same unrolling technique to the sum of the previous terms:

S(n - 1) = S(n - 2) + S(n - 3) + ... + S(2) + S(1)

We can notice that S(n-1) is essentially the same recurrence relation as T(n), but with a different initial condition. Therefore, we can rewrite S(n-1) as T(n-1) with a new initial condition:

S(n - 1) = T(n - 1) - T(1)

Substituting this back into the expression for T(n), we get:

T(n) = T(n - 1) - T(1) + n(n + 1)/2

We know that T(1) = 0, so we can simplify further:

T(n) = T(n - 1) + n(n + 1)/2

This is the final closed-form expression for the given recurrence relation. To calculate the value of T(n), you can either use this formula directly or implement it recursively or iteratively in a programming language.

Using the unrolling technique, we have transformed the original recurrence relation T(n) = T(n - 1) + n into a closed-form expression T(n) = T(n - 1) + n(n + 1)/2, which provides a more direct way to calculate the value of T(n) for any given n.

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To get another estimate using the velocities at the end of the time periods, repeat the process from (a), but this time, use the velocity values at the end of each interval as the heights of the rectangles.

To estimate the distance traveled by the motorcycle, we can use the velocities at the beginning or end of the time intervals to calculate the area under the velocity graph using rectangles.

(a) Using the velocities at the beginning of the time intervals, we can estimate the distance by adding up the areas of the rectangles formed by the velocity and time intervals. The distance estimate is the sum of these areas, which is approximately 156 meters.

(b) Using the velocities at the end of the time intervals, we can estimate the distance by adding up the areas of the rectangles formed by the velocity and time intervals. The distance estimate is the sum of these areas, which is approximately 175 meters.

(c) Since the velocity function is increasing over time, the estimate in part (a) using the velocities at the beginning of the time intervals is a lower estimate, and the estimate in part (b) using the velocities at the end of the time intervals is an upper estimate. This is because the velocity is increasing, and the rectangles using the beginning velocities will underestimate the distance, while the rectangles using the end velocities will overestimate the distance. Therefore, we can conclude that the estimates in parts (a) and (b) are respectively lower and upper estimates of the distance traveled by the motorcycle.

(a) To estimate the distance traveled using the velocities at the beginning of the time intervals, use the velocity values as the heights of rectangles and multiply them by the interval width (12 seconds). Sum up the resulting products to get an approximate distance.

(b) To get another estimate using the velocities at the end of the time periods, repeat the process from (a), but this time, use the velocity values at the end of each interval as the heights of the rectangles.

(c) The estimates in parts (a) and (b) can be considered as upper and lower estimates if the velocity function is strictly increasing or decreasing. If the velocity function is neither increasing nor decreasing consistently, then these estimates are not strictly upper or lower estimates. To determine which is which, analyze the given data and observe the behavior of the velocity function over time.

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Answer:

1. 130/6

2. 240/3

Step-by-step explanation:

make the whole numbers into a fraction by putting 1 as the denominator.

48/1.

then multiply together.

48 x 5 = 130

6 x 1 = 6

130/6

do the same with the other

120 x 2 = 240

1 x 3 = 3

240/3

Answer:

40

80

Step-by-step explanation:

5/6 × 48

5 × 48 = 240

240/6

= 40

120 × 2/3

120 × 2 = 240

240/3

= 80

Answer:

35 cents

Step-by-step explanation:

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If  his current total savings is 300m²+120m+180 dollars. The factorization that represent the months and monthly deposit is: 60(5m²+2m+3)

Given:

Expression=300m²+120m+180

Factorize

Extraction of common factor

60(5m²+2m+3)

Expand

60×5m²+60×2m+60×3

=300m²+120m+180

Therefore the factorization that represent the months and monthly deposit is: 60(5m²+2m+3).

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Answer: D

Step-by-step explanation:

Answer:

m<AOB = 50°

Step-by-step explanation:

<ACB = 25° is an inscribed angle of the circle.

<AOB is a central angle of the circle.

Thus, based on the inscribed angle theorem which states that an inscribed angle is ½ the measure of the central angle, therefore:

m<ACB = ½(m<AOB)

Substitute

25° = ½(m<AOB)

Multiply both sides by 2

2*25 = m<AOB

m<AOB = 50°

Answer:

44%

Step-by-step explanation:

60%-16% the answer is up ahead.

After 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6

Using the formula for compound interest:

A = \(P(1 + \frac{r}{n} )^{nt}\)

Where:

A = the future amount (the amount Dan will owe after 9 years)

P = the principal amount (the initial borrowed amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Given:

P = $8000

r = 18% = 0.18 (as a decimal)

n = 12 (monthly compounding)

t = 9 years

substitute the values into the formula:

A = \(8000(1 + \frac{0.18}{12} )^{12*9}\)

A = \(8000(1 + 0.015)^{108}\)

 = \(8000(1.015)^{108}\)

 = 8000(1.6487)

A = $13,189.6

Therefore, after 9 years with monthly compounding and no payments, Dan will owe approximately $13,189.6.

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Answer:

11.7b

Step-by-step explanation:

If you do 339.30 divided by 29 it equals 11.7 but the full equation would be c=11.7b

The proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

What is proportion?

The size, number, or amount of one thing or group as compared to the size, number, or amount of another. The proportion of boys to girls in our class is three to one.

Let's assume that each boxed lunch costs the same amount, denoted by the variable 'x'.

We are given that the company ordered 29 boxed lunches for a total cost of $339.30. Therefore, we can write the equation:

29x = 339.30

To find the cost 'c' for any number 'b' of boxed lunches, we can set up a proportion:

29x / 29 = 339.30 / b

Simplifying this equation, we get:

x = 339.30 / 29

Now, we can substitute this value of 'x' back into the equation:

c = bx = b * (339.30 / 29)

Therefore, the proportional equation for the total cost 'c' in terms of the number of boxed lunches 'b' is:

c = (339.30 / 29) * b

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A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.