Find the area of a regular octagon with an apothem length of 10 and a side length of 6.

the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

To find the derivative of the function y = (ln(x + 4))x using logarithmic differentiation, we can follow these steps:

Step 1: Take the natural logarithm of both sides of the equation:

  ln(y) = ln((ln(x + 4))x)

Step 2: Use the logarithmic property ln(a^b) = b ln(a) to simplify the right-hand side of the equation:

  ln(y) = x ln(ln(x + 4))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

  (1/y) * y' = ln(ln(x + 4)) + x * (1/ln(x + 4)) * (1/(x + 4))

Step 4: Simplify the expression on the right-hand side:

  y' = y * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Step 5: Substitute the original expression of y = (ln(x + 4))x back into the equation:

  y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]

Therefore, the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].

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Answer:

\(\dfrac{1}3\)

Step-by-step explanation:

When rolling a die successively, the probability of rolling a certain number(s) does not change because the die stays the same.

In this problem, we need to find the probability that a die roll will produce a number less than 3. First, we can list out those numbers:

all numbers:

numbers less than 3:

We can see that there are 6 total numbers and 2 numbers less than 3.

Therefore, we can represent the probability of rolling a number less than 3 as:

\(\dfrac{2}{6}\)

\(\boxed{=\dfrac{1}3}\)

First, we'll find the probability that a die is rolled only once.

There are 2 numbers that are less than 3, which are 1 and 2.

This makes the fraction 2/6, or simplified to 1/3.

The probability is 1/3.

9514 1404 393

Answer:

  d

Step-by-step explanation:

The geometric sequence is ...

  20, 10, 5

so has a common ratio of 10/20 = 5/10 = 1/2.

Only one answer choice shows that each successive term is 1/2 the one before. That is choice D.

Answer:

The expression √x+5+√1-x is defined for all values of x such that the value under the square root sign is non-negative. We can find the values of x that satisfy this condition by considering each of the square roots separately.

For the first square root, the value under the square root must be non-negative, so we have the following inequality:

x + 5 ≥ 0

x ≥ -5

For the second square root, the value under the square root must be non-negative, so we have the following inequality:

1 - x ≥ 0

x ≤ 1

Therefore, the expression is defined for all values of x that satisfy both of these inequalities. This means that the expression is defined for values of x in the range -5 ≤ x ≤ 1. The correct answer is therefore option D.

Answer:

The 75th term of the arithmetic sequence -17, -13, -9.... is:

\(a_{75}=279\)

Step-by-step explanation:

Given the sequence

\(-17, -13, -9....\)

An arithmetic sequence has a constant difference 'd' and is defined by  

\(a_n=a_1+\left(n-1\right)d\)

computing the differences of all the adjacent terms

\(-13-\left(-17\right)=4,\:\quad \:-9-\left(-13\right)=4\)

The difference between all the adjacent terms is the same and equal to

\(d=4\)

The first element of the sequence is:

\(a_1=-17\)

now substitute \(d=4\) and \(a_1=-17\) in the nth term of the sequence

\(a_n=a_1+\left(n-1\right)d\)

\(a_n=4\left(n-1\right)-17\)

\(a_n=4n-21\)

Now, substitute n = 75 in the \(a_n=4n-21\) sequence to determine the 75th sequence

\(a_n=4n-21\)

\(a_{75}=4\left(75\right)-21\)

\(a_{75}=300-21\)

\(a_{75}=279\)

Therefore,  the 75th term of the arithmetic sequence -17, -13, -9.... is:

\(a_{75}=279\)

Answer: Angle T is 45

Step-by-step explanation:

Yes, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.

A vector is a mathematical object that represents a quantity with both magnitude and direction. In the case of ℝ5, this set includes all possible lists of five real numbers, which can be thought of as five-dimensional vectors. Each number in the list represents a component or coordinate of the vector, indicating how far it extends in each of the five dimensions.

Therefore, any list of five real numbers can be considered a vector in the set of real numbers with dimension 5, denoted as ℝ5.


In mathematics, a vector is an element of a vector space, which is a set of objects that can be added together and multiplied by scalars (real numbers). The set ℝ⁵ is a vector space consisting of all 5-tuples (lists) of real numbers, written as (a₁, a₂, a₃, a₄, a₅), where each element aᵢ is a real number. Any list of five real numbers forms a vector in ℝ⁵ because it satisfies the required conditions to be an element of the vector space.

A list of five real numbers is indeed a vector in the set of real numbers ℝ⁵, as it meets the necessary criteria to be a part of the vector space.

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Answer:

1/49

Step-by-step explanation:

If i’m wrong my bad, but probability is desired out comes over possible. So there are 52 cards in a deck and there are 1 special card each in a suit= 3 or 4 but we are focusing on three, 52-3= 49 then there is one desired outcome since it’s “a” six of hearts. It’s 1/49

Answer:  The independant variable is the type of tennis ball.  The dependent variable is how high the ball bounces.

Step-by-step explanation:

A word problem that uses mixed numbers and asks to find the unit price of an item is " The price of a cup of rice is $2. Find the price of 3 1/2 cups.

From the information given, we want to find the word problem that uses mixed numbers and asks to find the unit price of an item.

This can be illustrated as the price of a cup of rice is $2. Find the price of 3 1/2 cups.

Therefore, the price of the cups of rice will be:

= 3 1/2 × $2

= $7

The price is $7.

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Bring like terms together

on number line, we will have

The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)

People eating hamburger P(h) =0.38

People eating burritos P(b) = 0.31

Number of people eating pizza = 35

    Let's suppose the total number of people is 1

So,

    By adding the total number of people eating hamburgers and burritos                                          

                                                           = 0.38+0.31

                                                            = 0.69

    The ratio of the total number of people eating pizza = 1.00 - 0.69

                                                                                            = 0.31

   So total number of people eating pizza = 0.31 = 35

   By solving :

              1 = 35 / 0.31

                = (35*100)/31

                = 3500/31

                 = 112.9 (we have to write it down in the nearest whole number)

Here we writing the approximate value of 112.9 = 113 (Approximate)

Hence, the total number of people in the food court in the nearest whole number is 113

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Answer: Area = 108 in. or 3/4 ft.

Step-by-step explanation: The formula for the area of a rectangle is l•w (length times width).

To get the area, you need to convert the units of measurement to one or the other (either inches or feet) because you cannot multiply them unless they are the same.

To get the area in inches, you convert 3 ft. to inches which is 36 inches, and then multiply it by 3 inches. You will get that the area = 108 inches.

To get the area in feet, you convert 3 inches to feet which is 1/4 (or 0.25) feet and then multiply it by 3 feet which gives you area = 3/4 ft. (or 0.75 ft.). Hope this helps.

The equation of the linear function is y = x - 5

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

The ordered pairs (0,-5) and (-2,-3)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 5

Using the other point (-2, -3), we have

-2m - 5 = -3

Evaluate the like terms

-2m = 2

Divide by 2

m = 1

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

y = x - 5

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Complete question

Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.

y = ___?___

Answer: 1/3

Step-by-step explanation:

1/3x1/3x1/3=1/27

Answer:

$5.00

Step-by-step explanation:

$3.50+$1.50=$5.00

Answer:

1/24

Step-by-step explanation:

We want to find the probability of picking a watermelon AND picking a green apple right after. These events are completely independent of each other as the watermelon is put back, and picking a watermelon/green apple does not affect the chances of getting the other the next/previous time. The formula for this is P(A) * P(B), with P(A) being the probability of event A happening and P(B) being the probability of event B happening. It does not matter which event is which.

Let's say picking a watermelon is event A and picking a green apple is event B.  There are 6 watermelons and 6+5+1 = 12 jolly ranchers, so there is a 6/12 = 1/2 chance of picking a watermelon. There is 1 green apple and still 12 jolly ranchers, so there is a 1/12 chance of picking a green apple jolly rancher.

Multiplying these two, we get (1/2) * (1/12) = 1/24

Answer:

g(x) =1

x-1

it's either g(x) or f(x)

a) Variables

• d: distance a person is from the pivot, in ft

• w: person's weight, in lbs

Since the variables are inversely proportional, then they are related by the next formula:

where k is constant.

b) Where w = 145 lbs, d = 6 ft. Substituting these values into the previous formula and solving for k:

Substituting into the formula with d = 5 ft and k = 870, and solving for w, we get:

c) Substituting into the formula with w = 87 lbs and k = 870, and solving for d, we get:

I HOPE THE ABOVE INFORMATION WILL HELP YOU.

THANK YOU.

Answer:

84

Step-by-step explanation:

Multiply 35 by 2.5

Answer:

75 windows

Step-by-step explanation:

35 ---- 7

x ----- 15

\(x=\frac{(35)(15)}{7} =75\)

Hope this helps

A sample is a subset of a population, containing the individuals that are actually observed.

In statistical analysis, a sample is a representative subset of a larger population. When studying a population, it is often impractical or impossible to gather data from every individual within that population. Instead, a sample is selected to provide insights into the characteristics, behavior, or properties of the entire population.

Samples are chosen using various sampling methods, such as random sampling, stratified sampling, or convenience sampling, depending on the research objective and available resources. The goal is to ensure that the sample is representative of the population, so that any observations or conclusions drawn from the sample can be generalized to the larger population.

Samples allow researchers to make inferences about the population based on the observed data. By analyzing the characteristics of the sample, statistical techniques can be applied to estimate population parameters, test hypotheses, and draw conclusions about the population as a whole. The validity and reliability of these inferences depend on the quality and representativeness of the sample selected.

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By using the formula of compound interest we can say that at the end of second year Mrs. Smith will have $65,771.58.

The interest earned from the initial deposit plus the cumulative interest is known as compound interest.

A = P(1 + r/n)^(nt), where P is the principle balance, r is the interest rate, n is the number of times interest is compounded per time period, and t is the total number of time periods, is the formula for compound interest.

Given that,

For first year,

P (principal) = $60,000.00

R = 4.3%

n  = 1

t = 1

First, convert R as a percent to r as a decimal

r = R/100

r = 4.3/100

r = 0.043 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 60,000.00(1 + 0.043/1)^(1×1)

A = 60,000.00(1 + 0.043)^(1)

A = $62,580.00

A = P + I  where,

P (principal) = $60,000.00

I (interest) = $2,580.00

So, by the end of second year Mrs. Smith will have $62,580.00.

Now, the amount calculated from first year will become the principle for second year.

For second year,

P (principal) = $62,580.00

R = 5.1%

n=1

t=1

First, convert R as a percent to r as a decimal

r = R/100

r = 5.1/100

r = 0.051 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 62,580.00(1 + 0.051/1)^(1×1)

A = 62,580.00(1 + 0.051)^(1)

A = $65,771.58

A = P + I where,

P (principal) = $62,580.00

I (interest) = $3,191.58

So, by the end of second year Mrs. Smith will have $65,771.58.

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The probability of rolling and odd number with both dice A and B is 1/4.

Probability simply means the likelihood that an event will occur on a scenario.

Since Dice A and dice B have ten sides,the numbers will be from 1 to 10. Therefore, there are 5 even numbers and 5 odd numbers.

Probability of odd number = 5/10 = 1/2

Probability of even number = 5/10 = 1/2

Probability of rolling both odd numbers will be:

= P(odd) × P(odd)

= 1/2 × 1/2

= 1/4

The probability is 1/4.

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Answer:

Perpendicular

neither

\(y=\frac{4}{5}x-2\)

Step-by-step explanation:

The base salary per year is $66,200, and she only gets the target for medication A, the 70% of the annual bonus of $22,500

(22,500 * 70)/ 100 = 15,750

So the total of her compensation (salary plus bonus) is:

$66,200 + $15,750 = $81950

Answer: A. line y = x

Step-by-step explanation: To determine if a transformation is a reflection across the line y = x, we can draw the line and plot the given points on either side of it. We can then draw a perpendicular line from each point to the line y = x, and see that the distance between the point and the line is equal on both sides.

- Lizzy ˚ʚ♡ɞ˚

Answer:

Step-by-step explanation:

Important fact: much as I hate to admit it, in all professional sports, there is no team that has made as many appearances in the sports final as the Canadiens.

The ratio you want is 10/32 = 5/16.

The ratio means that for every 5 appearances the rangers made, the Canadiens made 16 appearances.