Differentiate a Power Series Question use the power series representation f(x)-ln(1-3z) representation for g(z) T& on the interval (-1 , 1). (3z)",-1 〈 z 〈 3 to find a power ser 1 to find )--Σ 仁1 Select the correct answer below: n=1 2-1

By evaluating the linear function f(x) = x - 3 at x = 5 and discarding the another function in the table given, we conclude that f(5) = 2 belongs to that linear equation.

In this problem we must check if the given relationship between the independent variable (x) and the dependent variable (y) exists in any of the two functions: (i) a table, (ii) an expression.

After a quick analysis, we conclude that f(5) = 2 is a point of the linear function f(x) = x - 3. Here is the proof:

f(5) = 5 - 3

f(5) = 2

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Answer:A which is x-3

Step-by-step explanation:

The present age of John is 20 and the present age of Hlice is 5.

Let's solve the problem using algebraic equations and include the terms : John is 4 times as old as thice. In 20 years the Jolm will be twice as old, as Hlice. Find the present age of the both of them.

Let's assume the present age of Hlice = x and the present age of John = 4x (because John is 4 times as old as thice)In 20 years, the age of John = 4x + 20

In 20 years, the age of Hlice = x + 20 According to the problem, In 20 years the Jolm will be twice as old, as Hlice.(4x + 20) = 2(x + 20)4x + 20 = 2x + 40 4x - 2x = 40 - 204x = 20x = 5 (age of Hlice) Present age of John = 4x = 4 × 5 = 20

Therefore, the present age of John is 20 and the present age of Hlice is 5.

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Answer:

c = 7

d = 4

Step-by-step explanation:

To determine the values of c and d in the given equation, expand the brackets and rearrange the terms:

\(\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\2c-12x+5dx-d&=8x+10\\5dx-12x+2c-d&=8x+10\\(5d-12)x+(2c-d)&=8x+10\end{aligned}\)

To solve for d, equate the terms in x:

\(\begin{aligned}(5d-12)x&=8x\\5d-12&=8\\5d&=20\\d&=4\end{aligned}\)

To solve for c, equate the constants and substitute the found value of d:

\(\begin{aligned}2c-d&=10\\2c-4&=10\\2c&=14\\c&=7\end{aligned}\)

Therefore, the values of c and d are:

Check by substituting the found values of c and d into the original equation:

\(\begin{aligned}2(c-6x)+d(5x-1)&=2(4x+5)\\\\c=7,\;d=4\implies 2(7-6x)+4(5x-1)&=2(4x+5)\\14-12x+20x-4&=8x+10\\20x-12x+14-4&=8x+10\\8x+10&=8x+10\end{aligned}\)

Answer:

Step-by-step explanation:

Answer:

16=3=-16

"Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers." -Albert Einstein

Answer:

0.102048 ampere

Step-by-step explanation:

I α k / R

Current = 1/5 ; R = 8750

What is the current when the resistance is 17150 ​ohms

First obtain the value of k :

I = k/R

I = 1/5 ampere = 0.2 A

0.2 = k / 8750

k = 1750

What is the current when the resistance is 17150 ​ohms

I = 1750 / 17150

I = 0.1020408

I = 0.102048 ampere

Answer:

28 pillows

Step-by-step explanation:

\( = 10 \frac{1}{2} \div \frac{3}{8} \\ = \frac{21}{2} \div \frac{3}{8} \\ = \frac{21}{2} \times \frac{8}{3} \\ = 28\)

Answer:

the first one is 2/4 and 3/6

the second one is 4/6 and 6/8  and the equation is

3/4 times 4/6 = .5

Step-by-step explanation:

Expreion have a quotient of 6 is 0. 48 ÷ 0. 08.

What is quotient?

In mathematics, the quotient is the result of performing division operations on two integers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

0. 48 ÷ 0. 8

=0.06

The solution for Long Division of \($\frac{4.8}{8}$\) is 0.6

The solution for Long Division of \($\frac{0.48}{0.08}$\) is 6.

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The opposite diagonal is 5.95m long, exact as previous diagonal in length which indicates that the table's diagonal length is the same throughout.

According to the Pythagorean Theorem, the square of the length of the hypotenuse in every right triangle equals the sum of the squares of the lengths of the two legs.

Let's denote the width as w = 4.1m and the length as l = 4.1m. Then, the diagonal length d can be found as:

d² = w² + l²

Substituting the given values, we get:

d² = (4.1m)² + (4.1m)²

d² = 16.81m² + 16.81m²

d² = 2(16.81m²)

d = sqrt(2(16.81m²))

d ≈ 5.95m

So, we have found that the diagonal length across the table is approximately 5.95m.

Now, to prove that the diagonal length is the same length, we can repeat this calculation, but using the other diagonal of the table.

Let's denote the width as w = 4.1m and the length as l = 4.1m. Then, the other diagonal length d' can be found as:

d'² = w² + l²

Substituting the given values, we get:

d'² = (4.1m)² + (4.1m)²

d'² = 16.81m² + 16.81m²

d'² = 2(16.81m²)

d' = sqrt(2(16.81m²))

d' ≈ 5.95m

As a result, we have established that the other diagonal is roughly 5.95m long, the same as the first diagonal. This demonstrates that the table's diagonal length is the same throughout.

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Let's first write the vector equation of the two lines r1​ and r2​. r1​(t)=⟨3t+5,−3t−5,2t−2⟩r2​(t)=⟨11−6t,6t−11,2−4t⟩

​The direction vector for r1​ will be (3,-3,2) and the direction vector for r2​ will be (-6,6,-4).If the dot product of two direction vectors is zero, then the lines are orthogonal or perpendicular. But here, the dot product of the direction vectors is -18 which is not equal to 0.

Therefore, the lines are not perpendicular or orthogonal. If the lines are not perpendicular, then we can tell if the lines are distinct parallel lines or skew lines by comparing their direction vectors. Here, we see that the direction vectors are not multiples of each other.So, the lines are skew lines. Choice: The lines are skew.

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Answer:

I am 100% sure its 4.03 x 10^7

Step-by-step explanation:

Answer:

The percentage increase from 8000 to 10000 is 25%.

The percent of increase from 8000 to 10000 is given as 25%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100. The percent of increase or decrease can be found by taking the ratio of the increased or decreased value to the initial value.

The given numbers are 8000 and 10000.

The percent increase can be obtained as follows,

The increased value ÷ Initial number × 100

⇒ (10000 - 8000) ÷ 8000 × 100

⇒ 2000 ÷ 8000 × 100

⇒ 25%

Hence, the percent increase is obtained as 25%.

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The question states that 1/4 of students at International are in the blue house, with 1/5 votes for Adam and 1/4 for Franklin. To analyze the results, calculate the fraction of votes for each candidate and multiply by the total number of students.

Based on the information provided, 1/4 of the students at International are in the blue house. The vote went as follows: 1/5 of the votes were for Adam, and 1/4 of the votes were for Franklin.

To analyze the vote results, we need to calculate the fraction of votes for each candidate.

Let's start with Adam:
- The fraction of votes for Adam is 1/5.
- To find the number of students who voted for Adam, we can multiply this fraction by the total number of students at International.

Next, let's calculate the fraction of votes for Franklin:
- The fraction of votes for Franklin is 1/4.
- Similar to before, we'll multiply this fraction by the total number of students at International to find the number of students who voted for Franklin.

Remember, we are given that 1/4 of the students are in the blue house. So, if we let "x" represent the total number of students at International, then 1/4 of "x" would be the number of students in the blue house.

To summarize:
- The fraction of votes for Adam is 1/5.
- The fraction of votes for Franklin is 1/4.
- 1/4 of the students at International are in the blue house.

Please note that the question is incomplete and doesn't provide the total number of students or any additional information required to calculate the specific number of votes for each candidate.

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The quadratic equation that has (3·x + β) ans (3·x + a) as the roots can be presented as follows;

9·x² - 7.5·x - 3 = 0

A quadratic equation is an equation that can be expressed in the form; y = a·x² + b·x + c, where, a ≠ 0, and a, b, and c are numbers.

The quadratic equation -2·x² - 5·x + 6 = 0, divided by a factor of -1 indicates that we get;

2·x² + 5·x - 6 = 0

The quadratic formula indicates that we get;

x = (-5 ± √(5² - 4 × 2 × (-6))/(2 × 2) = (-5 ± √(73))/4

Let a = (-5 + √(73))/4 and let β =  (-5 - √(73))/4)

(3·x + ((-5 + √(73))/4)) × (3·x + (-5 - √(73))/4) = 9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4)

9·x² + 3·x·(-5 - √(73))/4) + 3·x·(-5 + √(73))/4) + ((-5 + √(73))/4)) × (-5 - √(73))/4) = 9·x² - 15·x/2 - 3 = 0

Therefore, the equation that has (3·x + β) ans (3·x + a) as roots is the equation

9·x² - 15·x/2 - 3 = 9·x² - 7.5·x - 3 = 0

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Answer:

≈ 197 students

Step-by-step explanation:

Let's start by writing what we know.

150 students sampled

68 prefer soccer

59 prefer basketball

23 prefer swimming

Part A

If 59 students prefer basketball out of the 150 students sampled then we divide 59/150 in order to get the percentage of students that prefer basketball.

59/150 ≈ 39.33%       Remember this is only a sample of the students so it is approximate.

Now that we have the percentage, we can multiply it by the entire student body to get an approximate number of all students that prefer basketball.

39.33% = .3933

.3933 * 500 = 196.66  ≈ 197 students   (because we can't have a partial student we round up)

The best approximation of the number of students in the school who prefer basketball is 197.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

The results from a random sample of 150 students' after-school activities at a school are shown.

68 students prefer soccer. 59 students prefer basketball. 23 students prefer swimming.

The percentage of students who prefer soccer will be

\(\rightarrow \dfrac{68}{150} = \dfrac{34}{75}\)

The percentage of students who prefer basketball will be

\(\rightarrow \dfrac{59}{150}\)

The percentage of students who prefer swimming will be

\(\rightarrow \dfrac{23}{150}\)

If there are a total of 500 students in the school. Then the best approximation for how many students in the school prefer basketball will be

\(\rightarrow \dfrac{59}{150} \times 500 = 196.667 \approx 197\)

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Answer:

15 hammers

Step-by-step explanation:

Let's first find how much money he has left after he buys the truck:

3750-3400=$350

Now let's find how many hammers he can purchase:

350/22=15.91

This means he can purchase 15 hammers since he cannot have .91 of a hammer.

Answer:

15

Step-by-step explanation:

Since John's truck costs 3,400, subtract that from 3,750

3750

-3400

-----------

350

22 goes into 350 fifteen times, hence giving you the answer 15.

Answer:

B. ½

Step-by-step explanation:

____________________

There are 39 elements in the intersection of the two sets.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Union: -

If set A and set B are two sets, then A union B is the set that contains all the elements of set A and set B. It is denoted as A ∪ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A union B is:

A ∪ B = {1,2,3,4,5,6}

Intersection:-

If set A and set B are two sets, then A intersection B is the set that contains only the common elements between set A and set B. It is denoted as A ∩ B.

Example: Set A = {1,2,3} and B = {4,5,6}, then A intersection B is:

A ∩ B = { } or Ø

Since A and B do not have any elements in common, so their intersection will give null set.

P(AUB) = P(A) + P(B) - P(A∩B)

Here, P (A) = the number of elements in the set A and so on.

We know that:

                     P (A)= 67

                     P (B)= 72

and                P (AUB) = 100

So, we can solve for the number in the intersection i.e.                     P(A∩B) = P(A) + P(B) - P(AUB)

P(A∩B) = 67 + 72 - 100

P(A∩B) = 139 - 100

P(A∩B) = 39.

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The required rate of change in radius of the sphere of change in volume 68ft^3/min is 0.11 ft/min.

We take his adjustment of distance ( 4 miles), and gap by the adjustment of the free factor, time ( 40 minutes or 23 hours). Separating the adjustment of distance by the adjustment of time, one acquires a typical speed, or pace of progress of distance regarding time, of 0.1 miles each moment (or 6 miles each hour).

We have,

Radius(r) = 7 feet, Change in volume = 68 ft^3/min.

To find : Rate of changing radius with respect to time.

So, V = 4πR^3/3

Differentiate w .r .t

dv/dt = 4π/3 d(r^3)/dt

dv/dt = 4π/3. 3r^2dr/dt

Putting the given values,

68 = (4×22×3)/(3 ×7) × (7)^2×dr/dt

dr/dt = 0.11 ft/min.

Thus, change in radius is 0.11 ft.min.

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The data which is given by the historian is used to find the population, variable, parameter, sample, data, and statistic. He estimated the mean number of children per household in New York City in 1900.

Population - all of the households in New York City in 1900.

Variable - a quantity equivalent to the number of children in a randomly selected household

Parameter -  the mean number of children per household in New York City in 1900

Sample - the 200 households selected by the historian

Data - the 200 records collected by the historian

Statistic -  the mean number of children per household in the historian's sample.

Complete question:

Suppose a historian wants to estimate the true mean number of children per household in New York City in 1900. The historian randomly selects 200 household census records from New York City. She records the number of children residing in each household. The historian then computes the mean number of children per household among these 200 households. Classify each description as one of a parameter, variable, population, sample, data, or statistic.

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

Its D if you think about it

Step-by-step explanation:in your mind move the triangle on the top right down 6 units and then turn your triangle 90 degrees counter clockwise (quick maths)

The only transformation that will move the triangle in quadrant 1 onto the similar triangle in quadrant three is;

Option D; translation 6 units down and rotation 90° counterclockwise

The y-coordinate of the right angle vertex of the triangle in quadrant 1 is y = -2. Meanwhile the y-coordinate of the same right angle point of the triangle in quadrant 3 is y = -4.

Thus, for the triangle in quadrant 1 to be on the same level with that in quadrant 3, we need to translate the triangle in quadrant 1 downwards by 6 units.

Now, since we want to map this newly translated triangle to the one in quadrant 3 and as such we need to rotate it 90° counterclockwise

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Answer:

The numbers are 410 , 82

Step-by-step explanation:

Let the another number be x

Positive number = \(\frac{1}{5}x\)

Their difference = 328

\(x - \frac{1}{5}x=328\\\\\frac{x*5}{1*5}-\frac{1}{5}x=328\\\\\frac{5x-x}{5}=328\\\\\frac{4x}{5}=328\\\\x=328*\frac{5}{4}\\\\x=82*5\\\)

x = 410

Positive number = \(\frac{1}{5}*410=82\)

The numbers are 410 , 82

A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothe

Answer:

9,948,394.

Step-by-step explanation:

Here, the other races is 4% of the total population. So we calculate 4/100 * 248,709,873=9,948,394.92. If you can't have a fractional amount of people is would be 9,948,394.

Answer:

A 3√4

Step-by-step explanation:

The 3 stays and 16 gives you 4 and 4 becomes positive

Answer:what are the numbers and I can tell u

Step-by-step explanation:ok

Answer:

https://www.algebra.com/algebra/homework/word/numbers/Numbers_Word_Problems.faq.question.826722.html

Step-by-step explanation:

go to this website, hope you understand it.

Answer:

first=19/5 or 3.8

second=2/5 or 0.4

Step-by-step explanation:

x+3y=5

2x+y=8

multiply by 3

6x+3y=24

subtract

5x=19

x=19/5

2×19/5+y=8

38/5+y=8

38+5y=40

5y=40-38=2

y=2/5

From the given graph, let's find the rate of change.

The rate of change can also be said to be the slope of the graph.

To find the rate of change, apply the slope formula:

Take the points on the graph:

(x1, y1) ==> (4, 21)

(x2, y2) ==> (2, 42)

Thus, we have:

Therefore, the rate of change is -10.5

This means the amount in Harold's savings account decreases by $10.5 each week.

ANSWER:

Rate of change = -10.5