The displacement of a particle on a vibrating string is given by the equation s(t)=3+ \frac{1}{5} sin (3πt)
where s is measured in centimeters and t in seconds. Find the velocity (in cm/s) of the particle after t seconds.\(\frac{1}{5}\)

Answer:

The answer for x is 37° to the nearest whole number

Answer:

the answer of X is 37° to the nearest whole number

If 0.4 Customers arrives after 1 minute-

0.4*5 = 2.0 cm

From 1947 to 1987, Willowbrook State School served Staten Island's Willowbrook neighborhood as a state-funded facility for youngsters with intellectual disabilities. The school had 6,000 students enrolled by 1965 despite being intended for 4,000.

Aerts entered through the doors of Willowbrook State School in 1971 with former Staten Island Advance writer Jane Kurtin, and took disturbing photos of children and adults with special problems who were confined in cages, hungry, and used as research experiments.

Geraldo Rivera, who was working as an investigative reporter for WABC-TV in New York at the time, began an investigation into Willowbrook soon after and found a number of appalling circumstances there, including overcrowding and subpar sanitary facilities.

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Step-by-step explanation:

Because of the 4:1 ratio, the cumulative number of pieces taken into account in that ratio is 4 + 1 = 5.

There is a total amount of money of $150 and 5 pieces.

150/5 = $30 is a single component number.

We know that Ivan consists of four pieces, while Tanya consists of one piece of $120 and 30.

As a result, we now split the amount of Ivan into the amount of Tanya: Ivan has 4 times more than Tanya, so Ivan has 4 times more money.

Hope that works!

Answer:

See below

Step-by-step explanation:

Ratio = 4 : 1

Let

Ivan's share = 4x

Tanya's share = 1x

So,

4x + 1x = £ 150

5x = 150

Divide both sides by 5

x = 150 / 5

x = 30

So,

Ivan's share = 4(30) = £ 120

Tanya's share = 1(30) = £ 30

Also,

Ivan has £ 90 more than that of Tanya.

\(\rule[225]{225}{2}\)

Hope this helped!

Given the functions f\((n)=0.1n^6−n^3 and$ g(n)=1000n^2+500\). To prove that either f(n)=O(g(n)) or g(n)=O(f(n)) by finding specific constants c and n0 for Definition 1: h(n)=O(k(n)).

Here, h(n)=f(n) and k(n)=g(n) We know that

\(f(n)=0.1n^6−n^3 and$\\ g(n)=1000n^2+500\).

The proof requires to prove that either f(n) <= c g(n) or g(n) <= c f(n) for large n.

To do this, we need to find some constant c and n0 such that either of the two conditions above hold. Let's prove that f(n)=O(g(n)).

For Definition 1, there exist constants c>0 and n0>0 such that 0 ≤ f(n) ≤ cg(n) for all n≥n0, where c and n0 are the constants to be determined.

\(f(n)=0.1n^6−n^3\\g(n)=1000n^2+500\)

Now, to prove that

f(n)=O(g(n)) or 0 ≤ f(n) ≤ cg(n),

we need to solve for c and n0 such that:

\(f(n) ≤ cg(n)0.1n^6−n^3 ≤ c\\g(n)0.1n^6−n^3 ≤ c(1000n^2+500)\)

Dividing by \(n^3, we get: 0.1n^3−1 ≤ c(1000+500/n^3)\)

As n approaches infinity, the RHS approaches c(1000).

Let's choose c(1000)=1, so c=1/1000.

Plugging this back into the inequality, we get:  \(0.1n^3−1 ≤ 1/1000(1000+500/n^3)0.1n^3−1 ≤ 1+n^-3/2\)

Multiplying by  \(n^3/10, we get:n^3/10−n^3/1000 ≤ n^3/10+n^(3/2)/1000\)

As n approaches infinity, the inequality holds.

Therefore, f(n)=O(g(n)) for c=1/1000 and n0=1

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Answer: -5

Step-by-step explanation:

im going to assume tomorrow means Two more.....

\(2+4x=-18\)

brilliant.

lets do opposite calculations to both sides. what is the opposite of 2? negative 2. so lets subtract 2 from both sides.

we get

\(4x=-20\)

ok so now we have 4 times x. what is the opposite of this? 4 DIVIDED BY x.

ok now lets do the same to the other side. what is negative 20 divided by 4?

\(x=-5\)

Answer:

the answer is 70

Step-by-step explanation:

52+58+q=180(angle on a straight line)

110+q=180

collect like terms

q=180-110

q=70

Answer:

A. standard form.

Step-by-step explanation:

Standard form = 750,000

Expanded form = 700,000 + 50,000

Answer:

This relation is a function--each value of x corresponds to exactly one value of y.

Answer:

The answer is C

Step-by-step explanation:

Need explanation??

Answer:

y=-3x+6

Slope:-3

y-intercept:6

h(x) = 2x + 4

let y =h(x)

y = 2x + 4

To find the inverse, we interchange the x and y

x = 2y + 4

we make y the subject of formula.

subtract 4 from both sides of the equation:

x - 4 = 2y + 4 - 4

x - 4 = 2y

DIvide both sides by 2:

(x-4)/2 = 2y/2

(x-4)/2 = y

Hence, the inverse of the function:

The proof for the statement "For all sets A, B, and C, if A ⊆ B and B ∩ C = ∅, then A ∩ C = ∅" follows a proof by contradiction approach. By assuming the negation of the desired conclusion and deriving a contradiction, it is shown that the original statement holds true.

The proof begins by assuming the negation of the statement, which states that there exist sets A, B, and C such that A ⊆ B, B ∩ C = ∅, and A ∩ C ≠ ∅.

Then, it is argued that if A ∩ C ≠ ∅, there must exist an element x that belongs to both A and C, denoted as x ∈ A ∩ C.

Next, using the fact that A ⊆ B, it is concluded that x ∈ B because any element in A must also be in B. Additionally, it is known that x ∈ C.

By the definition of intersection, it follows that x ∈ B ∩ C.

Then, using the definition of the complement, it is stated that (A ∩ C)c (the complement of A ∩ C) is equal to the universal set U.

From the definition of intersection, it can be deduced that x ∈ A and x ∈ C.

Assuming A = U by the definition of intersection, it leads to the contradiction that x ∈ B and x ∈ C, but B ∩ C = ∅.

This contradiction disproves the assumption that A ∩ C ≠ ∅, and therefore, the original statement holds true.

In conclusion, the proof establishes that for all sets A, B, and C, if A ⊆ B and B ∩ C = ∅, then A ∩ C = ∅.

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Answer:

# = number of tiles + 2

Step-by-step explanation:

So It would be 3,5,7 but your would add 2 to each number of tiles increased.

There were 0 tiles in step 0

Answer:

It can be observed that there is a pattern

Step 1

Step 2

Step 3

Step 4

Step n

Answer:

Step-by-step explanation:

sin 44° = \(\frac{63}{ST}\)

ST = \(\frac{63}{sin44}\)

ST ≈ 90.7

Answer: x = 5

Step-by-step explanation:

The inequality that can be used to determine the maximum number of people, x, who can go to the amusement park is: 20x + 6.50 ≤ 555Let's break down the components of the inequality.

We have x, representing the number of people going to the amusement park. Since each ticket costs $20, the total cost of tickets for x people is 20x. In addition to the ticket cost, there is also the cost of parking. The parking fee is $6.50, which is a fixed amount regardless of the number of people. The total amount spent on tickets and parking should not exceed $555, as mentioned in the problem. Therefore, we can set up the inequality: 20x + 6.50 ≤ 555 This inequality combines the cost of tickets (20x) and the cost of parking ($6.50) and ensures that the total amount spent does not exceed $555. By solving this inequality, we can determine the maximum value of x, representing the number of people who can go to the amusement park without exceeding the available budget.

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Answer: i think 336 i think

Step-by-step explanation: im pretty sure you have to just add 18 to the 318 to get 336

Answer:

336 is the answer.

Step-by-step explanation: To get this answer, you want to fill the eqation in as "y=120+18(12) and solve it.  The answer to the equation is the answer to the question.  Trust me, I just got it right.

area increase by ( n squared.)

Step-by-step explanation:

consider a square whose sides are 3 by 3.Its area will be 9. if its length becomes twice as long,i.e 6 by 6 ,the area is 36.The ratio between the areas is 1:4 ,hence does the area.In short ,its area increases by 4 times.

Answer:

For the first one it is 5x+2

Step-by-step explanation:

(9x+5) - (4x+3) = ?

First you minus the x's together so,

9x-4x which would equal 5x

then you minus the 5 and 3 together so,

5-3 which would equal 2

then you put the 5x and the 2 together and you get

5x+2 :-)

For the rest of the problems, use this as an example!

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

\( {6x}^{3} + {9x}^{2} - 18x + 3\)

Step-by-step explanation:

1. Expand by distributing sum groups.\(3x( {2x}^{2} + 5x - 1) - 3( {2x}^{2} + 5x - 1)\)

2. Expand by distributing terms.

\( {6x}^{3} + {15x}^{2} - 3x - 3( {2x}^{2} + 5x - 1)\)

3.Expand by distributing terms.

\( {6x}^{3} + {15x}^{2} - 3x - ( {6x}^{2} + 15x - 3)\)

4. Remove parentheses.

\( {6x}^{3} + {15x}^{2} - 3x - {6x}^{2} - 15x + 3\)

5. Collect like terms.

\( {6x}^{3} + {15x}^{2} - {6x}^{2} ) + ( - 3x - 15x) + 3\)

6. Simplify.

\( {6x}^{3} + {9x}^{2} - 18x + 3\)

Thus. the answer is,

\( {6x}^{3} + {9x}^{2} - 18x + 3\)

Marta leyó 1,625 veces la cantidad de páginas leída por su hermano.

En esta pregunta debemos determinar la razón (\(r\)) de la cantidad de páginas leída por Marta (\(x\)) a la cantidad de páginas leída por su hermano (\(y\)). Es decir,

\(r = \frac{x}{y}\) (1)

Si sabemos que \(x = 52\) y \(y = 32\), entonces la razón definida al principio de esta respuesta es:

\(r = \frac{52}{32}\)

\(r = 1,625\)

Marta leyó 1,625 veces la cantidad de páginas leída por su hermano.

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So as u can see we have to find whether the value of x is correct or not.

So:-

\( \\ \\ \)

\( \dashrightarrow \sf 2 {x}^{2} - 54 = 18\)

First write the equation

\( \\ \\ \)

\( \dashrightarrow \sf 2 {(6)}^{2} - 54 = 18\)

Put value of x I.e 6 in the equation.

\( \\ \\ \)

\( \dashrightarrow \sf 2 \times (6 \times 6 )- 54 = 18\)

To make it easy to understand I have covered square above 6 in it's original form I.e 6 ×6

\( \\ \\ \)

\( \dashrightarrow \sf 2 \times (36)- 54 = 18\)

multiply 6 with 6 to get 36

\( \\ \\ \)

\( \dashrightarrow \sf 72- 54 = 18\)

open the brakets and multiple 2 with 36 and then subtract 72 with 54

\( \\ \\ \)

\( \dashrightarrow \bf18 = 18\)

\( \\ \\ \)

\(\orange{\bf \dag LHS = RHS \dag}\)

\( \\ \\ \)

Hence proved ~

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Let the angle to be solved be x

Let the supplement/compliment by y

x+y=90 Complimentary angles add up to 90 degrees.

x+3y=180 Supplementary angles add up to 180 degrees, the other angle is thrice the other compliment.

Evaluating this as a system:

x+y=90 Isolate x:

x=90−y Input into the other equation:

(90−y)+3y=180 Combine like terms, isolate y and its coefficients:

2y=90 Isolate y

y=45 Input into the first equation:

x+45=90 Isolate x:

x=45degrees

f(x) = (π/3)x - (π³/81)x³ + O(x^5) (truncated to 10 terms).

The Maclaurin series expansion of the function f(x) = sin((πx)/3) can be found using the definition of a Maclaurin series. The Maclaurin series expansion of a function f(x) is given by:

f(x) = f(0) + f'(0)x + (f''(0)x²)/2! + (f'''(0)x³)/3! + ...

To find the Maclaurin series for f(x) = sin((πx)/3), we need to evaluate the function and its derivatives at x = 0. Let's start with the first few derivatives:

f(x) = sin((πx)/3)

f'(x) = (π/3)cos((πx)/3)

f''(x) = -(π²/9)sin((πx)/3)

f'''(x) = -(π³/27)cos((πx)/3)

Now, evaluating these derivatives at x = 0:

f(0) = sin(0) = 0

f'(0) = (π/3)cos(0) = π/3

f''(0) = -(π²/9)sin(0) = 0

f'''(0) = -(π³/27)cos(0) = -(π³/27)

Substituting these values into the Maclaurin series expansion formula, we get:

f(x) = 0 + (π/3)x + 0x² + (-(π³/27)x³)/3! + ...

Simplifying further:

f(x) = (π/3)x - (π³/81)x³ + ...

Therefore, the Maclaurin series expansion for f(x) = sin((πx)/3) is given by f(x) = (π/3)x - (π³/81)x³ + ... (continued to higher powers of x).

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Answer:

1/3 or 1:3

Step-by-step explanation:

since there is a 10/30 chance

to simplify divide by 2

10/30 ÷ 2/2 = 5/15

then divide by 5

5/15 ÷ 5/5 = 1/3

your answer is 1/3

another simple way to simplify

since there is a zero (0) in both the ones (1s) spot on both the numerator and denominator in 10/30, you may just cross out both zeros (0s) to simplify the value

10/30 simplified/taken away 0s = 1/3

hope this helps:)

The simplified ratio is 1 inch to 6 inches, or 1/6.

To express the ratio of 6 inches to 3 feet in its simplest form, we need to convert the measurements to a common unit. Since there are 12 inches in a foot, we can convert the feet to inches.

3 feet is equal to 3 x 12 = 36 inches.

So, the ratio becomes 6 inches to 36 inches.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio.

The part-to-part ratio denotes how two distinct entities or groups are related. For example, the ratio of boys to girls in a class is 12: 15, whereas, the part-to-whole ratio denotes the relationship between a specific group to a whole. For example, out of every 10 people, 5 of them like to read books. Therefore, the part to the whole ratio is 5: 10, which means every 5 people from 10 people like to read books.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD), which is 6 in this case.

6 ÷ 6 = 1

36 ÷ 6 = 6

Therefore, the simplified ratio is 1 inch to 6 inches, or 1/6.

Hence, the answer is 1/6.

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

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