PLEASE HELP ASAP
Write a polynomial of the smallest degree with roots 1, -3, and 4.

The smallest value of n greater than 8 among the options is 17. Therefore, the correct answer is e) n ≥ 17.

To find the appropriate value of n for the trapezoid rule to approximate the integral with an error less than 0.02, we can use the error-bound formula for the trapezoid rule:
Error ≤ (b - a)³ * M / (12 * n²)
where a and b are the limits of integration, M is the maximum value of the second derivative of the function in the interval [a, b], and n is the number of subintervals.
For the function f(x) = cos(3x), the second derivative is f''(x) = -9cos(3x). The maximum value of |f''(x)| in the interval [0, 5] is 9.
Plugging in the values, we get:
0.02 ≥ (5 - 0)³ * 9 / (12 * n²)
Now we solve for n:
0.02 ≥ 125 * 9 / (12 * n²)
n² ≥ 125 * 9 / (12 * 0.02)
n² ≥ 56.25
n ≥ √56.25 ≈ 7.5
Since n must be an integer, we round up to the nearest integer: n ≥ 8.
However, this value of n is not among the given options. The smallest value of n greater than 8 among the options is 17. Therefore, the correct answer is: e) n ≥ 17

The error bound for the trapezoid rule is given by:
|error| ≤ K(b-a)³ / (12n²)
where K is the maximum value of the second derivative of the function being integrated. In this case, K = 9, since the second derivative of cos(3x) is -9cos(3x).
We want to find n such that the error is less than or equal to 0.02. So we have:
0.02 ≤ 9(5-0)³ / (12n²)
0.02 ≤ 1125 / n²
n² ≤ 56250
n ≤ 237.16
Since n has to be an integer, the smallest value of n that satisfies this inequality is n = 238. Therefore, the answer is:
n ≥ 238 which is not one of the given choices. However, the closest choice is: b) n ≥ 69 which is incorrect. So the answer is none of the above.

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The missing length of the triangle using Pythagoras theorem is; x = 3

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle. The right angle triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

The formula to find the sides is;

hypotenuse² = opposite + adjacent²

We are given;

Hypotenuse = 5

Opposite = x

adjacent = 4

Thus;

5² = x² + 4²

x² = 5² - 4²

x² = 25 - 16

x = √9

x = 3

We conclude that it is the missing length of the triangle

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Answer:

15

Step-by-step explanation:

Since, we need a number that if added to -14, it'll give a positive result. The first number is gonna be 15, . Because, it's the first number that can give a positive number if summed up with -14.

Answer:

11

Step-by-step explanation:

30-2(7+2)-1

30-2(9)-1

30-18-1

12-1

11

Answer: Thy answer to ye question is 11

Step-by-step explanation:

The proceeds on the loan is $9600

Data;

To solve this problem, we need to calculate the simple interest of the loan which is done by the formula below

\(S.I = PRT\)

Let's substitute the values into the equation and solve

\(S.I = 800*0.1*120\\ S.I = 9600\)

The proceeds on the loan is $9600

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Answer:

32 Kilometers

Step-by-step explanation:

A Car travels 80 Kilometers in 2 and Half hours.

1 Hour =60 minutes, 2 & Half hours= 2.5*60= 150 minutes

Kilometers travelled by Car in a hour= 80/150*60= 32 Kilometers

Answer:

8

Step-by-step explanation:

81. Volume of a cone: 1. V = (1/3)πr2h 2. Slant height of a cone: 1. s = √(r2 + h2) 3. Lateral surface area of a cone: 1. L = πrs = πr√(r2 + h2) 4. Base surface area of a cone (a circle): 1. B = πr2 5. Total surface area of a cone: 1. A = L + B = πrs + πr2 = πr(s + r) = πr(r + √(r2 + h2))

hope this helps

By examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.

For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

We may find out the average number of successes by looking at the expected value of a binomial distribution with n trials.

Therefore, by examining the expected value of a binomial distribution with n trials, (1) we may determine the typical number of successes.

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Answer:

h = 440.94 feet

Step-by-step explanation:

It is given that,

An architect is standing 370 feet from the base of a building, x = 370 feet

The angle of elevation is 50°.

We need to find the approximate height of the building. let it is h. It can be calculated using trigonometry as follows :

\(\tan\theta=\dfrac{P}{B}\\\\\tan\theta=\dfrac{h}{x}\\\\h=x\tan\theta\\\\h=370\times \tan50\\\\h=440.94\ \text{feet}\)

So, the approximate height of the building is 440.94 feet

0.71%  is the probability micah is included in the group of students chosen.

Describe probability using an example?

the probability micah is included in the group of students chosen =

               3/28 = 10.71%

The probability of her getting picked is unlikely.

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The complete question is -

Micah is 1 of 28 students in a class. Micah's teacher is going to randomly select 3 students from their class to visit a classroom of younger students. What is the probability Micah is included in the group of students chosen?

Answer:

Make a line a bit close to -1

Step-by-step explanation:

-2 3/4 can be re-written as -2.75 therefore you have to mark close to the number -1

11 / 18 = 61%

39% discount given

Answer:

10x^9

Step-by-step explanation:

Add the exponents together and multiply normally

2x^6+5x^3

=10x^9

Answer:

2x^6x+5x^3

Step-by-step explanation:

First you want to

Add the exponents like you would with regular numbers

Which comes out to

2

Answer: 48

Step-by-step explanation:

The number of Pokemon cards in Steven's collection = x

The number of cards in Bob's collection is 4 times the amount in Steven's collection= 4x

The total number of Pokemon cards in both collections = 240

x + 4x = 240

5x = 240

x = 240/5

x = 48

The number of cards in Steven's collection is 48

No, Billy will not be able to reach the border before the cops arrive in 9 minutes.

To determine whether Billy can reach the border before the cops arrive, we need to calculate the time it would take him to cover the distance of 1.9 km.

Using the formula speed = distance / time, we can rearrange the formula to solve for time. Rearranging, we have time = distance / speed.

Given that Billy's speed is 13 km/h, we can calculate the time it would take him to cover 1.9 km.

time = 1.9 km / 13 km/h = 0.146 hours

To convert hours to minutes, we multiply by 60:

0.146 hours * 60 minutes/hour = 8.76 minutes

Therefore, it would take Billy approximately 8.76 minutes to reach the border. Since the cops are expected to arrive in 9 minutes, he would not be able to make it before they arrive.

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H(x,y) is a continuous function for all real values of x and y.

The function h(x, y) is defined as h(x, y) = g(f(x, y)) = g(2x + 3y − 6). We can calculate the value of h(x, y) by substituting f(x, y) into g(t):

h(x, y) = \((2x + 3y − 6)^2 + (2x + 3y − 6) = 4x^2 + 12xy − 24x + 9y^2 − 36y + 36 + 2x + 3y − 6 = 4x^2 + 14xy − 22x + 9y^2 − 33y + 42.\)

For h(x, y) to be continuous, the set of points at which the function is continuous must exist. This set includes all points (x, y) such that \(4x^2 + 14xy − 22x + 9y^2 − 33y + 42\) is defined, i.e. all real values of x and y. Thus, h(x, y) is continuous for all real values of x and y.

H(x,y) is a continuous function for all real values of x and y.

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A set of values for the decision variables that satisfy all the constraints and yields the best objective function value is a feasible solution that optimizes the objective function.

In optimization problems, decision variables are the quantities that we can control or adjust to achieve a desired outcome. Constraints are the limitations or conditions that these decision variables must satisfy. The objective function represents the goal or objective we want to optimize.

A feasible solution refers to a set of values for the decision variables that satisfy all the given constraints. This means that the solution meets all the specified requirements and does not violate any constraints. However, there can be multiple feasible solutions that meet the constraints.

Among these feasible solutions, the one that yields the best objective function value is the optimal solution. The objective function value is a measure of how well the solution aligns with the desired objective. The goal is typically to maximize or minimize this objective function value, depending on the problem.

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Step-by-step explanation:

I answered this already.

9514 1404 393

Answer:

  11.9 cm

Step-by-step explanation:

Arc length is given by ...

  s = rθ . . . . . . θ is the central angle in radians

Your central angle is 85°, so is (85/180)π radians = 17/36π radians.

Then the arc length is ...

  s = (8 cm)(17/36π) ≈ 11.9 cm

The length of the 85° arc is about 11.9 cm.

Answer:

£4244.83

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r)^t.  Here, P = £4000, r = 0.02 and t = 3 yrs

So:  A = £4000(1 + 0.02)^3, which comes to:

       A = £4000(1.061) = £4244.83

Multiply the upper system by -4:

\( - 7x - 5y = - 11\)

\(7x + 5y = 7\)

\(0 = - 3\)

\(this \: system \: admits \: no \: solutions\)

For every integer n > 7, we have shown that there exist positive integers a' and b' such that n = 2a' + 3b'.

An integer is a mathematical concept used to represent whole numbers, both positive and negative, without any fractional or decimal parts. Integers include zero (0) and the positive and negative counting numbers (1, 2, 3, ... and -1, -2, -3, ...). Integers can be expressed as numbers on the number line that extend infinitely in both the positive and negative directions.

To prove that for every integer n > 7, there exist positive integers a and b such that n = 2a + 3b, we can use the concept of the Chicken McNugget theorem, also known as the Frobenius coin problem.

The Chicken McNugget theorem states that for any two relatively prime positive integers a and b, the largest integer that cannot be expressed as a non-negative integer combination of a and b is ab - a - b.

In our case, a = 2 and b = 3 are relatively prime since their greatest common divisor (GCD) is 1.

Let's consider the number 6. We can express 6 as 2 * 1 + 3 * 2, so it is possible to represent 6 using positive integers a and b.

Now, let's consider any number n > 7. We know that n - 6 is a positive integer greater than or equal to 2. Therefore, n - 6 can be expressed as a non-negative integer combination of 2 and 3, using the Chicken McNugget theorem.

So, n - 6 = 2a + 3b, where a and b are positive integers. Adding 2 * 1 + 3 * 2 to both sides of the equation, we get:

n = 2a + 3b + 6

We can see that by choosing a = a + 1 and b = b + 2, we can rewrite the equation as:

n = 2(a + 1) + 3(b + 2) = 2a' + 3b',

where a' and b' are positive integers.

Therefore, for every integer n > 7, we have shown that there exist positive integers a' and b' such that n = 2a' + 3b'.

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Answer:

the answer is 4 x 10^4  or 40,000

Step-by-step

the answer is 40,000 but you need to put it in scientific notation which equals 4 x 10 to the 4th power

4 x 10^4

Based on the graph, the situation that best matches what the data on the table shows is C. Elyse soends $3 for movie rentals and the beginning balance in her account is $18. Her movie card balance decreases by $3 everytime she rents a movie.

The data on the graph shows the amount of money that was spent by Elyse for every movie she rented. She did so with the use of a gift card. Based on the fact that the graph begins at $18, this means that the amount on the gift card was $18.

The amount that Elyse spent per movie was:

= Change in amount on gift card / Change in movies rented

= (18 - 12) / (2 - 0)

= 6 / 2

= $3

Elyse therefore spent $3 whenever she rented a movie.

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Answer:

The value of x is -5 and y is 1

Step-by-step explanation:

Here,

y = -3x - 14

-2x - y = 9

Substitution Method

y = -3x - 14 ...(1)

-2x - y = 9 ...(2)

Now, substitute the value of y = -3x - 14 in equation (2) we get,

-2x - y = 9

-2x - (-3x - 14) = 9

-2x + 3x + 14 = 9

x = 9 - 14

x = -5

Now, put the value of x in equation (1) we get,

y = -3x - 14

y = -3(-5) - 14

y = 15 - 14

y = 1

Thus, The value of x is -5 and y is 1

y = -3x - 14

1 = -3(-5) - 14

1 = 15 - 14

1 = 1

-2x - y = 9

-2(-5) - 1 = 9

10 - 1 = 9

9 = 9

Hence, L.H.S = R.H.S

-TheUnknownScientist

If the amount of money Deon earns working at a store is given in the table. He will earn $20 in the 20 hours.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

The given data is represented by a table that gives a relation between the money earned and the hour he works.

It is obtained that there is a proportional relationship obtained from the money earned and the hour he works as,

The rate when he worked for 3 hours.

r=Money earned /  hour

r=$ 37.50 / 3

r=12.5

The rate when he worked for 6 hours.

r=Money earned /  hour

r=$ 62.50 / 6

r=12.5

The rate when he worked for 7 hours.

r=Money earned /  hour

r=$ 87.50 / 7

r=12.5

The amount he earned for 20 hour is the product of the amount he earned for the one hour and the number of hours,

=$ 12.5 × 20

= $250.00

Thus, the amount of money Deon earns working at a store is given in the table. He will earn $20 in the 20 hours.

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If the perimeter and area of the hexagon are $p$ and $a$, respectively, the value of $\frac{p^4}{a^2}$ is 192.

Regular hexagon has side length of 6

Perimeter of regular hexagon is given by 6*(side)

∴Perimeter = 6*(6) = 36

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

Area of Regular hexagon is composed of 6 equilateral triangles and is given by,

= 6* (1/2)*6² * √3/2

= 3√3/2 * 36

= 54√3

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

So fraction \(\frac{p^4}{a^2}\) = \(\frac{36^4}{(54\sqrt{3})^2 } = \frac{36*36*36*36}{54*54*3}\)  =192.

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A person bought two old scooters for Rs. 9000. By selling one at a profit of 25% and the other at a loss of 20%, to neither gain nor lose. The cost of each scooter is Rs. 4000 and Rs. 5,000.

Let the cost price of the first scooter be Rs. x and the cost price of the second scooter = Rs. (9000 - x)

Given, the first scooter was sold at a profit of 25%.

Selling price of first scooter = x + 0.25x = 1.25x

Given, the second scooter was sold at a loss of 20%.

Selling price of second scooter = 0.8(9000 - x)

Now, according to the question, there is no profit and no loss.

Therefore, Total Selling Price = Cost Price=> (1.25x) + 0.8(9000 - x) = 9000=> 1.25x + 7200 - 0.8x = 9000=> 0.45x = 1800=> x = Rs. 4000

So, the cost price of the first scooter is Rs. 4000.

The cost price of the second scooter is Rs. (9000 - 4000) = Rs. 5000

Therefore, the cost of each scooter is Rs. 4000 and Rs. 5,000.

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Answer:

x=1

Step-by-step explanation:

3/4x + 1/4 =2x

3/4x=2x-1/4

3/4x-2x= -1/4

3/4x-8/4x= -1/4

-5/4x= -1/4

x= -1/4+ 5/4

x=4/4

x=1

Answer:

x = 1/5

Step-by-step explanation:

Simplfy:

3x/4 + 1/4 = 2x

Join the denominators:

3x + 1/4 = 2x

Multiply both sides by 4:

3x + 1 = 8x

Subtract 3x from both sides:

1 = 8x - 3x

Simplify:

1 = 5x

Divide both sides by 5:

x = 1/5

Answer:

Poor physical health can lead to an increased risk of developing mental health can negatively impact on Physical health leading to an increased risk of some conditions

Step-by-step explanation:

The association between mental and physical health are poor mental is a risk factor for chronic physical conditions . if this is not correct don't report me or blame me just trying to help ......