Please help me and no links

Counterexample: The statement is not true. For n = 41, the expression n^3 + n^2 + 41 equals 41^3 + 41^2 + 41, which is divisible by 41 and therefore not prime.

To prove or disprove the statement, we need to find a counterexample, i.e., a natural number n for which n^3 + n^2 + 41 is not prime. By substituting n = 41 into the expression, we obtain 41^3 + 41^2 + 41. This expression is divisible by 41 since it can be factored as 41(41^2 + 41 + 1). Since a prime number is only divisible by 1 and itself, this means that the expression is not prime and thus disproves the statement. Therefore, the claim that n^3 + n^2 + 41 is prime for every natural number n is false.

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8,99,999 in international system:-

899,999= Eight hundred ninety-nine thousand nine hundred ninety-nine

The interval [μ - z (σ/sqrt(n)), μ + z (σ/sqrt(n))] within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

a. The interval is [166.01, 179.99].

b. The interval is [849.07, 898.93].

c. The interval is [74.47, 77.53].

a. μ = 173, σ = 20, n = 42.

Here, we have, μ = 173, σ = 20, n = 42.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 173 - 1.96(20/sqrt(42)) , 173 + 1.96(20/sqrt(42)) ]

i.e [ 166.01, 179.99 ]

Therefore, the interval is [166.01, 179.99].

b. μ = 874, σ = 12, n = 7.

Here, we have, μ = 874, σ = 12, n = 7.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 874 - 1.96(12/sqrt(7)) , 874 + 1.96(12/sqrt(7)) ]

i.e [ 849.07, 898.93 ]

Therefore, the interval is [849.07, 898.93].

c. μ = 76, σ = 2, n = 26.

Here, we have, μ = 76, σ = 2, n = 26.

Using the z-table, we get z = 1.96 (at 95% confidence level).

The interval is: [ 76 - 1.96(2/sqrt(26)) , 76 + 1.96(2/sqrt(26)) ].

i.e [ 74.47, 77.53 ]

Therefore, the interval is [74.47, 77.53].

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Answer:

y= -3

Step-by-step explanation:

Substitute x as 0

6(0)-3y=9

-3y=9

y= -3

For a graph with seven vertices, a minimum degree of 3 (8 = 3), and a maximum degree of 5 (Δ = 5), it can be shown that the graph must contain at least 12 edges. The largest number of edges possible in this graph is determined by the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges.

(a) To show that the graph must contain at least 12 edges, we can use the Handshaking Lemma. The sum of the degrees of all vertices in the graph is equal to twice the number of edges. In this case, with seven vertices and a minimum degree of 3, the sum of the degrees is at least 7 * 3 = 21. Therefore, the minimum number of edges is 21/2 = 10.5, which rounds up to 11. So the graph must contain at least 11 edges, but since the number of edges must be an integer, it must be at least 12.

(b) The largest number of edges possible in this graph can be determined by considering the maximum degree. In this case, the maximum degree is 5. Since the sum of the degrees of all vertices is equal to twice the number of edges, the sum of the degrees is at most 7 * 5 = 35. Therefore, the largest possible number of edges is 35/2 = 17.5, which rounds down to 17. So the largest number of edges possible in this graph is 17.

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Answer:

1.) it is the same way as subtracting a fraction be cause a pizza is cut into 8 so it will be 1/8th of each slice if some one ate a slice of pizza

Step-by-step explanation:

Answer:

l=8k

Step-by-step explanation:

Answer:

y=8k

Step-by-step explanation:

The solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

To find a solution of the second-order initial value problem (IVP) consisting of the differential equation y" - y = 0 and the given initial conditions y(1) = 0, y'(1) = e -x-1, we can follow these steps:

Determine the general solution of the differential equation y" - y = 0:

The characteristic equation is r^2 - 1 = 0. Solving this equation, we find two distinct roots: r = 1 and r = -1.

Therefore, the general solution is y(x) = c₁e^x + c₂e^(-x), where c₁ and c₂ are constants.

Apply the initial condition y(1) = 0:

Substituting x = 1 and y = 0 into the general solution:

0 = c₁e^1 + c₂e^(-1)

Dividing through by e:

0 = c₁ + c₂e^(-2)

Apply the initial condition y'(1) = e -x-1:

Differentiating the general solution:

y'(x) = c₁e^x - c₂e^(-x)

Substituting x = 1 and y' = e^(-1) into the differentiated solution:

e^(-1) = c₁e^1 - c₂e^(-1)

Dividing through by e:

e^(-2) = c₁ - c₂e^(-2)

We now have a system of two equations:

Equation 1: 0 = c₁ + c₂e^(-2)

Equation 2: e^(-2) = c₁ - c₂e^(-2)

Solving this system of equations, we can find the values of c₁ and c₂:

Adding Equation 1 and Equation 2:

0 + e^(-2) = c₁ + c₁ - c₂e^(-2)

e^(-2) = 2c₁ - c₂e^(-2)

Rearranging this equation:

2c₁ = e^(-2)(1 + c₂)

Substituting this value back into Equation 1:

0 = e^(-2)(1 + c₂) + c₂e^(-2)

0 = e^(-2) + c₂e^(-2) + c₂e^(-2)

0 = e^(-2) + 2c₂e^(-2)

-1 = 2c₂e^(-2)

Simplifying:

c₂e^(-2) = -1/2

Substituting this value back into Equation 1:

0 = c₁ - 1/2

c₁ = 1/2

Therefore, the values of c₁ and c₂ are c₁ = 1/2 and c₂ = -1/(2e^2).

Now we can write the particular solution to the IVP:

y(x) = (1/2)e^x - (1/(2e^2))e^(-x)

This is the solution to the second-order IVP consisting of the differential equation y" - y = 0 and the initial conditions y(1) = 0, y'(1) = e^(-1).

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Answer:

it is x=4÷2

Step-by-step explanation:

I just known the answer who cares about the steps

Answer:

i think it is A CiNiyah

Step-by-step explanation:

Answer:

-2[tex]x^{2}[/tex]+3xy+8[tex]y^{2}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is the equation of a circle with center at (-4, 6) and radius 4√3.

Answer:

$9015.20

Step-by-step explanation:

A = 4000[1 + (.063/4)]^13·4

Answer:

3276

Step-by-step explanation:

4000(6.3*13)÷100

Answer:

The volume of the cone is 3140cm³

Step-by-step explanation:

Volume of come = 1/3 × πr²h

r = diameter/2 = 20/2 = 10cm

h = 30cm

π = 22/7

Volume = 1/3 × 22/7 × 10² × 30

Volume = 1/3 × 22/7 × 100 × 30

Volume = 3142.86cm³

Volume = 3140cm³

Answer:

From the given information, we can see that when x = -3, f(x) = 1 and g(x) = -3. Since g(x) = kf(x), we can substitute the values of f(x) and g(x) to solve for k: g(x) = kf(x) -3 = k(1) k = -3 So the value of k is -3, which corresponds to answer choice D.

The series n=0 to infinity [tex]2^{n}[/tex] [tex]3^{n}[/tex] /n! is (e) convergent by ratio test and its sum is e⁶.

The given series can be written as:

S = Σ(n=0 to ∞) (2ⁿ * 3ⁿ) / n!

In order to determine if the series is convergent, let's apply the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, this can be expressed as:

lim(n→∞) |(a(n+1) / an)| < 1

Taking the ratio of a(n+1) to an is 6 / (n+1)

Now, let's take the limit as n approaches infinity:

lim(n→∞) |(6 / (n+1))| = 0

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The 95% confidence interval of the mean number of jobs is (6.7, 7.5).

Given that, a sociologist found that in a sample of 55 retired men, the average number of jobs they had during their lifetimes was 7.1 and the population standard deviation is 2.1.

The best point estimate of the mean is the sample mean.

Hence the best point estimate of the mean is 7.1.

Therefore, the 95% confidence interval of the mean number of jobs is (6.7, 7.5).

Hence the required solution.

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Answer:

35°

Step-by-step explanation:

Due to the parallelism, angle2=angle4

Answer:

Step-by-step explanation: The purpose of scientific notation is to make the numbers and quantities used easier to comprehend, to read and to write.

Express both numbers with the same power of ten.

Add the base numbers.

Bring the power of ten down to represent the new power of ten for the sum.

Simplify so that the base number is between 1 and 10.

Answer:

What is the purpose of scientific notation?

"to make the numbers and quantities used easier to comprehend, to read and to write. " <----- Credits to: Yahoo

How is scientific notation represented?

"To start with, scientific notation is a form of expressing very small or large numbers in a simpler form." <--------- Credits to: Yahoo

Answer:

8

x

3

+

2

x

2

−

3

x

+

18

Step-by-step explanation:

simply the answer thought bc i didn't simplify

Using area under normal curve and z-score, approximately 21.32% of shafts have a diameter between 19.987 mm and 20.000 mm.

To find the proportion of shafts with a diameter between 19.987 mm and 20.000 mm, we need to calculate the probability that a randomly selected shaft falls within this range.

Given that the diameters of the shafts are normally distributed with a mean of 20.003 mm and a standard deviation of 0.005 mm, we can use the properties of the normal distribution to determine the desired proportion.

To calculate this proportion, we need to find the area under the normal curve between the values of 19.987 mm and 20.000 mm.

Let's denote the random variable X as the diameter of the shafts. We want to find P(19.987 ≤ X ≤ 20.000).

To do this, we can standardize the values by converting them to z-scores using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

For 19.987 mm:

z₁ = (19.987 - 20.003) / 0.005

For 20.000 mm:

z₂ = (20.000 - 20.003) / 0.005

We can then use a standard normal distribution table or calculator to find the corresponding probabilities associated with these z-scores.

Using a standard normal distribution table, we find that P(Z ≤ z₁) ≈ 0.2119 and P(Z ≤ z₂) ≈ 0.4251.

To find the proportion of shafts between 19.987 mm and 20.000 mm, we subtract the probabilities:

P(19.987 ≤ X ≤ 20.000) = P(Z ≤ z₂) - P(Z ≤ z₁) ≈ 0.4251 - 0.2119

P(19.987 ≤ X ≤ 20.000) ≈ 0.2132

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Step-by-step explanation:

What is the measure of angle B in the triangle?

Enter your answer in the box.

m∠B=

°

A triangle labeled ABC with angle A as one hundred twenty degrees, angle B as X degrees and angle C as parenthesis X plus sixteen parenthesis degrees

the answer in the photo

The closest measurement in square inches to the overall surface area of the candle is 87.92 square inches.

To find the total surface area of the candle, we need to calculate the lateral surface area (excluding the top and bottom) and then add the areas of the two circular bases.

1. Lateral Surface Area:

The formula for the lateral surface area of a cylinder is given by A = 2πrh, where r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the candle is 4 inches, we can calculate the radius by dividing the diameter by 2:

Radius (r) = 4 inches / 2 = 2 inches

Height (h) = 5 inches

Using the formula, we can calculate the lateral surface area:

Lateral Surface Area = 2π(2 inches)(5 inches) = 20π square inches

2. Base Area:

The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle.

Using the radius calculated earlier (r = 2 inches), we can calculate the area of each circular base:

Base Area = π(2 inches)^2 = 4π square inches

3. Total Surface Area:

To find the total surface area, we add the lateral surface area and the areas of the two circular bases:

Total Surface Area = Lateral Surface Area + 2(Base Area)

Total Surface Area = 20π + 2(4π) = 20π + 8π = 28π square inches

Approximating the value of π to 3.14, we can calculate the approximate total surface area:

Total Surface Area ≈ 28(3.14) = 87.92 square inches

Therefore, the closest measurement to the total surface area of the candle in square inches is 87.92 square inches.

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A) Logical vector diagram of the flight is drawn below. B) The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°. C) The vacation island is approximately 1301 kilometers from the airport of departure.

A.  a logical vector diagram of the flight is given in image.

B. To determine the aircraft's ground velocity, we need to find the resultant vector of the aircraft's velocity and the wind vector. We can use vector addition to calculate this:

Aircraft's velocity = 250 km/hr at a heading of 170°

Wind velocity = 50 km/hr at a heading of 270° (since it's blowing from the south/west)

To add these vectors, we need to resolve them into their horizontal (x) and vertical (y) components:

Aircraft's velocity:

[tex]V_x[/tex] = 250 km/hr * cos(170°)

[tex]V_{y}[/tex] = 250 km/hr * sin(170°)

Wind velocity:

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°)

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°)

Now, we can add the horizontal and vertical components separately:

[tex]V_{x} total = V_x + V_{x}wind\\V_{y} total = V_y + V_{y}wind[/tex]

To find the magnitude and direction of the resultant vector, we can use the Pythagorean theorem and trigonometry:

Magnitude of the resultant vector (ground velocity):

[tex]V_{total} = \sqrt{V_x total^2 + V_y total^2}[/tex]

Direction of the resultant vector:

[tex]\theta = tan^{-1} 2(V_y total, V_xtotal)[/tex]

Let's calculate the values:

[tex]V_x[/tex] = 250 km/hr * cos(170°) ≈ -235.83 km/hr

[tex]V_y[/tex] = 250 km/hr * sin(170°) ≈ -62.85 km/hr

[tex]V_x[/tex]_wind = 50 km/hr * cos(270°) = 0 km/hr

[tex]V_y[/tex]_wind = 50 km/hr * sin(270°) ≈ -50 km/hr

[tex]V_x[/tex]_total = -235.83 km/hr + 0 km/hr = -235.83 km/hr

[tex]V_y[/tex]_total = -62.85 km/hr + (-50 km/hr) = -112.85 km/hr

[tex]V_{total}[/tex] =  [tex]\sqrt{((-235.83 km/hr)^2 + (-112.85 km/hr)^2) }[/tex] ≈ 260.2 km/hr

θ = [tex]tan^{-1} 2(-112.85 km/hr, -235.83 km/hr)[/tex] ≈ -153.7°

The aircraft's ground velocity is approximately 260.2 km/hr at a bearing of -153.7°.

C. If the entire flight took about 5 hours, we can calculate the distance traveled by multiplying the ground velocity by the time:

Distance = Velocity * Time

Distance = 260.2 km/hr * 5 hours = 1301 km

The vacation island is approximately 1301 kilometers from the airport of departure.

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Answer: 24/25

Step-by-step explanation:

Sin = opposite/hypotenuse

Sin = 24/25

The simplification based on Laurent series of the function (22-9)(2+3) centered at z = −3

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

The given problem involves finding the Laurent series of a function centered at z = -3 and evaluating the integral of another function over a specific interval. The Laurent series simplifies to a constant term of 65.

(a) To find the Laurent series of the function (22-9)(2+3) centered at z = −3, we can expand the function in powers of (z + 3):

(22-9)(2+3) = (13)(5) = 65

Since there are no negative powers of (z + 3), the Laurent series of the function is simply the constant term:

f(z) = 65

(b) To evaluate the integral ſc[−3,3] (z²−9)(z+3) dz, we can first simplify the integrand:

(z² - 9)(z + 3) = (z - 3)(z + 3)(z + 3) = (z - 3)(z + 3)²

Now, let's integrate the simplified expression:

∫[(z - 3)(z + 3)²] dz

Expanding the expression:

∫[z³ + 6z² + 9z - 27] dz

Integrating each term:

(1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z

Now, we can evaluate the integral over the given interval [−3, 3]:

∫[−3,3] (z²−9)(z+3) dz = [((1/4)z⁴ + (2/3)z³ + (9/2)z² - 27z)] evaluated from z = -3 to z = 3

Substituting the upper and lower limits into the expression and simplifying, we get:

[((1/4)(3)⁴ + (2/3)(3)³ + (9/2)(3)² - 27(3))] - [((1/4)(-3)⁴ + (2/3)(-3)³ + (9/2)(-3)² - 27(-3))]

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Answer:

x<-8

Step-by-step explanation:

x/8<-1

x<-1×8

x<-8

Answer:

10.7

Step-by-step explanation:

Hello There!

The image shown below shows the relationship between two chords formed inside of a circle

So the product of the lengths of the lines in the same chord is equal to the product of the other length of the chords lines if that makes sense

So basically 6 * 16 = 9 * x

we can now use this equation that was just made to solve for x

6 * 16 = 96

96 = 9x

*divide each side by 9*

96/9=10.66666667 *round to the nearest tenth* 10.7

9x/x

we're left with x = 10.7

Answer:

It is option one

Step-by-step explanation:

I don’t know why but I’m doing a quizzizz with the same question and i picked option 2 but option one was the correct answer