What is the value of C?

The required answer is  -

a. leaves a remainder of n² - 3n or (n - 6)(n + 7) ,the possible remainders are 0, 1, 4, 9, 5, 3

b .every n € Z that 121 | n² + 16n +20.

Explanation:-

(a) Remainder when n² + 16n + 20 is divided by 11:Let us first find out the value of n² + 16n + 20,n² + 16n + 20 = (n + 10)(n + 6) + 4As n and 11 are co-prime, by Fermat's Little Theorem, n¹⁰  ≡  1(mod 11)So, (n + 10)(n + 6) ≡ (n + 1)(n + 7) (mod 11)Hence, n² + 16n + 20 ≡ (n + 1)(n + 7) + 4 ≡ n² + 8n + 11 ≡ n² - 3n (mod 11).Therefore, when n² + 16n + 20 is divided by 11, it leaves a remainder of n² - 3n or (n - 6)(n + 7).

Thus, the possible remainders are 0, 1, 4, 9, 5, 3

(b) Prove that 121 | n² + 16n + 20 for every n ∈ Z . n ∈ Z, thenn² + 16n + 20 = (n + 8)² - 44(n + 8) + 324 = (n + 8 - 22)(n + 8 + 14) + 324= (n - 14)(n + 22) + 324.We know that 121 = 11² | (n - 14)(n + 22),

Therefore, 11 | (n - 14) or 11 | (n + 22)So, there exist k and l ∈ Z such that n - 14 = 11k or n + 22 = 11lWe have, n + 22 = n - 14 + 36Hence, n - 14 ≡ n + 22 (mod 11)If 11 | (n - 14), then 11 | (n + 22), if 11 | (n + 22), then 11 | (n - 14).Therefore, 121 | n² + 16n + 20. Thus, proved.

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The given quadratic expression is: $n^2 + 16n + 20$.

(a)We have to determine the possible remainders when this expression is divided by 11.

Let's solve for the remainder:$(n^2 + 16n + 20) \div 11$ $= \frac{(n + 8)^2 - 44}{11}$

We can write the given expression as $n^2 + 16n + 20 = (n + 8)^2 - 44$

Therefore,$\begin{aligned} (n^2 + 16n + 20) \div 11 & = \frac{(n + 8)^2 - 44}{11} \\ & = \frac{(n + 8)^2}{11} - 4 \end{aligned}$

For all possible values of $n$,

let's calculate the remainder of $\frac{(n + 8)^2}{11}$.

Let $a$ be the remainder when $n$ is divided by 11; then, $(n + 8) \div 11$ has a quotient of $q$ and a remainder of $r$. Therefore, $n + 8 = 11q + r$ $ \Right arrow n = 11q + r - 8$$\begin{aligned} n^2 & = (11q + r - 8)^2 \\ & = 121q^2 + r^2 + 64 + 22qr - 16q - 16r \end{aligned}$Let's now replace $n^2$

in the given expression:$(n^2 + 16n + 20) \div 11 = \frac{121q^2 + r^2 + 22qr - 16q + 6r + 64}{11}$

We have to find the remainders when $121q^2 + r^2 + 22qr - 16q + 6r + 64$ is divided by 11.

We observe that $121q^2$ is always divisible by 11, so we can ignore it.

We must find the remainders of $r^2 + 22qr + 6r + 64 - 16q$. $\begin{aligned} r^2 + 22qr + 6r + 64 - 16q & = r^2 + 2 \cdot 11qr + 11qr + 6r + 64 - 16q \\ & = (r + 11q)^2 + 6r - 16q + 64 \\ & = (r + 11q)^2 - 11(2q - r - 3) \end{aligned}$

The remainder is $r_0 = 11(2q - r - 3)$.

This remainder can take any value between $-10$ and $10$.

(b)We have to show that $121 | n^2 + 16n + 20$ for all integers $n$.We proved earlier that $n^2 + 16n + 20 = (n + 8)^2 - 44$.

We can restate this as $121 | (n + 8)^2 - 44$, which implies that $(n + 8)^2 - 44 = 121k$, where $k \in \mathbb{Z}$.Now we need to show that $k = \frac{n^2 + 16n + 20 - 121k}{121}$ is an integer.

Let's substitute $(n + 8)^2 - 44 = 121k$ into the given expression:$\begin{aligned} k & = \frac{(n + 8)^2 - 44}{121} \\ & = \frac{n^2 + 16n + 20 - 121k}{121} \\ & = \frac{n^2 + 16n + 20}{121} - k \end{aligned}$Thus, $k = \frac{n^2 + 16n + 20 - 121k}{121}$ is an integer for all $n \in \math bb{Z}$,

implying that $121 | n^2 + 16n + 20$ for all $n \in \math bb{Z}$.

Hence, we have proved that $121 | n^2 + 16n + 20$ for all $n \in \math bb{Z}$ using the method of mathematical induction.

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The holomorphic function f whose real part is u(x, y) = e^-2xy sin(x² - y²) is given by f(z) = e^(-z²)sin(z²).

This function is holomorphic because it satisfies the Cauchy-Riemann equations. The Cauchy-Riemann equations relate the partial derivatives of the real and imaginary parts of a holomorphic function with respect to the variables x and y.

In this case, the real part of f is u(x, y) = e^-2xy sin(x² - y²), and the imaginary part of f is v(x, y) = e^-2xy cos(x² - y²). By computing the partial derivatives of u and v with respect to x and y and checking that they satisfy the Cauchy-Riemann equations, we can verify that f is indeed holomorphic.

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If 19,000=19% Then 100,000=100%

100,000-900=99,100

Answer: $99,100 was his salary last year

Answer:

area = 84 in²

Step-by-step explanation:

area = (9x12) - (6x8x0.5) = 84 in²

Answer:

22.8906 sq in

Step-by-step explanation:

SA of a sphere = 4 π [tex]r^{2}[/tex]

r = 2.7 / 2 = 1.35

4 x 3.14 x [tex]1.35^{2}[/tex] = 22.8906

Answer:

.

Step-by-step explanation:

The value of [v]B1 is [[1][0]][[0][0]]

Suppose [v]B2 is as follows:

[v]B2 = [[11][14]]

[13][14]]

[7][6]]

[10]]

If the ordered bases are B1 = {a, b} and B2 = {c, d}, we want to find [v]B1.

To find [v]B1, we need to express the columns of [v]B2 in terms of the basis vectors of B1.

The first column of [v]B2 is [11, 13, 7, 10]. We want to express this column in terms of the basis vectors of B1: [a, b].

To do this, we set up the following equation:

[11][13][7][10] = [a][b]

Solving this equation, we find that:

11a + 13b = 11

13a + 14b = 13

7a + 6b = 7

10a = 10

From the last equation, we can see that a = 1.

Substituting this value of a into the first three equations, we can solve for b:

11 + 13b = 11

13 + 14b = 13

7 + 6b = 7

Simplifying these equations, we find that b = 0.

Therefore, [v]B1 is as follows:

[v]B1 = [[1][0]]

[0][0]]

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The complex number Z = (20 + 120i) can be expressed in polar form as Z = 2√370(cos(1.405) + isin(1.405)).

To express the complex number Z = (20 + 120i) in polar form, we need to find its magnitude (r) and argument (θ).

The magnitude of a complex number Z = a + bi is given by the formula:

|r| = √(a^2 + b^2)

In this case, a = 20 and b = 120.

Therefore, the magnitude of Z is:

|r| = √(20^2 + 120^2) = √(400 + 14400) = √14800 = 2√370.

The argument (θ) of a complex number Z = a + bi is given by the formula:

θ = arctan(b/a)

In this case, a = 20 and b = 120. Therefore, the argument of Z is:

θ = arctan(120/20) = arctan(6) ≈ 1.405 radians.

Now we can express Z in polar form as Z = r(cosθ + isinθ), where r is the magnitude and θ is the argument:

Z = 2√370(cos(1.405) + isin(1.405)).

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Answer:

110.45 inches cubed

Step-by-step explanation:

5in x 4.7in x 4.7in

Answer. 2, 3, 5, 7 , 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199

Step-by-step explanation:

There are 21 prime number between 100 and 200.

A number system is defined as a system of writing to express numbers.

A prime number is a whole number greater than 1 whose only factors are 1 and itself.

The prime numbers between 100 and 200 are

101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.

One hundred one, one hundred three, one hundred seven, one hundred nine, One hundred thirteen, one hundred twenty seven, One hundred thirty one, one hundred thirty seven, one hundred thirty nine, one hundred forty nine, one hundred fifty one, one hundred fifty seven, one hundred sixty three,  one hundred sixty seven, one hundred seventy three, one hundred seventy  nine, one hundred eighty one, one hundred ninty one, one hundred ninty three, one hundred ninty seven, one hundred ninty nine.

There are no numbers  between 100 and 200 have 11 as a prime factor.

Hence there are 21 prime number between 100 and 200.

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Answer: z= -0.5

Step-by-step explanation: mean m=120 and deviation s=10.

Z = (x-m)/s= (115-120)/10

Answer: z=−1.1

Step-by-step explanation:

z=\frac{x-\mu}{\sigma}

z=

σ

x−μ

​

z-score formula

z=\frac{104-115}{10}

z=

10

104−115

​

Plug in values

z=\frac{-11}{10}

z=

10

−11

​

Subtract

z=-1.1

z=−1.1

Divide

Answer:

x = 18

y = 27

Step-by-step explanation:

Answer:

x = 18

y = 27

Step-by-step explanation:

Answer:

1 1/4 cups

Step-by-step explanation:

3 3/4 cups = 3.75

1/3 = .33333

3.75 x .33333 = 1.25

1.25 = 1 1/4 cups

a) The correlation coefficient (r) is approximately 0.300, indicating a weak positive linear relationship between the ages of Best Actresses and Best Actors.

b) Based on the correlation coefficient (r), there is a weak positive linear correlation between the ages of Best Actresses and Best Actors, suggesting that as the ages of Best Actresses increase, the ages of Best Actors also tend to increase, but the relationship is not very strong.

To find the correlation coefficient (r), we can use the given ages of Best Actresses and Best Actors. The correlation coefficient measures the strength and direction of the linear relationship between two variables. Using a calculator or statistical software, we calculate the correlation coefficient to be approximately 0.300.

Based on the correlation coefficient (r) of approximately 0.300, there is a weak positive linear correlation between the ages of Best Actresses and Best Actors. This means that there is a tendency for the ages of Best Actresses and Best Actors to increase together, but the relationship is not very strong. The correlation coefficient ranges from -1 to +1, where 0 indicates no linear correlation, 1 indicates a strong positive linear correlation, and -1 indicates a strong negative linear correlation. In this case, the value of 0.300 suggests a weak positive linear relationship, indicating that as the ages of Best Actresses increase, the ages of Best Actors also tend to increase, albeit not strongly.

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The statement is false. The appropriate differential equation for the quantity Q of toxin in the tank is not given by dQ/dt = r (c/Vo).

In a tank problem with equal inflow and outflow rates and a constant input concentration c of a toxic substance, the appropriate differential equation for the quantity Q of toxin in the tank is dQ/dt = r(c - Q/Vo), where r is the inflow/outflow rate and Vo is the total volume of the mixture in the tank.

The term (c - Q/Vo) represents the difference between the input concentration and the concentration in the tank, scaled by the volume Vo. This equation accounts for the fact that the concentration in the tank changes over time due to the inflow of fresh mixture with concentration c and the outflow of the mixture with concentration Q/Vo.

Therefore, the correct differential equation is dQ/dt = r(c - Q/Vo), which reflects the balance between the inflow and outflow of the toxic substance and its accumulation or depletion in the tank.

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Answer:

[tex]y=2x-3[/tex]

Step-by-step explanation:

This is just algebraic manipulation. In order to solve for y, you need to isolate it. Start this by moving the 2x from the left side of the equation. You can do this by subtracting 2x from both sides and you should end up with:

[tex]-y=-2x+3[/tex]

After this, you still have a negative y, which means you just need to divide both sides of the equation by -1 to get rid of the negative. That should reverse the signs of all the variables in the equation, making it look like:

[tex]y=2x-3[/tex]

Answer:

Hi! The answer to your question is D. {(0,0),(0,1),(1,2)(1,3)}

Step-by-step explanation:

☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆

☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

The first three nonzero terms of two linearly independent solutions about x = 0 can be obtained by Taylor expanding the solutions in terms of the exponent r and truncating the series to the desired order.

To determine if x = 0 is a regular singular point of the differential equation xy'' + y = 0, we substitute y = x^r into the equation and solve for the exponent r. Differentiating y twice with respect to x, we have y'' = r(r - 1)x^(r - 2). Substituting these expressions into the differential equation, we get [tex]x(x^r)(r(r - 1)x^(r - 2)) + x^r = 0[/tex]. Simplifying, we obtain r(r - 1) + 1 = 0, which yields r^2 - r + 1 = 0. Solving this quadratic equation, we find that the exponents at the singular point x = 0 are complex and given by r = (1 ± i√3)/2.

To find the first three nonzero terms of two linearly independent solutions about x = 0, we can use the Taylor series expansion. Let's consider the solution y1(x) corresponding to the exponent r = (1 + i√3)/2. Expanding y1(x) as a series around x = 0, we have y1(x) =[tex]x^r = x^((1 +[/tex]i√3)/2) = x^(1/2) *[tex]x^(i√3/2[/tex]). Using the binomial series expansion and Euler's formula, we can write [tex]x^(1/2) and x^(i√3/2)[/tex] as infinite series.

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Answer:

72.25663

Step-by-step explanation:

C=2πr=2·π·11.5≈72.25663

Answer:

9

plz mark as brainliest

Answer:

9

Step-by-step explanation:

[tex]\sqrt{81} =9[/tex]

9 x 9 = 81

Answer:

Length = x + 3 meters

Step-by-step explanation:

Expression for the area of the rectangle = [tex]x^2 - 9 = (x + 3)(x - 3) m[/tex]

Expression for width of rectangle = ([tex]x - 3[/tex]) m

Area of a rectangle = [tex]Length \times Width[/tex]

⇒ Expression for length of rectangle = [tex]\frac{Area}{Width} = \frac{(x + 3)(x - 3)}{(x - 3)} = (x + 3) m[/tex]

Answer: C.

Step-by-step explanation: To find the volume of something, you multiply the length, width, and height together. Since they have already multiplied the length and width together to form the base, multiply 7 by 12 (base times height) to get 84 cubic inches.

The MGF of Y using the fact that Y = μ + oZ where Z ~ N(0, 1) is e^(tμ + t²/2).

The MGF of Y is given by,

E[exp(tY)] = E[exp(t(μ+Z))]

We know that if X is a normal random variable, X~N(μ, σ²) with μ as the mean and σ² as the variance.

The MGF of X is given by,

MGF_X(t) = E[e^(tx)] = e^(μt + (σ²t²)/2)

Here, Y ~ N(μ, 2) we have Y = μ + oZ where Z ~ N(0, 1)

MGF_Y(t) = E[exp(tY)] = E[exp(t(μ+Z))]MGF_

Y(t) = E[e^(tμ+tZ)]MGF_

Y(t) = e^(tμ) E[e^(tZ)]

We know that the MGF of Z is already derived in the lecture 1,

It is MGF_Z(t) = e^(t²/2)MGF_

Y(t) = e^(tμ) e^(t²/2)MGF_

Y(t) = e^(tμ + t²/2)

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Given information is that Y~ N(μ, 2), let's find the MGF of Y using the fact that Y = μ + oZ where Z~ N(0, 1).

The MGF of Y becomes:

MGF of [tex]Y = e^{t} \mu+ MGF\ of\ o \times e^{((t^2)/2)}[/tex]

Hence, the MGF of Y is [tex]e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex].

The MGF of Y is as follows:

MGF of Y = MGF of μ + MGF of oZ

The MGF of Y = MGF of μ + MGF of oMGF of Z

Since the mean of Y is μ, we can substitute the above equation with the following:

[tex]MGF\ of\ Y = e^{t}\mu + MGF\ of\ oMGF\ of\ Z[/tex]

Now let's find the MGF of Z: We know that the MGF of Z is given by;

MGF of [tex]Z = e^{((t^2)/2)}[/tex]

Therefore, the MGF of Y becomes: MGF of [tex]Y = e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex]

Hence, the MGF of Y is [tex]e^{t}\mu + MGF\ of\ o \times e^{((t^2)/2)}[/tex].

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Answer:

My brain...

Step-by-step explanation:

Answer:

i believe its A on plato

Step-by-step explanation:

The proof shows that if we assume the premises are true and the conclusion is false, it leads to a contradiction. Therefore, the argument is valid. The modus ponens and conjunction are used.

To construct a proof for the given argument, we'll use a proof by contradiction. We'll assume the premises are true and the conclusion is false, then we'll derive a contradiction. If a contradiction is reached, it means the original assumption was false, and thus the argument is valid.

Argument:

H ⊃ I

J ⊃ K

~K

H ∨ J

Conclusion: I

Proof by contradiction:

H ⊃ I (Premise)

J ⊃ K (Premise)

~K (Premise)

H ∨ J (Premise)

~I (Assumption for proof by contradiction)

H (Disjunction elimination from 4)

I (Modus ponens using 1 and 6)

~J (Assumption for proof by contradiction)

K (Modus ponens using 2 and 8)

~K ∧ K (Conjunction introduction of 3 and 9)

Contradiction: ~I ∧ I (Conjunction introduction of 5 and 7)

Conclusion: I (Proof by contradiction)

The proof shows that if we assume the premises are true and the conclusion is false, it leads to a contradiction. Therefore, the argument is valid.

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