pls help and show work i am so screwed if i don’t do well on this

:))))))

Step-by-step explanation:

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The values of k for which the function f(x, y, z) = kx² - kry + y² - 2yz - 22 has a nondegenerate local maximum at (0, 0, 0) are when k > 0.

To find the critical points of the function, we need to calculate the partial derivatives with respect to each variable:

∂f/∂x = 2kx ∂f/∂y = -kr + 2y - 2z ∂f/∂z = -2y

2kx = 0 => x = 0 (Equation 1) -kr + 2y - 2z = 0 => r = y - z (Equation 2) -2y = 0 => y = 0 (Equation 3)

From Equation 3, we can see that y = 0. Substituting this into Equation 2, we get:

r = 0 - z r = -z (Equation 4)

The Hessian matrix is given by:

H = | ∂²f/∂x² ∂²f/∂x∂y ∂²f/∂x∂z | | ∂²f/∂y∂x ∂²f/∂y² ∂²f/∂y∂z | | ∂²f/∂z∂x ∂²f/∂z∂y ∂²f/∂z² |

Calculating the second-order partial derivatives:

∂²f/∂x² = 2k ∂²f/∂y² = 2 ∂²f/∂z² = 0 ∂²f/∂x∂y = 0 ∂²f/∂y∂z = -2 ∂²f/∂z∂x = 0

Thus, the Hessian matrix becomes:

H = | 2k 0 0 | | 0 2 -2 | | 0 -2 0 |

D = ∂²f/∂x² ∂²f/∂y² ∂²f/∂z² + 2∂²f/∂x∂y ∂²f/∂y∂z ∂²f/∂z∂x - (∂²f/∂x² ∂²f/∂y∂z ∂²f/∂z∂x + ∂²f/∂y² ∂²f/∂z∂x ∂²f/∂x∂y ∂²f/∂z²)

Substituting the partial derivatives we calculated earlier:

D = (2k)(2)(0) + 2(0)(-2)(0) - (2k)(-2)(0) - (2)(0)(0) D = 0

If the determinant D is zero, the second derivative test is inconclusive. In such cases, we need to consider the eigenvalues of the Hessian matrix.

To find the eigenvalues, we solve the characteristic equation:

det(H - λI) = 0

where λ is the eigenvalue and I is the identity matrix. Substituting the values from the Hessian matrix:

| 2k-λ 0 0 | | 0 2-λ -2 | | 0 -2 -λ |

The characteristic equation becomes:

(2k - λ)((2 - λ)(-λ) - (-2)(0)) - (0)((2 - λ)(-2) - (0)(0)) = 0 (2k - λ)(λ² - 2λ) = 0

From this equation, we can see that one eigenvalue is (2k - λ) = 0, which implies λ = 2k.

For our case, we have one eigenvalue (λ = 2k). Thus, the sign of λ depends on the value of k.

When k < 0, the point (0, 0, 0) is a nondegenerate local minimum. When k = 0, the second derivative test is inconclusive, and further analysis would be required to determine the nature of the critical point.

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Step-by-step explanation:

Volume of Cylinder =

[tex]500 {cm}^{3} = \pi {r}^{2} h[/tex]

given d = 18

r = 1/2 x d = 9cm,

[tex]\pi( {9}^{2} )h = 500 \\ 81\pi \: h = 500 \\ h = \frac{500}{81\pi} cm[/tex]

I will leave the answer in terms of Pi as I am not sure how you want to leave your answer as.

The standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients is 1.6487.

Given that a healthcare research agency reported that 41% of people who had coronary bypass surgery in 2008 were over the age of 65 and twelve coronary bypass patients are sampled.

To determine the mean number of people over the age of 65 in a sample of 12 coronary bypass patients, we use the formula below:

Mean = np

Where n = 12 and p = 0.41.

Mean = 12(0.41)

Mean = 4.92

Therefore, the mean number of people over the age of 65 in a sample of 12 coronary bypass patients is 4.92.

To determine the standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients, we use the formula below:

Standard deviation, σ = √(n p q)

Where n = 12, p = 0.41, and q = 1 - p.

Standard deviation, σ = √(12 × 0.41 × 0.59)

Standard deviation, σ = √2.71948

Standard deviation, σ = 1.6487 (rounded to four decimal places).

Therefore, the standard deviation of the number of people over the age of 65 in a sample of 12 coronary bypass patients is 1.6487.

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(a) MLE of $\lambda$ is obtained by maximizing the log-likelihood. Suppose that X1,X2,…,XnX1,X2,…,Xn are independent and identically distributed exponential random variables with parameter λ, then the probability density function of XiXi is given by $$f(x_i;\lambda) =\lambda e^ {-\lambda x_i}, \quad x_i\geq0. $$

The log-likelihood function is given by$$\begin{aligned}\ln L(\lambda) &= \ln (\lambda^n e^{-\lambda(x_1+x_2+\cdots+x_n)}) \\&=n\ln \lambda-\lambda(x_1+x_2+\cdots+x_n).\end{aligned}$$

The first derivative of the log-likelihood function with respect to λλ is$$\frac {d\ln L(\lambda)} {d\lambda} = \frac{n}{\lambda}-x_1-x_2-\cdots-x_n.$$

The first derivative is zero when $$\frac{n}{\lambda}-\sum_{i=1} ^{n} x_i=0. $$Hence, the MLE of λλ is $$\hat{\lambda} =\frac{n}{\sum_{i=1} ^{n} x_i}. $$

Substituting the value of $\hat{\lambda} $ gives the maximum value of the log-likelihood. So, the MLE of $\lambda$ is given by $$\boxed{\hat{\lambda} =\frac{n}{\sum_{i=1} ^{n} x_i}}. $$

The MLE of $\lambda$ is $\frac {3} {\sum_{i=1} ^{n} x_i}$.

(b) The median of the exponential distribution is given by$$m = \frac {\ln (2)} {\lambda}. $$

Therefore, the log-likelihood function for median is given by$$\begin{aligned}\ln L(m) &= \sum_{i=1}^{n} \ln f(x_i;\lambda)\\&= \sum_{i=1}^{n} \ln \left(\frac{1}{\lambda}e^{-x_i/\lambda}\right)\\&= -n\ln\lambda-\frac{1}{\lambda}\sum_{i=1}^{n}x_i.\end{aligned}$$

The first derivative of the log-likelihood function with respect to mm is$$\frac {d\ln L(m)} {dm} = \frac {1} {\lambda}-\frac {1} {\lambda^2} \sum_{i=1} ^{n}x_i\ln 2. $$

The first derivative is zero when $$\frac {1} {\lambda} =\frac{1}{\lambda^2}\sum_{i=1}^{n}x_i\ln 2.$$Hence, the MLE of mm is $$\boxed{\hat{m} = \frac{\ln 2}{\bar{x}}}.$$where $\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i.$Therefore, the MLE of m is $\frac {\ln 2} {\bar{x}}. $

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Answer:

I found 2 answers for this one

Step-by-step explanation:

B- 2,5,10

D-12,16,20

The possible length in inches of the stick that will make a right angle triangle are as follows

A right angle triangle has one of its angles as 90 degrees.

The right angle triangle must obeys the Pythagorean theorem.

c² = a² + b²

where

Therefore, the sides that makes a right angle are as follows:

6, 8 , 10 : 6² + 8² = 10²

12, 16, 20 : 12² + 16² = 20²

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Answer:

5 drinks will be americanos

Step-by-step explanation:

2:8  (2/8)

simplify

1:4  (1/4)

divide 20 by 4

5:20

The number of next 20 drinks which may be Americanos is 5.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Given that,

Total drinks sold = 8

Number of drinks that is Americanos = 2

Probability of finding Americano = 2/8 = 1/4

If the total number of drinks next is 20,

Number of Americanos expected = Probability of Americanos × Number of drinks

= 1/4 × 20

= 5

Hence the number of Americanos expected is 5.

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Answer:

x<28

Step-by-step explanation:

Isolate x

First, subtract 4 on both sides

x/2+<14

Then, multiply both sides by 2 to get x alone

x<28

On a number line, there would be an open circle (not filled in dot) on 28, and the entire left side of the number line would be filled in

Answer:

x<28

Step-by-step explanation:

x/2+4<18

multiply the 2 on both sides to get rid of it

x+8<36

isolate the x

x<28

on the number line, it's an open circle with the arrow pointing to the left.

The function f(x) = e^(1+x) has at least one real root. The function f(x) = e^(1+x) cannot have more than one real root.

To show that f(x) has at least one real root, we need to find a value of x for which f(x) equals zero. Let's set f(x) = 0 and solve for x:

e^(1+x) = 0

Since e^(1+x) is always positive for any real value of x, there is no value of x that makes f(x) equal to zero. Hence, f(x) = e^(1+x) does not have any real roots. Therefore, we cannot show that f(x) has at least one real root.

b)

To show that f(x) cannot have more than one real root, we need to demonstrate that there cannot be two distinct real values, say c1 and c2, such that f(c1) = f(c2) = 0. Let's assume that f(x) = 0 at two distinct values, c1 and c2:

e^(1+c1) = e^(1+c2) = 0

However, this equation is not possible since e^(1+c1) and e^(1+c2) are always positive for any real values of c1 and c2. Therefore, f(x) = e^(1+x) cannot have more than one real root.

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Answer:

False

Step-by-step explanation:

A P E X

Answer:

fjekwnkewgnelwnlgnendndj

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

E is -1 and the absolute value is the posotive of any number. The positive of -1 is 1.

Answer:

$36

Step-by-step explanation:

Basically, every shirt is $6 because 30% of 20 is 6. If he buys 6 shirts, then 6 times 6 is 36 dollars spent, tax not included.

Answer:

a) 2x+(x+36)=90

Step-by-step explanation:

b) A1+A2=90°. (A=angle)

2x+(x+36)=90

2x+x+36=90

3x+36=90

3x=90-36

x=54/3

x=18

then A1=2x=2*18=36°

A2=x+36=18+36=54°

Answer:

the full answer is 215.859885inches cubed

Step-by-step explanation:

times the length, width and height together

Answer: squareroot of 58

You can solve this problem simply by using the distance formula . Using the distance formula we can solve this problem by just placing the numbers and then solving the equation.

Answer:

1 < -9

Step-by-step explanation:

A positive number can't be less than a negative

Answer:

Second One-

[tex] {5}^{14}. {5}^{ - 2} [/tex]

Fifth One-

[tex] {5}^{6} \: . \: {5}^{6} [/tex]

Sixth One-

[tex] \sqrt{ {5}^{24} } [/tex]

Seventh One-

[tex] {5}^{11} \: . \: 5 [/tex]

Answer:

$400

Step-by-step explanation:

all you do is add 320+540+230+450+280+580/6 and the asnwe comes out to 400

Answer:

45

Step-by-step explanation:

the correct choice is C.

By computing the pooled variance given the following data N_1 = 18, n_2 = 14, s_1 = 7, s_2 = 8, the pooled variance is 436.40.

To compute the pooled variance given N_1 = 18, n_2 = 14, s_1 = 7, s_2 = 8, we can use the formula below;

S_p² = [(n₁ - 1)S₁² + (n₂ - 1)S₂²] / (N - 2),

where S_p² = pooled variance, n₁ = sample size of first group, n₂ = sample size of second group, S₁² = variance of first group, S₂² = variance of second group, and N = total sample size.

To plug in the values, we have: N₁ = 18n₂ = 14S₁ = 7S₂ = 8

Substituting the values into the formula above we get;

S_p² = [(18 - 1)(7²) + (14 - 1)(8²)] / (18 + 14 - 2)S_p² = (17 × 49 + 13 × 64) / 30S_p² = 436.4

Round off to two decimal places to get 436.40.

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Answer:

Radius = 8 inches

Area = [tex]\pi {r}^{2} [/tex]

[tex]area = \pi( {8}^{2})[/tex]

[tex] = 64\pi \: square \: inches[/tex]

A = [tex]201.06 ^{2} \: inches[/tex]

Step-by-step explanation:

Hope it is helpful....

The logistic differential equation for the hyena population is given by:

dP/dt = r * P * (1 - P/K)

where P(t) is the hyena population at time t, r is the growth rate, and K is the carrying capacity.

We are given that:

P(t) = 40 + k * e^(-0.57t)

K = 200

To determine the value of k, we can plug in these values into the logistic differential equation and solve for k:

dP/dt = r * P * (1 - P/K)

dP/dt = r * P * (1 - P/200)

dP/dt = r/200 * (200P - P^2)

dP/(200P - P^2) = r dt

Integrating both sides, we get:

-1/200 ln|200P - P^2| = rt + C

where C is a constant of integration.

Using the initial condition P(0) = 40 + k, we can solve for C:

-1/200 ln|200(40+k)-(40+k)^2| = 0 + C

C = -1/200 ln|8000-480k|

Plugging in this value of C and simplifying, we get:

-1/200 ln|200P - P^2| = rt - 1/200 ln|8000-480k|

ln|200P - P^2| = -200rt + ln|8000-480k|

|200P - P^2| = e^(-200rt) * |8000-480k|

200P - P^2 = ± e^(-200rt) * (8000-480k)

Since the population is increasing, we choose the positive sign:

200P - P^2 = e^(-200rt) * (8000-480k)

Using the initial condition P(0) = 40 + k, we get:

200(40+k) - (40+k)^2 = (8000-480k)

8000 + 160k - 2400 - 80k - k^2 = 8000 - 480k

k^2 + 560k - 2400 = 0

(k + 60)(k - 40) = 0

Thus, k = -60 or k = 40. Since k represents a growth rate, it should be positive, so we choose k = 40. Therefore, the value of the constant k is option (A) 4.

For the second part of the question, the logistic equation that could model the growth in the graph is option (B) dM/dt = (20-M)*(M-50). This is because the carrying capacity is between 20 and 50, and the population growth rate is zero at both of these values (i.e. the population does not increase or decrease when it is at the carrying capacity).

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(a) To prove that the set N(R) = {x ∈ R: x is nilpotent} is an ideal of the commutative ring R with 1.

We need to show that it satisfies the two conditions of being an ideal: closure under addition and closure under multiplication by elements of R.

To demonstrate closure under addition, let x and y be nilpotent elements in N(R). This means that there exist positive integers m and n such that xm = 0 and yn = 0.

We want to show that x + y is also nilpotent. By expanding (x + y)^k using the binomial theorem, we can see that each term involves a product of powers of x and y. Since both x and y are nilpotent, their product is also nilpotent.

Therefore, the sum (x + y) raised to a sufficiently high power will result in zero, showing that x + y is indeed nilpotent. Hence, N(R) is closed under addition.

To prove closure under multiplication by elements of R, let x be a nilpotent element in N(R) and r be any element in R. We aim to show that rx is nilpotent. Since x is nilpotent, there exists a positive integer m such that xm = 0.

When we raise rx to a sufficiently high power, (rx)^k, it can be expanded as r^k * x^k. Since x^k is zero due to x being nilpotent, the product r^k * x^k is also zero. Therefore, rx is nilpotent, and N(R) is closed under multiplication by elements of R.

Hence, N(R) satisfies both conditions of being an ideal, and thus, it is an ideal of the commutative ring R.

(b) To prove that N(R/N(R)) = 0, we want to show that every element in R/N(R) is not nilpotent.

Let [x] be an element in R/N(R), where [x] represents the equivalence class of x modulo N(R). Our goal is to demonstrate that [x] is not nilpotent, meaning it is not equal to the zero element in R/N(R).

Suppose, for contradiction, that [x] = 0 in R/N(R). This would imply that x belongs to N(R), the set of nilpotent elements in R. However, if x is an element of N(R), it means that x is nilpotent, and by definition, there exists some positive integer n such that xn = 0. This contradicts our assumption that [x] = 0, since it would imply that x is not nilpotent.

Therefore, our assumption that [x] = 0 leads to a contradiction, and we conclude that every element in R/N(R) is not nilpotent.

Consequently, N(R/N(R)) = 0, indicating that the set of nilpotent elements in the quotient ring R/N(R) is empty.

In summary, we have shown that N(R/N(R)) = 0 and established that N(R) is an ideal of the commutative ring R.

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Answer: The correct answer is A or B

`

Step-by-step explanation:

a. To take a sample of the student population that would not represent the population well, Susan could use a biased sampling method.

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