Lulu's mum pours 210 ml of plant food into a watering con. She adds 150 ml more water than plant food into the watering can to get a mixture. She then pours all of the mixture equally onto 6 plants. How much of the mixture does she pour onto each plant?

a. To derive the bias of p(hat)2, we need to calculate the expected value (mean) of p(hat)2 and subtract the true value of p.

Bias(p(hat)2) = E(p(hat)2) - p

Now, p(hat)2 = (Y+1)/(n+2), and Y has a binomial distribution with parameters n and p. Therefore, the expected value of Y is E(Y) = np.

E(p(hat)2) = E((Y+1)/(n+2))

          = (E(Y) + 1)/(n+2)

          = (np + 1)/(n+2)

The bias of p(hat)2 is given by:

Bias(p(hat)2) = (np + 1)/(n+2) - p

b. To derive the mean squared error (MSE) for both p(hat)1 and p(hat)2, we need to calculate the variance and bias components.

For p(hat)1:

Bias(p(hat)1) = E(p(hat)1) - p = E(Y/n) - p = (1/n)E(Y) - p = (1/n)(np) - p = p - p = 0

Variance(p(hat)1) = Var(Y/n) = (1/n^2)Var(Y) = (1/n^2)(np(1-p))

MSE(p(hat)1) = Variance(p(hat)1) + [Bias(p(hat)1)]^2 = (1/n^2)(np(1-p))

For p(hat)2:

Bias(p(hat)2) = (np + 1)/(n+2) - p (as derived in part a)

Variance(p(hat)2) = Var((Y+1)/(n+2)) = Var(Y/(n+2)) = (1/(n+2)^2)Var(Y) = (1/(n+2)^2)(np(1-p))

MSE(p(hat)2) = Variance(p(hat)2) + [Bias(p(hat)2)]^2 = (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

c. To find the values of p where MSE(p(hat)1) < MSE(p(hat)2), we can compare the expressions for the mean squared errors derived in part b.

(1/n^2)(np(1-p)) < (1/(n+2)^2)(np(1-p)) + [(np + 1)/(n+2) - p]^2

Simplifying this inequality requires a specific value for n. Without the value of n, we cannot determine the exact values of p where MSE(p(hat)1) < MSE(p(hat)2). However, we can observe that the inequality will hold true for certain values of p, n, and the difference between n and n+2.

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In the given scenario, we have two estimators for the parameter p of a binomial distribution: p(hat)1 = Y/n and p(hat)2 = (Y+1)/(n+2). The objective is to analyze the bias and mean squared error (MSE) of these estimators.

The bias of p(hat)2 is derived as (n+1)/(n(n+2)), while the MSE of p(hat)1 is p(1-p)/n, and the MSE of p(hat)2 is (n+1)(n+3)p(1-p)/(n+2)^2. For values of p where MSE(p(hat)1) is less than MSE(p(hat)2), we need to compare the expressions of these MSEs.

(a) To derive the bias of p(hat)2, we compute the expected value of p(hat)2 and subtract the true value of p. Taking the expectation:

E(p(hat)2) = E[(Y+1)/(n+2)]

          = (1/(n+2)) * E(Y+1)

          = (1/(n+2)) * (E(Y) + 1)

          = (1/(n+2)) * (np + 1)

          = (np + 1)/(n+2)

Subtracting p, the true value of p, we find the bias:

Bias(p(hat)2) = E(p(hat)2) - p

             = (np + 1)/(n+2) - p

             = (np + 1 - p(n+2))/(n+2)

             = (n+1)/(n(n+2))

(b) To derive the MSE of p(hat)1, we use the definition of MSE:

MSE(p(hat)1) = Var(p(hat)1) + [Bias(p(hat)1)]^2

Given that p(hat)1 = Y/n, its variance is:

Var(p(hat)1) = Var(Y/n)

            = (1/n^2) * Var(Y)

            = (1/n^2) * np(1-p)

            = p(1-p)/n

Substituting the bias derived earlier:

MSE(p(hat)1) = p(1-p)/n + [0]^2

            = p(1-p)/n

To derive the MSE of p(hat)2, we follow the same process. The variance of p(hat)2 is:

Var(p(hat)2) = Var((Y+1)/(n+2))

            = (1/(n+2)^2) * Var(Y)

            = (1/(n+2)^2) * np(1-p)

            = (np(1-p))/(n+2)^2

Adding the squared bias:

MSE(p(hat)2) = (np(1-p))/(n+2)^2 + [(n+1)/(n(n+2))]^2

            = (n+1)(n+3)p(1-p)/(n+2)^2

(c) To compare the MSEs, we need to determine when MSE(p(hat)1) < MSE(p(hat)2). Comparing the expressions:

p(1-p)/n < (n+1)(n+3)p(1-p)/(n+2)^2

Simplifying:

(n+2)^2 < n(n+1)(n+3)

Expanding:

n^2 + 4n + 4 < n^3 + 4n^2 + 3n^2

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Answer:

???

Step-by-step explanation:

f(x) = x + 1 is the monic quadratic polynomial used here

Given,

The monic quadratic polynomial f(x)

The remainder when f(x) divided by x - 1 is 2

The remainder when f(x) divided by  x - 3 is 4

We have to find f(x).

Monic Quadratic Polynomial;-

A monic polynomial in algebra is a univariate polynomial with a single variable and a leading coefficient of 1. Its leading coefficient is the highest degree nonzero coefficient.

Here,

The remainder when f(x) divided by x - 1 is 2

Assume f(x) / x - 1 = 1

Then,

f(x) = (x - 1) × 1 + 2

f(x) = x - 1 + 2

f(x) = x + 1

Next,

The remainder when f(x) divided by  x - 3 is 4

Assume f(x) / x - 3 = 1

Then,

f(x) = (x - 3) × 1 + 4

f(x) = x - 3 + 4

f(x) = x + 1

That is,

The monic quadratic polynomial used here is, f(x) = x + 1

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Answer:

90 feet.

Step-by-step explanation:

The horizontal beam is parallel to the base of a triangular roof, and the vertical beam is perpendicular to the horizontal beam and the base of the roof. So the length of the horizontal beam is the same as the base of the roof which is 90 feet.

The limit does not exist. The left and right limits as x approaches 6 are different, so the overall limit does not exist. The function "jumps" at x = 6.

Consider the left and right limits as x approaches 6:

Since the left and right limits are different, the overall limit does not exist. Intuitively, this is because the function "jumps" at x = 6, taking on very different values on either side of the point. Therefore, the limit as x approaches 6 does not exist.

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Alright nevermind, imma delete this answer.

Answer: $5.40

Step-by-step explanation:

1 and 2/3 yards costs $9

5/3 yards costs $9 <--- changes 1 and 2/3 to improper

5 * 1/3 yards costs $9 <---- 5/3 = 5 * 1/3

1/3 yard costs $9/5 = $1.80 <--- divides the ratio by 5

1 yard costs $1.80 * 3 = $5.40

Answer: 0.32

Step-by-step explanation:

You are not going out of the same time for the same thing

Step-by-step explanation:

Uhgvhddfd dtcgxgstdd fhfgyfeywc

Gjufchhjjjjujch

Answer:

3^8

Step-by-step explanation:

please mark me as brainlest to all questions please

Answer:

(-2,4)

I just turned it in it was right

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer: Lol

B (-8,-5)

D (-10,-4)

C (-8,3)

Step-by-step explanation:

Answer:

191

Step-by-step explanation:

47+144=191

Answer:

equation: 144+ 47= 191

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

8/125cm3

Step-by-step explanation:

A=lxwxh

A=2/5 x 2/5 x 2/5

A=8/125cm

I hope this helps <3

↝ Quadratic Function has the domain of all real numbers. (Even not given the specific domain.)

↝ The equation \(y=-3(x-5)+8\) is a parabola with (5,8) as a vertex. We call the equation \(y=a(x-h)^2+k\) as vertex equation.

The domain of -3(x-5)+8 is all set of real numbers.

↝ Interval Notation ↝

Since the domain of the equation is set of all real numbers.

Therefore, the domain is x ∈ R or (-∞,∞) or -∞<x<∞

There of them work. Recall that the domain of quadratic function is all set of real numbers.

Answer:

20%

Step-by-step explanation:

12 / 60 = 0.2

0.2 x 100 = 20

20%

(% = Part / Whole × 100)

Answer:

The profit per sweater is 29 dollars.

Step-by-step explanation:

First find the total profit.

136 - 20

116 for all 4 sweaters

Now divide by 4 since there are 4 sweaters to find the profit per sweater.

116/4

29

The profit per sweater is 29 dollars.

Answer:

43

Step-by-step explanation:

divide 10 3/4 by 1/4

The probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).

We can use Bayes' theorem to calculate the probability that Ann picked a ball from the second box given that she selected an orange ball.

Let A be the event that Ann selected an orange ball, and B be the event that Ann picked a ball from the second box. We want to find P(B|A), the probability that Ann picked a ball from the second box given that she selected an orange ball.

We know that there are two boxes, each with a probability of 1/2 of being selected. The probability of selecting an orange ball from the first box is 3/7, and the probability of selecting an orange ball from the second box is 7/11. Therefore, the probability of selecting an orange ball overall is:

P(A) = P(A|B)P(B) + P(A|B')P(B')

= (7/11)(1/2) + (3/7)(1/2)

= 25/42

Now we can use Bayes' theorem:

P(B|A) = P(A|B)P(B)/P(A)

= (7/11)(1/2)/(25/42)

= 14/25

Therefore, the probability that Ann picked a ball from the second box given that she selected an orange ball is 0.56 or 56% (rounded to two decimal places).

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Answer:

Mean: \(93.2\; \rm ^{\circ} F\).

Standard deviation: \(4.086\; \rm ^{\circ} F\).

Step-by-step explanation:

Consider a random variable \(X\) with mean \(\overline{X}\) and variance \({\rm Var}(X)\).

If a random variable \(Y\) is obtained by linearly transforming \(X\) for some constants \(m \ne 0\) and \(b\), then the mean of \(Y\!\) would be:

\(\overline{Y} = m\, \overline{X} + b\).

\(\mathrm{Var}(Y) = m^{2} \, \mathrm{Var}(X)\).

The standard deviation of a random variable is the square root of its variance. Therefore, the standard deviation of \(Y\) would be:

\(\begin{aligned}\mathrm{SD}(Y) &= \sqrt{\mathrm{Var}(Y)} \\ &= \sqrt{m^{2}\, \mathrm{Var}(X)} \\ &= m\, \sqrt{\mathrm{Var}(X)} \\ &= m\, \mathrm{SD}(X)\end{aligned}\).

In this question, the random variable \(F\) is obtained by linearly transforming \(C\) using the constants \(m = (9/5)\) and \(b = 32\). That is:

\(F = (9/5)\, C + 32\).

It is given that mean \(\overline{C} = 34\) while standard deviation \(\mathrm{SD}(X) = 2.27\). The mean and standard deviation of \(F\) obtained from the linear transformation would be:

\(\begin{aligned}\overline{F} &= m\, \overline{C} + b \\ &= (9/5) \times 34 + 32\\ &= 93.2\end{aligned}\).

\(\begin{aligned}\mathrm{SD}(F) &= m\, \mathrm{SD}(C) \\ &= (9/5) \times 2.27 = 4.086\end{aligned}\).

Thus, when measured in degrees Fahrenheit, the corresponding mean would be \(93.2\; \rm ^{\circ} F\) and and standard deviation would be \(4.086\; \rm ^{\circ} F\).

Given the values (f = 7), (m = 0), and (l = 5) (corresponding to the number of letters in my first name, middle name, and last name, respectively), we can rewrite the differential equation as follows:

[5y^{\prime \prime} + 0y^{\prime} + 7y = e^{5x}, \quad y(0) = 0, \quad y^{\prime}(0) = 7.]

To solve this second-order linear homogeneous ordinary differential equation with constant coefficients, we first find the characteristic equation by assuming a solution of the form (y = e^{rx}). Substituting this into the differential equation, we get:

[5r^2 + 7 = 0.]

Solving this quadratic equation for (r), we have:

[r^2 = -\frac{7}{5}.]

Taking the square root of both sides, we obtain:

[r = \pm i\sqrt{\frac{7}{5}}.]

Since the roots are complex, we have two complex conjugate solutions: (r_1 = i\sqrt{\frac{7}{5}}) and (r_2 = -i\sqrt{\frac{7}{5}}).

The general solution to the homogeneous equation is given by:

[y_h(x) = c_1 e^{r_1 x} + c_2 e^{r_2 x},]

where (c_1) and (c_2) are arbitrary constants.

Next, we need to find a particular solution to the non-homogeneous equation. Since the right-hand side of the equation is (e^{5x}), we can assume a particular solution of the form (y_p(x) = Ae^{5x}), where (A) is a constant to be determined.

Substituting this into the differential equation, we have:

[5(5^2Ae^{5x}) + 7Ae^{5x} = e^{5x}.]

Simplifying, we get:

[25Ae^{5x} + 7Ae^{5x} = e^{5x}.]

Combining like terms, we obtain:

[32Ae^{5x} = e^{5x}.]

Dividing both sides by (e^{5x}), we find:

[32A = 1.]

Therefore, (A = \frac{1}{32}).

Hence, the particular solution is (y_p(x) = \frac{1}{32}e^{5x}).

The general solution to the non-homogeneous equation is the sum of the general solution to the homogeneous equation and the particular solution:

[y(x) = y_h(x) + y_p(x).]

Substituting the values of (r_1), (r_2), and (A), we have:

[y(x) = c_1 e^{i\sqrt{\frac{7}{5}}x} + c_2 e^{-i\sqrt{\frac{7}{5}}x} + \frac{1}{32}e^{5x}.]

To determine the constants (c_1) and (c_2), we use the initial conditions (y(0) = 0) and (y'(0) = 7).

From (y(0) = 0):

[c_1 + c_2 + \frac{1}{32} = 0.]

From (y'(0) = 7):

[i\sqrt{\frac{7}{5}}c_1 - i\sqrt{\frac{7}{5}}c_2 + 5\cdot \frac{1}{32} = 7.]

Simplifying the equations, we get:

[c_1 + c_2 = -\frac{1}{32},]

[i\sqrt{\frac{7}{5}}c_1 - i\sqrt{\frac{7}{5}}c_2 + \frac{5}{32} = 7.]

Adding the two equations, we find:

[2c_1 = 7 - \frac{1}{32}.]

Hence,

[c_1 = \frac{7}{2} - \frac{1}{64} = \frac{111}{32}.]

Substituting this value of (c_1) into the first equation, we obtain:

[\frac{111}{32} + c_2 = -\frac{1}{32}.]

Simplifying, we find:

[c_2 = -\frac{1}{32} - \frac{111}{32

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According to the question the median is most probably less than 36.

For a positively skewed distribution, the mode is the value that occurs most frequently, the mean is the average value, and the median is the middle value when the data is arranged in ascending order.

Given that the mode is \(\(x = 31\)\) and the mean is \(\(36\),\) we can infer that the majority of the data is clustered towards the left (lower values) and there are some relatively high values that pull the mean to the right.

Since the distribution is positively skewed, the median is expected to be lower than the mean. This is because the presence of outliers or higher values on the right side of the distribution affects the mean more than the median.

Therefore, the median is most probably less than 36.

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    Options (C) and (D) are the correct options.

          form of (a - b)(c - d).

          Here, a and c are the FIRST terms

                    a and d are the OUTER terms

                    b and c are the INNER terms

                    b and d are the LAST terms

           Multiply all FIRST, OUTER, INNER and LAST terms and add them.  

(a - b)(c - d) = a.c + a(-d) + (-b)c + (-b)(-d)

                  = ac - ad - bc + bd

                  = ac - (ad + bc) + bd

      Therefore, expressions given in options (C) and (D) are the correct options.

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The value of the required mean of the sampling distribution of sample means is approx. 21 ounces when this process is in control.

Sample mean: The arithmetic mean of the values of the variables in the sample. If the samples are drawn from probability distributions with a common expected value, the sample mean is an estimate of that expected value.

Sample means for all days using formula,

Monday = (23+22+23+24)/4 = 23

Tuesday = (23+21+19+21)/4 = 21

Wednesday = (20+19+20+21)/4 = 20

Thursday = (18+19+20+19)/4 = 19

Friday = (18+20+22+20)/4 = 20

We have to calculate the mean of sampling distribution of sample means.

Mean of the sampling distribution of sample means = Sum of sample means of all days / Number of days

= (23+21+20+19+20)/5

= 20.6 = 21 ounces

Hence, the required mean is approx. 21 ounces.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer: 697

Step-by-step explanation:

(9)(3)(9)(3)−(12)(3)+4

=(27)(9)(3)−(12)(3)+4

=(243)(3)−(12)(3)+4

=729−(12)(3)+4

=729−36+4

=693+4

=697

Answer:

5x+10y+5z

Step-by-step explanation:

hope this helped luis also other person is correct