The marginal PMFs for two INDEPENDENT random variables are given as follows 1/8 x = -1 Px(x) 1/2 = 0 3/8 1 = X = X = - py(y) = Py = 5/16 y=-1 9/16 y=0 1/8 = y = 1 a) Find the joint PMF for X, Y

Answer:

Length of rectangle = 51 cm

Width of rectangle = 24 cm

Step-by-step explanation:

Given:

Perimeter of rectangle = 150 cm

Find:

Length and width of the rectangle

Computation:

Assume;

Width of rectangle = a cm

Length of rectangle = 2a + 3 cm

Perimeter of rectangle = 2[l + b]

150 = 2[(2a + 3) + a]

2[3a + 3] = 150

6a + 6 = 150

6a = 144

a = 24

Width of rectangle = 24 cm

Length of rectangle = 2a + 3 cm

Length of rectangle = 2(24) + 3 cm

Length of rectangle = 51 cm

Answer:

x= 8

Step-by-step explanation:

17x + 3 = 139

17x = 136

x = 8

The probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.

We can use the binomial probability formula to solve this problem.

The formula is given as; $$P(X=k)={n\choose k}p^k(1-p)^{n-k}$$

Where;
n= sample size=12
k= number of green peas=8
p= probability of getting a green pea=3/4
q= probability of getting a yellow pea=1/4
Since we want the probability of exactly 8 green peas out of 12 peas,

we will plug in the values in the formula to get;

$$P(X=8)={12\choose 8}(\frac{3}{4})^8 (1-\frac{3}{4})^{12-8}$$$$

P(X=8)={12\choose 8}(\frac{3}{4})^8(\frac{1}{4})^{4}$$$$P(X=8)=495

(0.3164)(0.0039)$$$$P(X=8)=0.4749$$

Therefore, the probability of exactly 8 green peas is 0.475, rounded to three decimal places, i.e., 0.475.

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Using the CVP Formulas to solve the following. JBL Speakers has annual fixed costs of $2,450,000, and variable costs of $25 per unit. The selling price per unit is $90.

A) 37,692 units

B) 53,077 units

A) To calculate the annual revenue required to break even, we need to find the point where total revenue equals total costs.

Total cost (TC) = Fixed costs (FC) + Variable costs per unit (VC) * Quantity (Q)

Total revenue (TR) = Selling price per unit (SP) * Quantity (Q)

At the break-even point, total revenue equals total cost:

TR = TC

SP * Q = FC + VC * Q

Substituting the given values:

$90 * Q = $2,450,000 + $25 * Q

$90Q - $25Q = $2,450,000

$65Q = $2,450,000

Q = $2,450,000 / $65

Q ≈ 37,692.31

Therefore, approximately 37,692 units need to be sold to break even.

B) To calculate the annual unit sales required to make a $1,000,000 profit, we can use the following formula:

Profit (P) = (SP * Q) - (FC + VC * Q)

Substituting the given values and the desired profit:

$1,000,000 = ($90 * Q) - ($2,450,000 + $25 * Q)

$90Q - $25Q = $1,000,000 + $2,450,000

$65Q = $3,450,000

Q = $3,450,000 / $65

Q ≈ 53,076.92

Therefore, approximately 53,077 units need to be sold to make a $1,000,000 profit.

In conclusion, to break even, JBL Speakers needs to generate an annual revenue of approximately $2,450,000, and to make a $1,000,000 profit, they need to sell approximately 53,077 units annually.

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Answer:

(a + 4)(b + 1)

Step-by-step explanation:

ab + 4 + a + 4b

Rearrange the expression to find the GCF.

ab + a + 4b + 4

Now find the GCF.

a (b + 1) + 4 (b + 1)

Divide the whole thing by b+1

(a + 4)(b + 1)

The 90% confidence interval for the true population mean textbook weight, based on the given data, is approximately 41.44 ounces to 42.56 ounces.

To construct a confidence interval for the population mean textbook weight, we can use the formula:

Confidence Interval = sample mean ± (critical value * standard error)

Given that the sample mean is 42 ounces and the population standard deviation is 3.8 ounces, we need to determine the critical value and the standard error.

For a 90% confidence interval, the critical value corresponds to a two-tailed z-score of 1.645 (from the standard normal distribution).

The standard error can be calculated as the population standard deviation divided by the square root of the sample size. Since the sample size is not provided, we cannot calculate the exact standard error. However, if we assume a large sample size (usually considered to be greater than 30), we can use the formula for the standard error.

Assuming a large sample size, the standard error would be 3.8 ounces divided by the square root of the sample size.

Using the formula for the confidence interval, we can now calculate the range:

Confidence Interval = 42 ± (1.645 * standard error)

Substituting the values, we get:

Confidence Interval = 42 ± (1.645 * 3.8 / sqrt(sample size))

Since we do not know the sample size, we cannot calculate the exact confidence interval. However, based on the given data, we can conclude that the true population mean textbook weight falls between approximately 41.44 ounces and 42.56 ounces with 90% confidence.

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Answer:

15

Step-by-step explanation:

Prime Numbers Check

15: 5 * 3

30: 2 * 3 * 5

75: 3 * 5 * 5

Both 3 and 5 are prime numbers present in all 3 greater numbers, then you multiply them

3*5 = 15

GCF is 15

Answer:

16

Step-by-step explanation:

Alex will run 16 laps in the time it take for Carlos to run 12 laps.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given are the values related to the number of laps run by Alex and Carlos.

The number of laps run by Alex is forming the multiples of 4 or 4x.

Number of laps run by Carlos is forming the multiples of 3 or 3x.

When x = 1,

Alex : 4 × 1 = 4

Carlos : 3 × 1 = 3

When x = 2,

Alex : 4 × 2 = 8

Carlos : 3 × 2 = 6

When x = 3,

Alex : 4 × 3 = 12

Carlos : 3 × 3 = 9

When x = 4,

Alex : 4 × 4 = 16

Carlos : 3 × 4 = 12

Hence Alex ran 16 laps in the same time for which Carlos ran 12 laps.

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The unit impulse response of the system described by the equation y[n+2] + 2y[n+1] + y[n] = 2x[n+2] − x[n+1] is h[n] = 2δ[n+2] − δ[n+1] + δ[n], where δ[n] represents the unit impulse function.

To find the unit impulse response, we need to determine the output of the system when an impulse is applied at the input, i.e., x[n] = δ[n].

Substituting x[n] = δ[n] into the given equation, we have:

y[n+2] + 2y[n+1] + y[n] = 2δ[n+2] − δ[n+1].

Since δ[n] = 0 for n ≠ 0 and δ[0] = 1, we can simplify the equation:

y[n+2] + 2y[n+1] + y[n] = 2δ[n+2] − δ[n+1] + δ[n] = 2δ[n+2] − δ[n+1] + δ[n]δ[n].

Now, comparing the equation with the standard form of the unit impulse response:

h[n] = 2δ[n+2] − δ[n+1] + δ[n],

we can conclude that h[n] is the unit impulse response of the given system.

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Answer:

333 :)

Step-by-step explanation:

Answer:

d=2_f - 9h_f

Step-by-step explanation:

es la segunda opción

To express the function [tex]\(G\)[/tex] in the form [tex]\(f \circ g\)[/tex] , where [tex]\(y = f(g(x))\)[/tex] , we need to find suitable non-identity functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x)\)[/tex].

Let's choose [tex]\(g(x) = \frac{1}{x}\)[/tex]  and [tex]\(f(x) = x + 8\)[/tex].

Now, we can express [tex]\(G\)[/tex] as  [tex]\(G(x) = f(g(x))\)[/tex] , which becomes:

[tex]\[G(x) = f(g(x)) = f\left(\frac{1}{x}\right) = \frac{1}{x} + 8\][/tex]

Therefore, the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] that can be composed to yield [tex]\(G(x) = \frac{1}{x} + 8\) are \(f(x) = x + 8\)[/tex] and [tex]\(g(x) = \frac{1}{x}\)[/tex].

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Evaluating the quadratic function we will get:

g(-2) = -3

g(0) =  -5

g(3) = 31

Here we need to evaluate the quadratic function:

g(x) = -2x² + 3x - 5

To do so, just replace the value of x by the correspondent number.

For example, if x = -2

g(-2) = 2*(-2)² + 3*(-2) - 5 = -3

if x = 0

g(0) = 2*(0)² + 3*(0) - 5 = -5

if x = 3

g(3) = 2*(3)² + 3*(3) - 5 = 31

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Answer:

It depends on the type of function, but essentially the process is the same

Step-by-step explanation:

You gather up all of the y values and x values and plot them onto a coordinate grid. If you are using a calculator, go to the "y=" button and input the function and then hit "graph"

A spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. H represents heads, and T represents tails.

The sample space of outcomes is given below: Sample Space of Outcomes: {1H, 1T, 3H, 3T, 5H, 5T}Explanation: In this given problem, the spinner has three same-sized sectors numbered 1, 3, and 5. It indicates that the probability of each sector is equal. The spinner is spun once and a coin is tossed, where H represents heads, and T represents tails. It means that the spinner will land on one of three sectors, and the coin will land on either heads or tails.Therefore, the sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.

To determine the sample space of outcomes for this situation, we need to consider the possible combinations of the spinner's numbers (1, 3, 5) and the outcomes of the coin toss (H for heads, T for tails).

The spinner has three sectors numbered 1, 3, and 5. Therefore, there are three possible outcomes for the spinner.

The coin toss can result in two outcomes: heads (H) or tails (T).

To find the sample space, we need to consider all possible combinations of the spinner outcomes and the coin toss outcomes.

The sample space of outcomes can be listed as follows:

{1H, 1T, 3H, 3T, 5H, 5T}

Therefore, the sample space of outcomes for this situation consists of the six possible combinations: 1H, 1T, 3H, 3T, 5H, and 5T.

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Given information is that, a spinner has three same-sized sectors numbered 1, 3, and 5. The spinner is spun once and a coin is tossed. h represents heads, and t represents tails. We need to find the sample space of outcomes.

The required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.

We can use the formula for the sample space,

Sample space = Set of all possible outcomes.

The possible outcomes of the spinner are 1, 3, and 5. The possible outcomes of the coin are H and T. Therefore,

Sample space of outcomes = {1H, 1T, 3H, 3T, 5H, 5T}.

Hence, the required sample space of outcomes is {1H, 1T, 3H, 3T, 5H, 5T}.

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The hair color of the players on a tennis team would be considered nominal data. Therefore, the most appropriate answer is option (c): Nominal data.

In data classification, there are four main levels of measurement: nominal, ordinal, interval, and ratio. Nominal data is the lowest level of measurement and represents categories or labels that cannot be ranked or ordered. Hair color falls into this category as it represents different categories or labels such as blonde, brunette, red, etc. Nominal data does not have any inherent numerical value or order.

On the other hand, ordinal data represents categories that can be ordered or ranked but do not have a consistent interval between them. Interval and ratio data involve numerical values with a consistent interval and a true zero point, with ratio data having a meaningful zero point.

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At time t = 0, the capacitor in the circuit is charged to its maximum charge, qmax, and the circuit has zero current.

At t = 0, the capacitor in the circuit is fully charged, which means it has accumulated its maximum charge, qmax. The capacitor acts as a temporary energy storage device in the circuit. When the capacitor is fully charged, it contains potential energy. The charge on the capacitor creates an electric field, which opposes the flow of current through the circuit.

Since the capacitor is fully charged at t = 0, it resists any change in the current. Therefore, the circuit has zero current flowing through it. As time progresses, the capacitor will start to discharge, releasing the stored energy and allowing the current to flow. The discharge process is governed by the relationship between the voltage across the capacitor, the capacitance of the capacitor, and the resistance in the circuit.

Finally, at t = 0, the capacitor in the circuit is charged to its maximum capacity, qmax, and the circuit has zero current flowing through it.

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Based on the given sample, there is sufficient evidence to conclude that the mean is greater than 3.16 at a significance level of 5%.

To perform a hypothesis test, we need to state the null hypothesis and alternative hypothesis.

We want to test if the mean is greater than 3.16.

Null hypothesis (H0): μ ≤ 3.16 (Mean is less than or equal to 3.16)

Alternative hypothesis (Ha): μ > 3.16 (Mean is greater than 3.16)

Now, we can proceed with the hypothesis test.

We'll use a one-sample t-test since we don't know the population standard deviation and our sample size is relatively small.

The sample mean (X) and sample size (n) from the given data.

X= (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.5 + 3.7 + 2.8 + 4.4 + 4 + 5.2 + 3 + 4.8) / 15 = 3.66

n = 15

Now calculate the test statistic (t-value).

t = (X - μ) / (sd / √n)

= (3.66 - 3.16) / (1.05 / √15)

≈ 2.26

Since our alternative hypothesis is one-tailed (μ > 3.16), we need to find the critical value for a significance level of 5% in the right tail of the t-distribution.

Using a t-table, the critical value for a one-tailed test with α = 0.05 and degrees of freedom (df) = n - 1 = 15 - 1 = 14 is 1.761.

If the test statistic is greater than the critical value, we reject the null hypothesis.

t-value (2.26) > critical value (1.761)

Since the test statistic is greater than the critical value, we reject the null hypothesis.

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Answer: 7pi

Step-by-step explanation: If it completes the circumference distance (14pi) of the circle in 20 seconds, in 10 seconds it will complete half of that. or 7pi. Hope this helped!

:.the distance travelled after 10sec. =7πm

Answer:

in 20 sec distance travelled =2πr=2π×7=14πm

in 10 sec distance travelled=14πm×10/20=7πm

The value of the triple integral ∭E 4xy dV is 2/5. The limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.

To evaluate the triple integral ∭E 4xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = 0, y = 1, and x = 1, we need to set up the integral using appropriate limits of integration.

The region in the xy-plane is a triangle bounded by the lines y = 0, y = 1, and x = 1. Therefore, the limits of integration for x are from 0 to 1, and for y, the limits are from 0 to 1 - x, as y is bounded by the line x + y = 1.

Now, let's determine the limits for z. The plane z = 1 + x + y intersects the xy-plane at z = 1, and as we move up in the positive z-direction, the plane extends infinitely. Thus, the limits for z can be taken from 1 to infinity.

Now, we can set up the triple integral:

∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] ∫[1 to ∞] 4xy dz dy dx

The innermost integral with respect to z evaluates to z times the integrand:

∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] [4xy(1 + x + y)] evaluated from 1 to ∞ dy dx

Simplifying further:

∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] (4xy(1 + x + y) - 4xy(1)) dy dx

∭E 4xy dV = ∫[0 to 1] ∫[0 to 1-x] 4xy(x + y) dy dx

Now, we can integrate with respect to y:

∭E 4xy dV = ∫[0 to 1] [2xy²(x + y)] evaluated from 0 to 1-x dx

Simplifying further:

∭E 4xy dV = ∫[0 to 1] 2x(1-x)²(x + (1-x)) dx

∭E 4xy dV = ∫[0 to 1] 2x(1-x)² dx

Evaluating the integral:

∭E 4xy dV = 2/5

Therefore, the value of the triple integral ∭E 4xy dV is 2/5.

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24 years and 5 months

add 13 years to ten get 23 add 6 to 11 to get 1 year and 5 months

23 plus 1 years and 5 months = 24 years an 5months

have a nice day please mark brainliest

Answer:

p < 2

Step-by-step explanation:

hope this is right and have a good day

Answer:

First find the unit rate for julie

3 hours/45 dollars

0.066 hours/1 dollar

Now based off table, find Jacksons

y = 25x

if x = 1, y would be 25

25 - .066 = 24.934 dollars

Step-by-step explanation:

Answer:

2+3=5

Step-by-step explanation:

prime numbers =2 and 3

sum =5 which is odd