Suppose that a point (X_1, X_2, X_3) is chosen at random, that is, in accordance with the uniform p.d.f., from the following set S:
S = {(x_1, x_2, x_3): 0 ≤ x_i ≤ 1 for i=1,2,3}.
Determine:
(a) P ((X_1− 1/2)² + (X_2 −1/2)² + (X_3 -1/2)² ≤1/4)
(b) P(X_1^2 + X_2^2 + X_3^2 ≤ 1).

Answer: 126 degrees

there are 360 degrees in a circle.  

Answer: 5m

Step-by-step explanation:

The Initial water level means that level amount when the time equal to 0hrs, which is 5m.

The coefficients cn are related by the equation:

cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn

To begin, we can substitute the expression for y into the differential equation and see if it satisfies the equation. Taking the first and second derivatives of y with respect to x, we find:

y' = ∑n=0[infinity]cnxn-1

y'' = ∑n=0[infinity]cn(n-1)xn-2

Substituting these expressions into the differential equation yields:

∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n

=> 0[infinity]cnxn-1 - ∑n=0[infinity]cnxn+1 = 0

We can rearrange this equation to get:

∑n=0[infinity]cn(n+2)xn+1

=>  ∑n=0[infinity]cn(n-1)xn-2 + (3x-1)∑n=0[infinity]cnxn

Now, we can compare the coefficients of xn+1 on both sides of the equation to get:

cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn

This is a recurrence relation for the coefficients cn. To see how it relates to the equation given in the question, we can substitute n+1 for n and simplify:

cn+3 = (n+2)(n+3)cn+2 + (3n+2)cn+1

Now we can substitute cn+1 from the original recurrence relation:

cn+3 = (n+2)(n+3)(n+1)cn+1 + (n+2)(n+3)cn + (3n+2)cn+1

Simplifying gives:

cn+3 = (n+2)(n+3)cn+2 + [(n+2)(n+3)(n+1) + 3n+2]cn+1

This is exactly the same recurrence relation as the one given in the question. Therefore, we can conclude that the coefficients cn are related by the equation:

cn+2 = (n+1)(n+2)cn+1 + (3n-1)cn

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The value obtained for SSbetween is 20. The correct answer is (b) 20.

To calculate the sum of squares between (SSbetween) for an analysis of variance (ANOVA), we need to determine the variation between the sample means of the different treatment conditions. The formula for SSbetween is as follows:

SSbetween = n * Σ(M - m)²

where n is the sample size for each treatment condition, M is the individual treatment condition mean, and m is the overall mean.

In this case, the sample size for each treatment condition is n = 10, and the treatment condition means are M1 = 1, M2 = 2, and M3 = 3.

To calculate SSbetween, we first find the overall mean (m) by taking the average of the treatment condition means:

m = (M1 + M2 + M3) / 3

m = (1 + 2 + 3) / 3

m = 6 / 3

m = 2

Now, we can calculate SSbetween:

SSbetween = n * Σ(M - m)²

SSbetween = 10 * [(1 - 2)² + (2 - 2)² + (3 - 2)²]

SSbetween = 10 * [(-1)² + (0)² + (1)²]

SSbetween = 10 * (1 + 0 + 1)

SSbetween = 10 * 2

SSbetween = 20

Therefore, the value obtained for SSbetween is 20. The correct answer is (b) 20.

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Incomplete question:

An independent-measures research study compares three treatment conditions using a sample of n = 10 in each treatment. For this study, the three sample means are M1 = 1, M2 = 2, and M3 = 3. For the ANOVA, what value would be obtained for SSbetween?

a.30

b.20

c.10

d. 2

Janet's Co. has sales of $90,000, cost of goods sold (COGS) equal to 80% of sales, and operating expenses of $5,000. The task requires calculating the gross and net profits, the rate of markup based on cost, and the percent net margin.

a. The gross profit can be found by subtracting the COGS from the sales. In this case, the COGS is 80% of $90,000, which amounts to $72,000. Thus, the gross profit is $90,000 - $72,000 = $18,000. To calculate the net profit, we need to subtract the operating expenses from the gross profit. Therefore, the net profit is $18,000 - $5,000 = $13,000.

b. The rate of markup based on cost represents the percentage of profit added to the cost of goods sold. It can be calculated by dividing the gross profit by the COGS and multiplying by 100. In this case, the markup rate is ($18,000 / $72,000) * 100 = 25%.

c. The net margin is the percentage of net profit relative to the sales. It can be calculated by dividing the net profit by the sales and multiplying by 100. In this case, the net margin is ($13,000 / $90,000) * 100 = 14.44%.

In summary, Janet's Co. has a gross profit of $18,000 and a net profit of $13,000. The rate of markup based on cost is 25%, indicating the percentage of profit added to the cost of goods sold. The net margin, representing the percentage of net profit relative to sales, is 14.44%.

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After 6 million years, 25 percent of the radioactive isotope will be left.

The half-life of a radioactive isotope is the time it takes for half of the initial amount of the isotope to decay. In this case, the half-life is 3 million years. After the first half-life, half of the isotope will remain, which is 50 percent. After another 3 million years (a total of 6 million years), another half-life will have passed. Therefore, half of the remaining 50 percent will decay, leaving 25 percent of the original isotope.

To understand this further, let's consider the decay process. After the first 3 million years, 50 percent of the isotope will have decayed, leaving 50 percent. Then, after the next 3 million years, another 50 percent of the remaining isotope will decay, resulting in 25 percent remaining (50 percent of the original amount). This exponential decay pattern continues as each successive half-life cuts the remaining amount in half.

Therefore, after 6 million years, 25 percent of the radioactive isotope will be left, while 75 percent will have undergone radioactive decay.

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The confidence interval at an 80% confidence level is approximately $33.88 to $44.12.

To construct a confidence interval for the mean based on the given survey data, we can use the formula:

Confidence Interval = mean ± (critical value) * (standard deviation / √sample size)

In this case, the mean is $39, the standard deviation is $20, and the sample size is 25. The critical value corresponds to the desired confidence level, which is 80%. To determine the critical value, we can use a standard normal distribution table or a statistical calculator.

For an 80% confidence level, the critical value (z-score) is approximately 1.28.

Now, let's calculate the confidence interval:

Confidence Interval = $39 ± (1.28) * ($20 / √25)

= $39 ± (1.28) * ($20 / 5)

= $39 ± (1.28) * $4

= $39 ± $5.12

This means we can be 80% confident that the true mean amount spent on a child's last birthday gift falls within this range based on the given survey data.

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Answer:

Step-by-step explanation:

First, replace f(x) with y . ...

Replace every x with a y and replace every y with an x .

Solve the equation from Step 2 for y . ...

Replace y with f−1(x) f − 1 ( x ) . ...

Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.

The term of the geometric sequence 1, 3,9, ... which has a value of 19683 is :

To find which term of the geometric sequence has a value of 19683, we can use the formula for the nth term of a geometric sequence.

Here's the formula:

an = a₁ * r^(n - 1)

where an is the nth term of the sequence

a₁ is the first term of the sequence

r is the common ratio of the sequence

Given the sequence 1, 3, 9, ..., we can see that a₁ = 1 and r = 3.

To find the value of n that gives the term with a value of 19683, we can substitute these values into the formula and solve for n:

19683 = 1 * 3^(n - 1)

19683/1 = 3^(n - 1)

3^9 = 3^(n - 1)

Now we can equate the exponents:

9 = n - 1

n = 9 + 1

n = 10

Therefore, the 10th term of the geometric sequence 1, 3, 9, ... has a value of 19683. Thus, the answer is 10.

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Answer:

D 5.46 x 10^10

Step-by-step explanation:

Recall that  speed is the rate of change of distance with time and may be expressed mathematically as

speed = Distance/time

Distance = speed * time

Hence given that the speed of light

= 3 × 10^8 meters per second

Time taken for light to travel between the given distance

= 1.82 × 10^2 seconds

substituting the given values

Distance = 3 × 10^8 * 1.82 × 10^2

= 5.46 * 10^(8+2)

= 5.46 * 10^10 meters

Answer:

oh thats cool

Step-by-step explanation:

Answer:

they doubt if they're qualified or not

(A∪B)∩C = {9, 23, 31}.

To find the intersection of the sets (A∪B) and C, we first need to determine the union of sets A and B. The union of two sets consists of all the unique elements present in both sets.

A∪B = {3, 5, 7, 9, 13, 14, 22, 23, 31}

Next, we find the intersection of the obtained union (A∪B) and set C. The intersection of two sets contains the elements that are common to both sets.

(A∪B)∩C = {9, 23, 31}

Therefore, the intersection of the sets (A∪B) and C is {9, 23, 31}. These are the elements that are present in both (A∪B) and C.

In summary, (A∪B)∩C = {9, 23, 31}.

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Answer:

Since this is a multi-part question, just look at the bolded parts under each letter. I hope this helps a bit ;)

Step-by-step explanation:

A)  

All sides of a square are congruent. "s" represents the square's perimeter:

s=4x.

"r" is the rectangle's perimeter:

r= 4x+26

since the perimeter = 2W + 2L:

2W + 2L= 4x+ 26

and W=x, so:

2x + 2L= 4x + 26

Subtract from both sides:

2L= 2x +26

Divide both sides:

the length of the rectangle "L"= x +13.

B) Plug 5 into the equations:

L= 5+ 13 or 18.

2(18) + 2(5)= r

36+ 10 = r or 46

s= s+ 26

s= 46-26 or 20.

20/4= 5...

It seems (at least to me, feel free to give constructive criticism) that the only logical conclusion is that 5 could be the value of x.

C) You would likely need to use substitution to solve, but unless I am much mistaken, this looks like an infinite-solutions equation.

L=w+13

To evaluate the expression x² + y² - 1 in polar coordinates, we need to convert the Cartesian coordinates (x, y) to polar coordinates (r, θ).

In polar coordinates, x = rcos(θ) and y = rsin(θ). Substituting these values into the expression, we obtain r²cos²(θ) + r²sin²(θ) - 1. This expression can be simplified using trigonometric identities to obtain r²(cos²(θ) + sin²(θ)) - 1, which simplifies further to r² - 1.

When converting Cartesian coordinates (x, y) to polar coordinates (r, θ), we use the equations x = rcos(θ) and y = rsin(θ). Substituting these values into the expression x² + y² - 1, we have (rcos(θ))² + (rsin(θ))² - 1. Applying the trigonometric identity cos²(θ) + sin²(θ) = 1, we can simplify the expression to r²cos²(θ) + r²sin²(θ) - 1.

Since cos²(θ) + sin²(θ) = 1, the expression simplifies further to r²(1) - 1, which becomes r² - 1. Therefore, in polar coordinates, the expression x² + y² - 1 is equivalent to r² - 1. This means that when evaluating the expression in terms of polar coordinates, we only need to consider the square of the radial distance, r², and subtract 1.

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The series ∑ 3 / (n[ln(n)]^p is convergent for all values of p greater than 1.

To determine the values of p for which the series is convergent, we can use the integral test. According to the integral test, if the integral of the series converges, then the series itself converges.
Considering the series ∑ 3 / (n[ln(n)]^p, we can evaluate its convergence by integrating the series function. Integrating 3 / (n[ln(n)]^p with respect to n gives us ∫ (3 / (n[ln(n)]^p)) dn.By performing the integration, we obtain ∫ (3 / (n[ln(n)]^p)) dn = 3 ∫ (1 / (n[ln(n)]^p)) dn.
Simplifying further, we have 3 ∫ (1 / (n^1 * [ln(n)]^p)) dn = 3 ∫ (1 / (n^1 * n^p * [ln(n)]^p)) dn.
Now, we can observe that the integral is dependent on the value of p. For the integral to converge, the exponent of n^p must be greater than 1.
Therefore, we conclude that the series is convergent for all values of p greater than 1.

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Answer:Just add them all

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

First you have to find the percentage of pan crust to all the other crusts to do this you add all the crusts together:

397+220+167+196 = 980

Then divide 196 by 980:

196/980 = .2 or 20%

Then multiply 400 by 20%

400*20% = 80

Answer:

[tex]\angle T = 70[/tex]

Step-by-step explanation:

Given

[tex]\angle T= 2x[/tex]

[tex]\angle S= 75[/tex]

[tex]\angle R= x[/tex]

See attachment for triangle

Required

Calculate [tex]\angle T[/tex]

First, we add up the angles in the triangle;

[tex]\angle R + \angle S + \angle T = 180[/tex]

[tex]x + 75 + 2x = 180[/tex]

Collect like terms

[tex]x + 2x = 180 - 75[/tex]

[tex]3x = 105[/tex]

Solve for x

[tex]x = \frac{105}{3}[/tex]

[tex]x = 35[/tex]

Given that:

[tex]\angle T= 2x[/tex]

[tex]\angle T = 2 * 35[/tex]

[tex]\angle T = 70[/tex]

The vector equation of the plane P1 in R3 which passes through the given points is:  `(-36, -12, -9).(X - (2, 1, -4)) = 0`.

We have three points `A (2, 1, -4), B (3, 4, -4)` and `C (3, -9, 8)` that lie on plane P1. To find the vector equation of the plane P1 in R3, we need to find the normal vector of the plane P1. The normal vector is perpendicular to the plane P1. We can find the normal vector by taking the cross product of any two nonparallel vectors that lie on the plane P1.

Let's choose two vectors `AB` and `AC`.

`AB = B - A = (3, 4, -4) - (2, 1, -4) = (1, 3, 0)`

`AC = C - A = (3, -9, 8) - (2, 1, -4) = (1, -10, 12)`

Now, we take the cross product of `AB` and `AC` to get the normal vector `n`.

`n = AB × AC = (-36, -12, -9)`

The equation of the plane P1 with normal vector `n` and passing through the point A can be written as:

`(n . (X - A)) = 0` where `.` is the dot product.

Substituting the values, we get:

`(-36, -12, -9) . (X - (2, 1, -4)) = 0`

`(-36, -12, -9) . (X - 2, X - 1, X + 4) = 0`

`-36(X - 2) - 12(X - 1) - 9(X + 4) = 0`

`-36X + 72 - 12X + 12 - 9X - 36 = 0`

`-57X + 48 = 0`

`57X = 48`

`X = 48/57 = 16/19`

Therefore, the vector equation of the plane P1 in R3 which passes through the points A = (2, 1, –4), B= = (3, 4, –4), and C = (3, -9,8) is:

`(-36, -12, -9) . (X - 2, X - 1, X + 4) = 0`

`-36(X - 2) - 12(X - 1) - 9(X + 4) = 0`

`-36X + 72 - 12X + 12 - 9X - 36 = 0`

`-57X + 48 = 0`

`57X = 48`

`X = 16/19`

The answer is, `(-36, -12, -9).(X - (2, 1, -4)) = 0`.

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Answer. it is 5 or letter i

Answer:

The value of x is 5

Step-by-step explanation:

Using the linear pair theorem, both angles are supplementary and add up to 180 degrees. 180 minus 140 is 40. and 8 times 5 = 40. So x = 5.

The implicit solution to the initial value problem (2x − 6xy + xy)dx + (1 − 3x^2 + (2 + x^2)y)dy = 0 with y(1) = −4 is given by the equation:3xy − (x + 1)y^2 + 9x^2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2)The numerical value of lim y(x) rounded off to five significant figures is -1.3152.

Intermediate results obtained during the process include: implicit solution of initial value problem and explicit solution for y as a function of x. The implicit solution of the initial value problem is described by the equation:3 xy - (x + 1) y2 + 9 x2 = 0. The explicit solution for y as a function of x is given by the formula: y = (-1 + 3x^2 - 7/19 + 8x^2 + x)/(2 + x^2).

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The 95% confidence interval for p is  (0.47, 0.83)

Total subjects = 40

People preferring fresh brewed = 26

Calculating the sample proportion -

Sample proportion = Number of subjects preferring fresh brewed coffee / Total number of subjects

= 26 / 40

= 0.65

It is required to establish crucial values depending on chosen confidence level in order to generate the confidence interval. The z-value associated with a 97.5% cumulative probability to obtain a 95% confidence range is to be found. This is because the remaining 5% by 2 is divided to determine middle 95% of the standard normal distribution. The z-value for a 97.5% cumulative probability is around 1.96 using Table D or any other approach.

Using the formula for confidence interval -

[tex]CI = p + z x \sqrt ((px (1 - p) / n)[/tex]

Substituting the values -

[tex]CI = 0.65 ± 1.96 \sqrt{x} ((0.65 * (1 - 0.65)) / 40)[/tex]

[tex]= 0.65 ± 1.96 x \sqrt(0.2275 / 40)[/tex]

= 0.65 ± 1.96 x 0.0921

= 0.65 ± 0.1802

Rounding to two decimal places, the 95% confidence interval will be 0.47, 0.83)

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Answer:

11

Step-by-step explanation:

it says motor cycles combined with garbage so add both of them then subtract that from the bull dosers

motor =18

garbage=4

18+4=22

bulldosers=11

22-11= 11 more

Answer:

11

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

Answer:

b. data from our experiment

Step-by-step explanation:

Answer:

median is 90

Step-by-step explanation:

75, 88, 92, 100

(88+92)/2 = 90

Answer:

are you trying to look for the height or radius?

if you're looking for the height then you'll have to divide the volume by pi and the radius squared

if you're looking for the radius then you'll have to divide the volume by pu and the height and do the squareroot over the whole equation