36 draws are made at random with replacement from a box that has 7 tickets: -3, -2, -1, 0, 1, 2, 3 is the smallest possible the sum of the 36 draws can be?

The value of ∭E (x² + y²) dv over the region E between the given spheres.

To evaluate the integral ∭E (x² + y²) dv using spherical coordinates, we first need to express the volume element dv in terms of spherical coordinates.

In spherical coordinates, the volume element is given by dv = r² sin(φ) dr dφ dθ, where r represents the radial distance, φ represents the polar angle, and θ represents the azimuthal angle.

Since we are integrating over the region E between the spheres x² + y² + z² = 9 and x² + y² + z² = 16, the limits of integration for r, φ, and θ will be as follows:

r: from the lower sphere to the upper sphere, which corresponds to r = 3 to r = 4

φ: from 0 to π (since we are considering the entire range of polar angle)

θ: from 0 to 2π (since we are considering the entire range of azimuthal angle)

Now, let's substitute these values and evaluate the integral:

∭E (x² + y²) dv = ∭E (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ

Integrating over θ from 0 to 2π, and integrating over φ from 0 to π, we have:

∭E (x² + y²) dv = ∫[0,2π] ∫[0,π] ∫[3,4] (r² sin(φ) cos²(θ) + r² sin(φ) sin²(θ)) dr dφ dθ

Now, we can evaluate the integral by performing the integration step by step, starting from the innermost integral.

After evaluating the integral, the final result will give us the value of ∭E (x² + y²) dv over the region E between the given spheres.

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Answer:

=8x+4

Step-by-step explanation:

=2(4x+2)

a=2,b=4x,c=2

=2 x 4x + 2 x 2

Simplify- 2 x 4x + 2 x 2: 8x + 4

The 90% confidence lower bound for u is:  u>4.066

To find the confidence intervals for the true shear strength u, we will use the sample mean, sample standard deviation, and the given sample size.

a. Two-Sided 90% Confidence Interval for u:

The formula for the confidence interval is given by:

x' = z × s/√n  < u <  x' +z × s/√n

Where:

x' is the sample mean (given as 4.25)

s is the sample standard deviation (given as 1.30)

n is the sample size (given as 78)

z is the z-score corresponding to the desired confidence level (90% confidence level has z-score of 1.645)

Plugging in the values and simplifying:

4.25 - 0.184 < u < 4.25 + 0.184

Therefore, the 2-sided 90% confidence interval for u is:

4.066 < u < 4.434

b. 90% Confidence Lower Bound for u:

The formula for the confidence interval lower bound is given by:

x' - z × s/√n < u

Plugging and simplifying the values we get:

Simplifying the expression:

4.25 - 0.184 < u

Therefore, the 90% confidence lower bound for u is:

u > 4.066

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Answer:

Step-by-step explanation:

The correct answer is Always

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the correct answer was never. I appreciate your answer though.

.............................................................................................................................................................

P(A and B) means add A and B

if both A and B are both greater then 1/2

then when they are added they will always be greater than 1

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the correct answer was never. I appreciate your answer though.

Answer:The correct answer is Always

In Part A: Standard error = 3.5 / √100 = 3.5 / 10 = 0.35 years and in Part B: the mean of the sample means is 13.2 years.

Part A: The standard error of the sample means can be calculated using the formula: standard deviation / square root of the sample size. In this case, the standard deviation is 3.5 years and the sample size is 100. So, the standard error is given by:

Standard error = 3.5 / √100 = 3.5 / 10 = 0.35 years

Part B: The mean of the sample means is equal to the population mean, which is 13.2 years. When we take multiple samples from a population, the mean of those sample means is expected to be equal to the population mean. In this case, the mean of the sample means is 13.2 years. The standard error of the sample means is 0.35 years, indicating the average deviation of the sample means from the population mean. The mean of the sample means is 13.2 years.

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Hey there!

ASSUMING

2(3r + 4) - 3 (r + 1) = 11

IF SO

2(3r + 4) - 3 (r + 1) = 11

2(3r + 4) - 3 (1r + 1) = 11

DISTRIBUTE

2(3r) + 2(4) - 3(1r) - 1(1) = 11

6r + 8 - 3r - 1 = 11

COMBINE the LIKE TERMS

(6r - 3r) + (8 - 3) = 11

6r - 3r + 8 - 3 = 11

3r + 5 = 11

SUBTRACT 5 to BOTH SIDES

3r + 5 - 5 = 11 - 5

SIMPLIFY!

3r = 11 - 5

3r = 6

DIVIDE 3 to BOTH SIDES
3r/3 = 6/3

SIMPLIFY!

r = 6/3

r = 2

Therefore, the answer should be: r = 2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The function h(z) = 1 4iz + 2 defined on the extended complex plane,

(a) The function h(z) = 1/(4iz + 2) can be expressed as a composition of the linear function g(z) and reciprocal function f(z).

(b) The image of the line y = 2 under w = h(z) is the point z = -3/(8i).

(c) The image of the circle |z - i| = 1/2 under w = h(z) is the two points z = i + √7/2 and z = i - √7/2.

(a) To express the function h(z) = 1/(4iz + 2) as a composition of a linear function g(z) and reciprocal function f(z), we can rewrite h(z) as follows:

h(z) = 1/(4iz + 2)

= 1/(4i(g(z)) + 2)

= 1/f(g(z))

Here, g(z) represents the linear function and f(z) represents the reciprocal function. To determine g(z), we set g(z) = 4iz + 2.

Therefore, the composition of the linear function g(z) and the reciprocal function f(z) is:

h(z) = 1/f(g(z)) = 1/(4iz + 2)

(b) To find the image of the line y = 2 under w = h(z), we substitute y = 2 into the function h(z) and solve for z.

y = 2

1/(4iz + 2) = 2

To simplify the equation, we multiply both sides by (4iz + 2):

1 = 2(4iz + 2)

1 = 8iz + 4

8iz = -3

z = -3/(8i)

Therefore, the image of the line y = 2 under w = h(z) is the point z = -3/(8i).

(c) To determine the image of the circle |z - i| = 1/2 under w = h(z), we substitute z - i = 1/2 into the function h(z) and solve for w.

|z - i| = 1/2

|z - i|² = (1/2)²

(z - i)(z - i*) = 1/4

z² - iz - iz + i² = 1/4

z² - 2iz + 1 = 1/4

z² - 2iz + 3/4 = 0

Now we solve this quadratic equation using the quadratic formula:

z = (-(-2i) ± √((-2i)² - 4(1)(3/4))) / (2(1))

z = (2i ± √(-4i² - 3)) / 2

z = (2i ± √(4 + 3)) / 2

z = (2i ± √7) / 2

z = i ± √7/2

So, the image of the circle |z - i| = 1/2 under w = h(z) is the two points z = i + √7/2 and z = i - √7/2.

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Answer:

150*3= 450 miles

Hope this helped :)

Answer:

Distance= 15.3

Step-by-step explanation:

Answer:

I don't know

Step-by-step explanation:

I don't know

The confidence interval for the population mean would be 1.8 < u  < 3.4.

The practical use of the confidence interval is this: A The confidence interval can be used to estimate that, with 99% confidence, the interval from to actuality contains the true mean DNA base of all people.

The confidence interval expresses the probability that a given population parameter will be centered between a set of values. So, the practical use of the confidence interval is to indicate that if the experiment is repeated 100 times, 99 of those times will give a result that shows that the true mean of all people falls within the obtained values.

The confidence interval is obtained thus: μ ± Ζ s/√n

where μ = sample mean

Z = confidence level

s = standard deviation

n = sample size

From the question DNA samples or n = 10

Critical value = 2.262

Sample mean = 2.6

Standard deviation = 1.0749

The margin of error = 2.262 * 1.0749/√10

= 0.769

We can construct the 95% confidence level interval as follows:

x bar - E < u < x bar + E

= 2.6 - 0.7690 < u < 2.6 + 0.7690

= 1.8 < u  < 3.4.

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(i) The polar coordinates (r, θ) of the point (4, 3) are (5, arctan(3/4)). (ii) For a point with negative radius, the concept of polar coordinates is not applicable as polar coordinates are defined for points in the positive radial direction.

(i) To find the polar coordinates (r, θ) of the point (4, 3), we can use the formulas:

r = √(x² + y²) and θ = arctan(y/x).

Given that x = 4 and y = 3, we can calculate the values:

r = √(4² + 3²) = 5

θ = arctan(3/4)

Therefore, the polar coordinates of the point (4, 3) are (5, arctan(3/4)).

(ii) For a point with negative radius, the concept of polar coordinates is not applicable. In polar coordinates, the radius (r) is always defined as a positive value. Negative values of r would imply a direction opposite to the positive radial direction. However, the convention of polar coordinates focuses on the positive radial direction, so negative radius values are not considered.

In conclusion, polar coordinates are not defined for points with negative radius values, and therefore, the concept of polar coordinates does not apply to find the polar coordinates of a point with r < 0.

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Answer:

fixed - monthly rent, car payment, savings for new guitar

variable - movies, video games, snacks

Step-by-step explanation:

Fixed costs are costs that do not vary with output.

the amount of rent paid is fixed.  

Variable costs are costs that vary with production

the amount paid at the movies depend on the number of movies watched

Answer:

B) They estimate that 2.3% of those surveyed answered incorrectly

Step-by-step explanation:

hope it helps you dude

Answer: 13

Step-by-step explanation: the square root is 12.68925

so i rounded up to 13

Answer:

12.6885775404 or 13 if you need to round up

Step-by-step explanation:

The equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:

(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.

To find the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5), we can use the general equation for a sphere in three-dimensional space. The equation of a sphere with center (h, k, l) and radius r is given by:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2.

Using the given center (5, 8, 5), we have:

(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = r^2.

Since the sphere passes through the point (7, 3, -1), we can substitute these values into the equation:

(7 - 5)^2 + (3 - 8)^2 + (-1 - 5)^2 = r^2.

Simplifying the equation gives us:

4 + 25 + 36 = r^2.

65 = r^2.

Therefore, the equation of the sphere passing through the point (7, 3, -1) with center (5, 8, 5) is:

(x - 5)^2 + (y - 8)^2 + (z - 5)^2 = 65.

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Answer:

same

Step-by-step explanation:

The interior of S consists of all the points in S that are not in the boundary of S. These points are:

The rational numbers strictly between 13 and 16

The rational numbers strictly between 1 and 5

The rational numbers strictly between 5 and 7

The natural numbers strictly between 1 and 18, excluding 20

The set S consists of the rational numbers between 13 and 16 (inclusive), the open interval between 1 and 5, the open interval between 5 and 7, the singleton set {20}, and the set of natural numbers between 0 and 18.

To find the interior of S, we need to find all the points in S that have a neighborhood entirely contained in S. In other words, we need to find all the points in S that are not on the boundary of S.

The boundary of S includes the endpoints of the closed interval [13, 16] and the endpoints of the open intervals (1, 5) and (5, 7), as well as the points 20, 0, and 18.

Therefore, the interior of S consists of all the points in S that are not in the boundary of S. These points are:

The rational numbers strictly between 13 and 16

The rational numbers strictly between 1 and 5

The rational numbers strictly between 5 and 7

The natural numbers strictly between 1 and 18, excluding 20

Note that the point 20 is not in the interior of S because it is on the boundary of S. Similarly, the points 0 and 18 are not in the interior of S because they are in the boundary of S.

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Answer

3.7 or approximately 4 gallons

Step-by-step explanation:

7x2=14 total liters.

3.78 liters=1 gallon

14/3.78= 3.7 gallons

There are 10 ways to pick 4 jelly beans from a jar containing 5 red and 3 purple jelly beans, ensuring at least 2 are red.

To calculate the number of ways, we consider the cases where we choose exactly 2 red jelly beans, 3 red jelly beans, or all 4 red jelly beans.

Case 1: Choosing 2 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 2. This can be done in [tex]5C2 = 10[/tex] ways.

Case 2: Choosing 3 red jelly beans - There are 5 red jelly beans to choose from, and we need to select 3. This can be done in [tex]5C3 = 10[/tex] ways.

Case 3: Choosing all 4 red jelly beans - There are 5 red jelly beans, and we need to select 4. This can be done in [tex]5C4 = 5[/tex] ways.

Adding up the possibilities from all three cases, we get 10 + 10 + 5 = 25 ways. However, we need to subtract the case where we select all 4 purple jelly beans, which is only 1 way. Therefore, the final number of ways is 25 - 1 = 24 ways.

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a) Variables strongly/weakly positively/negatively correlated in the "airquality" data set can be identified through correlation analysis.

b) The t-test can be used to check if the temperature variable in the "airquality" data set is significantly different from 79.

c) The t-test can be used to check if the temperature variable is significantly different between samples A and B (observations 1 to 77 and 78 to 153, respectively) in the "airquality" data set.

a) To identify variables that are strongly/weakly positively/negatively correlated in the "airquality" data set, correlation analysis can be performed.

Correlation analysis measures the strength and direction of the linear relationship between variables.

By calculating correlation coefficients (such as Pearson's correlation coefficient), it is possible to determine if variables have a strong positive correlation (close to +1), weak positive correlation (between 0 and +1), strong negative correlation (close to -1), or weak negative correlation (between 0 and -1).

This analysis helps identify the nature of the relationships between variables in the dataset.

b) To check if the temperature variable in the "airquality" data set is significantly different from 79, a t-test can be conducted.

The t-test assesses whether the mean of a sample is significantly different from a hypothesized value (in this case, 79).

By comparing the t-statistic calculated from the sample data to the critical t-value at a given significance level, such as 0.05, it can be determined if the temperature is significantly different from 79.

If the calculated t-value falls outside the critical t-value range, the temperature variable is considered to be significantly different.

c) To check if the temperature variable is significantly different between samples A (observations 1 to 77) and B (observations 78 to 153) in the "airquality" data set, a t-test can also be used.

This comparison aims to determine if the means of temperature in samples A and B are significantly different.

By calculating the t-statistic and comparing it to the critical t-value at a chosen significance level, such as 0.05, it can be determined if the temperature variable differs significantly between the two samples.

If the calculated t-value falls outside the critical t-value range, it indicates a significant difference in temperature between samples A and B.

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Answer:

6/12,  2/4,

Step-by-step explanation:

6/12 because half of 12 is 6.

2/4 because half of 4 is 2.

Both can equal 1/2.

Given the function `y = (x-6) / (x^2 + 5x + 6)`, let's identify the vertical asymptotes and holes: Factoring the denominator, we get`(x^2 + 5x + 6) = (x+2)(x+3)`So, `y = (x-6) / (x+2)(x+3)`

The vertical asymptotes of the function are the roots of the denominator. Thus, the vertical asymptotes of the function are `x = -2` and `x = -3`.Now, we'll look for the holes in the function. A hole is a point where the function is undefined but can be simplified by canceling common factors.

In the given function, we notice that the numerator `(x-6)` and the denominator `(x+2)(x+3)` have a common factor of `(x-6)`. Thus, there is a hole at `x = 6`.We can cancel `(x-6)` from both numerator and denominator to obtain the simplified function `y = 1 / (x+3)`.Therefore, the vertical asymptotes are `x = -2` and `x = -3`, and there is a hole at `x = 6`.

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Answer:

Ice rental at the local skating rink is $150 for 2h. Skate rental is $3 per person. The Grade 8 class went skating. All students rented skates. The total cost was $231. How many students went skating?

Answer:

0.42846931021

Step-by-step explanation:

2(19-7) im pretty sure

a) the corresponding standardized value (z) for x = 4.1 is approximately 1.39.

b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.

a) To calculate the standardized value (z) for the point x = 4.1, we can use the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, x = 4.1, μ = 0.33, and σ = 2.69. Plugging these values into the formula:

z = (4.1 - 0.33) / 2.69

z ≈ 1.39

So, the corresponding standardized value (z) for x = 4.1 is approximately 1.39.

b) The area under the standard normal probability density function from negative infinity to z is interpreted as the probability that the random variable is less than or equal to z.

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Answer:

(x - 2)(3x^2 + 5)

Step-by-step explanation:

All four terms here have 3 as a factor.  Factor out 3:

3x^(3)-6x^(2)+15x-30 =>  3(x^3 - 2x^2 + 5x - 10)

The last two terms can be rewritten as 5(x - 2).  The first two terms can be rewritten as 3x^2(x - 2).  So (x - 2) is a factor of 3(x^3 - 2x^2 + 5x - 10).  We get:        

3x^2(x - 2) + 5(x - 2) = (x - 2)(3x^2 + 5)