Work Problems (30+30) 01) Let E = {(x,y,z): z= - x2 +9, z = 2, y=-6, and y=0} be the enclosed region. a) (10 pts) Draw E b) (20 pts) Evaluate the following integral SSS( 12xy-2) dv=? E Q2) S v2=* -6 a) (10 pts) Convert the following integral into the spherical coordinates 36-y? √36x² - y² (x?z+y?z+z2+2 z) dzdxdy=? 36-y-V36-72-72 b)(20 pts) Evaluate the following integral 38-y 36-x-y? ( x2 + y2 +7-2) dzdxdy=? 36 -x?y? S S 1 () = SV26 -6 36

Answer:

x = 5.88

Step-by-step explanation:

1.5x / 7 = 6.3 / 5

Cross multiply

7.5x = 44.1

Divide both sides by 7.5

x = 5.88

I hope this helped and please mark me as brainliest!

Answer: 5.88

Step-by-step explanation: Answer confirmed on test as correct

Answer:

11. 40.5

12. 84

Step-by-step explanation:

The slope of the line is a measure of the rate of change between two points and is calculated by dividing the change in y-values by the change in x-values. In this case, the slope is -6, which means that for every 1 unit increase in x, there is a 6 unit decrease in y.

The slope of the line is a measure of the rate of change between two points. It is calculated by dividing the change in y-values by the change in x-values. To find the slope of the line represented by the table of values, we need to first identify two points on the line. We will use the points (x1, y1) and

(x2, y2).

We can choose any two points, but for this example, we will use

(x1, y1) = (-7, 9) and (x2, y2) = (8, -15).

The slope of the line is then calculated by finding the difference between the y-values

(y2 - y1 = -15 - 9 = -24)

and the difference between the x-values

(x2 - x1 = 8 - (-7) = 15)

and dividing these two values:

-24/15 = -6.

This means that for every 1 unit increase in x, there is a 6 unit decrease in y.

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A 21-ft ladder leans against a building so that the angle between the ground and the ladder is 63 How high does the ladder reach on the building?

We have given: A 21-ft ladder leans against a building so that the angle between the ground and the ladder is 63.We need to find: How high does the ladder reach on the building?

We can see from the above diagram that:ladder = 21ftThe angle between the ground and the ladder is 63We have to find the height that the ladder reaches on the building.

Hence, from the figure we see that:tan(θ) = opp/adj

Where θ = 63, opp = height and adj = base of the ladder We need to find the height which can be given as:height = opp= ladder × tan(θ) = 21 × tan(63) = 45.51 ft

Thus, the height that the ladder reaches on the building is 45.51ft (approximately).Hence, the required answer is 45.51 ft.

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a. the equation for the hyperbola is x^2 / 4 - y^2 / 12 = 1. b. the equation for the hyperbola is [(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.

A) To find the equation for the hyperbola with vertices (±2, 0) and foci (±4, 0), we can use the standard form equation for a hyperbola:

[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,

where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and c is the distance from the center to the foci.

In this case, the center is at (0, 0) since the vertices are symmetric with respect to the y-axis. The distance from the center to the vertices is a = 2, and the distance from the center to the foci is c = 4.

Using the formula c^2 = a^2 + b^2, we can solve for b^2:

b^2 = c^2 - a^2 = 4^2 - 2^2 = 16 - 4 = 12.

Now we have all the necessary values to write the equation:

[(x - 0)^2 / 2^2] - [(y - 0)^2 / √12^2] = 1.

Simplifying further, we get:

x^2 / 4 - y^2 / 12 = 1.

Therefore, the equation for the hyperbola is:

x^2 / 4 - y^2 / 12 = 1.

B) To find the equation for the hyperbola with foci (4, 0) and (4, 6) and asymptotes y = 1 + (1/2)x and y = 5 - (1/2)x, we can use the standard form equation for a hyperbola:

[(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1,

where (h, k) represents the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the foci.

From the given information, we can determine that the center of the hyperbola is (4, 3), which is the midpoint between the two foci.

The distance between the center and each focus is c, and in this case, it is c = 4 since both foci have the same x-coordinate.

The distance from the center to the vertices is a, which can be calculated using the distance formula:

a = (1/2) * sqrt((4-4)^2 + (6-0)^2) = (1/2) * sqrt(0 + 36) = 3.

Now we have all the necessary values to write the equation:

[(x - 4)^2 / 3^2] - [(y - 3)^2 / b^2] = 1.

To find b^2, we can use the relationship between a, b, and c:

c^2 = a^2 + b^2.

Since c = 4 and a = 3, we can solve for b^2:

4^2 = 3^2 + b^2,

16 = 9 + b^2,

b^2 = 16 - 9 = 7.

Plugging in the values, the equation for the hyperbola is:

[(x - 4)^2 / 9] - [(y - 3)^2 / 7] = 1.

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Answer:96

Step-by-step explanation:

Answer: slope =1/2  y intercept (0,6)

Step-by-step explanation: use the slope and y intercept form y=mx + b

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

Im pretty sure just one

x= -20

Step-by-step explanation:

Answer: Dante slices 8.5 potatoes per minute.

Explanation: To find the unit rate look at the steps below.

102:12

12/12 gives us 1 minute and 102/12 gives us 8.5 We divide both numbers by 12 because if we divide 12 by 12 we get one minute and when we divide the other side it tells us how many potatoes Dante slices in one minute.

Answer:

47 days

Step-by-step explanation:

Since the patch of pads doubles in size every day, the lake would be half covered just one day before it was covered entirely.

Answer:

So, the correct answer is (30.104, 32.896).

Step-by-step explanation:

To find the 95% confidence interval for the mean number of pounds of trash per person per week, we can use the following formula:

CI = X + Zα/2 * (σ/√n)

σ = population standard deviation = 7.8 pounds

n = sample size = 120

Plugging in the values, we get:

CI = 31.5 ± 1.96 \times(7.8/√120)

CI = 31.5 ± 1.96 \times 0.711

CI = 31.5 ± 1.39

Therefore, the 95% confidence interval for the mean number of pounds of trash per person per week is (30.11, 32.89).

So, the correct answer is (30.104, 32.896).

This problem is about the rule of three.

The given ratio is 20 minutes for 3 tasks done. We need to find the number of taks done after 8 hours.

First, we know that 1 hour is 60 minutes, so the total number of minutes is

Now, the rule of three is about the total number of tasks done after 480 minutes, if three tasks take 20 minutes only.

Answer:

where is the question ⁉️

Answer:

36 in

Step-by-step explanation:

7+7+11+11= 36

Answer:

36 inches

Step-by-step explanation:

2 7inch sides plus 2 11 inch sides

2x7= 14

2x11= 22

14+22= 36 inches

Answer:

I believe the answer is A and I'm sorry if I'm wrong

graph best represents the solution set of -4x <- 6y - 54 graph C. Option C is the correct option.

graph best represents the solution set of -4x < -6y - 54.

Inequality can be defined as the relation of an equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Since the Question seems to be incomplete, The Correct inequality in the question could be  -4x < -6y - 54.
Here, graph C represents the inequality. Because y-intercept is y = -9
and the x-intercept for the inequality is x = 13.5. And it's below shaded and no boundary element can be included because of < sign.

Thus, the graph best represents the solution set of -4x < -6y - 54 graph C. Option C is the correct option.

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The question given is incomplete, Answer is correct for the solution is based on the assumed data mentioned in the question.

The proportion of defective circulators can be calculated by weighting the defect rates of each company by their respective proportions in the contractor's inventory. Thus, the proportion of defective circulators can be expected to be 0.0065 (0.60*0.005 + 0.40*0.010).Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

To calculate the probability that a defective circulator came from the first company, we can use Bayes' theorem.

Let A denote the event that a circulator is defective, and let B denote the event that the circulator came from the first company.

We want to find P(B|A), the probability that the circulator came from the first company given that it is defective.

This can be calculated using the formula P(B|A) = P(A|B)*P(B)/P(A), where P(A|B) is the probability of a defective circulator given that it came from the first company (0.005),

P(B) is the probability that a circulator came from the first company (0.60), and P(A) is the overall probability of a defective circulator (0.0065).

Plugging in these values, we get P(B|A) = (0.005*0.60)/0.0065 = 0.046, or approximately 4.6%.

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Answer:

There are no values of  p  that make the equation true.

(No solution)

Step-by-step explanation:

Answer:

\(\mathrm{No\:Solution}\)

Step-by-step explanation:

\(p-4=-9+p\)

Step 1: Subtract \(p\) from both sides

\(p-4-p=-9+p-p\\\\-4=-9\)

Since negative four is not equal, and does not equal negative 9, the answer is \(\mathrm{No\:Solution}\), NOT that there is NO SOLUTION.

The Taylor series for ln(x) centered at 9 is:

ln(x) = ln(9) + (1/9)(x-9) - (1/281)(x-9)^2 + (2/3729)(x-9)^3 + ...

To find the Taylor series for ln(x) centered at a=9, we first need to find the derivatives of ln(x).

The first derivative of ln(x) is 1/x, the second derivative is -1/x^2, the third derivative is 2/x^3, and so on.

Next, we need to evaluate these derivatives at a=9 to find the coefficients of the Taylor series.

The first coefficient is f(9), which is ln(9).

The second coefficient is f'(9), which is 1/9.

The third coefficient is f''(9), which is -1/81.

The fourth coefficient is f'''(9), which is 2/729.

We can then use the formula for the Taylor series to write the series for ln(x) centered at a=9.

The series will converge to ln(x) for values of x that are close to 9.

f(x) = ln(x), a = 9

f(9) = ln(9)

f'(x) = 1/x

f'(9) = 1/9

f''(x) = -1/x^2

f''(9) = -1/81

f'''(x) = 2/x^3

f'''(9) = 2/729

The Taylor series for ln(x) centered at 9 is:

ln(x) = ln(9) + (1/9)(x-9) - (1/281)(x-9)^2 + (2/3729)(x-9)^3 + ...

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We need to determine the number of integers between 1 and 9,999 (inclusive) whose digits sum up to 12. For example, the integer 66 satisfies this condition because 6 + 6 = 12, while 812 does not because the sum of its digits is not 12. We will calculate the count of such integers.

To find the number of integers in the interval [1, 9,999] whose digits sum up to 12, we can consider different cases for the number of digits in the integer.

Case 1: 4-digit integers

In this case, we need to find four-digit integers whose digits sum up to 12. Since the integer must be between 1 and 9,999, the first digit cannot be zero. We can use techniques such as combinatorics to determine the number of combinations of digits that satisfy the condition.

Case 2: 3-digit integers

Similarly, we need to find three-digit integers whose digits sum up to 12. The first digit cannot be zero, and we can apply combinatorics to count the number of valid combinations.

Case 3: 2-digit integers

For two-digit integers, the sum of the digits must be 12. Again, we exclude numbers starting with zero and calculate the count using combinatorics.

Case 4: 1-digit integers

In this case, the only possibility is the integer 12 itself. By summing up the counts from each case, we can determine the total number of integers in the interval [1, 9,999] whose digits sum up to 12.

We need to consider different cases for the number of digits in the integer and apply combinatorics to count the number of integers satisfying the condition. The final count will give us the number of integers between 1 and 9,999 (inclusive) with digits summing up to 12.

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Answer:

16777216

Step-by-step explanation:

64 times 64 equals 4096. 4096 to the power of 2 is 16777216.

The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Answer:

70mm

Step-by-step explanation:

(14*10)/2=70

Height and Width multiplied against each other divided by two is the area of a triangle

Answer: when one of the variables is dichotomous; when you need to measure the relationship between a continuous variable and a dichotomous variable.

Step-by-step explanation:

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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