(1 point) Let F(x,y,z)=3z2xi+(y3+tan(z))j+(3x2z+4y2)kF(x,y,z)=3z2xi+(y3+tan⁡(z))j+(3x2z+4y2)k. Use the Divergence Theorem to evaluate ∫SF⋅ dS∫SF⋅ dS where SS is the top half of the sphere x2+y2+z2=1x2+y2+z2=1 oriented upwards.

Answer:

The area of a circle can be calculated using the formula:

Area = π x radius^2

where π (pi) is a mathematical constant approximately equal to 3.14159.

Since each rug has a radius of 4 feet, the area of one rug is:

Area = π x 4^2

Area = 16π square feet

To find the total area covered by the three rugs, we need to multiply the area of one rug by three:

Total area = 16π square feet x 3

Total area = 48π square feet

Using a calculator, we can approximate the value of π to two decimal places as 3.14, so the total area covered by the three rugs is:

Total area ≈ 48 x 3.14 square feet

Total area ≈ 150.72 square feet

Therefore, Joanna's bedroom floor will be covered by approximately 150.72 square feet of rugs.

(a) 99% certain that a burglar is detected by at least one alarm, the bank should use at least 21 alarms.

To determine the number of alarms needed to be 99% certain that a burglar is detected by at least one alarm, we can use the concept of complementary probability.

Let's assume each alarm operates independently, and the probability of a single alarm not detecting a burglar is 1 - 0.55 = 0.45.

The probability that none of the alarms detect the burglar can be calculated by multiplying the probability of each alarm not detecting the burglar together.

If we have n alarms, this probability is (0.45)^n.

To find the number of alarms needed to be 99% certain that the burglar is detected by at least one alarm, we need to solve the following equation:

(0.45)^n ≤ 1 - 0.99

Taking the logarithm of both sides:

n * log(0.45) ≤ log(1 - 0.99)

n ≥ log(1 - 0.99) / log(0.45)

Using a calculator, we can evaluate the right side of the equation:

n ≥ 3.171 / (-0.152)

n ≥ -20.86

Since the number of alarms cannot be negative, we take the ceiling value of -20.86, which gives us n = 21.

Therefore, to be 99% certain that a burglar is detected by at least one alarm, the bank should use at least 21 alarms.

(b) Rounding to two decimal places, the expected number of alarms that will detect a burglar is 6.05.

If the bank installs eleven alarms, we can calculate the expected number of alarms.

that will detect a burglar by multiplying the number of alarms (11) by the probability that a single alarm detects a burglar (0.55).

Expected number of alarms = 11 * 0.55 = 6.05

Rounding to two decimal places, the expected number of alarms that will detect a burglar is 6.05.

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The function f(x) = 2x² + 2 attains its average value f(c) at c = ±(√1607)/3.

Let the function be f(x) = 2x² + 2.

For the given function, the average value f(c) is given by

f(c) = (1/(b - a)) ∫ [a, b] f(x) dx

Given that f(x) dx = 1072/3.

Also, the interval [a, b] is not given.

We can still find the value of c using the following method:

Let c be such that

f(c) = (1/(b - a)) ∫ [a, b] f(x) dx

We have

f(c) = (1/(b - a)) ∫ [a, b] f(x) dx = (1/(b - a)) × (1072/3)

f(c) = (2/3) × [(b³ - a³)/3 + 2(b - a)]

Using the above expression for f(c) and simplifying, we get:

(2/3) × [(b³ - a³)/3 + 2(b - a)] = 2c² + 2

Multiplying both sides by (3/2), we get:

[(b³ - a³)/3 + 2(b - a)] = 3c² + 3

Multiplying both sides by 3, we get:

(b³ - a³) + 6(b - a) = 9c² + 9

Rearranging, we get:

9c² = (b³ - a³) + 6(b - a) - 9

Taking 9 common on the RHS, we get:

9c² = (b³ - a³ - 9) + 6(b - a)

Adding 9 on both sides, we get:

9c² + 9 = (b³ - a³ - 9) + 6(b - a) + 9

Simplifying, we get:

9(c² + 1) = b³ - a³ + 6(b - a)

Now, we need to find the value of c for which the above equation holds true.

We can do this by using the given value of f(x) dx as follows:

Given, f(x) dx = 1072/3

Also, we know that

∫ [a, b] f(x) dx = [(b³ - a³)/3 + 2(b - a)]

Substituting this value of ∫ [a, b] f(x) dx in the given equation,

we get:(b³ - a³)/3 + 2(b - a) = (1072/3) / (2/3)

Multiplying both sides by 3/2, we get:

(b³ - a³)/3 + 2(b - a) = 536

Multiplying both sides by 3, we get:

(b³ - a³) + 6(b - a) = 1608

Substituting this value in the earlier equation, we get:

9(c² + 1) = 1608

Simplifying, we get:

c² + 1 = 1608/9

c² = 1607/9

c = ±(√1607)/3

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Answer:

Step-by-step explanation:

Decrease £262 by 39%

----------------------------------------------------------------

In short you could put this as:

Answer:

Step-by-step explanation:

This question looks trivial but its not and its apparent you didn't think so either. It uses the very important word(s) of more than and less than. These two words in higher science give more trouble that a flock of magpies give a bunch of robins in spring when they are nesting.

So Here's the solution

1 foot = 12 inches.

12 feet is going to be MORE THAN 12 inches.

That's the first answer in the right column. Watch out for more than and less than. They are real trouble.

The standard form equation of this circle is (x - 3)² + (y + 2)² = 7²

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² - 6x + y²+ 4y = 36

x² - 6x + (-6/2)² + y² + 4y + (4/2)² = 36 + (4/2)² + (-6/2)²

x² - 6x + 9 + y² + 4y + 4 = 36 + 4 + 9

(x - 3)² + (y + 2)² = 49

(x - 3)² + (y + 2)² = 49

Therefore, the center (h, k) is (3, -2) and the radius is equal to 7 units.

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Answer:

The correct answer is B. 0.13 cm^2

Step-by-step explanation:

Correct on EDG.

Answer:

B. 93.75 ft

Step-by-step explanation:

The area of a trapezoid is found by the equation Area=1/2(base 1 + base 2)*height

Known:

Base 1 = 12.5 ft

Base 2 = .5*Base 1 = .5*12.5 = 6.25 ft

Height = 10 ft

We can plug these numbers into the formula

Area=1/2(12.5+6.25)*10

Solving the equation, we get Area = 93.75 ft

The probability of at least one is a Samsung in the purchase collection of two independent LED HDTV is equal to 0.376.

Percent of all LED display manufactured by Samsung = 21%

Probability that at least one purchase is Samsung

= 1 - Probability that both purchases are not Samsung

Probability that the first purchase is not Samsung is 1 - 0.21 = 0.79.

The probability that the second purchase is also not Samsung is also 0.79.

Since the purchases are independent,

Multiply these probabilities to get the probability that both purchases are not Samsung,

P(neither is Samsung)

= 0.79 x 0.79

= 0.6241

The probability that at least one purchase is Samsung is,

P(at least one is Samsung)

= 1 - P(neither is Samsung)

= 1 - 0.6241

= 0.3759

Rounding to 3 decimal places, we get,

P(at least one is Samsung) = 0.376

Therefore, the probability that in a collection of two independent LED HDTV purchases, at least one is a Samsung is 0.376.

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9514 1404 393

Answer:

  linear

Step-by-step explanation:

We notice that adjacent x-values all differ by 1.

Similarly, we notice that all y-values differ by 0.5. When differences are constant, the function is linear.

Given an infinite grid, initial cell position (x, y) and a sequence of other cell position which needs to be covered in the given order.

The task is to find the minimum number of steps needed to travel to all those cells.

Note: Movement can be done in any of the eight possible directions from a given cell that is from cell (x, y) you can move to any of the following eight positions:(x-1, y+1), (x-1, y), (x-1, y-1), (x, y-1), (x+1, y-1), (x+1, y), (x+1, y+1), (x, y+1) is possible

Examples:

Input: points[] = [(0, 0), (1, 1), (1, 2)]

Output: 2

Move from (0, 0) to (1, 1) in 1 step(diagonal) and

then from (1, 1) to (1, 2) in 1 step (rightwards)

Input: points[] = [{4, 6}, {1, 2}, {4, 5}, {10, 12}]

Output: 14

Move from (4, 6) -> (3, 5) -> (2, 4) -> (1, 3) ->

(1, 2) -> (2, 3) -> (3, 4) ->

(4, 5) -> (5, 6) -> (6, 7) ->

(7, 8) -> (8, 9) -> (9, 10) -> (10, 11) -> (10, 12)

Since all the given points are to be covered in the specified order.

Find the minimum number of steps required to reach from a starting point to next point, then the sum of all such minimum steps for covering all the points would be the answer.

One way to reach from a point (x1, y1) to (x2, y2) is to move abs(x2-x1) steps in the horizontal direction and abs(y2-y1) steps in the vertical direction, but this is not the shortest path to reach (x2, y2).

The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction.

If we look closely this just reduces to the maximum of abs(x2-x1) and abs(y2-y1).

Traverse for all points and summation of all diagonal distance will be the answer.

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Using the fundamental theorem of calculas the derivative of function g(x)=\(xt^{3}+t^{5}\) at x=0 is \(t^{3}\).

Given a function g(x)=\(xt^{3}+t^{5}\).

We are required to find the derivative of the function g(x) at x=0.

Function is relationship between two or more variables expressed in equal to form. The values entered in a function are part of domain and the values which we get from the function after entering of values are part of codomain of function. Differentiation is the sensitivity to change of the function value with respect to a change in its variables.

g(x)=\(xt^{3}+t^{5}\)

Differentiating with respect to x.

d g(x)/dx=\(t^{3}\)+0  [Differentiation of x is 1 and differentiation of constant is 0]

=\(t^{3}\)

Hence using the fundamental theorem of calculas the derivative of function g(x)= \(xt^{3}+t^{5}\) at x=0 is \(t^{3}\).

The function given in the question is incomplete. The right function will be g(x)=\(xt^{3}+t^{5}\).

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.

Answer:

1) 4/29

2) 3/29

3) 16/29

4) 23/29

5) 22/29

The forecast value for time period 2 is 210, and the forecast error is -110 when the actual value is 100. Option B

To calculate the forecast value for time period 2, we substitute W = 2 into the regression equation:

y = 200 + W + 2W^2

= 200 + 2 + 2(2^2)

= 200 + 2 + 2(4)

= 200 + 2 + 8

= 210

Therefore, the forecast value for time period 2 is 210.

To calculate the forecast error, we compare the forecasted value with the actual value for time period 2. Given that the actual value is 100, the forecast error can be calculated as the difference between the actual value and the forecast value:

Forecast error = Actual value - Forecast value

= 100 - 210

= -110

Hence, the forecast error is -110.

Therefore, the correct answer is:

Forecast value = 210; forecast error is -110. So Option B is correct.

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50

Step-by-step explanation:

you just subtract the 29 from 79

There are 50 candies left in the jar.

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

There are 79 candies in the Jar.

Aaron remove 29 candies from the jar.

Now,

Total number of candies in the jar =n 79

And, Aaron remove 29 candies from the jar.

Thus, Left candies in the jar = 79 - 29

                                           = 50

Therefore, There are 50 candies left in the jar.

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Answer:

(1067)(6740)

=7191580

Step-by-step explanation:

I hope this help you :)

If you need another thing just let me know.

The shape of the probability distribution for the random walk problem depends on the values of p and q. When p = q, the distribution is symmetric, while if p and q have different values, the distribution becomes asymmetric.

The shape of the probability distribution for the problem of the random walk can be determined by considering the values of p and q, where p represents the probability of moving in one direction and q represents the probability of moving in the opposite direction.
(a) In this case, we are given that p = q = 1/2, which means that there is an equal probability of moving in either direction.
When p = q = 1/2, the probability distribution for the random walk problem will have a symmetric shape. This means that the probabilities of moving to the left and the right are the same. For example, if we start at position 0 and take 20 steps, the probability of ending up at position +10 will be the same as the probability of ending up at position -10.
It is important to note that the specific values of p and q do not affect the shape of the distribution. As long as p = q, the distribution will be symmetric.

(b) Now, let's consider a different scenario where p = 0.6 and q = 0.4. In this case, the probability of moving in one direction is greater than the probability of moving in the opposite direction. This will result in an asymmetric probability distribution.
For example, if we start at position 0 and take 20 steps, the probability of ending up in a positive position will be higher than the probability of ending up in a negative position. The distribution will be skewed towards the positive position.

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Answer:

$30

Step-by-step explanation:

Just multiply

Answer:

$30

Step-by-step explanation:

7.5 x 4= 30

Answer:

12

Step-by-step explanation:

First you have to add the amount of pencils each person has

14 + 9 + 12 + 13 + 12

Which equals 60

Then, you have to divide the total by the answer you got from above

60 / 5

Which equals 12

Answer:

2.94

Step-by-step explanation:

multiply them like normal multiplication

remember that 2 negatives equal positive

Answer:

25

Step-by-step explanation:

When calculating a percentage of a number always multiply it by the percentage divided by 100. In this case that would be 0.05, 500*0.05=25

We have created our own arithmetic sequence which is: a₁ = 3; a₂ = 6; a₃ = 9

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.

An arithmetic progression is another name for an arithmetic sequence.

So, make up your own arithmetic order. the first three terms in writing.

Think about the numbers 3, 6, 9, 12, 15, etc.

a₁ = 3

a₂ = 6

a₃ = 9

Therefore, we have created our own arithmetic sequence which is: a₁ = 3; a₂ = 6; a₃ = 9

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Correct question:

An arithmetic sequence is a sequence with a common difference. It can be represented by the recursive formula a1 = a (where a is the first term of the sequence); an = an - 1 + d. Create your own arithmetic sequence. Write out the first 3 terms.

The number of reindeer in St. Elsewhere in 1920 will be approximately 475.

The growth rate of .12 indicates an annual increase of 12%, meaning that each year the number of reindeer will be multiplied by 1.12. To find the number of reindeer in 1920, we need to use this growth rate over the 20-year period from 1900 to 1920.
Starting with the initial 52 reindeer, we can multiply by 1.12 for each year. This gives us:
Year 1: 52 * 1.12 = 58.24
Year 2: 58.24 * 1.12 = 65.10
Year 3: 65.10 * 1.12 = 72.90
Year 4: 72.90 * 1.12 = 81.60
Year 5: 81.60 * 1.12 = 91.15
Year 6: 91.15 * 1.12 = 101.66
Year 7: 101.66 * 1.12 = 113.27
Year 8: 113.27 * 1.12 = 126.13
Year 9: 126.13 * 1.12 = 140.43
Year 10: 140.43 * 1.12 = 156.36
Year 11: 156.36 * 1.12 = 174.16
Year 12: 174.16 * 1.12 = 194.10
Year 13: 194.10 * 1.12 = 216.45
Year 14: 216.45 * 1.12 = 241.58
Year 15: 241.58 * 1.12 = 269.87
Year 16: 269.87 * 1.12 = 301.72
Year 17: 301.72 * 1.12 = 337.62
Year 18: 337.62 * 1.12 = 378.10
Year 19: 378.10 * 1.12 = 423.77
Year 20: 423.77 * 1.12 = 475.30
Therefore, the number of reindeer in St. Elsewhere in 1920 will be approximately 475.

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False. Scaling, in the context of graphics, refers to the process of resizing an image or graphic while maintaining its aspect ratio. It involves changing both the vertical and horizontal size of the graphic by the same percentage.

When scaling a graphic, the goal is to resize it proportionally, preserving the original aspect ratio. This means that both the vertical and horizontal dimensions are changed by the same factor or percentage. For example, if an image is scaled by 50%, both its height and width will be reduced by 50% of their original values. This ensures that the graphic maintains its original proportions and does not appear distorted.

Scaling graphics is commonly used in various applications, such as graphic design, image editing, and web development, to resize images without distorting their appearance. It allows for consistent resizing across different devices or platforms while maintaining the integrity of the original graphic.

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Answer:

(2,1)

Step-by-step explanation:

Well first we single out y or x in one of the equations,

we’ll use 2x + y = 5 and single out y.

2x + y = 5

-2x to both sides

y = -2x + 5

So we can plug in -2x + 5 into y in 2x - 2y = 2.

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

2x + 4x - 10 = 2

combine like terms,

6x - 10 = 2

Communicarice property

+10 to both sides

6x = 12

divide 6 to both sides

x = 2

If x is 2 we can plug 2 in for x in 2x + y = 5.

2(2) + y = 5

4 + y = 5

-4 to both sides

y = 1

(2,1)

Thus,

the solution is (2,1).

Hope this helps :)