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The line integral of xy dx + x^2 dy around the given rectangle is 0.

To evaluate the line integral ∮C (xy dx + x^2 dy) along the given rectangle C with vertices (0, 0), (5, 0), (5, 1), and (0, 1), we can break it down into four line integrals along each side of the rectangle and sum them up.

Along the bottom side:

Parametrize the line segment from (0, 0) to (5, 0) as r(t) = (t, 0), where t ranges from 0 to 5. The differential element along this line segment is dr = (dt, 0). Substituting these values into the line integral, we get:

∫[0,5] (t*0) dt = 0.

Along the right side:

Parametrize the line segment from (5, 0) to (5, 1) as r(t) = (5, t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, dt). Substituting these values into the line integral, we get:

∫[0,1] (5t0 + 25dt) = ∫[0,1] 25*dt = 25.

Along the top side:

Parametrize the line segment from (5, 1) to (0, 1) as r(t) = (5-t, 1), where t ranges from 0 to 5. The differential element along this line segment is dr = (-dt, 0). Substituting these values into the line integral, we get:

∫[0,5] ((5-t)*0 + (5-t)^2 * 0) dt = 0.

Along the left side:

Parametrize the line segment from (0, 1) to (0, 0) as r(t) = (0, 1-t), where t ranges from 0 to 1. The differential element along this line segment is dr = (0, -dt). Substituting these values into the line integral, we get:

∫[0,1] (0*(1-t) + 0) dt = 0.

Summing up all the line integrals, we have:

0 + 25 + 0 + 0 = 25.

Therefore, the line integral of xy dx + x^2 dy around the given rectangle is 25.

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

9 weeks :)

Step-by-step explanation:

First we subtract :)

2145 - 952.50 = 1192.50

Now we divide :)

265/2 = 132.5

Now we divide 1 more time :)

1192.50/132.50 = 9

It will take 9 weeks :)

Have an amzing day!!

Please rate and mark brainliest!!

Answer:

y<1/2+2

Step-by-step explanation:

Answer:

I think the answer is A because I learned about slope last year

Answer:

It is C and D

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.95 is the correct answer

Answer:

its correct

Step-by-step explanation:

Each term of 6x^2+4x-9 is placed along the top of the table. Each term of 5x+1 is placed along the right side of the table.

We have 3 terms in 6x^2+4x-9 and 2 terms in 5x+1

So there are 3 columns and 2 rows leading to 3*2 = 6 cells total.

Each cell is filled in by multiplying the outer terms

For instance, row 1, column 1 has 6x^2*5x = (6*5)*(x^2*x) = 30x^3

The other cells are filled in the same way.

After the table is completed, you then combine like terms

20x^2 and 6x^2 is one pair which add to 26x^2

4x and -45x is another pair which add to -41x

The other terms are just added on, but not combined/simplified. This leads to the final answer shown on your paper.

Step-by-step explanation:

the formula is ax^2+bx+c

the vertex is (-b/2a)i^

find it and put it on function and the j^ of the vertex is found which is -delta/4a

The domain of the function g/f is x ∈ (0, ∞), which is written in interval notation as (0, ∞).

Given f(x) = √x and g(x) = |x-3|, we need to find g/f, which is the division of g(x) by f(x).

Substituting the given functions into the expression g/f, we have:

g/f = |x-3| / √x

To simplify this expression, we need to consider two cases: x ≥ 3 and x < 3, as the absolute value function |x-3| behaves differently in these cases.

Case 1: x ≥ 3

For x ≥ 3, |x-3| simplifies to x - 3. Thus, the expression becomes:

g/f = (x-3) / √x

Case 2: x < 3

For x < 3, |x-3| simplifies to -(x - 3) = 3 - x. Thus, the expression becomes:

g/f = (3-x) / √x

Next, let's determine the domain of the function g/f. To have a well-defined division, the denominator √x cannot be equal to zero.

Therefore, x must be greater than zero since we're taking the square root of x.

Hence, the domain of the function g/f is x ∈ (0, ∞), which is written in interval notation as (0, ∞).

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The equation that can be formed from the given set of numbers

1) (3 + 4) * 6 + 7 = 24

2) 3 + 4 * (6 + 7) = 24

3) 3 + 4 + 6 + 7 = 20, so (3 + 4 + 6 + 7) * 1 = 24

4) 3 * 4 * 6 * 7 = 168, so 168 / 7 = 24

Mathematical Operations :

The mathematical “operation” refers to calculating a value using operands and a math operator. The symbol of the math operator has predefined rules to be applied to the given operands or numbers.

Mathematical Equations :

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

BODMAS

According to the BODMAS rule, mathematical equations containing numerous operators must be resolved in the order of BODMAS, starting from the left.

Keep in mind that the order in which you perform the operations will affect the result. Parentheses are used to indicate the order in which operations should be performed.

In the first example above, the operation inside the parentheses (3 + 4) is done first, and then that result is multiplied by 6 and added to 7.

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Answer:

\(\frac{1}{81}\)

Step-by-step explanation:

Using the rule of exponents

\(a^{-m}\) = \(\frac{1}{a^{m} }\) , then

\(3^{-4}\) = \(\frac{1}{3^{4} }\) = \(\frac{1}{81}\)

Answer:

1) \(10\sqrt{10\)

3) \(15\)

5) \(9\sqrt3\)

7) \(35\sqrt7\)

Step-by-step explanation:

We can simplify these values by factoring the value underneath the square root sign.

1) We can factor 1000 as:

\(1000 = 10 \cdot 10 \cdot 10\)

From this factorization, we can see that there is a pair of 10s. So, we can represent this as one 10 outside the square root.

\(\sqrt{1000}\)

\(= \sqrt{10 \cdot 10 \cdot 10}\)

\(= \boxed{10\sqrt{10}}\)

3) We can factor 225 as:

\(225 = 5 \cdot 5 \cdot 3 \cdot 3\)

We can see that there is a pair of 5s and a pair of 3s. So, we have one 5 and one 3 outside the square root.

\(\sqrt{225}\)

\(= \sqrt{5\cdot 5 \cdot 3 \cdot 3}\)

\(= 5 \cdot 3 \sqrt{1}\)

\(= \boxed{15}\)

5) We can factor 243 as:

\(243 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3\)

We can see that there are two pairs of 3s. So, there will be two 3s outside the square root.

\(\sqrt{243\)

\(= \sqrt{3 \cdot 3 \cdot3 \cdot 3\cdot 3\)

\(= 3 \cdot 3\sqrt3\)

\(=\boxed{9\sqrt3}\)

7) We can factor 175 as:

\(175 = 5 \cdot 5 \cdot 7\)

We can see that there is a pair of 5s. So, there will be one 5 outside the square root multiplied by the 7 that is already there.

\(7\sqrt{175\)

\(= 7\sqrt{ 5 \cdot 5 \cdot 7}\)

\(= 7 \cdot 5\sqrt7\)

\(= \boxed{35\sqrt7}\)

We can see that the values of H can be found dividing each value of G by 4. So, the answer is:

Each term in Pattern G is 4 times the corresponding term in Pattern H.

Answer:

\(\mathbf{\beta=140\ dB}\)

Step-by-step explanation:

The Logarithm Function

The sound level is usually calculated as a logarithm by the formula:

\(\displaystyle \beta=10\log\frac{I}{I_o}\)

Where

I   = Sound intensity in W/square meter

Io = Smallest sound intensity that can be heard.

\(I_o=1\cdot 10^{-12}\ W/m^2\)

The blue whale can emit a sound of I=106.8 W/square meter, thus the sound level is:

\(\displaystyle \beta=10\log\frac{106.8}{1\cdot 10^{-12}}\)

\(\displaystyle \beta=10*14\)

\(\mathbf{\beta=140\ dB}\)

Answer:

D

Step-by-step explanation:

The midpoint of PQ is the average of the coordinates of P and Q

y = \(\frac{12-1}{2}\) = \(\frac{11}{2}\) = 5.5 ← y- coordinate of midpoint

Answer:

we need an out of sorry -_-

Answer:

the probability would be 4/6 or 66.67%

Step-by-step explanation:

The reason is because out of the 6 numbers on a 6-sided die, the odd numbers are 1, 3, and 5.

Now if you add the number 4 to the mix, you get a probability of 4 out of the 6 total numbers being either 1, 3, 5, or 4.

Answer:

\(\bold{18, 36, 54, 72, 90, 108, 126, 144, 162, 180}\)

Step-by-step explanation:

Hi there!

18 has infinitely many multiples.

These are the first 10 multiples of 18:

\(\bold{18, 36, 54, 72, 90, 108, 126, 144, 162, 180}\)

I hope it helps! Enjoy your day!

~Just a teenage girl willing to help

\(\bold{Besties4Ever}\)

Answer:35.4

Step-by-step explanation:

for this one you would subtract 172.5-137.1 for the answer 35.4 which is where the shark will end up.

The radius of Deimos to one significant digit in meters is approximately 9.4 m

.

Given the ratio of the Sun-from-Mars distance to Deimos-from-Mars distance is 365,000, the distance between Mars and Deimos can be found to bedeimos distance = Sun-Mars distance / 365,000

Next, we can find the diameter of Deimos by noting that 550 of its diameters is equal to the distance it takes to transit the shadow of Mars during a lunar eclipse.

Let's call the diameter of Deimos "d", so we can

diameter = 1/550 * deimos distance

Finally, the Sun appears about 8.4 times as large as Deimos in the Martian sky. If we call the radius of Deimos "r", then the radius of the Sun is 8.4r.

Using the information given, we can set up the following equation:

deimos distance / (3,000,000 + r) = 8.4r / (3,000,000)Simplifying and solving for r,

we get:r = 9.39 m (rounded to one significant digit)

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Jason's trip was 9 minutes longer than his usual drive to work.

Given that,

Distance from Jason's home to office = 20 miles

Speed of driving from home to office = 50 miles/hour

Total time taken to reach from home to office = distance ÷ speed = 20/50 = 0.4 hours = 24 minutes

Thus, on a normal day, Jason takes 0.4 hours to reach his office from home.

Now, Jason drove for 12 minutes when his car broke down,

The taxi arrived 15 minutes later and drove at 40 miles/hour,

Total time spent to reach office from taxi= distance ÷ speed = 20/40 = 0.5 hours= 30 minutes

Although he already spent 12 minutes driving before the taxi arrived so,

30 - 12 = 18 minutes.

But, he waited for the taxi to arrive for 15 minutes so,

18+15 = 33 minutes.

Thus, today Jason took 33 minutes to reach the office from his home.

Therefore, Jason took (33- 24)minutes which is equal to 9 minutes longer than his usual drive to work.

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Answer:

C and D is the answer.

Step-by-step explanation:

If m∠5 = x°, according to the Corresponding Angle Theorem, m∠9 will equal the same, and because 9 and 12 are vertical angles, both of these will be the same measure.

She should order 8 large pizzas to serve 36 guests.

We know that two large pizzas serve 9 people. To determine the number of pizzas she should order to serve 36 guests, we can set up a proportion:

2 pizzas / 9 people = x pizzas / 36 people

Cross-multiplying, we get:

2 * 36 = 9 * x

72 = 9x

Dividing both sides of the equation by 9, we find:

x = 8

Therefore, she should order 8 large pizzas to serve 36 guests.

To serve 36 guests, she should order 8 large pizzas based on the information that two large pizzas serve 9 people.

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Answer:

\(\huge\boxed{\sf tan \ 28 = x / 14}\)

Step-by-step explanation:

Since opposite and adjacent is given, we will use tan as trigonometric ratio.

Hence,

opposite = x , adjacent = 14 and \(\theta\) = 28

So,

\(\sf tan \theta = opposite / adjacent\)

tan 28 = x / 14

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:180

Step-by-step explanation:

hope this helps

Answer:

0.8 mm

Step-by-step explanation:

Given that you require the actual size.

The ant has been magnified by 15 X

To find the actual size divide magnified size by 15

actual size = 12 mm ÷ 15 = 0.8 mm

Answer:

a. 7 times

b. 74.7 km

Step-by-step explanation:

a. From Albany to Pittsburgh, there are 739.7 km.

She stopped to rest after every 95 kilometres:

Therefore, let us find how many times she stopped:

739.7 / 95 = 7.79

We only need the quotient, that is, 7

So she stopped 7 times.

b. After her last stop, she had traveled:

7 * 95 = 665 km

Therefore, the distance she has left after her last stop is:

739.7 - 665 = 74.7 km

The table of values is

X |f(x)

-6 | 11

-3 | 7

0 | 4

3 | -1

The value of f(6) is -5

The y-intercept is 3

From the question, we have the following parameters that can be used in our computation:

4x + 3y = 9

Make y the subject

So, we have

y = 3 - 4/3x

We have the x values to be

x = -6, -3, 0, and 3

Substitute the known values in the above equation, so, we have the following representation

y = 3 - 4/3 * -6 = 11

y = 3 - 4/3 * -3 = 7

y = 3 - 4/3 * 0 = 4

y = 3 - 4/3 * 3 = -1

We have

y = 3 - 4/3x

This means that

f(6) = 3 - 4/3 * 6

f(6) = -5

For the y-intercept, we set x = 0

So, we have

f(0) = 3 - 4/3 * 0

f(0) = 3

So, the y-intercept is 3

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Answer:

0.7208 = 72.08% probability that this whole shipment will be accepted.

Step-by-step explanation:

For each tablet, there are only two possible outcomes. Either it meets the required specifications, or it does not. The probability of a tablet meeting the required specifications is independent of any other tablet, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

4% rate of defects

This means that \(p = 0.04\)

26 tablets

This means that \(n = 26\)

What is the probability that this whole shipment will be accepted?

Probability that at most one tablet does not meet the specifications, which is:

\(P(X \leq 1) = P(X = 0) + P(X = 1)\)

Thus

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{26,0}.(0.04)^{0}.(0.96)^{26} = 0.3460\)

\(P(X = 1) = C_{26,1}.(0.04)^{1}.(0.96)^{25} = 0.3748\)

Then

\(P(X \leq 1) = P(X = 0) + P(X = 1) = 0.3460 + 0.3748 = 0.7208\)

0.7208 = 72.08% probability that this whole shipment will be accepted.

Answer:

D) (4,5)

Step-by-step explanation:

the ordered pair (4, 5) is the only one that, when substituted into each inequality statement, made both of them true