Consider the following system of linear equations 3x X2 + X₂ 1 3x1 + 6x2 + 2x2 = 0 3x1 + 3x2 + 7x, = 4 (a) Find the first three iterations of the Gauss-Seidel method using x(0) = 0 (6)Find the first three iterations of the Jacobi's method using x( ) = 0

The final result of the given expression is 49.4.

Part A: In  the missing expression should be the result of squaring three and adding four.

This is because the expression in Step 2 states "the quantity of the sum of three squared plus four divided by 0.25.

" Therefore, to continue simplifying the expression, we need to evaluate the value of the sum of three squared plus four.

The quantity of [tex](3^2 + 4)[/tex] divided by 0.25

To solve Step 3, we first evaluate the expression inside the parentheses:

[tex]3^2 + 4 = 9 + 4 = 13[/tex]

So, Step 3 becomes:

The quantity of 13 divided by 0.25

Part B: In the missing expression should be the result of dividing 13 by 0.25.

This is because in Step 4, the expression is "the quotient of the quantity 13 divided by 0.25 end quantity minus 10.4 divided by 4."

To simplify further, we need to calculate the value of 13 divided by 0.25.

13 divided by 0.25

To solve Step 6, we perform the division:

13 ÷ 0.25 = 52

So, it becomes:

52 minus 10.4 ÷ 4

Following the remaining steps:

52 minus (10.4 ÷ 4) = 52 - 2.6 = 49.4

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Answer:

$35,000

Step-by-step explanation:

The amount that would be repaid = amount borrowed + interest earned on loan

interest earned on deposit can be determined by determining the simple interest

Simple interest = principal x time x interest rate

principal = the amount deposited = 20,000

Time = the duration of the deposit =5  

interest rate = the percentage on deposit that would be earned = 15

20,000 x 5 x 0.15 = $15,000

total = 20,000 + 15,000 = $35,000

The 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%)

Let's denote p as the proportion of orders that are not accurate.

The sample proportion of orders that are not accurate is given by:

p(bar) = 70 / (239 + 70)

= 70 / 309

≈ 0.226

The standard error of the proportion is calculated as:

SE = √[(p(bar)(1 - p(bar))) / n]

= √[(0.226(1 - 0.226)) / 309]

≈ √(0.1785 / 309)

≈ 0.0267

To find the margin of error, we need to multiply the standard error by the critical value corresponding to a 95% confidence level. For a 95% confidence level, the critical value is approximately 1.96.

Margin of error = 1.96 × SE

≈ 1.96 × 0.0267

≈ 0.0523

Now we can construct the confidence interval:

Lower limit = p(bar) - Margin of error

= 0.226 - 0.0523

≈ 0.1737

Upper limit = p(bar) + Margin of error

= 0.226 + 0.0523

≈ 0.2783

Therefore, the 95% confidence interval estimate of the percentage of orders that are not accurate is approximately (17.37%, 27.83%).

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Answer:

Step-by-step explanation:

1. Write the question.

17 - 2x = -11

2. Subtract 17 from both sides

-17          -17

    - 2x = -28

3. Negatives cancel

      2x = 28

4. Divide both sides by 2

        /2     /2

        x = 14

5. Check the answer, write the equation.

17 - 2x = -11

6. Substitute x with the value

17 - 2(14) = -11

17 - 28 = -11

-11 = -11

The answer is correct!

Hope this helped,

Kavitha

We have:

[tex]2x \cdot (5^2)[/tex]

[tex]= 2x \cdot 25[/tex]

[tex]= \boxed{50x}[/tex]

Answer: Nicole can spend up to 7 hours in the boat.

Step-by-step explanation:

Based on the information given in the question, the possible number of hours that can be used will be calculated as thus:

(6 × t) - 9 ≤ 33

6t - 9 ≤ 33

Collect like terms

6t ≤ 33 + 9

6t ≤ 42

Divide both side by the coefficient of t

6t/6 ≤ 42/6

t ≤ 7

Nicole can spend up to 7 hours in the boat.

Answer:

1.04 mill

Step-by-step explanation:

15 inches to mill = 381

[tex]365\sqrt{381}[/tex] = 1.04 ( rounded )

Answer:

x=50 degrees

Step-by-step explanation:

I'm not sure but hope this helps and have a  wonderful day!!!!

Answer:

x = 48

Step-by-step explanation:

2x + 10 + x + 26 = 180

3x + 36 = 180

3x = 180 - 36

3x = 144

x = 48

Answer:

a. -12n^3 + 8n^2 - 2n

b. n^4 - n/2

c. 6b^7 + 2b^6 - b^5

Step-by-step explanation:

btw photomath (the app) is really good for this type of stuff

Answer:

2) $1797

3) $152

4) $5,378

Answer:

This theorem states that 'if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. ' This is kind of like the SAS, or side-angle-side postulate. But SAS requires you to know two sides and the included angle.

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

√196

Calculate the square root of 196 and get 14.

14

The decimal number (25679)₁₀ is equivalent to the octal number (62117)₈. The base conversion method, also known as the radix conversion method, is a systematic approach to converting numbers from one base to another.

To convert the decimal expansion (25679)₁₀ to an octal expansion, we can use the base conversion method.

Step 1: Divide the decimal number by 8 and keep track of the remainders.

25679 ÷ 8 = 3209 remainder 7

3209 ÷ 8 = 401 remainder 1

401 ÷ 8 = 50 remainder 1

50 ÷ 8 = 6 remainder 2

6 ÷ 8 = 0 remainder 6

Step 2: The remainders from bottom to top form the octal expansion.

Therefore, (25679)₁₀ = (62117)₈.

Hence, the decimal number (25679)₁₀ is equivalent to the octal number (62117)₈.

The question should be:

Use base conversion method, convert the decimal expansion (25679)₁₀ to an Octal expansion.

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Step-by-step explanation:

The first composite shape is a combination of a rectangular prism and a pyramid. To find the volume of the entire shape you find the volume of each individual shape and add them together. The second figure consists of a cylinder and a hemisphere.

Hope that helps :)

Answer:

W is either less than or( less than or equal to)

Step-by-step explanation:

I do not know what shows if something is equal to so the best answer I can think if is less than -2 as it looks like W is everything lower or equal to -2

Answer:

11t -2

Step-by-step explanation:

3t - 5 + 8t + 3

Combine like terms

3t +8t- 5  + 3

11t -2

Start by changing the problem to 3t + -5 + 8t + 3.

Now combine like terms.

Combine like terms → your numbers

and your "t" terms.

So 3t + 8t is 11t and -5 + 3 is -2.

So the answer is 11t - 2.

Answer:

x=0

I used phone math!!!!!!!!

Answer:

1 hour: $12.75

Step-by-step explanation:

Easy divide 38.25 by 3 which is 12.75

Answer:

[tex]4 \sqrt{2 - 3 = 1[/tex]

Answer:

(-2,8), (-1,6), (0,4), (1,2), (2,0), (3,-2)

Step-by-step explanation:

Insert these points in graph and draw a line. You will get the answer. ^_^

sorry had to edit because of a blunder

Answer:

12

Step-by-step explanation:

To determine the number of discs, divide the area of the metal sheet by the area of the discs

The metal sheets are in the shape of a rectangle, thus the area of a rectangle would be used to determine the area of the sheet

Area of a rectangle = length x breadth

56 x 33 = 1848 cm^2

The disc is in the shape of a circle.

area of a circle = πr²

π = 3.14

r = radius

3.14 x 7² = 153.86 cm²

Number of discs = 1848 /153.86 = 12

Step-by-step explanation:

[tex]90 = 4x - 6 \\ 96 = 4x \\ x = 24[/tex]

[tex]2x - 8 = \\ = 48 - 8 = \\ = 40[/tex]

The borrower would need to make payments of approximately $943.57 per year to pay off the loan in 5 years.

To determine the payment rate required to pay off the loan in 5 years, we can use the continuous compound interest formula:

A = P * [tex]e^{(rt)[/tex],

where A is the final amount, P is the initial principal, e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate, and t is the time in years.

In this case, the initial principal is $6600, the annual interest rate is 10%, and the time is 5 years. We want to find the payment rate, so let's set A equal to zero, indicating that the loan is fully paid off:

0 = 6600 * [tex]e^{(0.10 * 5)[/tex]- k * 5,

Simplifying the equation, we have:

[tex]e^{(0.5)[/tex] = k / 6600.

Now, we can solve for k by multiplying both sides of the equation by 6600:

k = 6600 * [tex]e^{(0.5)[/tex],

Using a calculator or software, we find that k is approximately $943.57 per year.

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Answer:

A

Step-by-step explanation:

(6,4)

3x-1y=14

-y= 3x-14

y=-2x+16

sub in first equation

3x-14 =-2x+16

3x+2x= 16 +14

5x = 30

x = 6

plug in x

y=-2x+16

y = -2(6)+16

y = 4

(6,4)

Events A and B are considered independent if and only if the probability of their intersection (P(A ∩ B)) is equal to the product of their individual probabilities (P(A) * P(B)).

Independence: Two events A and B are independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

Joint Probability: The joint probability P(A ∩ B) represents the probability of both events A and B occurring together.

Multiplication Rule: According to the multiplication rule for independent events, if events A and B are independent, the probability of their intersection is equal to the product of their individual probabilities.

P(A ∩ B) = P(A) * P(B)

Interpretation: If the equation holds true, events A and B are considered independent since the probability of their intersection can be determined solely by multiplying their individual probabilities.

Dependence: If the equation does not hold true, it implies that the occurrence of one event affects the probability of the other event, indicating dependence between the two events.

In summary, the multiplication rule for independent events states that events A and B are independent if and only if P(A ∩ B) = P(A) * P(B).

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The correct answers for the given data are (a) b = 6, (b) arg(z - 9) = -π/4, and (c) ||w/w|| = 1.

(a) To determine z/w, we first need to express z and w in terms of their real and imaginary parts. Given 2 = 3 + 6i, we can rewrite it as z = 3 + 6i. Similarly, w = a + bi. Now, let's calculate z/w:

z/w = (3 + 6i)/(a + bi)

To make z/w real, the imaginary part of the denominator should cancel out the imaginary part of the numerator. This means 6/a = 6i/b. Simplifying further, we get ab = 6a + 6bi. Since a and b are real numbers, the only way for the equation to hold is if b = 6 and a = 1. Therefore, b = 6.

(b) To determine arg(z - 9), we need to subtract 9 from z = 3 + 6i:

z - 9 = (3 + 6i) - 9 = -6 + 6i

The argument (or angle) of -6 + 6i can be calculated as:

arg(-6 + 6i) = arctan(6/(-6)) = arctan(-1) = -π/4

(c) To determine ||w/w|| (the magnitude of w divided by the magnitude of w), we need to find the magnitude of w. Given w = a + bi, the magnitude of w is given by:

||w|| = √(a^2 + b^2)

Now, substituting a = 1 and b = 6 (from part a):

||w|| = √(1^2 + 6^2) = √37

Therefore, ||w/w|| = ||w||/||w|| = 1.

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Answer:

The hikers are 5 miles apart.

Step-by-step explanation:

East + West = 3 miles apart (x-axis)

North + South = 4 miles apart (y-axis)

Then use the pythagorean theorem to find the distance between them.

sqrt(distance) = sqrt(3^2+4^2)

distance = sqrt(25)

distance = 5 miles

Answer:

Step-by-step explanation:

1/5 + 1/5 = 2/5

1/7 + 1/7 = 2/7

1/3 + 1/3 = 2/3

There are an infinite number of these fractions. They must be 1 and 1 in the numerator, and the denominator must be relatively prime  to 2. The examples I have picked are prime in the denominator, but the rule is not without many exceptions. For example

1/9 + 1/9 = 2/9

I don't think you can pick an even denominator because it will reduce when put with two.  Oh wait 2/18 + 2/18 = 4/18 = 2/9 But these could be reduced before adding. Still, it might count. It depends on who is marking the question.

What about an odd and even denominator?

1/9 + 1/18 = 3/18 = 1/6  There must be something that works, but I can't come up with an example.

Answer:

area of trapezoid = 1/2×(a+b)×height

area of trapezoid =1/2×(15m+7m)×7m

area of trapezoid =1/2×22m×7

area of trapezoid =77m²

area of trapezoid =1/2×(a+b)×height

area of trapezoid =1/2×(9ft+12ft)×4ft

area of trapezoid =1/2×21ft×4ft

area of trapezoid =42ft²