The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article "Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds" (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s-136s) presents several equations for computing the oxygen equivalence number of a weld. One equation, designed to predict the hardness of a weld, is X=O+2N+(2/3)C, where X is the oxygen equivalence, and O,N, and C are the amounts of oxygen, nitrogen, and carbon, respectively, in weight percent, in the weld. Suppose that for welds of a certain type, μ o
​
=0.1668,μ N
​
=0.0255,μ C
​
=0.0247, σ o
​
=0.0340,σ N
​
=0.0194, and σ C
​
=0.0131 a. Find μ X
​
. b. Suppose the weight percents of O,N, and C are independent. Find σ X
​
.

cos(90° - x) = x/4.5.

In a right triangle, the sum of the measures of the two acute angles is always 90 degrees. Therefore, if one angle measures x degrees, then the other acute angle measures 90 - x degrees.

We are given that sin(x°) = x/4,5. The sine function represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. In this case, the side opposite the angle x° has a length of x, and the hypotenuse has a length of 4.5.

To find cos(90° - x), we need to determine the cosine of the other acute angle, which is 90 - x degrees.

Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can find the cosine of 90° - x as follows:

sin^2(x) + cos^2(x) = 1

(cos^2(x) = 1 - sin^2(x))

cos^2(90° - x) = 1 - sin^2(90° - x)

cos(90° - x) = √(1 - sin^2(90° - x))

Since sin(90° - x) = cos(x), we can substitute cos(x) for sin(90° - x):

cos(90° - x) = √(1 - cos^2(x))

Now, we need to find the value of cos(x). Given that sin(x°) = x/4.5, we can solve for cos(x) as follows:

sin^2(x) + cos^2(x) = 1

(x/4.5)^2 + cos^2(x) = 1

cos^2(x) = 1 - (x/4.5)^2

cos(x) = √(1 - (x/4.5)^2)

Substituting this expression back into cos(90° - x), we have:

cos(90° - x) = √(1 - (√(1 - (x/4.5)^2))^2)

cos(90° - x) = √(1 - (1 - (x/4.5)^2))

cos(90° - x) = √(x/4.5)^2

cos(90° - x) = x/4.5

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Answer:

Undermentioned explanation, similarity & dissimilarity between long division & multiplication of polynomials

Step-by-step explanation:

Long Division of Polynomial steps :

Complete missing terms in divisor with zero coefficients, sort terms in decreasing exponential order

Divide leading term, multiply divisor x quotient, subtract partial product & carry down remainder ............ (continue same)

Multiplication of Polynomial steps :

Multiply the 1st, 2nd, 3rd term(s) in the first polynomial with 1st, 2nd, 3rd consecutive term(s) in the second polynomial........... (go on)

Similarity (ies) : Both involve term by term treatment, multiplying monomial & polynomial

Dissimilarity (ies) : Division includes subtracting of exponential power. However, multiplication includes adding of exponential power

Answer:

D

Step-by-step explanation:

Hope this helps

Answer:

\(x < 80000\)

Step-by-step explanation:

\(3600 + 1.02x < 2000 + 1.04x \\ \frac{ \: \: \: \: \: \: \: \: \: \: \: \: - 1.04x < \: \: \: \: \: \: \: \: \: \: \: \: \: - 1.04x}{3600 - 0.02x < 2000} \\ \\ 3600 - 0.02x < 2000 \\ \frac{ - 3600 \: \: \: \: \: \: \: \: \: < - 3600}{ - 0.02x < - 1600} \\ \\ \frac{ - 0.02x}{ - 0.02} < \frac{ - 1600}{ - 0.02} \\ \\ x < 80000\)

The absolute maximum value of f(x) on the closed interval (-1, 3) is 30, which occurs at x = 0.

To find the absolute maximum value of the function f(x) = 24 - 8x^2 + 6 on the closed interval (-1, 3), we need to follow these steps:

1. Find the critical points by taking the first derivative of f(x) and setting it equal to 0.
2. Evaluate the function at the critical points and endpoints of the interval.
3. Compare the values and determine the absolute maximum.

Step 1:
f(x) = 24 - 8x^2 + 6
f'(x) = d/dx (24 - 8x^2 + 6) = -16x

Now, set f'(x) equal to 0:
-16x = 0
x = 0 (this is the critical point)

Step 2:
Evaluate the function at the critical point and endpoints:
f(-1) = 24 - 8(-1)^2 + 6 = 22
f(0) = 24 - 8(0)^2 + 6 = 30
f(3) = 24 - 8(3)^2 + 6 = -54

Step 3:
Compare the values:
f(-1) = 22
f(0) = 30
f(3) = -54

The absolute maximum value of f(x) on the closed interval (-1, 3) is 30, which occurs at x = 0.

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salary : $12 per hour

Let M be a nxn upper triangular matrix with nonzero diagonal entries. To prove that the columns of M are linearly independent, we will use proof by contradiction.

Suppose, to the contrary, that the columns of M are not linearly independent. This means that there exists a non-zero vector x = (x_1, x_2, ..., x_n) such that Mx = 0, where 0 is the zero vector.

Now, we can write Mx as the following product of a matrix and vector:
Mx = (m_11, m_21, m_31, ..., m_n1)x_1 + (m_12, m_22, m_32, ..., m_n2)x_2 + ... + (m_1n, m_2n, m_3n, ..., m_nn)x_n

Since M is an upper triangular matrix, the entries of M below the main diagonal are all equal to 0. Therefore, the above equation simplifies to:
Mx = (m_11, 0, 0, ..., 0)x_1 + (m_12, m_22, 0, ..., 0)x_2 + ... + (m_1n, m_2n, m_3n, ..., m_nn)x_n

Since Mx = 0, each term of the equation above must equal 0. But, since each diagonal entry of M is non-zero, this implies that each corresponding x_i must equal 0. Since this holds for all i, we conclude that x = 0, contradicting the initial assumption that x is non-zero. Therefore, we have proven that the columns of M are linearly independent.

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Answer:

Step-by-step explanation:

Sorry bro imma 6th grader i have no clue what any of that means

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the value of Jeans property tax.

Jean's new home are 4. 23% of the value of the home. For a home of $238500:

x = 4.23% of $238500 = 0.0423 * $238500 = $10088.55

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

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The result of the multiplication is 24,000.

Multiplication is simply repeated addition, and it is a crucial skill to master.

For the given multiplication;

= 10 x 20 x 30 x 40

This could be written in the terms of 10.

= 10 x 2 x 10 x 3 x 10 x 4 x 10

Simply count the 10 and put the same number of zero after 1 and multiply remaining.

= 2 x 3 x 4 x 10000

= 24 x 10,000

Now, put the same number of zero after the number 24.

= 240,000

Therefore, the given multiplication is solved using simple mental maths.

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The correct question is -

Explain how using basic facts can help you find 10 x 20 x 30 x 40 mentally.

To prove that the products r1·r2 and n1·n2 are quadratic residues modulo p, we need to show that they are perfect squares modulo an odd prime p.

1. Quadratic residues are integers that have a square root modulo p. Let's assume that r1 and r2 are quadratic residues modulo p. This means that there exist integers a1 and a2 such that r1 ≡ a1^2 (mod p) and r2 ≡ a2^2 (mod p).

2. Using the properties of congruence, we can rewrite the products as r1·r2 ≡ (a1^2)·(a2^2) (mod p). Simplifying, we get r1·r2 ≡ (a1·a2)^2 (mod p).

3. Since a1·a2 is an integer, (a1·a2)^2 is a perfect square. Therefore, r1·r2 is a quadratic residue modulo p.

4. Now let's consider n1 and n2, which are quadratic nonresidues modulo p. This means that there are no integers b1 and b2 such that n1 ≡ b1^2 (mod p) and n2 ≡ b2^2 (mod p).

5. Similar to the previous step, we can express the product as n1·n2 ≡ (b1^2)·(b2^2) (mod p). Simplifying, we have n1·n2 ≡ (b1·b2)^2 (mod p).

6. Since there are no integers b1 and b2 that make n1·n2 a perfect square, we can conclude that n1·n2 is not a quadratic residue modulo p.

In summary, the products r1·r2 and n1·n2 are quadratic residues modulo an odd prime p, while the product r1·n1 is not a quadratic residue modulo p.

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If Kayla as 110 nickels and 90 pennies in her change purse, then she has a total of $6.40. If she has xx nickels and yy pennies, then she has $(5xx + yy)/100 in dollars.

We shall convert the pennies and nickels into same unit before adding to get the expression for the number of coins in dollars Kayla will have in total.

A nickel = 5 cents so;

110 nickels = 110 × 5 cents

110 nickels = 550 cents

A penny = 1 cent, so

90 pennies = 90 cents

110 nickels + 90 pennies = 640 cents

110 nickels + 90 pennies = $ 640/100

110 nickels + 90 pennies = $6.40

A nickel = 5 cents so;

xx nickels = xx × 5 cents

A penny = 1 cent, so

yy pennies = yy cents

xx nickels + yy pennies = (5xx + yy) cents

xx nickels + yy pennies = $(5xx + yy)/100

Therefore, $6.40 is the total value in dollars for Kayla if she has 110 nickels and 90 pennies. And the expression $(5xx + yy)/100 represent the total value if she has xx nickels and yy pennies.

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As t increases the curve is changing according to the plot points given by the parametric equations.

Define parametric equations?

The coordinates of the points that make up a geometric object, such as a curve or surface, are frequently expressed using parametric equations; in this case, the equations are collectively referred to as a parametric representation or parameterization (alternatively spelled as parametrisation) of the object. It describes a collection of numbers that represent functions with one or more independent variables. The parameters used here are the independent variables. For the representation of the coordinates that make up geometric objects like curves and surfaces, parametric equations are used. Additionally, a curve that is not a function can be drawn using parametric equations.

The equations are

x=1-t²

y=2t-t²,-1≤t≤2

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To represent decimal values ranging from 0 to 12,500, we need 14 bits.

To determine the number of bits needed to represent decimal values ranging from 0 to 12,500, we need to find the smallest number of bits that can represent the largest value in this range, which is 12,500.

The binary representation of a decimal number requires log base 2 of the decimal number of bits. In this case, we can calculate log base 2 of 12,500 to find the minimum number of bits needed.

log2(12,500) ≈ 13.60

Since we can't have a fraction of a bit, we round up to the nearest whole number. Therefore, we need at least 14 bits to represent values ranging from 0 to 12,500.

Using 14 bits, we can represent decimal values from 0 to (2^14 - 1), which is 0 to 16,383. This range covers the values 0 to 12,500, fulfilling the requirement.

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Answer:

how many masks can she make from one yard of fabric?

If her fabric was on sale for $3.00 per yard, what is the fabric cost of one mask?

If her fabric is regularly priced at $9.00 per yard, what is the fabric cost of one mask?

a. The amount remaining in the account after x week  is 700 - 40x

b. Olivia can withdraw can withdraw money from her account money for  approx. 13 weeks.

Let x represent the number of weeks. Then the amount of withdrawal in this time is 40x

So, the amount remaining in the account after x weeks is 700 - 40x

Since he needs 150$ in the account for safety net, we must have

700 – 40x ≥ 150

So,

700 - 150 ≥ 40x

550 ≥ 40x

550/40 ≥ x

x ≤ 13.75

Hence, he can withdraw money for  approx. 13 weeks.

Withdrawal involves removing money from a bank account, savings plan, pension or trust. In some cases, conditions must be met for funds to be withdrawn without penalty, and an early withdrawal penalty usually occurs when a condition of the investment agreement is violated. Withdraw money from account: With this account you can withdraw a maximum of $500 per day. withdraw money/money/savings With the financial crisis, people had to withdraw their savings.

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Answer:  23-s ≥ 5

Step-by-step explanation:

I hope you will be happy

Answer: $15

Step-by-step explanation:

Given:

The equation is:

\(x^2+5x=2\)

To find:

The solution of the given equation by completing the square.

Solution:

We have,

\(x^2+5x=2\)

We need to add the square of half of the coefficient of x on both sides.

Adding \(\left(\dfrac{5}{2}\right)^2\) on both sides, we get

\(x^2+5x+\left(\dfrac{5}{2}\right)^2=2+\left(\dfrac{5}{2}\right)^2\)

\(\left(x+\dfrac{5}{2}\right)^2=2+\dfrac{25}{4}\)

\(\left(x+\dfrac{5}{2}\right)^2=\dfrac{8+25}{4}\)

\(\left(x+\dfrac{5}{2}\right)^2=\dfrac{33}{4}\)

Taking square root on both sides, we get

\(x+\dfrac{5}{2}=\pm \sqrt{\dfrac{33}{4}}\)

\(x=\pm \dfrac{\sqrt{33}}{2}-\dfrac{5}{2}\)

\(x=\dfrac{\pm \sqrt{33}-5}{2}\)

\(x=\dfrac{\sqrt{33}-5}{2}\) and \(x=\dfrac{-\sqrt{33}-5}{2}\)

Therefore, the solutions of the given equation are \(x=\dfrac{\sqrt{33}-5}{2}\) and \(x=\dfrac{-\sqrt{33}-5}{2}\).

Answer: d and e

Step-by-step explanation:

edge 2021 :)

y=3

Step-by-step explanation:

2x-y=1

if x=2 then

2(2)-y=1

4-y=1

y= 4-1

y=3.

Answer:

y = 3

Step-by-step explanation:

2x - y = 1 ← substitute x = 2 into the equation

2(2) - y = 1

4 - y = 1 ( subtract 4 from both sides )

- y = - 3 ( multiply both sides by - 1 )

y = 3

Answer:

The y-intercept moves 13 spaces lower

Step-by-step explanation:

Answer:

The y-intercept moves 13 spaces lower

Step-by-step explanation:

In linear equation,112.8 is the solution .

What is a linear equation example?

=  157.8 - ( 3² + 6) × 3

=  157.8 - ( 9 + 6) × 3

=  157.8 - 15 × 3

=  157.8 - 45

=  112.8

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Answer:

Second option

Step-by-step explanation:

Check the relationship between the x digits and compare with y digits. It must be the same all through

In the second option x =2y for all the digits

4:2, 7:3.5,8:4,10:5

The equation of an ellipse with center (h,k), horizontal axis of length 2a, and vertical axis of length 2b is given by (x-h)^2/a^2 + (y-k)^2/b^2 = 1.

Given that the center is at (2,2), we have h = 2 and k = 2. We know that one focus is at (10,2), which is 8 units to the right of the center, so a = 8. Using the distance formula, we can find that the distance between the center and the point (2,6) is 4 units, which is the value of b.

Finally, we can use the formula for the distance from the center to a focus (c) to find that c = 6.

Now we can plug in our values for h, k, a, b, and c into the equation for an ellipse to get (x-2)^2/64 + (y-2)^2/16 = 1. Simplifying this equation gives us the left side of the equation of the ellipse, which is (x-2)^2/64 + (y-2)^2/16.

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The next three letters in the sequence J F M A M J J A are S, O, N.

To find the next three letters in the sequence J F M A M J J A, we need to identify the pattern or rule that governs the sequence. In this case, the sequence follows the pattern of the first letter of each month in the year.

The sequence starts with 'J' for January, followed by 'F' for February, 'M' for March, 'A' for April, 'M' for May, 'J' for June, 'J' for July, and 'A' for August. The pattern repeats itself every 12 months.

Therefore, the next three letters in the sequence would be 'S' for September, 'O' for October, and 'N' for November.

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The next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.

The given sequence "J F M A M J J A" represents the first letters of the months in a year, starting from January (J) and ending with August (A). To find the next three letters in the sequence, we need to continue the pattern by considering the remaining months.

The next month after August is September, so the next letter in the sequence is "S". After September comes October, represented by the letter "O". Finally, the month following October is November, which can be represented by the letter "N".

Therefore, the next three letters in the sequence "J F M A M J J A" are "S O N", indicating the months of September, October, and November.

It is important to note that the given sequence follows the pattern of the months in the Gregorian calendar. However, different cultures and calendars may have different sequences or names for the months.

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Answer:

-1/2

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Domain is what x values are allowed in a function

The solution for the inequalities is x > - 1 OR x < -1.

The mathematical expression for inequality states that neither side is equal. In mathematics, inequality occurs when the relationship results in a non-equal comparison between two expressions or numbers. Any of the inequality symbols, such as greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).

Given  : 5x - 29 > -34 OR 2x + 31 < 29.

to solve the equations,

5x - 29 > -34 OR 2x + 31 < 29.

For 5x - 29 > -34

On adding both sides by 29.

5x > - 34 + 29 .

5x > -5

On dividing both sides by 5.

x > - 1 .

For 2x + 31 < 29.

On subtracting both sides by 31

2x < 29 -31

2x < - 2

On dividing both sides by 2.

x < -1

So , x > - 1 OR x < -1 .

Therefore, option A is correct.

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Answer:

x > 6

Step-by-step explanation:

Given

3(x + 4) - 5(x - 1) < 5 ← distribute and simplify left side

3x + 12 - 5x + 5 < 5

- 2x + 17 < 5 ( subtract 17 from both sides )

- 2x < - 12

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative value.

x > 6