express the distance between the given numbers using absolute value. then find the distance by evaluating the absolute value expression. 3 and 18

The matrix of the system is [tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

The complete question is added as an attachment

From the question, we have the following system of equations that can be used in our computation:

11x + 3y = 20

x - 2y = 5

Remove the variables

So, we have the following representation

x    y

11   3   20

1     -2   5

Next, we input the numbers in a matrix

This gives

[tex]\left[\begin{array}{cc}11&3\\1&-2\end{array}\right] \left[\begin{array}{c}20&5\end{array}\right][/tex]

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Z = x + yi times its conjugate x – yi is the square of its absolute value |z|²

A complex number z = x + yi times its conjugate x – yi is simply verified to be the square of its absolute value |z|². As a result, 1/z equals z divided by the square of its absolute value |z|². A complex number z is one that can be represented as x+iy, where x and y are real integers and I is an imaginary unit, i²=1. In this equation, x represents the complex number’s real portion and y represents its imaginary part.

The discriminant, b 2 4 a c, demonstrates the different forms of quadratic equation solutions. If the discriminant is equal to zero, the equation has one genuine solution.

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The chance that the third number is bigger than twice the first number is equal to the number of combinations where the first number is between 1 and 5 (inclusive) and the third number is between 2 * first number + 1 and 10 (inclusive).

Here's the calculation:

Therefore, the answer is:

= 21/1000

= 21/10^3

= 0.021

which is closest to choice B, so the answer is B.

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Yes, that's correct. The Pareto Chart also called bar charts, named after Vilfredo Pareto, is a graphical tool used in quality control and continuous improvement methodologies such as Six Sigma to help identify the most significant causes of problems.

In a Pareto Chart, the bars are arranged in descending order of height, with the most frequently occurring cause appearing first on the left. This allows you to quickly see which issues are the most pressing and require the most attention. By focusing on the most impactful causes, organizations can achieve the greatest improvement in their processes.

A bar chart gives a visual representation of the information.

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Answer:

10 gallons is still in the tank.

Step-by-step explanation:

We have to calculate 5/8 of 16.

(5/8)*16 = 10.

Answer:

[tex]r=14\mathring{}[/tex]

Step-by-step explanation:

[tex](5r-5)\mathring{}+(8r+3)\mathring{}=180\mathring{}\\5r-5+8r+3=180\mathring{}\\13r-2=180\mathring{}\\13r=180\mathring{}+2\\13r=182\mathring{}\\r=\frac{182}{13} \\\\r=14\mathring{}[/tex]

Answer:

B 49/3

Explanation:

I did the work, unlike your lazy ahh! :)

the amount that results from the given investment $500 invested at 12% compounded quarterly after a period of 3 years is:  $711.66. This can be solved using the concept of compound interest.

When calculating compound interest, the starting principle amount is multiplied by one together with the yearly interest rate raised to the number of compound periods minus one. The resultant value is then reduced by the whole initial loan amount. When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. Compound interest accelerates the growth of your money since it calculates interest on both your original principle and the interest that has accrued over time. The initial investments and the revenue generated by those investments increase simultaneously as a result of compounding, which can have a snowball effect.

Principal amount (P) = $500

interest rate (r) = 12%

time (t) = 3 years

period (n) = 3

Final amount = A

As we know, A = P ( 1 + r/n) ^{nt}

or, A = 500 (1 + 0.12 / 3)^{3*3}

or, A = $711.66

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The cost of each ranch chicken sandwich before tax is, $14.99

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

3 Coffee 5.85

1 Diet Bev. – lg. 3.38

1 Sparkling Water 2.50

3 Ranch Chicken Sandwich 44.97

1 Classic Burger 12.95

1 Thai Stir-fry Special 11.50

2 Club Sandwich 22.98

Subtotal 104.13

Tax (13%) 13.54

Total 117.67

The cost of each ranch chicken sandwich before tax.= ?

Total Amount = 44.97

⇒  For 1 ranch chicken sandwich = 44.97/3                                                             =  14.99

Therefore, the cost for 1 ranch chicken sandwich is $44.97/3

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Answer:

$20584

Step-by-step explanation:

using of proportion

if $20,750 = 2000

than ? = 1984

=1984/2000 × 20750

=4116,8000/2000

=$20584

Mean of the sampling distribution of sample means is 5.9 years.

A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.

Population mean, μ = 5.9 years

Population standard deviation, σ = 0.8 years

If the sample size is at least 30, we can use the normal approximation of sampling distribution of sample means.

Here, sample size for the sampling distribution, n = 68 > 30.

For a sample which is drawn from a normally distributed population, mean of the sampling distribution of sample means is equal to the population mean and standard deviation = σ / √n.

Mean of the sampling distribution of sample means = μ = 5.9 years.

Hence mean is same as the population mean.

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If Miss Shaw has some counters. If she gives her pupil 3 counters each, she will have 12 counters left.

a) The number of pupils that are there is 24.

b) The number of counters she have is 84.

a) Let's p represent the number of pupils

3p + 12 = number of counters

4p = number of counters + 24

We can substitute the first equation into the second:

4p = (3p + 12) + 24

4p = 3p + 36

p = 24 pupils

Counters:

3p + 12

= 3 * 24 + 12

= 84 counters

Therefore the number of pupils that are there is 24 and the number of counters she have is 84.

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Answer:

Step-by-step explanation:

To solve the equation x/75 = 25, you can multiply both sides by 75 to isolate x:

x/75 * 75 = 25 * 75

x = 1875

a) The probability that an employee does not know C/C++ = 0.4

(b) The probability that an employee knows either C/C++ or R = 0.8

(c) The probability that an employee knows R and does not know C/C++ =  0.2

(d) The probability that an employee knows at least one of the languages = 0.8

Let us assume that an event A:  employee knows C/C++ languages

here, 60% know C/C++

So, P(A) = 0.6

event B:  employee knows R

here, 50% know R

This means, P(B) = 0.5

30% know both languages

This means, P(A ∩ B) = 0.3

Also, 20% know neither language.

⇒  P(A ∪ B)c = 0.2

a.  the probability that an employee does not know C/C++ would be,

1 - P(A)

= 1 - 0.6

= 0.4

b. the probability that an employee knows either C/C++ or R

We know that the formula, P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.6 + 0.5 - 0.3

P(A∪B) = 0.8

c.  the probability that an employee knows R and does not know C/C++

P(B) - P(A∩B)

= 0.5 - 0.3

= 0.2

d.  the probability that an employee knows at least one of the languages

1 - P(A ∪ B)c

= 1 - 0.2

= 0.8

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Answer:To calculate the total interest paid on a mortgage, you can use the following formula:

Total Interest = (Interest Rate/12) * (Total Number of Payments) * (Loan Amount)

In this case, the loan amount is the total cost of the mortgage, which is not specified in the question. However, we know that the payments are made for 15 years or 15*12 = 180 months.

We can use the formula above to find the total interest:

Total Interest = (0.04/12) * (2000 * 180) = 53,333.33 dollars

So, you paid $53,333.33 in interest over the life of the mortgage.

Step-by-step explanation:

The value of m + n is 53.

Let's consider the first roll "a". The second, third, and fourth rolls will be represented as "b", "c", and "d".

The first roll of a can be any integer from 1 to 6.

For the second roll of b, there are 5 possible integers that are greater than or equal to the first roll "a".

For the third roll of c, there are 4 possible integers that are greater than or equal to the subsequent roll "b".

For the fourth roll of d, there are 3 possible integers that are greater than or equal to the third roll "c".

Thus, the total number of possible outcomes that meet the rules is 6 * 5 * 4 * 3 = 360.

The total number of possible outcomes for rolling a fair die multiple times is 6 * 6 * 6 * 6 = 1296.

This is how the probability of every one of the last three rolls being in some measure as extensive as the roll going before it is 360/1296, which can be improved to 5/18.

In this way, m + n = 5 + 18 = 23.

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If we randomly choose a point on which Federer served and get distracted before seeing his first serve but look up in time to see Federer win the point , then the probability that he missed his first serve given he won the point is (a) 0.3000

To calculate the probability that Federer missed his first serve given that he won the point, we Let , event A is = Federer missed his first serve and

event B is = Federer won the point.

So, probability of Federer missing his first serve = (100-63)% = 37% = 0.37,

probability of Federer winning point given he missed his first serve= 57%.

⇒the probability he first serve and misses point = (0.37)(0.57) = 0.2109  .

The probability of Federer winning the point, regardless of whether he made his first serve or not, can be calculated as

⇒ (0.63)(0.78) + (0.37)(0.57) = 0.7023  .

So , the probability of Federer missing his first serve given that he won the point is 0.2109/0.7023 = 0.300    .

The given question is incomplete , the complete question is

Tennis great Roger Federer made 63% of his first serves in a recent season. When Federer made his first serve, he won 78% of the points. When Federer missed his first serve and had to serve again, he won only 57% of the points. Suppose you randomly choose a point on which Federer served. You get distracted before seeing his first serve but look up in time to see Federer win the point.

What is the probability that he missed his first serve given he won the point?

(a) 0.3000

(b) 0.37

(c) 0.63

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As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

It is possible either multiply, distribute, add, or negate in mathematics. The trying to follow is how a expression is put together: Number, expression, and scientific operator The ingredients of a mathematical expression include numbers, variables, and operations (such as addition, subtraction, multiplication or division etc.) It is possible to combine expressions and phrases. An expressions, often known as an arithmetic operation, is any mathematical statement that contains variables, numerals, and a numerical operation between them. That instance, the word m there in given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as is the variable m in the phrase 4m + 5.

given

To address this issue, we just need to determine the total or difference that yields 2x2 + 2x + 2

Option A: ( x2 + 4x -2) + (x2 - 2x - 4) = 2x2 + 2x - 6

Option B: ( x2 + 4x - 2 ) + ( x2 + 2x + 4 ) = 2x2 + 6x + 2

Option C: ( x2 + 4x - 2) - ( -x2 + 2x - 4)= x2 + 4x - 2 + x2 - 2x + 4

= 2x2 + 2x + 2

As a result, choice C is the equation that best represents the algebraic tiles since we only need to determine the total or difference.

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The complete question is:-

Select the correct answer.

Which sum or difference is modeled by the algebra tiles?

A. (-x2 + 2x + 3) − (x2 − 2x − 1) = -2x2 + 2

B. (-x2 + 2x + 3) − (-x2 + 2x + 1) = -2x2 + 2

C. (-x2 + 2x + 3) + (-x2 + 2x + 1) = -2x2 + 2

D. (-x2 + 2x + 3) + (-x2 − 2x − 1) = -2x2 + 2

The statement states that the rectangular garden has the following measurements: length = -4 and width = -2.

Sums with terms of something like the form kxn, where k has been any variable & n is a real number, make up polynomials. For instance, the polynomial 3x+2x-5. a description of radicals. The concepts degrees, standard form, monomial, binomial, and trinomial are all covered in this video.

A rectangle's area is represented by the polynomial [tex]x2 + 6x + 8,[/tex] which may be solved in (x + a)(x + b), in which a and b are indeed the rectangle's length and breadth.

So,[tex]x^2 + 6x + 8 = (x + a)(x + b).[/tex]

Solving for a and b, we find that a = -4 and b = -2, so the dimensions of the rectangular garden are length = -4 and width = -2.

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The fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.

Finding the smallest common multiple between any two or more integers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple.

The given fractions are:

A:

5/8 and 2/3

Using the least common multiple take a common denominator:

Here LCM = (8)(3) =24

5/8 multiply the numerator and denominator by 3.

5/8 = 15/24

Similarly, 2/3 multiply the numerator and denominator by 8.

2/3 = 16/24

15/24 < 16/24

B: Using LCM:

1/6 and 2/9

6/36 and 8/26

6/36 < 8/36

C: 7/12 and 5/8

Using LCM:

14/24 < 20/24

Hence, the fractions are 15/24 < 16/24, 6/36 < 8/36, and 14/24 < 20/24. This can be found using LCM.

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Answer:

23cm

Step-by-step explanation:

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's characteristics. Commutative and associative properties of multiplication, respectively.

Multiplication's "Distributive Property"

Multiplication's identity property.

The Japanese technique of multiplication is only a graphic representation of the four stages. Two integers are multiplied by each of the four smaller products represented by each cluster of intersections.

6666652222 - 12

6666652210 * 2 / 78 = 175438216.05

6666652210 * 6 / 78 = 512819400.76

6666652210 * 8 /78 = 701752864.21

6666652210 * 9 / 78 = 789471972.23

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Answer:

x = 7/3

Step-by-step explanation:

Given equation,

→ 4x - 5 = -2x + 9

Now the value of x will be,

→ 4x - 5 = -2x + 9

→ 4x + 2x = 9 + 5

→ 6x = 14

→ x = 14/6

→ [ x = 7/3 ]

Hence, value of x is 7/3.

In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. Therefore, we can use the Pythagorean theorem to find the length of the legs of a right triangle given the length of the hypotenuse.

Pythagorean theorem: c^2 = a^2 + b^2

where c is the hypotenuse and a and b are the legs of the right triangle.

If the length of the longer leg is x, then the length of the other leg is 2x.

Using the Pythagorean theorem:

25^2 = x^2 + (2x)^2

625 = x^2 + 4x^2

625 = 5x^2

x = √(625/5) = √125 = 5

So, the length of the longer leg is 5 units.

Answer:

12

Step-by-step explanation:

[tex] ( {5}^{2} - {3}^{2} ) - (5 - 3) {}^{2} [/tex]

is 12

Answer:

x + 9

Step-by-step explanation:

Sum is addition

The J (Jenny) has $15 , C (Charlie) has $20 and A(Aldo) has $30 in their wallets with total sum of $65.

Since Jenny, Charlie and Aldo have a total of $65 in their wallets. This could be represented as

J + C + A = 65      (equation 1)

Jenny has $5 less than Charlie

J = C - 5         (equation 2)

Aldo has 2 times what Jenny has

A = 2 * J   (equation 3)

Now we can solve the above equations by substitution.

Rearranging Equation 2 as

C = J + 5

Now substituting the values of A and C in equation 1 from 2 and 3. So equation 1 would become

J + (J+5) + (2*J) = 65

Solving the above equation

J + J + 5 + 2J = 65

4J = 65-5

4J = 60

J = 60/4

J = 15

Now if we insert the value of J in equation 2 and 3 we will get C and A.

C = J + 5

C = 15 + 5

C= 20

And

A = 2*J

A= 2*15

A = 30

The J (Jenny) has $15 , C (Charlie) has $20 and A(Aldo) has $30 in their wallets with total sum of $65.

The complete question is,

Jenny, Charlie, and Aldo have a total of $65 in their wallets. Jenny has $5 less than Charlie. Aldo has 2 times what Jenny has. How much do they each have in their wallets?

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[tex](1.7\times 10^{4})(8.5\times 10^{-2})\implies (1.7\times 8.5)(10^4\times 10^{-2}) \implies (1.7\times 8.5)(10^{4-2}) \\\\\\ (1.7\times 8.5)(10^2)\implies (14.45)(10^2)\implies 14.45\times 100\implies 1445[/tex]

the daily balance equals the previous day's balance plus new purchases minus the payments and credits

New purchases included indicates that at the conclusion of each day, the firm adds any new purchases to the balance. In other words, the daily balance is equal to the previous day’s amount plus any new purchases less any payments or credits. Credit card issuers will also impose a late fee if payment is not received by the due date.

The daily balance approach calculates your finance fee based on your actual amount on each day of your billing cycle rather than an average of your balance throughout the course of the billing cycle. Finance costs are computed by adding each day’s amount and multiplying it by the daily rate, which is 1/365th of your APR.

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