Solve the system by the elimination method.
R - 9S = 2
3R - 3S = -10

A. {(-4, -8/3)}
B. {(-4, -3/2)}
C. {(-4, -2/3)}

Each installment will be approximately $15,280.55.

To calculate the equal six-monthly installment, we can use the formula for the present value of an annuity.

Principal amount (P) = $500,000

Interest rate (r) = 12% per annum = 12/100 = 0.12 (compounded monthly)

Number of periods (n) = 20 (since there are 20 equal six-monthly installments)

The formula for the present value of an annuity is:

\(P = A * (1 - (1 + r)^(-n)) / r\)

Where:

P = Principal amount

A = Equal installment amount

r = Interest rate per period

n = Number of periods

Substituting the given values into the formula, we have:

$500,000 = \(A * (1 - (1 + 0.12/12)^(-20)) / (0.12/12)\)

Simplifying the equation:

$500,000 = A * (1 - (1.01)^(-20)) / (0.01)

$500,000 = A * (1 - 0.6726) / 0.01

$500,000 = A * 0.3274 / 0.01

$500,000 = A * 32.74

Dividing both sides by 32.74:

A = $500,000 / 32.74

A ≈ $15,280.55

Therefore, each installment will be approximately $15,280.55.

Learn more about Principal amount here:

https://brainly.com/question/30163719

#SPJ11

To find the counterclockwise circulation of the vector field C around the triangle with vertices (0, 0), (1, 0), and (1, 4), we can break it down into three line integrals along each side of the triangle.

1. Line integral along the line segment from (0, 0) to (1, 0):

We parameterize this line segment as r(t) = (t, 0) for t ranging from 0 to 1.
The differential vector dr(t) = (dt, 0).

The circulation along this line segment can be calculated as:

C1 = ∫C F · dr = ∫[from 0 to 1] (xy dx + x²y³ dy) · (dt, 0) = ∫[from 0 to 1] (t * 0) dt = 0.

2. Line integral along the line segment from (1, 0) to (1, 4):

We parameterize this line segment as r(t) = (1, t) for t ranging from 0 to 4.

The differential vector dr(t) = (0, dt).

The circulation along this line segment can be calculated as:

C2 = ∫C F · dr = ∫[from 0 to 4] (xy dx + x²y³ dy) · (0, dt) = ∫[from 0 to 4] (0 + t⁴) dt = ∫[from 0 to 4] t⁴ dt = (1/5) * t⁵ [from 0 to 4] = (1/5) * (4⁵) = 102.4.

3. Line integral along the line segment from (1, 4) to (0, 0):

We parameterize this line segment as r(t) = (1 - t, 4 - 4t) for t ranging from 0 to 1.

The differential vector dr(t) = (-dt, -4dt).

The circulation along this line segment can be calculated as:

C3 = ∫C F · dr = ∫[from 0 to 1] (xy dx + x²y³ dy) · (-dt, -4dt) = ∫[from 0 to 1] (-t(1 - t) dt - (1 - t)²(4 - 4t)³ * 4dt) = ∫[from 0 to 1] (-t + t² - 4(1 - t)²(4 - 4t)³) dt.

To calculate C, we need to add up C1, C2, and C3:
C = C1 + C2 + C3 = 0 + 102.4 + ∫[from 0 to 1] (-t + t² - 4(1 - t)²(4 - 4t)³) dt.

To find the final value of C, we need to evaluate the remaining integral..

However, since the integrand involves higher powers and nested functions, it might not have a simple closed-form solution.

You can evaluate the integral using numerical methods or a computer algebra system for a more precise result.

To know more about counterclockwise circulation visit;

https://brainly.com/question/30173684

#SPJ11

The line integral of $C$ over the given triangle is $2 + \frac{16}{5} + \frac{64}{7}$.

The line integral of $C$ over the given triangle is equal to the integral of the function $Cxy\,dx + x^2y^3\,dy$ over the curve $C$, where $C$ represents the counterclockwise path around the triangle with vertices $(0, 0)$, $(1, 0)$, and $(1, 4)$.

To evaluate this line integral, we need to parametrize the curve $C$. Since $C$ is a triangle, we can split it into three line segments.

First, let's consider the line segment from $(0, 0)$ to $(1, 0)$. We can parametrize this segment as $x = t$ and $y = 0$, where $t$ ranges from 0 to 1.

Next, we have the line segment from $(1, 0)$ to $(1, 4)$. We can parametrize this segment as $x = 1$ and $y = 4t$, where $t$ ranges from 0 to 1.

Finally, we consider the line segment from $(1, 4)$ to $(0, 0)$. We can parametrize this segment as $x = 1 - t$ and $y = 4(1 - t)$, where $t$ ranges from 0 to 1.

Now, we can substitute these parametric equations into the line integral expression:

\[\int_{C} Cxy\,dx + x^2y^3\,dy = \int_{0}^{1} (t)(0)\,dt + (t^2)(0)^3(0)\,dt + \int_{0}^{1} (1)(4t)\,dt + (1^2)(4t)^3\,dt + \int_{0}^{1} (1 - t)(4(1 - t))\,dt + (1 - t)^2(4(1 - t))^3\,dt\]

Simplifying this expression, we get:

\[\int_{C} Cxy\,dx + x^2y^3\,dy = \int_{0}^{1} 4t\,dt + \int_{0}^{1} 64t^3\,dt + \int_{0}^{1} 4(1 - t)(1 - t)^2(4(1 - t))^3\,dt\]

Evaluating each integral, we find:

\[\int_{C} Cxy\,dx + x^2y^3\,dy = 2 + \frac{16}{5} + \frac{64}{7}\]

Learn more about line integral :

https://brainly.com/question/30763905

#SPJ11

Step-by-step explanation:

keep in mind that, to get the inverse expression of any relation, we start off by doing a quick switcheroo on the variables, and then solve for "y", so let's do so,

Answer:

\(y = \frac{\sqrt{x+4} }{3}, \ y = -\frac{\sqrt{x+4} }{3}\)

Step-by-step explanation:

To  find inverse we replace  and y first.

\(y = 9x^2 - 4 \ becomes \ x = 9y^2 -4\)

\(Then \ solve \ for \ y\\\\9y^2 = x+ 4\\\\y^2 = \frac{x+4}{9}\\\\y = \pm \sqrt{\frac{x+4}{9}} \\\\y = \pm {\frac{\sqrt{x+4}}{3}\)

297 mm is  nearest millimetre complete this statement .

The definition of convert units?

1 cm = 10mm

the length of a sheet of paper = 29.7 cm

the nearest millimetre = 29.7 * 10 = 297 mm

Learn more about convert units

brainly.com/question/11875738

#SPJ9

(11) The measure of angle IGJ is  46⁰.

(12) The measure of arc JH is determined as 138⁰.

The measure of the arc or central angle indicated is calculated as follows;

(11) The measure of angle IGJ is calculated as follows;

m∠LGK =  arc angle LK (interior angle of intersecting secants)

m∠LGK = 48⁰

m∠HGI = m∠LGK = 48⁰ (vertical opposite angles are equal)

m∠IGJ + m∠HGI + m∠JGK = 180⁰  (sum of angles in a straight line)

m∠IGJ + 48⁰ + 86⁰ = 180

m∠IGJ = 180 - 134

m∠IGJ = 46⁰

(12) The measure of arc JH is calculated as follows;

arc JH = arc JI + arc IH

arc JI = arc FG

arc FG = 180 - 137⁰ (sum of angle in a straight line)

arc FG = 43⁰

arc FG = arc JI (vertical opposite angles are equal)

arc JH = arc JI + arc IH

arc JH = 43⁰ + 95⁰

arc JH = 138⁰

Learn more about arc angles here: https://brainly.com/question/30543683

#SPJ1

Answer:

 0.0714

Step-by-step explanation:

The probability that the first is "working in nature" is 3/8.

The probability that the 2nd is "working in nature" is 2/7.

The probability that the 3rd is "not working in nature" is 5/6.

The probability that the 4th is "not working in nature" is 4/5.

Thus the probability that the first two of 4 opportunities are "working in nature" is ...

  (3·2·5·4)/(8·7·6·5) = 1/14 ≈ 0.0714

While there is a positive correlation between clouds and rain, this does not necessarily mean that one variable causes the other.

Correlation is a statistical measure that describes the strength and direction of a relationship between two variables.

The relationship "the more clouds there are, the more rain will fall" is a positive correlation. Positive correlation means that as one variable increases, the other variable also increases.

However, it's important to note that correlation does not imply causation. In this case, the relationship between clouds and rain is not necessarily causal. While it is true that more clouds can lead to more rain, there are also other factors that can influence rainfall, such as temperature, humidity, and wind patterns.

Additionally, it is possible that rain could cause more clouds to form, rather than the other way around.

Therefore, while there is a positive correlation between clouds and rain, this does not necessarily mean that one variable causes the other.

To know more about correlation visit:

https://brainly.com/question/13879362

#SPJ1

As per dr. Chidi Anagonye, self esteem and success on school project results in low distinctiveness.

The focus of attribution theory is on how people make sense of events and how this influences their perceptions and actions. Heider (1958) was the first to suggest a psychological theory of attribution, but Wener and his colleagues (e.g., Jones et al., 1972; Wener, 1974, 1986) created a theoretical framework that has grown to be a significant research paradigm in social psychology. Attribution theory assumes that people try to figure out why people do what they do, i.e., attribute causes to behavior. If someone is trying to figure out why someone else did something, they could assign one or many reasons to that action. An attribution is based on a three-stage process: (1) the person must notice or watch the activity, (2) the person must think that the behavior was done purposefully.

Education, legislation, clinical psychology, and the field of mental health have all seen extensive use of Wener's thesis. Achievement and one's self-concept are closely related. Causal attributions control how we feel about success and failure, according to Wener (1980). For example, one is unlikely to feel satisfaction in achievement or competence while obtaining a 'A' from a professor who only delivers that grade, or when defeating a tennis opponent who always loses... An 'A' from a teacher who gives few high grades, on the other hand, or a victory over a highly rated tennis player after a lot of practice has a big impact. Higher self-esteem students and students who perform well academically have a tendency to credit success to internal, stable, uncontrolled causes.

In order to learn more about the attribution theory, visit:

brainly.com/question/14544027

#SPJ4

Step-by-step explanation:

Given:

\(\pounds1=1.55 CHF\)

Multiply \(\pounds 145\) by 1.55 to represent 145 pounds in Swiss Frances currency.

\(145 \times 1.55 = 224.75\)

Compare:

\(193.75 < 224.75\)

The watch in Geneva is cheaper.

How Much?

Divide 193.75 CHF by 1.55

\(193.75 \div 1.55 = 125\)

Subtract:

145 - 125 = 20.

The watch is 20 Pounds cheaper.

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(4(y - 3) + 2(3x + 2y) = \)

\(4y - 12 + 6x + 4y = \)

\(6x + 4y + 4y - 12 = \)

\(6x + 8y - 12\)

If u wanna in factored form :

\(2(3x + 4y - 6)\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer:

The area will be "34 unit²".

Step-by-step explanation:

The diagram is missing throughout the given question. Below is the figure attached.

According to the question,

The side of squares will be:

=  \(\sqrt{(5)^2+(3)^2}\)

=  \(\sqrt{25+9}\)

=  \(\sqrt{34} \ units\)

Hence,

The area of square will be:

=  \((side)^2\)

=  \((\sqrt{34} )^2\)

=  \(34 \ unit^2\)

The nullity of the matrix A, where each element aᵢⱼ is equal to 3 times i minus j, can be determined as follows: (a) If n > 3, the nullity of A is 0. (b) If n = 3, the nullity of A is 1. (c) If n < 3, the nullity of A is n - 3.

To find the nullity of matrix A, we need to determine the dimension of its null space, which is the set of all vectors x such that Ax = 0. The matrix A has n rows and n columns, and each element aᵢⱼ is given by 3i - j. This implies that the row vectors of A are linearly independent, as each row has a distinct combination of 3i - j values. Therefore, the system of equations Ax = 0 will have only the trivial solution when the number of unknowns (n) is greater than the number of equations (n), i.e., n > 3. In this case, the nullity of A is 0, as there are no non-trivial solutions.

If n = 3, the system of equations Ax = 0 will have a non-trivial solution, indicating the presence of a free variable. Thus, the nullity of A is 1. If n < 3, the number of unknowns is less than the number of equations. In this case, the system of equations Ax = 0 will have n - 3 free variables, leading to non-trivial solutions. Hence, the nullity of A is n - 3. In summary, the nullity of matrix A depends on the value of n:

(a) If n > 3, the nullity of A is 0.

(b) If n = 3, the nullity of A is 1.

(c) If n < 3, the nullity of A is n - 3.

to know more about nullity, click: brainly.com/question/3149728

#SPJ11

Answer:

Step-by-step explanation:

1.  4x = angle 4

x = angle 1

Angle 1 + angle 4 = 180

4x + x = 180

5x = 180

2. 55 = angle 2

angle 1 = 68

angle 3 = 55 + 68 = 123 = 180 - 123 = 57

Angle 4 = 57

Hope this helped,

kavitha

To guarantee accuracy within 0.00002 for trapezoidal and midpoint rule approximations for ∫21 1x dx, we must take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

To guarantee that the trapezoidal and midpoint rule approximations for ∫21 1x dx are accurate to within 0.00002, we need to find the value of n that satisfies the following inequalities:

|ET| ≤ (b-a)³ / (12n²) * M₂ for the trapezoidal rule
|EM| ≤ (b-a)³ / (24n²) * M₂ for the midpoint rule

Where M₂ is the maximum value of the second derivative of the function f(x) = 1/x on the interval [1,2], b-a = 2-1 = 1, and ET and EM are the true errors for the trapezoidal and midpoint rules, respectively.

Taking the second derivative of f(x), we get f''(x) = 2/x³. The maximum value of this function on the interval [1,2] is M₂ = 2.

Plugging in the values of M₂, b-a, and the desired accuracy into the inequalities, we get:

|ET| ≤ (1)³ / (12n²) * 2 ≤ 0.00002
|EM| ≤ (1)³ / (24n²) * 2 ≤ 0.00002

Solving for n, we get:

n² ≥ (1)³ / (12 * 0.00002) * 2 = 8333.33 for the trapezoidal rule
n² ≥ (1)³ / (24 * 0.00002) * 2 = 4166.67 for the midpoint rule

Taking the square root of both sides, we get:

n ≥ 91.29 for the trapezoidal rule
n ≥ 64.55 for the midpoint rule

Therefore, to guarantee that the trapezoidal and midpoint rule approximations are accurate to within 0.00002, we should take n ≥ 92 for the trapezoidal rule and n ≥ 65 for the midpoint rule.

Learn more about trapezoidal and midpoint rule: https://brainly.com/question/17218343

#SPJ11

Answer: I believe the answer is M= -4

Step-by-step explanation:

Answer:

Please mark brainliest and I hope this helps :)

Step-by-step explanation:

1.5a^12b^6

2.xy^10

3.6x^144

4.9a^12b^4

5.4x^4

6.-9bc^2

23/111 is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade.

Probability theory deals with numerical evaluations of the likelihood that an event will occur.

Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.

A probability represents the likelihood or chance that a particular occurrence will take place. Probabilities can be expressed as ratios between 0 and 1, or as percentages between 0% and 100%.

March Madness Movies served 23 lemonades out of a total of 111 fountain drink last weekend.

The probability that the a fountain drink ordered is a lemonade will be :-

  P=  \(\frac{Number of lemonade}{Total fountain drink}\)

 = 23/111

Based on this data, the reasonable estimate of the probability that the next fountain drink ordered is a lemonade = 23/111.

To learn more about Probability, Visit:

https://brainly.com/question/30034780

#SPJ4

\(\\ \rm\rightarrowtail x^2-3x-10=0\)

\(\\ \rm\rightarrowtail x^2-5x+2x-10=0\)

\(\\ \rm\rightarrowtail x(x-5)+2(x-5)=0\)

\(\\ \rm\rightarrowtail (x+2)(x-5)=0\)

\(\\ \rm\rightarrowtail x=-2\;or\:5\)

Given,

\(\small\bold{x² – 3x – 10 =0}\)

Taking LHS,

\(\small\bold\red{ → }\small\bold{x^2 – 5x + 2x – 10}\)

\(\small\bold\red{ → }\small\bold{ x(x – 5) + 2(x – 5)}\)

\(\small\bold\red{ → }\small\bold{ (x – 5)(x + 2)}\)

The roots of this equation, x² – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore,\( \small\bold{x – 5 = 0 \: or \: x + 2 = 0}\)

\(\small\bold\red{ → }\small\bold{x = 5 \: or \: x = -2 }\)

Answer:

1/3

Step-by-step explanation:

The exponent -1 indicates that we need to take the reciprocal of the base 3.

So, 3^(-1) = 1/3

Therefore, the answer is 1/3.

Answer:

1/3

Step-by-step explanation:

Rewrite the expression using the negative exponent rule \(b^{-n}\) = \(\frac{1}{b^{n} }\)

The answer is 1/3

The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin⁡(5x)dx. We are given that y=cos(5x)=π/30y=cos⁡(5x)=π/30 and x=0.055x=0.055.

We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:

Δy≈dy≈dy=-5sin(5x)dx

Plugging in the values of y, x, and dxdx, we get:

Δy≈-5sin(5(0.055))(0.005)≈-0.00679

Therefore, the estimated change in yy using differentials is -0.00679.

To learn more about differential click here : brainly.com/question/31383100

#SPJ11

Answer:

x = 8

Step-by-step explanation:

180 - (88 + 50) = 42

5x + 2 = 42

     - 2     -2

  5x = 42

5x/5    42/5

   x = 8

(sorry I'm not great at typing out work)

Answer:

48

Step-by-step explanation:

2 hours gives you 4 inches so one hour give u 2 inches 24x2 =48

Answer:

B. obtuse triangle

Step-by-step explanation:

Obtuse triangles are triangles with one obtuse angle and two acute angles. Define obtuse angles as angles over 90 degrees and acute angles as angles less than 90 degrees.

In this triangle:

118 degrees - obtuse angle

19 degrees - acute angle

43 degrees - acute angle

Thus, this triangle is an obtuse triangle.

Answer:

3 and -4

Step-by-step explanation:

this is simple but difficult

let the number be x and second number be y

3x + 2y=1

x-y/2=5

from the 2nd equation

x-y/2=5

x=5+y/2

substitute value for x into equation 1

3x + 2y=1

3(5+y/2) + 2y= 1

15 +3y/2 +2y=1

15 + 7y/2=1

7y/2= 1 - 15

7y/2=-14

cross multiply

7y= -28

y= -28/7

y= -4

therefore second number is -4

substitute value for y into 1st equation

3x + 2y=1

3x + 2(-4) = 1

3x - 8= 1

3x= 1+8

3x= 9

x= 9/3

x= 3

therefore first number is 3

therefore two numbers are;

3 and -4

Answer:

1.48 meters

Step-by-step explanation:

let the sum of the heights of the girls and the boys be Y and x respectively

\( \frac{x}{14} = 1.56 \: \: \: \: \frac{x + y}{32} = 1.515 \: \\ x = 21.84 \: \: \: \: x + y = 48.48 \\ y = 48.48 - 21.84 = 26.64 \\ \: the \: number \: of \: girls \: in \: aclass \: is \: 32 - 14 = 18 \\ then \: the \: mean \: will \: be \: \\ \frac{26.64}{18} = 1.48\)

X=6 x+y=

Answer:

mean (average height) of the girls is 1.48 metres

Step-by-step explanation:

Number of boys × average height  = 14 × 1.56 = 21.84

All students × average height = 32 × 1.515= 48.48

Number of girls × average height = 18 x

32-14 boys = 18 girls

Total height of all = Total height of boys + Total height of girls

 48.48 = 21.84 + 18x

48.48 - 21.84 = 18x

   26.64 = 18x

  26.64 ÷ 18 = x

           1.48 = x the average height of the girls

The Least-squares problem that has minimal norm can be given using factorization.

The least squares method is used to find the best fit for a set of data points by minimizing the sum of the offsets from the plotted curve. Singular value decomposition (SVD) is a factorization of a real or complex matrix.

It is a widely used technique to decompose a matrix into several component matrices, exposing many of the useful and interesting properties of the original matrix. The singular value decomposition, guaranteed to exist, is A=UΣV.

When we have the equation system Ax=b, we calculate the SVD of A as A=UΣVT. The matrices U and VT have a very special property. They are unitary matrices. One of the main benefits of having unitary matrices like U and VT is that if we multiply one of these matrices by its transpose (or the other way around), the result equals the identity matrix.

The singular value decomposition (SVD) of matrix A is very useful in the context of least squares problems. It is also very helpful for analyzing the properties of a matrix.

To know more about the Least square method,

brainly.com/question/22513087

brainly.com/question/29560177

#SPJ4