Debt payments of $2,100 and $1,950 are due in six months and nine months, respectively. What single payment is required to settle both debts in one month? Assume a simple interest rate of 6.30% p.a. and use one month from now as the focal date.

Answer:

= 53/42

Step-by-step explanation:

10/12 is equivalent to: 70/84

3/7 is equivalnt to: 36/84

Then:

10/12 + 3/7 = 70/84 + 36/84

= (70 + 36) / 84

= 106 / 84

= 53 / 42

The solutions that match the given differential equation are a)y=0 and b)y=2x.

The differential equation is a homogeneous linear differential equation with constant coefficients, which can be written in the form of y" + p(x)y' + q(x)y = 0. The general solution to this type of equation is y = c1e^(rx) + c2e^(rx) where r is the root of the characteristic equation r^2 + p(x)r + q(x) = 0.

In this case, the equation is of the form xy'' - y' = 0. By dividing both sides by x, we get y'' - (1/x)y' = 0, which is a homogeneous linear differential equation with constant coefficients. The characteristic equation is r^2 - (1/x)r = 0. The roots of this equation are r1 = 0 and r2 = 1/x.

Therefore, the general solution to this differential equation is y = c1 + c2x.

y=0 is a solution of the differential equation since it satisfies the equation when plugged in.

y=2x is also a solution of the differential equation since it also satisfies the equation when plugged in.

y=2x^2 and y=2 are not solutions of the differential equation because when plugged into the equation they don't satisfy it.

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Translations between points B and B' and points S and S' are result of using translation vector T(x, y) = (- 3, - 1).

In this problem we find the case of two points being translated by rigid transformation formula. Translations are defined by following equations:

P'(x, y) = P(x, y) + T(x, y)

Where:

First, derive translation vector from translation formula:

T(x, y) = B'(x, y) - B(x, y)

T(x, y) = (- 9, - 2) - (- 6, - 1)

T(x, y) = (- 3, - 1)

Second, check that point S' is the image of point S:

S'(x, y) = S(x, y) + T(x, y)

S'(x, y) = (5, 1) + (- 3, - 1)

S'(x, y) = (2, 0)

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A power function is a type of function with a variable in the form of an exponent. An exponential function is a type of function that contains a variable in the form of an exponent.

The most common example of this is y = xn, where n is the exponent and x is the independent variable. For example, y = (π)x is a power function with an exponent of x and an independent variable of π.

Exponential Function: An exponential function is a type of function that contains a variable in the form of an exponent. The most common example of this is y = bx, where b is the base and x is the independent variable. For example, y = xy is an exponential function with a base of x and an independent variable of y.

Polynomial: A polynomial is a type of function that has a degree, which is the highest exponent of its variables. For example, y = x2 (2-x3) is a polynomial with a degree of 2 since the highest exponent of its variables is 2.

Trigonometric: A trigonometric function is a type of function that involves trigonometric ratios. The most common example of this is y = tan t â cos t, which uses the trigonometric ratios of tangent and cosine.

Algebraic Function: An algebraic function is a type of function that can be expressed as a combination of polynomials. The most common example of this is y = s / 1+s, which is a combination of polynomials with a numerator of s and a denominator of 1+s.

Root Function: A root function is a type of function that involves a root of a polynomial. The most common example of this is y = sqrt(x3 â 1) / 1+ 3sqrt(x), which uses the root of the polynomial x3 â 1 in the numerator and 3sqrt(x) in the denominator.

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The linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

What is proportional relationship?

Relationships between two variables where their ratios are equal are known as proportional relationships. The fact that one variable is always a constant value multiplied by the other in a proportionate connection is another way to conceive of them. This parameter is referred to as the "constant of proportionality".

We are given points as (2,14.5), (4,29), (6,43.5) and the origin (0,0).

We know that in a proportional relationship the ratios are equal i.e.

[tex]\frac{y_{1} }{x_{1}} = \frac{y_{2} }{x_{2} } = \frac{y_{n} }{x_{n} }[/tex]

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

Since, the ratios are same, therefore the linear relationship is a proportional relationship.

The graph of the given situation has been plotted and it can be seen that the graph passes through the origin i.e. (0,0)

Hence, the linear relationship is a proportional relationship because the ratios between each pair of values are equivalent and the graph passes through the point (0,0).

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Answer:

3/4 > 4/7

Step-by-step explanation:

1. Find the LCM of 4 and 7, which is 28

2. Take 3/4 and multiply the numerator and the denominator by 7 (because 7x4=28)

You will end up with 21/28

3. Take 4/7 and multiply the numerator and the denominator by 4 (because 4x7=28)

You will end up with 16/28

Now that the denominators are the same,  the fraction with the bigger numerator is the greater fraction. Therefore, 3/4 is the greater than 4/7.

The expression to represent how much Jamie spends in all. we may state,0.40x + 0.40y is 8, 0.30x + 0.30y is 6

Set variables to represent the amounts we wish to identify.

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From the given table the greatest frequency is 40,

midpoint of greatest frequency =$2100.

Relative frequency is also referred to as the empirical probability, which is calculated by the division of each frequency by the total number of frequency in the sample.

We can answer the question creating the following table:

Class            Frequency       Rel. Frequency

$600-$800             3                  3/120=0.025

$800-$1000            7                  7/120=0.059

$1000-$1200          11                  11/120=0.092

$1200-$1400          22                22/120=0.183

$1400-$1600          40                40/120=0.333

$1600-$1800          24                24/120=0.2

$1800-$2000         9                  9/120=0.075

$2000-$2200        4                  4/120=0.033

Total                       120                      1

From the above table the greatest frequency is 40,

midpoint of greatest frequency =$2100.

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The public increased the amount of currency it held and that banks increased the reserve-deposit ratio is $0.66 million.

Now, According to the question:

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

We know that:

Bank deposits = (Bank reserves)/(Desired reserve-deposit ratio).

The Fed injected $0.30 billion (the public held $0.23 billion as currency and reserves increased by $0.07 billion was held as reserves). However, the money supply still fell by $3.3 billion.

It would have taken an additional 0.109 × $3.3 billion = $0.36 billion in reserves to support $3.3 in additional deposits.

So the answer is $0.30 billion + $0.36 billion = $0.66 billion.

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The given question is incomplete, complete question is :

Based on the information in the table, what quantity of reserves would the Federal Reserve have had to inject into the economy in 1932 to prevent the money supply from falling, given that the public increased the amount of currency it held and that banks increased the reserve-deposit ratio?

December 1921

-Currency held by public: $4.59

-Reserve Deposit ratio: 0.095

-Bank reserves: $3.11

-Money supply: $37.3

December 1932

-Currency held by public: $4.82

-Reserve Deposit ratio: 0.109

-Bank reserves: $3.18

-Money supply: $34.0

The two equivalent expressions to the given one are the ones in options C and E.

C (100y + 32) - (200y + 16)

E -(-100y + 16 + 200y - 32)

We want to see which expressions are equivalent to:

-4*(-25y + 4 + 50y - 8)

Let's distribute that product so we will get:

-4*(-25)*y - 4*4 - 4*50y - 4*-8

100y - 16 - 200y + 32 = -(-100y + 16 + 200y - 32)

Then option E is a correct option

And also is C: (100y + 32) - (200y + 16)

If we keep simplifying this we wil get:

100y - 16 - 200y + 32 = -100y + 16

And here we end.

The only two equivalent expressions are E and C.

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Answer:this is so ez

Step-by-step explanation: 2/5

The sample used in the study is b) the 4200 Florida residents surveyed. surveyed. To obtain the answer following steps are :
1. Read the question and identify the key words: sample, Florida residents, 4200
2. Consider the given options and eliminate those that don't match
3. Based on the given information and the options, the answer is b) the 4200 Florida residents surveyed.

This is because the sample used in the study was the 4200 Florida residents who were surveyed, and this sample was used to estimate the proportion of all Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters.

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Expressed the answers to the given operations with the proper number of significant figures:

(a) (1.600 × 10-¹)(2.1 × 10³) = 336

(b) (1.33)³ = 2.352637

(c) 1.93.x 2.651 = 5.11643

(d) 4.4/2.200 = 2

In calculation, single integers called integers are used to represent values. To represent all fine values, the figures 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are employed in colorful combinations and reiterations.

A number is a symbol that can be used to represent any of the ten integers ranging from 0 to 9. an illustration of a two- number.

When a number has two integers, it's called a 2- number . 2- number figures have two integers and range from 10 to 99.

They're unfit to begin with zero since it'll also be regarded as a single- number .

Any number between 1 and 9 can be used as the number in the knockouts place. For case, the figures 45, 78, and 12 have two integers.

a) (1.600 × 10-¹)(2.1 × 10³)

= 1.6 × 2.1 × 10⁻¹⁺³

= 3.36 × 10²

= 336

b) (1.33)³

= 2.352637

c) 1.93 × 2.651

= 5.11643

d) 4.4/2.200

= 2.0

= 2

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Elementary row operations are always applied to an augmented matrix after the solution has been found. So the option D is correct.

Elementary row operations:

1. It is possible to convert a system of linear equations into an equivalent system, or into a new system of equations that has the same solutions as the original system, using these straightforward techniques.

2. In order to convert a matrix to row echelon form, Gaussian elimination is used.

3. Simple row operations on an augmented matrix never alter the underlying linear system's solution set.

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The best name for this shape is rectangle. There are two sets of parallel sides and two pairs of equal opposite sides in every rectangle.

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The measure of an exterior angle of the regular polygon shown in the figure is 60°.

The angle between a side of a polygon and an extended adjacent side is called its exterior angle.

Given is a polygon, since, it has six vertices, so we can say it is a regular hexagon,

We know that, the sum of interior angles of regular hexagon is 720°

Therefore, one interior angle = 720 / 6 = 120°

If we extend a side of the hexagon, (refer to figure attached in solution)

Then, the interior angle and an exterior angle "A" will make a linear pair,

Therefore,

120° + A = 180°

A = 60°

Hence, the measure of an exterior angle of the regular polygon shown in the figure is 60°.

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At that level of output and price, profit is maximized when marginal revenue and the marginal cost of production are equal:

MR = *TR/*Q

MC = *C/*Q

Eq.  = MR = MC

where, MR = Marginal Revenue

MC = Marginal Cost

* = Change in

TR = Total Revenue

Q = Quantity

C = Cost

The marginal revenue rule states that by selecting the amount at which marginal revenue equals marginal cost, we can maximize the net benefit of any action. The activity's net benefit is maximum at this amount.

The corporation eventually reaches the point at which manufacturing any more units will raise the cost of production per unit, which is known as its optimum production level.

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By solving a subtraction, we can write the difference between the lengths as:

|x + 7|

Here we want to find the difference between the two lenghts below:

L₁ = (7x + 2)

L₂ = (6x - 5)

The difference between these can be written as the absolute value of the subtraction, then we will get:

| L₁ - L₂|

We use the absolute value because we don't know which one is the larger value.

Replacing the expressions we will get:

| (7x + 2) - (6x - 5)|

|7x + 2 - 6x + 5|

| x + 7|

That is the difference.

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Vector v and w have lengths of 11 and contain elements of 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2 respectively. The addition, multiplication, and sorting of both vectors were calculated, as well as the means, maximums, and minimums.

a) The lengths of the vectors v and w are both 11.

b) Vector v contains the elements 21, 10, 32, 2, -3, 4, 5, 6, 7, 4, -22 and vector w contains the elements -18, 72, 11, -9, 10, 2, 34, -5, 18, 9, 2.

c) Elements 3 through 7 of vector v are 2, -3, 4, 5, 6 and elements 3 through 7 of vector w are 10, 2, 34, -5, 18.

d) The sum of the elements in vector v is 60 and the sum of the elements in vector w is 91.

e) The mean of vector v is 5.454545454545455 and the mean of vector w is 8.272727272727273.

f) Vector v is sorted in descending order as 32, 21, 10, 7, 6, 5, 4, 4, 2, -3, -22 and vector w is sorted in descending order as 72, 34, 18, 11, 10, 9, 2, 2, -9, -5.

g) The addition of vectors v and w is 53, 82, 28, 2, 7, 13, 6, 8, -7, 4, -20.

h) The multiplication of vectors v and w is -378, 720, 352, -18.

i) Elements in vector v that are greater than zero are 21, 10, 32, 2, 4, 5, 6, 7, 4.

j) Elements in vector w that are less than zero are -18, -9, -5.

k) Vector v multiplied by 6 is 126, 60, 192, 12, -18, 24, 30, 36, 42, 24, -132.

l) The maximum of vector v is 32 and the minimum of vector v is -22. The maximum of vector w is 72 and the minimum of vector w is -9.

m) In vector v, all negative values are replaced with the average of all numbers in the vector, which is 5.454545454545455. In vector w, all negative values are replaced with the average of all numbers in the vector, which is 8.272727272727273.

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The average speed throughout the given time was [1,2] = -2.00 cm/sii. -0.26 cm/siii for [1,1.1]. [1.1,1.01] = 0.17 cm/siv. [1.1,1.001] = 0.02 cm/s

The particle's displacement divided by the passage of time represents its average velocity at each time interval. The displacement of the particle for the above motion equation is given by s = 2 sint + 4 cost. By subtracting the displacement at the beginning and end of the period and dividing it by the change in time, we can determine the average velocity for each time period. As an illustration, the displacement for the time period [1,2] is 2 sin + 4 cos at the beginning of the period and 2 sin + 4 cos at the end of the period. These two figures differ by -4, and one second has passed between them.

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I think you want to know what written out means? If yes it means when someone writes something down on a book or paper.

The value of N would be N = q/(9 + 4uz).

What is algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

Given:

q - 4Nuz = 9N

To find the value of N, we can use algebraic manipulation.

9N + 4Nuz = q

N(9 + 4uz) = q

N = q/(9 + 4uz)

Hence, the value of N would be N = q/(9 + 4uz).

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Answer:

Step-by-step explanation:

[tex]-63y^2+27y[/tex]

[tex]-63yy+27y[/tex]

[tex]-9\cdot \:7yy+9\cdot \:3y[/tex]

[tex]9y\left(-7y+3\right)[/tex]

The value of the variable x = π³ - π/π

Algebraic expressions are described as mathematical expressions that are comprised of variables, factors, constants, terms and coefficients.

These algebraic expressions are also comprised of arithmetic operations, such as;

From the information, we have that;

y = π³

y = πx + π

Substitute the values, we get;

π³ =  πx + π

collect like terms

π³ - π = πx

Divide both sides by the coefficient of x

x = π³ - π/π

Thus, the value is x = π³ - π/π

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There were 0-5 Listeners when the song was released.

The approximate number of listeners who had heard the song after the hour 5 was 15- below 50

The number of listeners was about 29,458 after hour 5842.62/

Alternative forms

Y= 4,637(1.26)ˣ

292131/50,5842,31/50,5.84262 =10³

5842.62

Including polynomial components, such as squared or cubed predictors, is the most popular technique to fit curves to data using linear regression. Typically, the model order is determined by the number of bends required in your line. Each exponent increment causes one additional bend in the curved fitting line.

Curve of Best Fit: a scatter plot curve that best approximates the trend. If the data looks to be quadratic, we use quadratic regression to get the equation for the best-fit curve. We do a cubic regression if it looks to be cubic.

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The required point that divides the line into 5:1 is given by (-5,0)

Let M(x, y) be the point which divides line segment PQ internally in the ratio m : n. PA, MN and QR are drawn perpendicular to x- axis. PS and MB are drawn parallel to x – axis. This is known as section formula.

Given here: A line segment with end points  (−10,−10) to ( − 4 , 2 )

Now the coordinates of the point that divides a line in the ratio m:n is given by

x= mx₂+nx₁ /m+n

y=my₂+ny₁/m+n

Thus the co-ordinates are x=5×-4+1×-10 / 5+1

                                             =-30/6

                                             = -5

And y= 5×2+1×-10 / 6

         =0

Hence, The required point that divides the line into 5:1 is given by (-5,0)

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When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

Division is the process of splitting a number or an amount into equal parts.

Given is an expression, 3x³+x-200 which is divided by x-4,

Therefore,

(3x³+x-200) / (x-4)

Divide the leading term of the dividend by the leading term of the divisor:

3x³/x = 3x²

Multiply it by the divisor: 3x²(x−4)=3x³−12x²

Subtract the dividend from the obtained result:

(3x³+x−200)−(3x³−12x2) = 12x²+x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 12x²/x = 12x

Multiply it by the divisor: 12x(x−4) = 12x²−48x

Subtract the remainder from the obtained result:

(12x²+x−200)−(12x²−48x) = 49x−200

Divide the leading term of the obtained remainder by the leading term of the divisor: 49x / x = 49

Multiply it by the divisor: 49(x−4) = 49x−196

Subtract the remainder from the obtained result:

(49x−200)−(49x−196) = −4

Hence, When will divide (3x³+x-200) by (x-4) will get 3x²+12x+49 and -4 as remainder.

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The probability of a person that has the disease and indication of the test also shows the presence of the disease is given by 0.92.

Let us consider 'A' represents the test indicate the presence of disease when it was actually present

A = 96%

  = 0.96

And 'B' represents the population percent actually has the disease

B = 2%

  = 0.02

A' represents the population who represents the disease when actually disease is not present.

A' = 0.08

Probability of a person that has the disease when test also indicates its presence is given by :

P ( A/ B) = P( A∩B) / [ P(A∩B) + P(A'∩B) ]

             = ( 0.02 × 0.96 ) / [ ( 0.02 × 0.96 ) + ( 0.02 × 0.08 ) ]

             = 0.0192 / 0.0208

             = 0.92

Therefore, the required probability of a person having disease when test also indicates it is equal to 0.92.

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Answer:

656 cm sq

Step-by-step explanation:

2 x 10 x 2 x 10 = 400

8 x 2 x 8 x 2 =256

256+400 = 656