How much must be deposited today into the following account in order to have $50,000 in 7 years for a down payment on a house? Assume no additional deposits
are made.
An account with quarterly compounding and an APR of 5.9%

The constant of proportionality between the total cost and the number of songs is 0.72.

The constant of proportionality is the ratio that supplies the variable cost per unit of each song.

Other names for the constant of proportionality include:

Determining the constant of proportionality can help us formulate the total cost equation as y = 0.72x.

Number of Songs    Total Cost    Unit Cost

          13                     $9.36         $0.72 ($9.36/13)

          17                     $12.24        $0.72 ($12.24/17)

         19                     $13.68         $0.72 ($13.68/19)

Check:

y = 0.72x

y = 0.72(13)

y = $9.36

Thus, the constant of proportionality is 0.72, showing that a downloaded song costs $0.72 each.

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Answer:

Real, Irrational

Step-by-step explanation:

5sqrt2 is NOT:

Natural (1,2,3...)

Whole (0,1,2,3...)

Integer (...-3,-2,-1,0,1,2,3...)

Rational (can be written like a ratio)

Imaginary (have the number i in it.)

It IS Irrational, will have neverending decimal with no repeating pattern.

5sqrt2 = 7.0710678119...

It IS REAL and IRRATIONAL.

By using normal distribution of probability, it can be inferred that

For [tex]x_1 = 325[/tex], z = -1.5

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex], z = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by-

[tex]f(x) = \frac{1}{\sigma \sqrt{2\pi}}}e^{-\frac{z^2}{2}[/tex]

where  [tex]z = \frac{x - \mu}{\sigma}[/tex], [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

For [tex]x_1 = 325[/tex]

[tex]z = \frac{325 - 496}{114} = -1.5[/tex]

This means  325 is 1.5 standard deviation below the mean.

For [tex]x_2 = 366.21[/tex]

[tex]z = \frac{366.21 - 496}{114}[/tex] = -1.1385

This means 366.21 is 1.1385 standard deviation below the mean.

[tex]x_1 = 325[/tex] is 1.5 standard deviation below the mean.

[tex]x_2 = 366.21[/tex] is 1.1385 standard deviation below the mean.

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Answer:

I = (2350)(0.0277)(6)

Step-by-step explanation:

We're told the principal, rate, and time so we just plug in.

We must convert the 2.77% to a decimal by moving the period two places to the left to get the rate 0.0277

By using the concept of growth, it can be calculated that

Value of coin in 8 years is $3.52

[tex]3(\frac{51}{50})^x[/tex] is the required exponential function

Domain of the function is all positive real number

Range is [tex](0, \infty)[/tex]

y- intercept is 3

This means initial value of the coin is $3

What is growth?

Growth is the exponential increase in the value of the product at a certain rate over a certain period of time

Here, concept of growth has been used

Present value of the coin = $3

Rate = 2%

Time = 8 years

Future value =

[tex]3(1 + \frac{2}{100})^8\\\\3(1 + \frac{1}{50})^8 \\\\3(\frac{51}{50})^8[/tex]

= $3.52

If the time is x years, the given exponential function is

y =

[tex]3(1 + \frac{1}{50})^x\\\\3(\frac{51}{50})^x[/tex]

This is the required exponential function.

Since x represents time here, then x has to be positive

Domain of the function is all positive real number

Now

As  [tex]x\rightarrow \infty[/tex], [tex]f(x) \rightarrow \infty[/tex]

As  [tex]x\rightarrow -\infty[/tex], [tex]f(x) \rightarrow 0[/tex]

Range is [tex](0, \infty)[/tex]

For y- intercept, x = 0

Putting x = 0, we get y = 3

y- intercept is 3

This means initial value of the coin is $3

The graph of the function has been attached here

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Answer:

Here,

Let the age of Adam be x

and ,Brian be y

so,x=y+20.........eqn 1

and ,2(y+2)=x

or,2y+4=x......eqn 2

Now ,

subtracting eqn1 and eqn 2

so, x=y+20

x=2y+4

- - -

______________

0 = -y+16

so,y=16 and x=y+20 =16+20=36 .

so Adam is 36 years old and brian is 16.

The number of cupcakes sold will be 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.

The number of cupcakes sold will be,

N = (1/3) + (3/8) +[(2-1/3-3/8)]+3

N = (1/3)+(3/8) + (7/24)

N = 96 / 24

N = 4

Therefore, the number of cupcakes sold will be 4.

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Answer:_______________________________

1) y = 3x+2, where slope is 3 and point is(3, -5).

2) y+6 = 4(x-5) is the equation for the given slope and point.

                      y = mx + b

                       Slope = m = tan θ = (y2 - y1)/(x2 - x1)

1) y + 5 = 3(x-1)x-x

Compare this equation to y - y₁ = m(x - x₁)

y = 3x - 3 + 5

y = 3x + 2

2) Given:

Slope = 4; point (5, -6)

y - y₁ = m(x - x₁)

y + 6 = 4(x -5 )

Option A

Hence, i) y = 3x+2, where slope is 3 and point is(3, -5) and ii) y+6 = 4(x-5) is the equation for the given slope and point.

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His tuition was increased by 10.34%

A quantity or ratio stated as a fraction of 100 is known as a % in mathematics (from the Latin per centum, "by a hundred").

The Latin word per centum, which means "hundred" or "by the hundred," is the source of the word "percent." The Italian phrase per cento, which means "for a hundred," gradually shrank to become the symbol for "percent," which is now used globally. It finally vanished totally. The word "per" was frequently shortened to "p." Two circles and a horizontal line made up the "cento," which is how the contemporary "%" symbol is now represented.

Given, Larry's tuition for last semester was $5510

% increase= (6080-5510)/5510

=0.10344

=0.10344*100

=10.34%

His tuition was increased by 10.34%

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Answer:

4

Step-by-step explanation:

5-3m>-10

-5.     -5

-3m>-15

/-3.   /-3

m<5

so 4 is the highest integer since 4 is less than 5

Hopes this helps please mark brainliest

By doing addition and subtraction of integers, the result obtained is

Mohammed had $5290 at the end of the month

What is addition and subtraction of integers?

At first it is important to know about integers

Integers are those numbers which has no fractional part. Integer can be positive, negative and zero is also an integer.

Suppose there are many integers, and we need to find the sum total of all those integers, then the operation used in this case is called addition.

To find how big or small one integer is from the other, then the operation used is called subtraction of integers.

Here we will use addition and subtraction of integers

Bank balance of Mohammed = $8376

Amount of money taken out by Mohammed next month to buy a car = $4595

Amount of money needed to buy new tires for his car = $1200

Amount of salary received by Mohammed next day = $2709

Amount of money Mohammed had at the end of the month =

$(8376 - 4595 - 1200 + 2709)

= $5290

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Answer:

12 ft, 13 ft , 17 ft

Step-by-step explanation:

let x be the length of the second side , then

one side is x + 1

third side is x + 5

the perimeter P is the sum of the 3 sides, then

P = x + x + 1 + x + 5 ← collect like terms

P = 3x + 6

given P = 42 , then equating gives

3x + 6 = 42 ( subtract 6 from both sides )

3x = 36 ( divide both sides by 3 )

x = 12

x + 1 = 12 + 1 = 13

x + 5 = 12 + 5 = 17

the 3 sides are 12 ft, 13 ft , 17 ft

Answer:

Step-by-step explanation:

Here by using the ascending property:

-75, -28, -3, 13, 103, 341, 619

The artist will take 5 hours to decorate 25 clay pots.

Given,

Number of pots to be decorated in 3 hours =40

Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]

So, the artist took 3 hours to decorate 15 pots instead of 40 pots.

It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]

So, to decorate 25 pots he need time,

[tex]time=\frac{1}{5}*25= 5 hours[/tex]

Thus, the artist need 5 hours to decorate 25 clay pots.

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Answer:

---------------------------

Answer:

Step-by-step explanation:

1) v + 8w = 4v, for v?

→ v + 8w = 4v

→ 8w = 4v - v

→ 8w = 3v

→ [ v = (8w)/3 ]

Thus, value is (8w)/3.

2) -m + 5n = -2, for n?

→ -m + 5n = -2

→ 5n = -2 + m

→ 5n = m - 2

→ [ n = (m - 2)/5 ]

Thus, value is (m - 2)/5.

A solution to this inequality |y + 4| < 1 in as an interval is: A. −5 < y < –3.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Adding -1 to both sides of the inequality, we have:

|y + 4| + (-1) < 1 + (-1)

|y + 4| - 1 < 0

Evaluating the absolute value function, we have the following:

y + 4 < ±1

For the positive interval, we have:

y < -4 + 1

y < -3

For the negative interval, we have:

y < -4 - 1

y < -5

Finally, we would express the solution to this inequality as an interval as follows:

-5 < y < -3.

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Complete Question:

What is a solution to this inequality |y + 4| < 1?

A. −5 < y < –3

B. –3 < y < 5

C. –4 < y < 1

D. 1 < y < 4

The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:

                                          FIFO          LIFO

Ending inventory          $10,250     $12,800

Cost of goods sold       $17,000     $14,450

FIFO, which means First-in, First-out, computes the cost of goods sold based on the assumption that the physical flow of goods sold depends on the earlier inventory in stock.

FIFO can be applied under both the perpetual and periodic inventory systems, unlike LIFO.

LIFO means Last-in, First-out, and as a cost flow assumption assigns the cost of goods sold based on the latest inventory purchases.

LIFO cannot be used under the perpetual inventory system.

Date        Activities                       Units     Unit Rate      Total Cost

April 1     Beginning inventory       220          $50             $11,000

April 5    Purchases                        100          $60                6,000

April 10   Purchases                         50          $45                2,250

April 16   Sales                              -300          $80

April 25  Sales                                -20          $95

April 30  Purchases                      200          $40                8,000

Total                                              570                             $27,250

Units sold                                      320

Ending inventory                         250

FIFO:

Ending Inventory = $10,250 (200 x $40 + 50 x $45)

Cost of goods sold = $17,000 ($27,250 - $10,250)

LIFO:

Ending Inventory = $12,800 (220 x $50 + 30 x $60)

Cost of goods sold = $14,450 ($27,250 - $12,800)

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The equation of line passing through points (4,−2) and (8, 3) is 4y - 5x + 28 = 0

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

Given pair of points are  (4,−2) and (8, 3).

The equation of line passing through two points (x₁, y₁) and (x₂, y₂) is given as,

y = ((x - x₁) / (x₁ - x₂)) (y₁ - y₂) + y₁

Substitute the respective values to get the equation of line as,

y = ((x - 4 ) / (4 - 8)) (-2 - 3) + (-2)

y = ((x - 4 ) / 4) × 5 - 2

4(y + 2) = 5(x - 4)

4y - 5x + 28 = 0

Hence, the equation of line for the given points is 4y - 5x + 28 = 0.

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The value of TV for the similar triangles is 25

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different.

Similar triangles are not the same as congruent triangles though.

triangle UXW and UTV are similar since line TV cuts lines UX and UW in the same proportion.

Let UV = p, it means also that WV = P. which means WU = 2p

so since the two triangles are similar, the ratio of their corresponding lengths are equal

meaning,

UV/UW = TV/XW

substituting their values, we have

p/2p = TV/50

by cross multiplying,

2p x TV = 50p

2TV = 50

TV = 50/2 = 25

In conclusion,  the value of TV is half the value of WX = 25

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solution: [tex]x > -175[/tex]

interval notation:  (-175, ∞)

explanation:

[tex]-\frac{1}{5}x + 4 < 39\\[/tex]

Subtract 4 from both sides

[tex]-\frac{1}{5}x +4-4 < 39-4\\[/tex]

Simplify

[tex]-\frac{1}{5}x < 35[/tex]

Multiply both sides by -1 (reverse the inequality)

[tex](-\frac{1}{5}x )(-1) > 35(-1)[/tex]

Simplify

[tex]\frac{1}{5}x > -35\\[/tex]

Multiply both sides by 5

[tex]5[/tex] ·[tex]\frac{1}{5}x > 5(-35)[/tex]

Simplify

[tex]x > -175[/tex]

Answer:

The answer is x=4.5

Step-by-step explanation:

I hope this helps

The ellipse given by x^2+xy+2y^2=7. The y-coordinate(s) of all points are -11.3, 11.2, -5.665, 5.585 where the ellipse has a vertical tangent line.

Differentiation is the process of determining a function's derivative. Differentiating algebraic functions, trigonometric functions, and exponential functions are the three fundamental derivatives.

Given,

Ellipse given,

x²+ xy + y ² = 7

Differentiating:

dy/dx

x²+ xy + y² = 7

d/dx(x² + xy + y²) = d/dx(7)

2x + 1y + x dy/dx + 2y dy/dx = 0

dy/dx = 2x + y/ x + 2y

dy/dx = 0

2x + y = 0

x + 2y = 0

Now, we have 2 equations,

x² + xy + y² = 0

y = -2x

Solving equations by substitution method,

x² + x(-2x) + (-2x)² = 7

x² - 2x² + 4x² = 7

3x² = 7

x = ±√21/3

Using y = -2x

Points are:

( -2√21/3 , √21/3) and (2√21/3 , -√21/3)

±√21/3 = ±1.528

x² + xy + y² = 7 [-11.3, 11.2, -5.665, 5.585]}

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The amount that $100 will be able to buy in 20 years, given an inflation rate of 4% is $44.20

When given the inflation rate, know that this rate is the rate at which the value of money decreases per year.

If given a rate of 4% as inflation, then the value of a dollar would decrease by 4% a year.

In 20 years therefore, the value of $100 would be:

Value in 20 years = Value today x (1 - inflation rate) ^ number of years

= 100 x (1 - 4%) ²⁰

= $44.20

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Answer: f (x)= -2x + 4

As per the concept of transformation, the image of the polygon after a reflection in the line y = - x is has vertices at A(0,-2), B(-4,-3), C(-4,-6), D(0,-5) as shown in the diagram attached below.

Transformation:

Transformation refers the movement of a point from the initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

Given,

Here we have the vertices A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the equation for line y = -x.

Now we have to plot the graph  with the given vertices and its image after a reflection in the line y = -x .

Here reflection refers flipping of a figure.

Therefore, if a point A(x, y) is reflected about the line y = - x, the new point would be at A'(-y, -x)

For the given the polygon with vertices at A(2, 0), B(3, 4), C(6, 4), D(5, 0) and the image of the polygon after a reflection in the line y = -x has vertices at:

A(0,-2), B(-4,-3), C(-4,-6), D(0,-5)

The image of the polygon is attached below.

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The unit rate of the equation y = -4x + 2 is -4

From the question, we have the following equation

y = -4x + 2

The above equation is a linear equation

Linear equations are represented as

y = mx + c

Where

When the equations y = mx + c and y = -4x + 2 are compared, we have

Unit rate, m = -4

Y-intercept, c = 2

Note that all linear equations have a constant rate of change

Hence, the unit rate in the linear equation is -4

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Answer:

7.8

Step-by-step explanation:

Switch 8 and 7, it round to 8 and end in tenths.

Answer:

7.8

Step-by-step explanation:

7.8 rounds to 8, because 8 is greater than 5, and then we end in the tenths place.

The required volume of the given shape is given as 432 cubic feet.

Given that,
A 3-dimensional shape with a hexagonal profile is given with dimension,
a = 6 in, H = 6 in and h = 4 in as shown in figure.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

here,
The volume of the given shape is,
Volume = 6/2[ah] × H
Substitute the value in the above expression,
Volume = 3 [4×6] × 6
Volume = 432 cubic feet,

Thus, the required volume of the given shape is given as 432 cubic feet.

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