A newspaper editor starts a retirement savings plan in which $275 per month is deposited at the beginning of each month into an account that earns an annual interest rate of 6.4% compounded monthly. Find the value of this investment (in dollars) after 20 years. (Round your answer to the nearest cent.)

Answer:

To prove that 7^7 - 7^6 is divisible by 6, we can factor out 7^6 from the expression:

7^7 - 7^6 = 7^6 (7 - 1)

Simplifying the expression, we get:

7^7 - 7^6 = 7^6 (6)

We can see that 7^6 is a common factor in the expression, and 6 is also a factor. Therefore, we can conclude that 7^7 - 7^6 is divisible by 6.

Step-by-step explanation:

The required y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).

We can use the two given points (5,8) and (7,14) to find the slope of the line passing through them, and then use the slope and the x-coordinate of the third point (8) to find the y-coordinate.

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:

[tex]$m = \frac{y2-y1}{x2-x1}$$[/tex]

Using the points (5,8) and (7,14), we get:

[tex]$m = \frac{14-8}{7-5} = \frac{6}{2} = 3$$[/tex]

So the slope of the line passing through these two points is 3.

Now we can use the slope and the x-coordinate of the third point (8) to find the y-coordinate. We use the point-slope form of the equation of a line:

[tex]$y - y1 = m(x - x1)$[/tex]

where (x1,y1) is one of the given points, and m is the slope.

Using the point (5,8), we get:

y - 8 = 3(x - 5)

Simplifying this equation, we get:

y = 3x - 7

Now we can use this equation and the x-coordinate of the third point (8) to find the y-coordinate:

y = 3(8) - 7 = 17

So the y-coordinate of the third point is 17. Therefore, the ordered pair is (8,17).

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When it happens, the ratio of their corresponding side will not change. The value of x is 8.

What are properties of triangle?

The sum of the interior angles of a triangle is always 180°.

When two triangle sides are linked together, they will always be longer than the triangle's third side.

Half of a triangle's base plus height is considered to be its surface area.

Already mentioned the ΔDEF and ΔXYZ are similar.

When it happens, the ratio of their corresponding side will not change.

So,

7/14=6/12=2x-5/22

We take last two,

6/12=2x-5/22

Or, 24x-60=132

Or, x= 192/24

Or, x=8

Hence, the value of x is 8.

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8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.

Let x be the number οf TV advertisements, y be the number οf radiο advertisements, and z be the number οf οnline advertisements.

The οbjective is tο maximize the tοtal audience, which is given by:

Tοtal audience = 140,000x + 18,000y + 30,000z

The cοnstraints are:

Cοst cοnstraint: 1500x + 200y + 550z ≤ 24,100

TV cοnstraint: x ≥ 0.15(x + y + z)

Radiο cοnstraint: y ≤ 0.45(x + y + z)

Maximum media usage cοnstraint: x ≤ 15, y ≤ 19, z ≤ 12

Nοn-negative cοnstraint: x ≥ 0, y ≥ 0, z ≥ 0

Using a sοlver, we get the fοllοwing οptimal sοlutiοn:

x = 8, y = 9, z = 12

Therefοre, 8 TV advertisements, 9 radiο advertisements, and 12 οnline advertisements shοuld be run tο maximize tοtal audience cοntact.

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The amount of water drained from the tank between 5 pm and 6 pm is given as follows:

143 liters.

An exponential function is modeled as follows:

y = ab^x.

In which the parameters are represented as follows:

The parameter values for this problem are given as follows:

Hence the function giving the amount of water in x hours after 1 pm is presented as follows:

y = 1870(0.86)^x.

At 5pm and 6 pm, the amounts are given as follows:

Hence the amount drained is of:

1023 - 880 = 143 liters.

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Answer: 6

Step-by-step explanation:

Answer:

I tried my best by helping

Step-by-step explanation:

So it is asking what are the probability of you getting the power ball lottery a player must get 5 white balls and a red one. I don’t get what question a is asking but letter b is the overall probability of the player winning the power ball lottery is 1/35 so in the graph it show 1 in 195,249,054. So that will be the answer of explaining the probability.

Accοrding tο the transfοrmatiοn prοperty, the cοrrect answer is οptiοn (c): (x, y) → (- y + 2, x + 2)

Transfοrmatiοn is a functiοn that maps οne set οf pοints tο anοther set οf pοints in a way that preserves sοme structure οr prοperties οf the οriginal set. The mοst cοmmοn types οf transfοrmatiοns are geοmetric transfοrmatiοns, which preserve distance, angle, and shape, and algebraic transfοrmatiοns, which preserve algebraic prοperties such as the sum, prοduct, οr symmetry οf functiοns.

Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal. Therefοre, tο determine whether a transfοrmatiοn maps triangle ABC tο a similar, but nοt a cοngruent triangle, we need tο examine hοw the transfοrmatiοn affects the angles and sides οf triangle ABC.

Let's assume that triangle ABC has vertices A(a₁, a₂), B(b₁, b₂), and C(c₁, c₂).

a) (x, y) → (x + 2, - y - 2)This transfοrmatiοn is a translatiοn that mοves each pοint οf the plane twο units tο the right and twο units dοwn. Therefοre, this transfοrmatiοn dοes nοt change the size οr shape οf triangle ABC. It οnly changes its pοsitiοn in the plane. Hence, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

b) (x, y) → (- 4x, - 4y)

This transfοrmatiοn scales each cοοrdinate by a factοr οf -4, which reflects the triangle acrοss the οrigin and changes its size. Hοwever, this transfοrmatiοn alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

c) (x, y) → (- y + 2, x + 2)

This transfοrmatiοn is a rοtatiοn οf 90 degrees cοunterclοckwise arοund the pοint (2, 2). Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a rοtatiοn, it preserves the angles οf the triangle. Tο check if it preserves the sides, we need tο cοmpute the length οf each side οf the transfοrmed triangle and cοmpare it tο the cοrrespοnding side οf the οriginal triangle:

AB: distance between (- a₂ + 2, a₁ + 2) and (- b₂ + 2, b₁ + 2) is equal tο the distance between A(a₁, a₂) and B(b₁, b₂)

AC: distance between (- a₂ + 2, a₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between A(a₁, a₂) and C(c₁, c₂)

BC: distance between (- b₂ + 2, b₁ + 2) and (- c₂ + 2, c₁ + 2) is equal tο the distance between B(b₁, b₂) and C(c₁, c₂)

Since the angles and sides are preserved, this transfοrmatiοn maps triangle ABC tο a similar, but nοt cοngruent triangle.

d) (x, y) → (- y, - x)

This transfοrmatiοn is a reflectiοn acrοss the line y = x. Tο see if it maps triangle ABC tο a similar, but nοt cοngruent triangle, we need tο check if the angles and sides οf the triangle are preserved. Since this transfοrmatiοn is a reflectiοn, it preserves the angles οf the triangle. Hοwever, it alsο changes the οrientatiοn οf the triangle. Therefοre, this transfοrmatiοn dοes nοt map triangle ABC tο a similar, but nοt cοngruent triangle.

Therefοre, the answer is οptiοn (c): (x, y) → (- y + 2, x + 2)

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A

i had this question it's right

If mDA =(23x -14), mDB =(9x-4), and mx=?Arc DA= ?

Answer:

169.188 _[tex]\geq[/tex]__ 169.098

Step-by-step explanation:

The equation of the graph is option (c) i.e. y = 0.5 csc [0.5(x + π/2)] - 1 which is solve below.

In elementary mathematics, term "graph" denotes a plot or a function graph. A graph, in the language of mathematicians, a set of points and connections between some subset of those points (which may empty).

If the equation y = A csc (B(x + C)) + D

Amplitude is A, the Amplitude is the height from the centre line to the peak . Or we can measure height from highest to lowest points and divide that by 2

Period is 2π/B, the Period goes from one peak to the next

Phase shift is C (positive is to the left), the Phase Shift is how far the function is shifted horizontally from the usual position.

Vertical shift is D, Vertical Shift is how far the function is shifted vertically from the usual position.

If y = csc(x), then A = 1 , B = 1 , C = 0 , D = 0

That means amplitude is 1, the period is 2π, So there is no phase shift or vertical shift

Now lets solve the problem from the graph

[tex]The\ amplitude = \frac{(-0.5 - (-1.5))}{2} = 0.5[/tex]

∴ [tex]A = 0.5[/tex]

The period is from 2.5π to -1.5π

∴ [tex]The \ period\ is\ 4\pi[/tex]

∵ [tex]The\ period = \frac{2\pi }{B}[/tex]

∴ [tex]4\pi = \frac{2\pi }{B}, by\ cross \ multiplication[/tex]

∴ [tex]B = \frac{2\pi }{4\pi } = \frac{1}{2} = 0.5[/tex]

There is only one answer which has value A = 0.5 and B = 0.5

∴ y = 0.5 csc[0.5(x + π/2)] - 1

So, The Correct equation of the graph is 0.5 csc[0.5(x + π/2)] - 1

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Answer:

The answer is c

Step-by-step explanation:

edge

The area of the figure is 72 square meters

From the question, we have the following parameters that can be used in our computation:

A composite figure

The area of the figure is calculated as

Area = Sum of areas of the individual figures

From the figure, we have

Number of rectangles that make up the composite =3

Using the above as a guide, we have the following:

Area = 8 * 5 + 4 * 7 + 2 * 2

Evaluate

Area = 72

Hence, the area is 72 square meters

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Answer:

I, IV, V

Step-by-step explanation:

To determine which of the given expressions are equivalent, we can expand and simplify them.

I. (x - 4)² - 1

Expanding the square, we get:

(x - 4)² = x² - 8x + 16

So, (x - 4)² - 1 = x² - 8x + 15

II. x² - 8x - 17

III. x² + 15

IV. x² - 8x + 15

V. (x - 5)(x - 3)

Expanding the product, we get:

(x - 5)(x - 3) = x² - 8x + 15

VI. x² - 17

From the above expressions, we can see that the following expressions are equivalent:

I. (x - 4)² - 1 and IV. x² - 8x + 15

Also, V. (x - 5)(x - 3) is equivalent to both I. and IV.

Therefore, the answer is (C) I, IV, V.

The graph of the sinusoidal function shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters.

we can use a general form of sinusoidal function

h(t) = A sin(ωt + φ) + C

where:

A = amplitude (maximum displacement from the mean position)

ω = angular frequency (radians per second)

φ = phase angle (initial position of the oscillation)

C = vertical displacement (position of the mean or equilibrium position)

Since the mass is released from rest, we can assume that the initial displacement is zero, i.e., C = 0. Also, we know that the period of the oscillation is 1/f, where f is the frequency. Therefore, we can find the frequency from the given time period of 0.8 seconds.

Let's assume that the height of the mass oscillates with an amplitude of 0.1 meters and a frequency of 5π radians per second (corresponding to a period of 0.4 seconds), and the phase angle is 0.

h(t) = 0.1 sin(5πt)

We can plot this function for t ranging from 0 to 0.8 seconds using a graphing tool or by hand. Here is the resulting graph

    |

0.1 +                 . * .

    |             .*         *.

    |           .              .

    |         *                 *

    |        *                    *

    |      .                        .

    |     .                            .

    |   .*                                *.

    | .*                                      *.

-0.1 +----------------------------------------------

    0        0.2        0.4        0.6        0.8

The x-axis represents time in seconds, and the y-axis represents the height of the mass in meters. The graph shows that the mass oscillates up and down around the equilibrium position with an amplitude of 0.1 meters. The maximum height occurs at t = 0.1 seconds and t = 0.5 seconds, while the minimum height occurs at t = 0.3 seconds and t = 0.7 seconds. At t = 0.4 seconds and t = 0.8 seconds, the mass returns to the equilibrium position.

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Answer:

Kevin has 11 CDs.

The numerator of the rational expression 7/V + 3/V is 10. In this rational expression, we are adding two fractions that have the same denominator (V).

To add these fractions, we need to find a common denominator, which is already given to us as V.

Then, we add the numerators of the two fractions, which are 7 and 3, to get:

7/V + 3/V = (7+3)/V

Simplifying the numerator by adding 7 and 3, we get:

10/V

The numerator for the rational expression 7/V + 3/V is:

7 + 3 = 10

Therefore, the numerator is 10.

Therefore, the numerator of the rational expression 7/V + 3/V is 10.

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Answer:10-2= 8

Step-by-step explanation:

7

the first order pair is always x and the second is y

slope m =Y2_Y1 ÷ X2_X1

then 24_ 17 ÷3 _2= 7

The two 2×2 matrices A and B with real entries  sucah that (AB)^2 is not equal to A^2 B^2 is given below:

Let A = [[1, 0], [0, -1]] and B = [[0, 1], [1, 0]] be two 2x2 matrices with real entries. Then,

AB = [[0, 1], [-1, 0]] and AB^2 = [[-1, 0], [0, -1]]

A^2 = [[1, 0], [0, 1]] and B^2 = [[0, 1], [1, 0]]

So, A^2B^2 = [[0, 1], [1, 0]] and (AB)^2 = ABAB = [[0, 1], [-1, 0]][[0, 1], [-1, 0]] = [[-1, 0], [0, -1]]

Therefore, (AB)^2 is not equal to A^2B^2 for the matrices A and B defined above.

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After addressing the issue at hand, we can state that As a result, the equation truck travelled 1830.18 miles between fill-ups.

A mathematical statement which then proves both the equality of two traits linked by an equal sign '=' is known as an equation. 2x - 5 = 13, for example. 2x-5 and 13 are two expressions. The symbol '=' connects the two expressions. An equation is a mathematical formula with two algebraic expressions from either side of an equal sign (=). It represents the relationship of equivalence between left and right formulas. In any formula, LHS = RHS (left side = right side).

Because the truck used 241 gallons of diesel fuel between Monday and Friday, the distance travelled can be calculated using the truck's fuel efficiency.

T Previous fill-up odometer reading = 78467

At the current fill-up, the odometer reads 80293

Traveled distance = 80293 - 78467 = 1826 miles

241 gallons of fuel were consumed.

Mileage = Distance travelled / Fuel Consumption

Mileage = 1826 divided by 241

7.58 miles per gallon = mileage

We can now use the mileage to determine the distance travelled between fill-ups:

Distance travelled = Fuel consumption x Mileage

241 divided by 7.58 equals the distance travelled.

The total distance travelled is 1830.18 miles.

As a result, the truck travelled 1830.18 miles between fill-ups.

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Answer: 30 Child tickets 6 Adult tickets.

Step-by-step explanation:

Set up your system of equations to solve.

36 tickets are purchased, meaning a number of child tickets, and a different number of adult tickets add up to 36. We can write this as x+y=36.

The price of the tickets add up to 252 dollars. We can write this as 6 (the child price) times x + 12 (the adult price) times y = 252

So, x+y=36 and 6x+12y=252.

I will solve this using the substitution method.

So, first, we need to isolate a variable, I will choose the first equation to do so.

x+y=36 ---> x=36-y

Now, plug the value of x into the second equation.

6(36-y)+12y=252.

Distribute.

216-6y+12y=252

Combine like terms.

216+6y=252.

Subtract 216 from both sides.

6y=36

Divide by 6 on both sides.

y=6

Now plug this value of y into the previous equation to get x.

x+6=36

Subtract 6 from both sides.

x=30

Remember x was children's tickets and y was adult tickets. (It is better to use variables like C and A in this case).

Answer:

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The volume of the prism is 115.5 cubic centimeters.

A three-dimensional structure called a right rectangular prism has six rectangular faces, each of which has four right angles. The length, breadth, and height of a right rectangular prism are perpendicular to one another, and the opposing sides are congruent and parallel to one another. The prism's dimensions—also referred to as its length, breadth, and height—can be utilised to determine its volume. Multiplying the prism's length, width, and height yields the volume of a right rectangular prism.

The volume of the rectangular prism is given by the formula:

Volume = Length x Width x Height

Substituting the values we have:

Volume = 3.5 cm x 6 cm x 5.5 cm

Volume = 115.5 cubic centimeters

Hence, the volume of the prism is 115.5 cubic centimeters.

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The answer of the question based on the rate of interest is a)  $23,900, b) $1,146.37 c) $1,289.78.

An interest refers to cost of borrowing money, typically expressed as percentage of amount borrowed over period of time. When you borrow money, you generally have to pay back  amount borrowed plus interest, which compensates  lender for risk and opportunity cost of lending you  money.

a) The down payment is 10% of the home price, which is:

10% of $239,000 = 0.10 x $239,000 = $23,900

To find the loan amount, we subtract the down payment from the home price:

Loan amount = $239,000 - $23,900 = $215,100

b) To calculate the monthly payment at an interest rate of 5%, we use the formula for a fixed-payment loan:

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

First, we need to find the monthly interest rate, which is the annual interest rate divided by 12:

Monthly interest rate = 5% / 12 = 0.00416667

Total number of payments = 30 years x 12 months/year = 360

Now we can plug in these values to find the monthly payment:

M = $215,100 * 0.00416667 * (1 + 0.00416667)^360 / ((1 + 0.00416667)^360 - 1) = $1,146.37

Therefore, the monthly payment at an interest rate of 5% is $1,146.37.

c) To calculate the monthly payment at an interest rate of 6%, we use the same formula as before, but with a different interest rate:

Monthly interest rate = 6% / 12 = 0.005

Total number of payments = 30 years x 12 months/year = 360

M = $215,100 * 0.005 * (1 + 0.005)^360 / ((1 + 0.005)^360 - 1) = $1,289.78

Therefore, the monthly payment at an interest rate of 6% is $1,289.78.

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Answer: 1/3 or 1 divided by 3 is equivalent to 0.333333

Answer:

0,33

Step-by-step explanation:

this for sure.......

Answer:

B

Step-by-step explanation:

the graph of the function is a parabola

Devaluation of 5%:

125+(125x5%)=187,5

Many US dollars can be bought if Nepali currency is devaluated by 5%=

62.500:187,5=333 dollar

Answer:

5divided by 14 is 2 with a remainder of 3

Answer:

x+6=y

Step-by-step explanation: