3000 dollars is invested in a bank account at an interest rate of 7 percent per year, compounded continuously. Meanwhile, 20000 dollars is invested in a bank account at an interest rate of 5 percent compounded annually.

To the nearest year, when will the two accounts have the same balance?

Answer:

[tex]y=-2(sin(2x))-7[/tex]

Step-by-step explanation:

1. Approach

Given information:

What conclusions can be made about this function:

Therefore, one has the following information figured out:

[tex]y=-n(sin(ax))+b[/tex]

Now one has to find the following information:

2. Midline

The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:

y = -7

2. Amplitude

The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline: [tex]y=-7[/tex]

Amplitude: 9 - |-7| = 9 - 7 = 2

3. Period

The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline intersection: [tex](0, -7)[/tex]

Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]

However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).

[tex]a=\frac{2\pi}{\pi}=2[/tex]

4. Assemble the function

One now has the following solutions to the variables:

[tex]n =-16\\a=2\\b=-7\\[/tex]

Substitute these values into the function:

[tex]y=-2(sin(2x))-7[/tex]

Answer:

Un número decimal exacto es algo de la forma:

3.27

Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.

Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)

así obtenemos:

3.27*(100)/(100) = 327/100

Entonces la fracción 327/100 genera un decimal exacto.

Así, encontrar 10 fracciones es trivial, 10 ejemplos son:

7/10 = 0.7

314/100 = 3.14

27/10 = 2.7

27/100 = 0.27

2/10 = 0.2

25/100 = 0.25

31/10 = 3.1

12/10 = 6/5 = 1.2

131/10 = 13.1

142/100 = 1.42

Ahora, un decimal inexacto puro es algo de la forma:

3.33...

donde el 3 se repite infinitamente.

Tratemos de reescribir este número como una fracción:

primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:

3.33*10 = 33.33...

Ahora, podemos restar el numero original:

33.333... - 3.333... = 30

Entonces tenemos que:

3.33*9 = 30

3.33 = 30/9

La fracción:

30/9 nos da in decimal inexacto puro.

Ahora que sabemos construirlas, 10 ejemplos pueden ser:

30/9 = 3.33....

1/3 = 0.33...

40/9 = 4.44...

50/9 = 5.55...

60/9 = 6.66...

70/9 = 7.77...

20/9 = 2.22...

55/9 = 6.11...

544/99 = 5.5959...

10/9 = 1.11...

Finalmente, un periódico mixto es algo de la forma:

1.2343434...

Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.

Para construirlos, podemos tomar una fracción exacta, como

1.1 y una periódica, como 1.11...

Si las sumamos, obtenemos:

1.1 + 1.11... = 2.211...

donde el uno se repetirá infinitamente.

Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:

7/10 + 55/9 = 613/90 = 0.7 +  6.11... = 6.8111....

7/10 +  10/9 = 163/90 = 0.7 + 1.11... = 1.811....

31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...

31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...

31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...

27/10 + 20/9 =  443/90 = 2.7 + 2.22... = 4.922...

37/10 + 20/9 =  533/90 = 3.7 + 2.22... = 5.922...

4/10 +  10/9 = 136/90 = 0.4 + 1.11... = 1.511....

3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...

4/10 +  20/9 = 236/90 = 0.4 + 2.22... = 2.622....

Answer:

Since this number is small we know that the exponent will be negative.

In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.

1.2 x 10 ^-11

Step-by-step explanation:

Answer:

its letter a

Step-by-step explanation:

I hope you help

Answer:

a)2x-3y

b)4(9a-4)

Step-by-step explanation:

we want to expand the following expression:

[tex] \displaystyle - \frac{1}{4} ( - 8x + 12y)[/tex]

well to do so we consider distributive property thus distribute:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y)[/tex]

reduce fraction which yields:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y) \\ \\ \displaystyle 2x + ( - 3y)[/tex]

simplify Parentheses:

[tex] \displaystyle \boxed{ 2x - 3y}[/tex]

in the expression there's a common factor of 4 therefore factor it out:

[tex] \displaystyle 9.4a - 4.4 \\ \\ \displaystyle \boxed{4(9a - 4)}[/tex]

Answer:

7/10

Step-by-step explanation:

½ of a cup of cheddar=½ x 1=½

⅕ of a cup of parmesan=⅕ x 1=⅕

all cheese used=½ + ⅕= 7/10

Answer:

hi?

Step-by-step explanation:

Answer:

The sum of the first 50 is 5200

Step-by-step explanation:The given sequence is a linear sequence.

So, first we calculate the common difference

d=t2-t1

d=10-6=4

The sum of the first 50 terms is then calculated using: sorry it wont let me copy and paste my explo and im lazy

Answer:

5,200

Step-by-step explanation:

6, 10, 14, ...

Sum = [ number of terms(first term+last term) ] / 2

-we know there are 50 terms

-we now the first term is 6

-we need to find the last term

last term = first term + (n-1)* difference between first and second term

last term = 6 + (50-1) * (10-6)

last term = 6 + 49*4 = 202

Sum = [ number of terms(first term+last term) ] / 2

Sum = [ 50 ( 6 + 202) ] / 2 = 5,200

Answer:

19 + 1 + 9 + 1

put any of those in the slots

Answer:

19 + 1 + 9 + 1

peace

Answer:

there is no diagram ......

Answer:

Step-by-step explanation:

{ 2/3 x+y=6

+

{ -2/3x-y=2

= 0=6

Hence,no solution.

Answer:169

Step-by-step explanation:13 x 13 = 169

You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.

Answer:

there is only one way to to roll a 3

1/36 = .044 = 4.4%

Step-by-step explanation:

Answer:

$43,799.50

Step-by-step explanation:

USing the formula:

A = P(1+r)ⁿ

n is the time = 5

1 + r = 1.04

P = 36,000

Substitute the values into the formula

A = 36000(1.04)⁵

A = 36,000(1.2166529024)

A = 43,799.50

Hence the value in the fifth year will e $43,799.50

Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(

Answer:

96 in²

36 in²

60 in²

6.51 in

Step-by-step explanation:

Given that :

Dimension of paper = 12 in by 8 in

Dimension of right triangles :

2 in by 9 in ; 3 in by 6 in

Area of sheet of paper = 12 in * 8 in = 96 in²

Area of triangle = 1/2 base * height

Therefore, area of remnant right triangle :

2 * 1/2 * 2 * 9 = 18 in²

2 * 1/2 * 3 * 6 = 18 in²

Combined area of triangle left = 18in + 18in = 36 in²

Area of parallelogram = Area of sheet - Area of triangles left

Area of parallelogram = 96in² - 36in² = 60 in²

Base, b of parallelogram = 9.22 in

Area of parallelogram = base * altitude,h

60in² = 9.22h

h = 60 / 9.22 = 6.51 in

Answer:

answer A

Step-by-step explanation:

A=(-4,7)

C=(2,-5)

midpoint = U=((-4+2)/2, (7+(-5))/2)=(-1,1))

B=(3,0)

D=(-5,2)

midpoint = V=((3+(-5))/2,(0+2)/2)=( -1,1)

Diagonals have the same middle, the quadrilater is a parallogram.

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

See this attachment

Answer:

f the mean of this set is equal to 20, we can write down the below equation,

20 = (x1 + x2 +x3 + .... + x10)/10

x1 + x2 + x3 + ... x10 = 200

Then we can also write an equation for the mean of the given numbers as below,

Mean  = [(x1+4) + (x2+8) + (x3+12) + .... + (x10+40)]/10

          = (x1 + x2 + x3 + ... + x10 + 4 + 8 + 12 + ... + 40)/10

Then we can use above equation (1) to replace x1 + x2 + x3 + ... + x10 by 200

Mean = (200 + 4 + 8 +12 + 16 + 20 + 24 + 28 + 32 + 36 + 40)/10

        = 420/10

        = 42

If you remember Arithmetic Progressions you can simply add together the above number set.

If you closely look above, you can find that there is an Arithmetic Progression : 4, 8, 12, ... , 40

Here we want the addition of 10 terms. So we can use,

Sn = n/2(a+l)

S10 = 10/2(4+40)

      = 220

Then you can easily get the answer,

Mean = (200 + 220)/10

         = 42

Answer:

64 = 2(3x + x)

Step-by-step explanation:

Perimeter of the rectangle = 64 cm

Width of the rectangle = x

Length of the rectangle = 3x

Perimeter of a rectangle = 2(length + width)

The equation is

64 = 2(3x + x)

64 = 6x + 2x

64 = 8x

x = 64/8

x = 8 cm

Width of the rectangle = x = 8 cm

Length of the rectangle = 3x

= 3(8 cm)

= 24 cm

Answer:

100 mm

Step-by-step explanation:

Square root the area to find the length of each side

[tex]\sqrt[]{625} =25[/tex]

Multiply 25 by 4 to get the sum of all four sides for the perimeter

25 x 4 = 100

Answer:

Please find the complete question and the graph in the attached file.

Step-by-step explanation:

On the basis of the data,

The level of importance is [tex]\alpha = 0.01[/tex]

Freedom levels [tex]= n -1 = 13 -1 = 12[/tex]

For the right-tailed test, the critical value is [tex]t_c = 2.681[/tex]

(Partially t-table permitted [tex]\alpha = 0.01 \ and\ df =12[/tex])

Answer:

51

Step-by-step explanation:

1. Approach

One is given the polygon, (ABCDE); the problem asks one to find the area of this polygon. The most logical step to take is to divide this polygon into easier parts, find the area of each part, and then add up the area to find the total area of the figure.

One way to divide this figure up is to draw the line (AC). This will create the triangle (ABC) and rectangle (ACDE).

2. Find the area of (ABC)

The formula to find the area of a triangle is the following:

[tex]A=\frac{b*h}{2}[/tex]

Where (b) is the base of the triangle, and (h) is the height. The base of the triangle (ABC) is (AC), which has a measure of (6) units. The height of the triangle is the distance from the base of the triangle to the vertex opposite the base. This measurement is (3) units. Substitute these values into the formula and solve for the area:

[tex]A=\frac{b*h}{2}[/tex]

Substitute,

[tex]A=\frac{6*3}{2}\\\\A=\frac{18}{2}\\\\A=9[/tex]

3. Find the area of (ACDE)

The formula to find the area of a rectangle is as follows:

[tex]A=b*h[/tex]

The base of the rectangle is the segment (AE), with a measure of (7) units. The height of the rectangle is the segment (AC) with a measurement of (6) units. Substitute these values into the formula and solve for the area:

[tex]A=7*6\\\\A=42[/tex]

4. Find the area of the total figure

To find the area of the total figure, add up the area of the triangle, and the area of the rectangle:

[tex]9+42= 51[/tex]

Answer:

d = 8t

Step-by-step explanation:

Answer:

The answer is 80

Step-by-step explanation:

we know that

the outlier is 50, as it is not around the other numbers in the data set.

therefore

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80

Answer:

80

Step-by-step explanation:

mean=[76+ 79 + 80 + 82+ 78 + 83 + 79 + 81 + 82]/9

mean=[720]/9

mean=80