You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never
withdraw money from the account. How much money will be in the account after 4 years?

Answer:

5m - 10

Step-by-step explanation:

Use distributive property;

5(m - 2)

(5 x m) (5 x -2)

5m - 10

Answer(s):

[tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}) \\ y = 4cos\:2x[/tex]

Step-by-step explanation:

[tex]\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{4}} \hookrightarrow \frac{-\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 4sin\:2x,[/tex]in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-\frac{\pi}{4}} = \frac{-\frac{\pi}{2}}{2}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 4sin\:(2x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph WILL hit [tex]\displaystyle [-1\frac{1}{4}\pi, 0],[/tex]from there to [tex]\displaystyle [-\frac{\pi}{4}, 0],[/tex]they are obviously [tex]\displaystyle \pi\:units[/tex]apart, telling you that the period of the graph is [tex]\displaystyle \pi.[/tex]Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

Answer:

5 years ago

Step-by-step explanation:

5 years ago, they were 35 years old and 3 years old. 35*3=105.

Answer:

B is the answer

Step-by-step explanation:

Hope it helps.

Answer:

The expected value is $375

The profit is $6,500,000

Step-by-step explanation:

15000, 30000, 70000

1/100, 1/200, 1/400

So the expected value of the claim is:

15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475

Given that an insurance policy sells for $800 and the expected value of the claim is $475.

So, the expected value of the companies profit is = $(800 – 475) = $325.

If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000

Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.

-TheUnknownScientist 72

Apply Pythagorean theorem

[tex]\\ \rm\rightarrowtail B^2=2.2^2-2^2[/tex]

[tex]\\ \rm\rightarrowtail B^2=5-4[/tex]

[tex]\\ \rm\rightarrowtail B^2=1[/tex]

[tex]\\ \rm\rightarrowtail B=1[/tex]

Area:-

Answer:6

Step-by-step explanation:

I did the test

Answer:

(x−4)(x−2)(x+5)

Step-by-step explanation:

Answer:

un rhgdb tennis felicidades ID remix estoy do do ID do ID Rockband do ID do TX

Step-by-step explanation:

120 ÷ 1.6 = 75.

so 75 miles per hour.

75 × 2 = 150

therefore 150 miles in 2 hours

Answer:

120 km/ 1 hour

We need to convert kilometers into miles, so given the information below (1 mile = 1.6 km), we divide 120 km by 1.6 km because 1.6 km is equivalent to 1 mile.

120km/1.6km

= 75 miles, so therefore the cars rate will be:-

75 miles/ 1 hour

To see how many miles are in 2 hours, we must multiply the unit rate(75 miles/ 1 hour) by 2.

75 miles/ 1 hour x 2/2 hours

75 x 2

______ = 150/2, so the car will travel 150 miles in 2 hours.

 1 x 2

Answer:

19 and 13

Step-by-step explanation:

width = x

length = x + 6

2x + 2(x + 6) = 64

2x + 2x + 12 = 64

4x = 64 - 12

4x = 52

x = 13

x + 6 = 19

Answer:

19 and 13

Step-by-step explanation:

Answer:

D should be the answer because the rate of Mason and Evan is 3 pages per a minute because three goes into both like so 30÷10=3 and 12÷4=3. Which is why D is your answer.

By using the parallel condition and the fact that the distance to the origin is the same, we will see that a = 1 and b = 2.

First, remember that two lines are parallel if have the same slope and different y-intercept.

In this case, we know that

y = a*x - 1

b*y - (a + 1)*x = 2

Are parallel, if we write both of them in the slope-intercept form, we get:

y = a*x - 1

y = (a + 1)*x/b + 2/b

Note that because both of the lines are parallel, the slopes must be equal, then we have that:

(a + 1)/b = a

Then if we know that the distance of both lines to the origin is the same, we have that:

|-1/(√(a^2 + 1))| = | (2/b)/(√(((a + 1)/b)^2 + 1))|

Because the slopes are equal the denominators are equal, this means that:

|-1| = |2/b|

And the y-intercepts must be different, this means that:

b = 2

now we can solve:

(a + 1)/b = a

(a + 1)/2 = a

a + 1 = 2a

1 = 2a - a = a

a = 1 and b = 2.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491

Answer:

p=7/2

Step-by-step explanation:

Rember that a p series can be represented by

[tex] \frac{1}{k {}^{p} } [/tex]

Here, notice that

[tex] \frac{1}{8 \sqrt{2} } = \frac{1}{2 {}^{3} \sqrt{2} } = \frac{1}{2 {}^{3} \times 2 {}^{ \frac{1}{2} } } = \frac{1}{2 {}^{ \frac{7}{2} } } [/tex]

This is true for all parts of the series because

[tex]27 \sqrt{3} = 3 {}^{ \frac{7}{2} } [/tex]

So p=7/2

Answer:

[tex]\sf \dfrac29[/tex]

Step-by-step explanation:

From the table:

[tex]\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}[/tex]

[tex]\sf \implies P(Girl)=\dfrac{18}{30}[/tex]

[tex]\sf \implies P(Freshman \cap Girl)=\dfrac{4}{30}[/tex]

[tex]\begin{aligned}\sf P(Freshman|Girl)& = \sf\dfrac{P(Freshman \cap Girl)}{P(Girl)}\\\\ & = \sf \dfrac{4}{30} \div \dfrac{18}{30}\\\\ & \sf=\dfrac{4}{30} \times \dfrac{30}{18}\\\\ & = \sf \dfrac29\end{aligned}[/tex]

[tex]\left\{\begin{matrix}x=4\\y=10\\\end{matrix}\right.[/tex]

[tex]\left\{\begin{matrix}-5x+y=-10\\-4x-y=-26\\\end{matrix}\right.[/tex]

_____________________________________

[tex]-5x+y+(-4x-y)=-10+(-26)[/tex]

____________________________

[tex]-5x+y-4x-y=-10-26[/tex]

_________________________________________________

[tex]-5x-4x=-10-26[/tex]

___________________________________________

[tex]-9x=-10-26[/tex]

______________________________________________

[tex]-9x=-36[/tex]

________________________________________________

Divide both sides of the equation by the coefficient of variable

[tex]x=\frac{-36}{-9}[/tex]

____________________________________________________

Determine the sign for multiplication or division

[tex]x=\frac{36}{9}[/tex]

_________________________________________

Cross out the common factor

[tex]x=4[/tex]

[tex]-4\times4-y=-26[/tex]

____________________________________________________

Calculate the product or quotient

[tex]-16-y=-26[/tex]

______________________________________________________

Rearrange variables to the left side of the equation

[tex]-y=-26+16[/tex]

_____________________________________________

Calculate the sum or difference

[tex]-y=-10[/tex]

_________________________________________-

Divide both sides of the equation by the coefficient of variable

[tex]y=10[/tex]

I hope this helps you

:)

Answer:

150 minutes

Step-by-step explanation:

Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds

As there are 3.2 rounds to go in 8 hours, so the time for 1 round will be: 8/3.2= 2 hours and 30 minutes

Answer:

150 minutes

Step-by-step explanation:

16/5 = 3.2  turns

8 hours /3.2 turns  = 2.5 hours (150 minutes)

Answer:

4 squares

Step-by-step explanation:

If the rectangle is only 3 cm wide, only one square will be able to fit in a row. Since the square is 12 cm long, 4 squares can fit. This can be found by 12/3 which = 4

Answer:

ok

Step-by-step explanation:

40 America-nos

Explanation:

make proportional equation

Answer:

Step-by-step explanation:

Use ratios

Solve for x

Answer:

Width=28 1/3 Length=51 2/3

Step-by-step explanation:

1. Create an equation

x+(2x-5)=80

2. Solve

x+(2x-5)=80

3x-5=80

3x-5+5=80+5

3x/3=85/3

x=28 1/3

So, if x=28 1/3

85/3x2=170/3

56 2/3-5

So, Length=51 2/3

Answer:

Step-by-step explanation:

let the eq. be

y=a(x-2)(x-4)+b

x=0,y=-2

-2=a(0-2)(0-4)+b

-2=8a+b

when x=6,y=-2

-2=a(6-2)(6-4)+b

-2=8a+b

when x=8,y=-6

-6=a(8-2)(8-4)+b

-6=24a+b

16a=-4

a=-1/4

-2=-2+b

b=0

y=-1/4(x-2)(x-4)

y=-1/4(x^2-6x+8)

y=-1/4x^2+3/2x -2

when x=1

y=-1/4(1-2)(1-4)

y=-3/4

Add the two together:

15 + 17 = 32

total miles = 32

Answer:

$4.75

Step-by-step explanation:

To find the unit price (price for one), just divide $9.30 by 2. You get that one clay pot (the price for one unit) is $4.75.

Hopefully this helps- let me know if you have any questions!

Answer:

Parallelogram

Step-by-step explanation:

Instead of one pair of parallel sides like in a trapezoid, a parallelogram has two pairs of opposite sides (for example a rectangle)

Answer:

m<BAC = 85°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of its intercepted arc.

m<BAC = 170°/2

m<BAC = 85°

Answer:

Θ = (π/6) + πn

Θ = (5π/6) + πn

Step-by-step explanation:

4sin²Θ + 4 = 5

            -4    -4

4sin²Θ = 1

÷4         ÷4

sin²Θ = (1/4)

√sin²Θ = √(1/4)

sinΘ = (1/2), (-1/2)

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

Θ = arcsin (1/2)

Θ = (π/6)

to find the quadrant subtract π

Θ = π - (π/6)

Θ = (5π/6)

Find the period

2π / |b|

b = 1

2π/1 = 2π

The sin Θ function is 2π, so values will repeat 2π in both directions.

Θ = (π/6) + 2πn (n is the variable)

Θ = (5π/6) + 2πn

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

sin Θ = (-1/2)

Θ = arcsin (-1/2)

Θ = (-π/6)

To find the second function add π

Θ = 2π + (π/6) + π

Θ = (7π/6)

Find the period

2π/|b|

2π/1

2π

(-π/6) + 2π

2π       6         π

----- ×  ----- -  -----

1           6        6

Θ = (11π/6) will repeat every 2π in both directions

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

Θ = (π/6) + 2πn

Θ = (5π/6) + 2πn

Θ = (7π/6) + 2πn

Θ = (11π/6) + 2πn

(π/6) + π = (7π/6)

(5π/6) + π = (11π/6)

Θ = (π/6) + πn

Θ = (5π/6) + πn

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

I hope this helps!

Answer:

a=20

Step-by-step explanation:

a-10+a=30

a+a-10=30

2a-10=30

2a=30+10

2a=40

a=20

Answer:

See attached graph

Step-by-step explanation:

We need to convert the polar coordinates into Cartesian coordinates using the rules [tex]x=r\:cos\theta[/tex] and [tex]y=r\:sin\theta[/tex] (see table in attached file).

The converted points will start to resemble a circle with a horizontal pole and a diameter of 4, so by connecting the points, we get our equation [tex]r=4\:cos\theta[/tex].