Tiana invests $83,927 in a start-up company. She will be repaid at the end of 7
years at 7% interest compounded annually. Find the amount of interest she will
earn on this investment.
DO NOT ROUND ANY NUMBERS UNTIL YOUR FINAL ANSWER!
Round to the nearest dollar.

Answer:

13.1 cm² (nearest tenth)

Step-by-step explanation:

Use the sine rule for area of a triangle with 2 sides and an included angle (SAS).

Sine rule for area

[tex]\textsf{Area ABC}=\dfrac12ab \sin C[/tex]

(where [tex]a[/tex] and [tex]b[/tex] are the side lengths and [tex]C[/tex] is the included angle)

Given:

[tex]\implies \textsf{Area}=\dfrac12\cdot 8 \cdot 7 \cdot\sin (28\textdegree)[/tex]

               [tex]=13.14520376...[/tex]

               [tex]= 13.1 \textsf{ cm}^2 \textsf{ (nearest tenth)}[/tex]

Use sine rule

Area:-

[tex]\\ \sf\longmapsto \dfrac{1}{2}Base\times Height sin\theta[/tex]

[tex]\\ \sf\longmapsto \dfrac{1}{2}(8)(7)sin28[/tex]

[tex]\\ \sf\longmapsto 28sin28[/tex]

[tex]\\ \sf\longmapsto 13.1cm^2(Approx)[/tex]

Answer:

[tex]\displaystyle y = \frac{1}{2}sin\:524\pi{x}[/tex]

Step-by-step explanation:

[tex]\displaystyle \boxed{y = \frac{1}{2}cos\:(524\pi{x} - \frac{\pi}{2})} \\ \\ 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 \frac{C}{B} \hookrightarrow \boxed{\frac{1}{1048}} \hookrightarrow \frac{\frac{\pi}{2}}{524\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{1}{262}} \hookrightarrow \frac{2}{524\pi}\pi \\ Amplitude \hookrightarrow \frac{1}{2}[/tex]

OR

[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 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{1}{262}} \hookrightarrow \frac{2}{524\pi}\pi \\ Amplitude \hookrightarrow \frac{1}{2}[/tex]

You will need the above information to help you interpret the graph. First off, keep in mind that although the exercise told you to write the sine equation based on the speculations it gave you, if you plan on writing your equation as a function of cosine, 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 = \frac{1}{2}cos\:524\pi{x},[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine 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 cosine graph [photograph on the right] is shifted [tex]\displaystyle \frac{1}{1048}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{1}{1048}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{1}{1048}} = \frac{\frac{\pi}{2}}{524\pi}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle y = \frac{1}{2}cos\:(524\pi{x} - \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have the exercise to wourk with, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]It displays the formula on how to define each wavelength of the graph. You just need to remember that the B-term has [tex]\displaystyle \pi[/tex]in it as well, meaning both of them strike each other out, leaving you with just a fraction. Now, the amplitude is obvious to figure out because it is the A-term, so this is self-explanatory. 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 one-half unit beyond the midline, hence, your amplitude. So, no matter what the vertical shift is, that will ALWAYS be the equation of the midline, and if viewed from a graph, no matter how far it shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

If x  represent the number of seconds then the function is f(x)=0.5sin(52π(x))

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that the middle C key on a piano has a frequency of 262 cycles per second.

Frequency = 262

It has an amplitude of 0.5 unit

Amplitude = 0.5

We have to find the function.

y=Asin(2πf(x))

A is amplitude and f is the function.

y=0.5sin(2π262(x))

y=0.5sin(52π(x))

Hence, if x  represent the number of seconds then the function is f(x)=0.5sin(52π(x))

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ3

Answer:

Step-by-step explanation:

Here it is given that ,l ines PV , QW and RX are parallel .That is ,

[tex]\longrightarrow PV \ || \ QW \ || RX [/tex]

And we would like to find out the value of ,

[tex]\longrightarrow m\angle STW \ \& \ \angle TSV [/tex]

As we know that when a transversal intersects two parallel lines then ,

Here ,

[tex]\angle STW [/tex] and [tex]\angle TUX [/tex] are corresponding angles .So they must be equal.

[tex]\longrightarrow x = 2y \dots (i)[/tex]

Again here [tex]\angle VST[/tex] and [tex]\angle STW[/tex] are co- interior angles. So ,

[tex]\longrightarrow x + (x +5y) = 180^o \dots (ii) [/tex]

Substitute the value from equation (i) into (ii) ,

[tex]\longrightarrow 2y + 2y +5y =180^o \\[/tex]

[tex]\longrightarrow 9y = 180^o\\[/tex]

[tex]\longrightarrow y =\dfrac{180^o}{9}\\[/tex]

[tex]\longrightarrow y = 20^o [/tex]

[tex]\rule{200}4[/tex]

Therefore , we may find out the required angles as ,

[tex]\longrightarrow m\angle STW = x \\ [/tex]

[tex]\longrightarrow m\angle STW = 2y\\ [/tex]

[tex]\longrightarrow m\angle STW = 2(20^o)\\ [/tex]

[tex]\longrightarrow \underline{\underline{m\angle STW = 40^o}} [/tex]

[tex]\rule{200}4[/tex]

Again ,

[tex]\longrightarrow m\angle TSV = x + 5y \\ [/tex]

[tex]\longrightarrow m\angle TSV = 40^o 5(20^o)\\[/tex]

[tex]\longrightarrow m\angle TSV = 40^o + 100^o\\ [/tex]

[tex]\longrightarrow \underline{\underline{ m\angle TSV = 140^o }} [/tex]

And we are done!

[tex]\rule{200}4[/tex]

Answer:

x=6

Step-by-step explanation:

7+5(×-3)=22

expand the brackets:

7 + 5x - 15 = 22

simplify:

5x - 8 = 22

add 8 to both sides:

5x = 30

divide both sides by 5

x = 6

hope this helps

brainliest plz?

x

Answer:

7+5 (x-3)=22

7+5x-15=22

5x+ -8=22

5x=30

x=6

Step-by-step explanation:

PEMDAS

First distribute in the parentheses

Then add like terms together

once you have -8, add it on both sides

then divide 5 from both sides to leave the unknown variable by itself

Finally you have the answer

I hope this helps! :)

Answer:

5:12

Step-by-step explanation:

you can't simplify your answer so it will be

5:12

9514 1404 393

Answer:

  2/7

Step-by-step explanation:

Put the number where x is and do the arithmetic.

  [tex]14x^{-2}=\dfrac{14}{x^2}=\dfrac{14}{7^2}=\dfrac{7\cdot2}{7\cdot7}=\boxed{\dfrac{2}{7}}[/tex]

Answer:

B

Step-by-step explanation:

the values of t from the table are 7 times the corresponding values of s , so

t = 7s

Answer:

evaluate

Step-by-step explanation:

um duh

but I hope I helped in some way

Answer:

Distance between  the observer and the red car is [tex]250 Sin \frac{\pi}{3}t[/tex]

Step-by-step explanation:

Diameter of field = 500 m

Radius of field =[tex]\frac{Diameter}{2}=\frac{500}{2}=250 m[/tex]

Let R be the radius and the speed at which the car completes race be w

So,[tex]w=\frac{2\pi}{T}[/tex]

Car finished 5 laps in minutes = 30

Car finished 1 lap in minutes = [tex]\frac{30}{5}=6[/tex]

So, [tex]w=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]

Refer the attached figure

Angle between car and observer = wt

So, Distance between  the observer and the red car is give as A sin wt

So, Distance between  the observer and the red car=[tex]250 Sin \frac{\pi}{3}t[/tex]

Step-by-step explanation:

Tulis 689.802.473 dalam angka

six hundred eighty nine million eight hundred two four hundred and seventy three

sorry if wrong

Answer:

.23

Step-by-step explanatio

45 of the seeds will be yellow. So the probability of a yellow flower is

45/300 = .15

Total probability = probability of white + probability of yellow + probability of red

or

1 = P(W) + P(Y) + P(R)

we know P(W) = .62. So let x = probability of a red flower

1 = .62 + .15 + x

1 = .77 + x

x = .23

Answer:

a^8/b^12 --> a.k.a answer d

Step-by-step explanation:

when there's an exponent outside of a parenthesis of exponents inside, you're basically just going to multiply them together. not add or anything

2 * 4 = 8

3 * 4 = 12

and we cant divide or do anything else with the product b/c a and b are both different variables and we don't know what they are

Answer:

a=2x-b

Step-by-step explanation:

[tex]x=\frac{a+b}{2}\\\\\frac{a+b}{2} = x\\ a+b = 2x\\a= 2x-b\\[/tex]

Answer:

Highest common factor of 63 and 45 is 9.

Therefore there can be 9 bouquets each with 5 roses and 7 carnations

Step-by-step explanation:

hope this helped!

Step-by-step explanation:

Length=l

Width=w

l=3w

Perimeter of a rectangle=2(l+w)

2(l+w)=88

l+w=44

3w+w=44

4w=44

w=11

l=3w=33

Let l be the symbol for length

Let w be the symbol for width

[tex]l = 2w - 5[/tex]

Our first equation is built according to the given that the length is twice the width subtracted by 5

Our second equation is built on the definition of perimeter. A perimeter is the sum of all sides of a polygon. A rectangle has 4 sides (2 lengths and 2 widths)

So the perimeter of a rectangle is=l+l+w+w=2l+2w

[tex]2l + 2w = 26[/tex]

This will be our second equation;

I can make a system of equations of 2 unknowns using my 2 equations;

[tex]2l + 2w = 26[/tex]

[tex]l -2w = - 5[/tex]

Add the two systems together by adding everything that is before the equal sign together and everything after it together.

[tex]2l + l + 2w - 2w = 26 - 5[/tex]

[tex]3l = 21[/tex]

[tex]l = \frac{21}{3} = 7 \: meters[/tex]

To find the width substitute L=7 in any equation;

[tex]l = 2w - 5[/tex]

[tex]7 = 2w - 5[/tex]

[tex]7 + 5 = 2w[/tex]

12=2w

w=12/2=6

The app is bugging, the width is 6 meters and the length is 7 meters

Answer:

Negative

Step-by-step explanation:

A quadratic that does not touch the x-axis always has a negative discriminant.

positive

[tex]As\ shown\ in\ the\ figure[/tex]

[tex]when\ g(x)=0,\ have\ 2\ real\ roots\ (b^2-4ac > 0,\ \ have\ 2\ real\ roots)[/tex]

[tex]So\ the\ discriminant\ of\ g\ positive[/tex]

I hope this helps you

:)

Answer:

6,000,000

Explanation:

42,000 acres is the area you get after you multiply the number of acres of old-growth trees by 0.7%. So you would divide 42,000 by 0.7% to get the number of acres of old-growth trees.

# of acres of old-growth trees * 0.7% = 42,000

# of acres of old-growth trees = 42,000/0.7%

# of acres of old-growth trees = 6,000,000

PS. 0.7% = 0.007

Answer: 1/4/7=1/28

You’re welcome good luck to whatever you’re working on. Give brainliest please for my answer.

Answer:

the answer is A

Step-by-step explanation:

please make me brainliest

Answer:

da te

Step-by-step explanation:

Answer:

[tex]\sqrt{32}[/tex]

Step-by-step explanation:

The square root of 4 is 2.

The square root of 16 is 4.

The square root of 32 is 5.65685425.

The square root of 64 is 8.

Therefore [tex]\sqrt{32}[/tex] is irrational.

Hope this helped! :)

By rewriting the linear function we will see that the correct option is A.

"an increasing line that passes through (0, 4)"

Here we have the linear function:

2y  = 4x + 8

We can rewrite it to get the function in the slope-intercept form:

y = (4x + 8)/2

y = 2x + 4.

So, the slope is positive, this implies that we will have an increasing line.

We also can see that the y-intecept is 4, this means that the line passes through the point (0, 4).

From that, we can conclude that the correct option is A.

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

https://brainly.com/question/4025726

Answer:

12 boys

Step-by-step explanation:

i took the 7 that represents the girls and multiplied by 3 to get 21 (how many girls are there)

So then i took 4 multiplied 3 and thats how i got the answer 12 (brainllist Plz!)

Answer:

If Sarah has three times as many pencils as Mike she has 3  times the number of pencils Mike has which is equivalent to 3 * m. That means Mike has m pencils and Sarah has 3m pencils. they have m + 3m pencils. The expression would be total:  m + 3m.

Step-by-step explanation:

Answer:

None of the above

Step-by-step explanation:

According to the divergence test, if the limit of a sequence as n approaches infinity does not equal 0, then the series diverges.  (Notice that if the limit does equal 0, the series doesn't necessarily converge).

According to the geometric series test, a geometric series converges if -1 < r < 1, and diverges otherwise.

The first series is a geometric series with r = -5/3.  So it diverges.

The second series is also a geometric series:

3ⁿ⁻¹ / 2ⁿ = ⅓ (3ⁿ / 2ⁿ) = ⅓ (3/2)ⁿ

r = 3/2, so it diverges.

For the third series, the limit as n approaches infinity equals 1.  This fails the divergence test, so this series also diverges.

For the fourth series, the limit as n approaches infinity equals 1.  This fails the divergence test, so this series also diverges.

Answer:

Bar graph

Step-by-step explanation:

Hopes this helps

Answer:

n + 3 ≤ -8

Step-by-step explanation:

Answer: n + 3 is greater than or less than to -8

The symbol ≤ means less than or equal to.

I hope this helped remember any number that has a negative combined with a positive depending on the number it will rise or fall. In this matter we are adding a positive to a negative so the number gets closer to 0.