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3 years ago

Find the annual interest rate.

Mathematics

2 answers:

Salsk061 [2.6K]3 years ago

7 0

Answer:

20.50

Step-by-step explanation:

lidiya [134]3 years ago

3 0

Answer:

12.05%

Step-by-step explanation:

You might be interested in

What is the easiest way to find a geometric mean?

zubka84 [21]

GM= ( II i = 1 xi) 1/N
for example, {3,4,2,6}.
GM = (3*4*2*6) 1/4
GM = 144*1/4
GM ~ 3.464

6 0

4 years ago

Graph the line that passes through the points (-1,7) and (-3,5) and determine

kari74 [83]

Answer:

y = x + 8

Step-by-step explanation:

find slope first:

m = 7-5 / -1-(-3)

m = 2 / 2

m = 1

now find the y-intercept using either ordered pair; plug 'y', 'x', and 'm' into

y = mx + b to solve for 'b'

7 = 1(-1) + b

7 = -1 + b

8 = b

put 'm' and 'b' into slope-intercept equation of a line, y = mx + b to get:

y = x + 8

5 0

3 years ago

Please help! thank you to anyone who does:)

Sav [38]

Answer: it is th

Step-by-step explanation:

3 0

3 years ago

Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

docker41 [41]

By De Moivre's theorem,

$\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}$

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let $x=\dfrac\pi5$ and let $c=\cos x$ . Then recall that

$\cos5x=c^5-10c^3\sin^2x+5c\sin^4x$

$\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)$

$\cos5x=16c^5-20c^3+5c$

On the left, $5x=\pi$ so that

$16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0$

Since $c=\cos\dfrac\pi5\neq1$ , we're left with

$4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4$

because we know to expect $\cos x>0$ . Then from the Pythagorean identity, and knowing to expect $\sin x>0$ , we get

$\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}$

Both $\cos$ and $\sin$ are $2\pi$ -periodic, so that

$\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5$

and

$\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5$

so that the answer we left in trigonometric form above is equal to

$\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}$

7 0

3 years ago

Li had 5 2/3 gallons of juice. He served 2 3/4 gallons at breakfast. How many gallons does Li have left? Enter your answer in th

Sholpan [36]

Total quantity of juice Li had = 5 2/3 gallons.

In breakfast used quantity = 2 3/4 gallons.

Number of gallons of juice does Li have left = Total quantity - used quantity.

Therefor, number of gallons of juice does Li have left = 5 2/3 gallons - 2 3/4 gallons.

Let us convert those mixed fractions into improper fracions first.

5 2/3 = (5*3+2)/3 = 17/3.

2 3/4 = (2*4+3)/4 = 11/4.

5 2/3 gallons - 2 3/4 gallons = 17/3 -11/4.

Subtracting fractions by taking common denominator (lcd).

We have common denominator of 3 and 4 = 3*4 = 12.

So, 17/3 -11/4 = 17*4/3*4 - 11*3/4*3

= 68/12 - 33/12.

= (68-33)/12.

= 35/12

Let us convert 35/12 into mixed fraction now.

Dividing 35 by 12 we get quotient 2 and remainder 11.

So, 35/12 can be wriiten in mixed fractions as 2 11/12.

And final answer would be, Li have left 2 11/12 gallons.

7 0

3 years ago