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lisov135 [29]
9 months ago
10

A bank features a savings account that has an annual percentage rate of 4.8 % with interest compounded monthly. Umbrosia deposit

s $6,500 into the account.
How much money will Umbrosia have in the account in 1 year?
What is the annual percentage yield (APY) for the savings account?
Mathematics
1 answer:
Scilla [17]9 months ago
5 0

S(8)=3500(1+(.047/4))^32

S(8)=$5086.40 in the account after 8 years.

a)The relative growth rate is .25, or 25%

b)at t=0, the population is 955e^.25(0)=955

c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.

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He will eventually make enough money to buy his car

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△klm, lm=20 sqrt 3 m∠k=105°, m∠m=30° find: kl and km
Anarel [89]

Answer:

KL =  \frac{20\sqrt{6}}{1+\sqrt{3}} = 17.93

MK =  \frac{40\sqrt{3}}{1+\sqrt{3}} = 25.36


Explanation:

According to the Law of Sines:

\frac{a}{sinA}=\frac{b}{sinB}= \frac{c}{sinC}

where:

A, B, and C are angles

a, b, and c are the sides opposite to the angles


First of all, let's find m∠L: the sum of the angles of a triangle is 180°, therefore

m∠K + m∠L + m∠M = 180°

m∠L = 180° - m∠K - m∠M

m∠L = 180° - 105° - 30°

m∠L = 45°


Now, we can apply the Law of Sines to our case (see picture attached):

\frac{LM}{sinK}=\frac{MK}{sinL}=\frac{KL}{sinM}


Let's solve one side at the time:

\frac{LM}{sinK}=\frac{MK}{sinL}

\frac{20\sqrt{3}}{sin(105)}=\frac{MK}{sin(45)}

MK = \frac{20\sqrt{3} }{sin(105)} \cdot sin(45)

MK = \frac{40\sqrt{3} }{1+\sqrt{3} } = 25.36


Similarily:

\frac{LM}{sinK}=\frac{KL}{sinM}

\frac{20\sqrt{3}}{sin(105)}=\frac{KL}{sin(30)}

KL = \frac{20\sqrt{3} }{sin(105)} \cdot sin(30)

KL = \frac{20\sqrt{6}}{1+\sqrt{3}} = 17.93

8 0
2 years ago
Which concept is used to prove that the opposite sides of a parallelogram are congruent?
Neko [114]

Answer:

  congruent triangles

Step-by-step explanation:

You can eliminate useless answers based on their wording. "Similar" anything cannot be used to prove congruence. "Rectangles" will not help you prove congruence of parallelogram sides. The only reasonable choice is ...

  congruent triangles

_____

Typically, a diagonal is drawn through the figure, and the two triangles created are shown to be congruent, often by ASA. Then, by CPCTC, sides of the parallelogram are shown to be congruent.

7 0
2 years ago
Read 2 more answers
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