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Fofino [41]
3 years ago
5

119. Beatrice decides to deposit $100 per month at the end of every month in a bank with an annual interest rate of 5.5% compoun

ded monthly.
a. Write a geometric series to show how much she will accumulate in her account after one year.
Mathematics
1 answer:
sveta [45]3 years ago
3 0

Answer:

Beatrice will accumulate $1230.72 at the end of the year.

Step-by-step explanation:

We can write:

(1+\frac{0.055}{12})=z

100=C for deposits

The first month would have only the deposit reflected in her balance, then, expanding some steps of the calculation would yield:

S_{1}=C\\S_{2}=Cz + C\\S_{3}=Cz^{2}+Cz + C\\S_{n}=Cz^{n-1} +...+Cz+C

A geometric series is given by:

1+x+...+x^{m}=\frac{x^{m+1}-1}{x-1}

Translating our series to the short form:

S_{n}=C(\frac{z^{n}-1}{z-1} )

plugin in the values for the 12 month gives:

S_{12}=100(\frac{(1+\frac{0.055}{12})^{12} -1}{\frac{0.055}{12}})=1230.7169

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Answer:

49

Step-by-step explanation:

588  divided by 12                        49

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Hope this helped, click thanks if it did

6 0
3 years ago
Need to know number 2.
melomori [17]

Answer:

when the radicand is negative

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
A train travels train travels 288 kilometre at a uniform speed. If the speed had been 4 kilometre per hour more it would have ta
kiruha [24]

Answer:

Let the speed of the train be x km/h.

Case 1:

Distance = 288 km

Speed = x km/h

Time = Distance/Speed

= 288/x h

Case 2:

Distance = 288 km

Speed = (x+4) km/h

Time = 288/x + 4 h

Since 288/x > 288/x + 4

288/x - 288/x+4 = 1

288[1/x - 1/x+4 ] = 1

[ x + 4 - x / x(x + 4) ] = 1/288

[4 / x^2 + 4x ] = 1/288

x^2 + 4x = 1152

x^2 + 4x - 1152 = 0

x^2 + 36x - 32x - 1152 = 0

x(x + 36) - 32(x + 36) = 0

(x + 36)(x - 32) = 0

x + 36 = 0 , x - 32 = 0

x = -36 , x = 32

x = -36 , rejected since speed cannot be negative.

Therefore , speed of the train = 32 km/h

4 0
3 years ago
DUE BY 11:59 PM!!<br><br>HELP GREATLY APPRECIATED!!​
aksik [14]

Answer:

Step-by-step explanation:

1. There are only 4 numbers including 5 that follow the "five or more" requirment, and the probability of spinning it once is 4/8, or 1/2. (The total sections is 8) Then we multiply 1/2 and 1/2 together to get the "two times in a row" requirement done. (1/2)*(1/2)= 1/4 is the probability.

2. There are two values on the spinner that are a multiple of 3, 3 itself and 6. Again, the total amount of numbers/sections is 8, so the probability of spinning a multiple of three is 2/8 or 1/4. The probability of spinning an odd number is 4/8 or 1/2. (1/2)*(1/4)=1/8 is the probability.

3. The probability of spinning one odd number is 1/2, and so we multiply 1/2 by itself four times. (1/2)*(1/2)*(1/2)*(1/2)=1/16 is the probability.

4. There are 6 numbers greater than two on the number wheel not including two itself. So the probability of that is 6/8, or 3/4. Then we multiply 3/4 by itself 3 times as it asks. (3/4)*(3/4)*(3/4)*(3/4)=81/256 is the probability.

Note that I am not really sure about the answer myself, but I hope that this can help in some way. Good luck! :)

5 0
3 years ago
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