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horsena [70]
3 years ago
5

Write an explicit formula for the arithmetic sequence 15.6, 15, 14.4, 13.8,..., and then find the 32nd term.

Mathematics
1 answer:
uysha [10]3 years ago
5 0

Answer: the 32nd term is - 3

Step-by-step explanation:

The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = 15.6

d = 15 - 15.6 = 14.4 - 15 = - 0.6

n = 32

The explicit formula for the arithmetic sequence is

Tn = 15.6 - 0.6(n - 1)

We want to determine the value of the 32nd term, T32. Therefore,

T32= 15.6 - 0.6 (32 - 1)

T32 = 15.6 - 18.6

T32 = - 3

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Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.
anzhelika [568]
Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
V_{0} =(1+ i_{a} ) ^{1}
Where
V_{0} = initial investment.
i_{a} = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
V_{0} =(1+ i_{q} ) ^{4}
Where
V_{0} = initial investment.
i_{q} = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
(1+ i_{a} )=(1+ i_{q} ) ^{4}
Notice that we are not using the initial investment V_{0} since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
(1+0.07)=(1+ i_{q} ) ^{4}
1.07=(1+ i_{q} ) ^{4}
\sqrt[4]{1.07} =1+ i_{q}
 i_{q} = \sqrt[4]{1.07} -1
i_{q} =0.017
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.


6 0
3 years ago
Ramp 10 feet high and 32 long
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A. IMA = 32/10 = 3.2

8 0
3 years ago
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lesantik [10]
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Since their no zeros (0) here's your answer:

6.174798604×10^9
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kondor19780726 [428]
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3 0
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Write L if it is likely to happen and U if unlikely to happen.
maria [59]

Answer:

Probabilities

        Likely to happen (L)      Unlikely to happen (U)

a.      4/5                                 5/8

b.     3/5                                  3/8

c.     4/5                                  4/7

d.    0.3                                  0.09

e.    5/6 and 4/5                   2/3

Step-by-step explanation:

Probabilities in Percentages:

a. The probability of 4/5 = 80% and 5/8 = 62.5%

b. The probability of 3/8 = 37.5% and 3/5 = 60%

c. The probability of 4/5 = 80% and 4/7 = 57%

d. The probability of 0.3 = 30% and 0.09 = 9%

e. The probability of 2/3 = 67% and 4/5 = 80% and 5/6 = 83%

b) To determine the relative values of the fractional probabilities, it is best to reduce them to their fractional or percentage terms.  When this is done, the relative sizes become obvious, and then, comparisons can be made.

3 0
2 years ago
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