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Snowcat [4.5K]
3 years ago
7

Maya open a savings account that pays 3.5% annual interest compounded semiannually.If she deposited $2,000 into the account and

made no other deposits or withdrawals, how much money did she have in the account after one year?​
Mathematics
1 answer:
dalvyx [7]3 years ago
4 0
That would be $2,070 because 3.5% of 2000 is 70
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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co
jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

5 0
3 years ago
If breadth of a rectangle is 19m and perimeter is 80m, find the length of the rectangle.
soldi70 [24.7K]

Answer: 21

Step-by-step explanation:

since 19 is the breadth and the perimeter is 80m, so 19*2=38 and 80-38= 42 so 42/2=21. The answer is 21

3 0
3 years ago
Find d<br><br> a * a * a = 216<br> a * b * c = 96<br> b * c = 52<br> a + b + c = d
Slav-nsk [51]

a\cdot a\cdot a=216\\\\a^3=216\to a=\sqrt[3]{216}\\\\\boxed{a=6}\\\\\text{Substitute}\ b\cdot c=52\ \text{to the second expression}\ a\cdot b\cdot c=96:\\\\abc96\ \wedge\ bc=52\to a(52)=96\qquad\text{divide both sides by 52}\\\\a=\dfrac{96}{52}\to a=\dfrac{24}{13}\neq6

a = 6 and a = 24/13  FALSE!!!

<h3>Answer: NO SOLUTION.</h3>
3 0
4 years ago
A rectangle that has a width of 18 inches and a length of 36 inches has a diagonal of 43 inches. True or false
astra-53 [7]

Answer:

fals it is smaller than that

4 0
3 years ago
Question is below in photo
horrorfan [7]

what about using 20-30-40-5

Step-by-step explanation:

the sequence is that you are skipping ten to get the second nb which is 30 and keep on going on to get 50

3 0
3 years ago
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