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3 years ago

You deposit $ 1200 in an account. The annual interest rate is 3%. How long will it take you to earn $108 in simple interest?

Mathematics

1 answer:

alukav5142 [94]3 years ago

5 0

The correct answer is 3

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What is the greatest common factor of 3 and 6? O3 O 6 O 18 O 36

Arada [10]

Answer:

3 I believe

Step-by-step explanation:

The factors of 3 are: 1, 3

The factors of 6 are: 1, 2, 3, 6

Then the greatest common factor is 3.

6 0

3 years ago

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Find the measurement of ∠DOC Round your answer to the nearest whole number.

polet [3.4K]

Answer:

61.2 degrees

Step-by-step explanation:

You want to isolate x on one side of the equation and the numbers on the other side

3x + 2x + 27 = 180

3x + 2x +27 - 27 = 180-27

5x = 153

x = 153/5

x = 30.6

<DOC = 2x

2x = 30.6 x 2

61.2 degrees

7 0

3 years ago

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Radical 2 squared plus 7 squared

ololo11 [35]

Answer: 51

Step-by-step explanation: (sqrt(2))^2 + 7^2

The squareroot and square cancel, leaving 2. 7^2=7*7=49

49+2=51

7 0

3 years ago

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the larger triangle is a dilation of the smaller triangle with a center of dilation at (2,-1). Whatbis the scale factor of the d

leva [86]

I think it’s 2. You can see this because if you count the squares in the smaller triangle it is 3 along. You would then need to double the amount of squares on all sides. This makes the larger triangle now 6 squares along. 6/3 is 2 making the scale factor 2. (This is only if I have read the question correctly and we are calculating small to big. If I have read it wrong and it is big to small it would be 1/2)

5 0

3 years ago

For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[

Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

$1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

Solve point 1 that is $\sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\$ :

when,

$k= 1 \to s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\$

$= \frac{1}{2} - \frac{1}{3}\\\\$

$k= 2 \to s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\$

$= \frac{1}{3} - \frac{1}{4}\\\\$

$k= 3 \to s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\$

$= \frac{1}{4} - \frac{1}{5}\\\\$

$k= n^ \to s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\$

Calculate the sum $(S=s_1+s_2+s_3+......+s_n)$

$S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\$

When $s_n \ \ dt_{n \to 0}$

$=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\$

$\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}$

In point 2: $\sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}$

when,

$k= 1 \to s_1 = \frac{1}{(1+6)(1+7)}\\\\$

$= \frac{1}{7 \times 8}\\\\= \frac{1}{56}$

$k= 2 \to s_1 = \frac{1}{(2+6)(2+7)}\\\\$

$= \frac{1}{8 \times 9}\\\\= \frac{1}{72}$

$k= 3 \to s_1 = \frac{1}{(3+6)(3+7)}\\\\$

$= \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\$

$k= n^ \to s_n = \frac{1}{(n+6)(n+7)}\\\\$

calculate the sum: $S= s_1+s_2+s_3+s_n\\$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\$

when $s_n \ \ dt_{n \to 0}$

$S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066$

$\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}$

8 0

3 years ago