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olga nikolaevna [1]
4 years ago
8

You deposit $300 in an account earning 5% interest compound annually. How much will you have in the account after 10 years

Mathematics
1 answer:
Alja [10]4 years ago
7 0

Answer:

450

Step-by-step explanation:

5% of 300 = 15

300+10(15)=450

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Answer:

1. Change each number to an improper fraction.

2. Simplify if possible.

3. Multiply the numerators and then the denominators.

4. Put answer in lowest terms.

Step-by-step explanation:

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If a > b > c > d, then which is larger, a+c or b+d ? Can we tell from a > b > c > d which of a+d and b+c is la
victus00 [196]

Answer:

1. a+c is larger than b+d

2. No way to tell whether a+d or b+c is larger.

Step-by-step explanation:

<u>1. Which is larger, a+c or b+d?</u>

Let a, b, c, and d be any numbers such that a > b > c > d.

Specifically, note that a > b, and subtracting b from both sides of the inequality, observe that a-b > 0.

Similarly, c > d, and subtracting d from both sides of the inequality, observe that c-d > 0.

From this, <u>add "a-b"</u> (a positive number, as proven above) to both sides of the inequality.

(a-b)+(c-d) > (a-b)+0

Addition by zero (<u>the additive identity</u>) doesn't change anything, so the right side remains "a-b"...

(a-b)+(c-d) > a-b

... and <u>"a-b" is positive</u>...

(a-b)+(c-d) > a-b > 0

... so, by the <u>transitive property</u> of inequality...

(a-b)+(c-d) > 0

Recall that <u>subtraction is addition by a negative</u> number...
a+(-b)+c+(-d) > 0

...and that <u>addition is associative and commutative</u>, so things can be added in any order, so the middle two terms on the left side can be rearranged...

a+c+(-b)+(-d) > 0

<u>Adding b + d</u> to both sides of the inequality

(a+c+(-b)+(-d))+(b+d) > 0+(b+d)

... and <u>simplifying</u>

a+c > b+d

So, a+c is larger than b+d.

<u>2. Which is larger, a+d or b+c?</u>

Consider the following two examples:

<u>Example 1</u>

Suppose a=10; b=3; c=2; d=1.

Note that a > b > c > d (10 > 3 > 2 > 1) and, also observe that a+d=(10)+(1)=11, and b+c=(3)+(2)=5, so a+d is larger than b+c.

<u>Example 2</u>

However, suppose a=10; b=9; c=8; d=1.

Note that a > b > c > d (10 > 9 > 8 > 1) but that a+d=(10)+(1)=11, and b+c=(9)+(8)=17, so a+d is smaller than b+c.

So, in one example, a+d is bigger, and in the other, a+d is smaller.  Therefore, there is no way to tell which of a+d or b+c is larger from only the given information.

5 0
2 years ago
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