The Colorado River is 1,450 miles long. This is 752 miles shorter than the Mississippi River. Write an equation that describes t
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The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
<h3>How to find the sum of consecutive integers?</h3>What are the properties of summation?</h3>
where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).
For the given case, the considered summation can be written symbolically as:
It is evaluated as;
Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
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$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Step-by-step explanation:
Susan purchased company ABC's stock and invested the balance in her money market account
- ABC's stock yielded 13% last year and her money market account yielded 5% last year
- Susan's initial investments amount to $15000, and the annual income is $1070
We need to find how much money is invested in stock and how much is invested in her money market account
Assume that she invested $x in ABC's stock and $y in her money market account
∵ She invested $x in ABC's stock
∵ She invested $y in her market account
∵ Her initial investments amount is $15000
∴ x + y = 15000 ⇒ (1)
The interest formula is I = Prt, where P is the initial investment, r is the rate of interest in decimal and t is the time
In ABC's stock:
∵ She invested $x
∴ P = x
∵ The rate is 13%
∴ r = 13% = 13 ÷ 100 = 0.13
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = x(0.13)(1)
∴ = 0.13x
In her market account:
∵ She invested $y
∴ P = y
∵ The rate is 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = y(0.05)(1)
∴ = 0.05y
∵ Her annual income is $1070
- Add the interest of ABC's stock and the interest of her market
account, equate the sum by 1070
∴ 0.13x + 0.05y = 1070 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.05 to eliminate y
∵ -0.05x - 0.05y = -750 ⇒ (3)
- Add equations (2) and (3)
∴ 0.08x = 320
- Divide both sides by 0.08
∴ x = 4000
- Substitute value of x in equation (1) to find y
∵ 4000 + y = 15000
- Subtract 4000 from both sides
∴ y = 11000
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
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You can learn more about the system of equations in brainly.com/question/2115716
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