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Andrew [12]
3 years ago
8

Rose and Dennis each open a savings account at the same time. Rose invests $2,600 in an account yielding 4.1% simple interest, a

nd Dennis invests $2200 in an account yielding 5.7% simple interest. After nine years, who has the greater total amount of money, and how much greater is it? a. Rose has $230.80 more than Dennis. b. Rose has $559.40 more than Dennis. c. Dennis has $169.20 more than Rose. d. Dennis has $512.00 more than Rose.
Mathematics
1 answer:
densk [106]3 years ago
4 0
The formula is
A=p (1+rt)
A future value
P present value
R interest rate
T time

Rose investment
A=2,600×(1+0.041×9)
A=3,559.4

Dennis investment
A=2,200×(1+0.057×9)
A=3,328.6

Rose investment is greater by
3,559.4−3,328.6=230.8

So the answer is A

Hope it helps!
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Sonbull [250]

Answer:

The positive value of k will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0 (1)

Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

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Step-by-step explanation:

..................

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Answer:

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Step-by-step explanation:

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