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dusya [7]
2 years ago
11

On Melissa's 6th birthday, she gets a $2000 CD that earns 7% interest compounded quarterly. If the CD matures on her 13th birthd

ay, how much money will be available?​
Mathematics
1 answer:
Alexandra [31]2 years ago
8 0

Answer:

A\simeq3250.83

Step-by-step explanation:

The amount formula in compound interest is:

A=P(1+\frac{r}{n} )^{nt}

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $2000

r = 7\% = \frac{7\%}{100\%}=0.07

t = 7 (number of years from 6th to 13th bday)

n = 4 (quarterly in a year)

Then,

A=2000(1+\frac{0.07}{4} )^{(4)(7)}\\\\A=2000(1+\frac{0.07}{4} )^{28}\\\\A=3250.825792\\\\A\simeq3250.83

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Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y =
Dovator [93]

Answer:

V = π ∫₀² (y² − 8y + 6√(2y)) dy

or

V = π ∫₀² (6x − 5x² + x³) dx

Step-by-step explanation:

y₁ = 0.5x²

y₂ = x

First, find the intersections of the curves.

0.5x² = x

x² = 2x

x² − 2x = 0

x (x − 2) = 0

x = 0 or x = 2

So the points of intersection are (0, 0) and (2, 2).

When we revolve this region about the line x = 3, we get a hollow shape that looks like an upside-down funnel, or a volcano.

One option is to use washer method to find the volume, by cutting a thin horizontal slice of thickness dy, inner radius 3−x₁ = 3−√(2y), and outer radius of 3−x₂ = 3−y.

V = ∫₀² π [(3−y)² − (3−√(2y))²] dy

V = ∫₀² π (9 − 6y + y² − 9 + 6√(2y) − 2y) dy

V = π ∫₀² (y² − 8y + 6√(2y)) dy

Another option is to use shell method to find the volume, by cutting a thin vertical slice of thickness dx, radius 3−x, and height y₂−y₁ = x−0.5x².

V = ∫₀² 2π (3 − x) (x − 0.5x²) dx

V = ∫₀² 2π (3x − 1.5x² − x² + 0.5x³) dx

V = ∫₀² 2π (3x − 2.5x² + 0.5x³) dx

V = π ∫₀² (6x − 5x² + x³) dx

The second option is arguably easier to evaluate, but either one will get you the same answer (V = 8π/3).

7 0
3 years ago
PLZZZ I BEGGG PLZZZ HELP ME!!!!
Tom [10]

Answer:

100

Step-by-step explanation:

There are 4 numbers less than 5 on the spinner.

4/6=2/3

150*2/3=100

4 0
2 years ago
Read 2 more answers
Which of these is closest to the time in years that it will take an investment to triple when it is invested in an account that
kkurt [141]

Answer:

20.4 years

Step-by-step explanation:

The nper formula in excel comes handy in this scenario:

=nper(rate,pmt,-pv,fv)

Rate is the monthly rate of 5.4%/12

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The triple amount would be $5,000*3=$15,000 which is future value fv.

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=nper(5.4%/12,0,-5000,15000)= 244.68  months

Yearly it can be expressed as = 244.68/12  =20.39  years

When rounded to one decimal place it becomes 20.4 years

5 0
2 years ago
Emily flipped a coin 30 times the coin landed heads up nine times and tails up 21 times
lara [203]
Part A)
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Part B)
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8 0
3 years ago
Which letter on this number line is at -2.25?
svlad2 [7]

Answer:

A.

Step-by-step explanation:

7 0
3 years ago
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