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ch4aika [34]
3 years ago
6

The National Science Foundation (NSF) offers grants to students who are interested in pursuing a college education. The student

must be enrolled full time (12 credit hours or more), and hold a grade point average of 3.8. The NSF will pay $9,500 per year towards tuition for 4 years. The initial amount is placed into an account paying 7.8% compounded annually, and the tuition is drawn from the account until the remaining balance is zero dollars. Determine the initial amount invested by the NSF. Round your answer to the nearest dollar.
a.
$30,000
c.
$35,036
b.
$31,606
d.
$38,000
Mathematics
2 answers:
Kruka [31]3 years ago
6 0
PVAO=9500[(1-(1+0.078)^(-4))/0.078]
PVAO=31605.79
So the answer is 31606
Elodia [21]3 years ago
3 0

Answer:

The answer is option b.  $31,606

Step-by-step explanation:

The NSF will pay $9,500 per year towards tuition for 4 years.

So, p = 9500

r = 7.8% or 0.078

t = 4

We can find the initial amount invested by:

p(\frac{1-(1+r)^{-t} }{r})

Putting values in the formula we get

9500(\frac{1-(1.078)^{-4} }{0.078} )

9500(\frac{1-0.74050}{0.078} )

= $31605.769

Rounding this to nearest whole number, we get $31606.

So, option B is the correct answer.

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6 0
2 years ago
1. Find the area of parallelogram ABCD.
LUCKY_DIMON [66]

Answer:

1: C =69.3 m2

2: F = ll units

3. C:  3 in.

4. G =65 units

Step-by-step explanation:

1: C =69.3 m2

We see from the figure that height of the parallelogram ABCD is not known and the base is 10 m

Taking the right angled triangle the height is given by

Sine theta= height/hypotenuse

height = hypotenuse* sine theta

         = 8* sine 60

         = 8* 0.866= 6.928

Area of parallelogram= base * height

                   = 10 * 6.928

                   = 69.28

                  =69.3 m²

2: F = ll units

We see from the figure that height of the parallelogram DEFG is not known and the base is 13 cm

Area of parallelogram= base * height

                  143 = 13 * height

           Height = 143/13= 11 units

3. C:  3 in.

The area of the triangle = 1/2 * base * height

Let the height be x then the base is 3x

54= 1/2*x*3x

54= 3x²/2

27= 3x²

x²=27/3

x²= 9

x= 3

The height is 3 inches

4. G =65 units

Area of the quadrilateral = 1/2 *PR*QO + 1/2 *PR*OS

                                      = 1/2*13*4+ 1/2*13*6

                                        =26+ 39

                                        = 65 units

These measurements are given in the diagram .

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Answer:

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