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jonny [76]
3 years ago
13

Nate borrowed $62,000 at 9.4% interest per year if he owed a total of $910.90 in when he repaid the loan how many days do they k

eep the money for
Mathematics
1 answer:
OverLord2011 [107]3 years ago
6 0
The formula for simple annual interest is:

I = Prt

where,

I = Interest accumulated = $910.90
P = Principal Amount = $62000
r = Interest rate = 9.4% = 0.094
t = time in years

Using the values in above equation, we get:

910.90 = 62000 x 0.094 x t

⇒ t = 910.90/(62000 x 0.094) = 0.156

This is the time in years. Since there are 365 days in a year, the time in days will be:

t = 0.156 x 365 = 57 (rounded to nearest day)

This means, Nate kept the borrowed money for 57 days
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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by
11111nata11111 [884]

Answer:

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is V=l\times b\times h

V=(11-2x)\times (7-2x)\times x

V=4x^3-36x^2+77x

Derivate w.r.t x,

V'(x)=4(3x^2)-2(36x)+77

V'(x)=12x^2-72x+77

The critical point when V'(x)=0

12x^2-72x+77=0

Solve by quadratic formula,

x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}

x=4.607,1.392

Derivate again w.r.t x,

V''(x)=24x-72

Now, V''(4.607)=24(4.607)-72=38.568>0 (+ve)

V''(1.392)=24(1.392)-72=-38.592 (-ve)

So, there is maximum at x=1.392.

The length of the box is l=11-2x

l=11-2(1.392)=8.216

The breadth of the box is b=7-2x

b=7-2(1.392)=4.216

The height of the box is h=1.392.

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is V=l\times b\times h

V=8.216\times 4.216\times 1.392

V=48.217\ in.^3

The volume of the box is 8.217 cubic inches.

5 0
3 years ago
Factor completely:
maw [93]

Answer:

d

Step-by-step explanation:

Given

12x^{5} + 6x³ + 8x² ← factor out 2x² from each term

= 2x²(6x³ + 3x + 4) → d

7 0
3 years ago
I need to know the answer to the question with the circle
KATRIN_1 [288]
___________________________

◆ AREA RELATED TO CIRCLES ◆ ___________________________

As shown in the figure ,

Radius of circle = 5 cm

Side of square = 2 × (Radius of inscribed circle)

Side of square = 2 × 5 cm

Side of square = 10 cm = a

___________________________

Now ,
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Area of shaded region =
{a}^{2} - \pi {r}^{2}

Area of shaded region =
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Area of shaded region = 100 - 78.571

= 21.428 \: ans.

7 0
3 years ago
the sum of 3 decimal numbers is 6. Exactly one of the numbers is less than 1 what could those numbers be.
kati45 [8]
There are infinitely many solutions to this problem (which is why it asks what could those numbers be), so you just have to make one up!

Start with the first sentence.
x + y + z = 6.0

Now one of those numbers has to be less than 1. I'll choose x. And I'll choose a random number, say, 0.7.

0.7 + y + z = 6.0

Now I'll subtract 0.7 from both sides to see what y and z have to add up to.

0.7 + y + z - 0.7 = 6.0 - 0.7
y + z = 5.3

Now I'll choose a random number for y that's less than 5.3.

2.6 + z = 5.3

And subtract 2.6 from both sides to find z.

2.6 + z - 2.6 = 5.3 - 2.6
z = 2.7

And now we have our numbers!
x = <u>0.7</u>
y = <u>2.6</u>
z = <u>2.7</u>
3 0
3 years ago
Bill paid $2.49 for 5 pounds of rice. What could be cost of 9 pounds
Nadya [2.5K]

Answer:

\boxed{\sf Cost \ of \ 9 \ pounds \ rice =\$ 4.482}

Given:

5 pounds rice cost $2.49

To Find:

Cost of 9 pounds rice

Step-by-step explanation:

5 pounds rice cost $2.49

1 pound rice will cost $ \sf \frac{2.49}{5}

So,

9 pounds rice cost = 1 pound rice cost × 9

= $ \sf \frac{2.49}{5} \times 9

= $0.498 × 9

= $4.482

3 0
3 years ago
Read 2 more answers
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