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Lina20 [59]
3 years ago
8

How many half miles are in 12 miles?

Mathematics
1 answer:
adoni [48]3 years ago
3 0
There are 24 half miles in 12 miles.

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Eli invested $ 330 $330 in an account in the year 1999, and the value has been growing exponentially at a constant rate. The val
Cloud [144]

Answer:

The value of the account in the year 2009 will be $682.

Step-by-step explanation:

The acount's balance, in t years after 1999, can be modeled by the following equation.

A(t) = Pe^{rt}

In which A(t) is the amount after t years, P is the initial money deposited, and r is the rate of interest.

$330 in an account in the year 1999

This means that P = 330

$590 in the year 2007

2007 is 8 years after 1999, so P(8) = 590.

We use this to find r.

A(t) = Pe^{rt}

590 = 330e^{8r}

e^{8r} = \frac{590}{330}

e^{8r} = 1.79

Applying ln to both sides:

\ln{e^{8r}} = \ln{1.79}

8r = \ln{1.79}

r = \frac{\ln{1.79}}{8}

r = 0.0726

Determine the value of the account, to the nearest dollar, in the year 2009.

2009 is 10 years after 1999, so this is A(10).

A(t) = 330e^{0.0726t}

A(10) = 330e^{0.0726*10} = 682

The value of the account in the year 2009 will be $682.

4 0
3 years ago
Need help please, thanks!
MakcuM [25]
Given:
1 inch : 18 kilometers

Let us use the ratio and proportion method:

a:b = c:d where ad = bc

0.8 inches is <u>14.4 kilometers</u>

1 : 18 = 0.8 : x
x = 0.8 * 18
x = 14.4 km

1.4 inches is <u>25.2 kilometers</u>

1: 18 = 1.4 : x
x = 18 * 1.4
x = 25.2 km

2.1 inches is <u>37.8 kilometers</u>

1 : 18 = 2.1 : x
x = 18 * 2.1
x = 37.8 km

4 0
2 years ago
Gavyn, Pip and Mark share £102 in a ratio 1:2:3. How much money does each person get?
rosijanka [135]

Answer:

see explanation

Step-by-step explanation:

sum the parts of the ratio , 1 + 2 + 3 = 6 parts

divide the amount by 6 to find the value of one part of the ratio

£102 ÷ 6 = £17 ← value of 1 part of the ratio , then

2 parts = 2 × £17 = £34

3 parts = 3 × £17 = £51

Gavyn gets £17

Pip gets £34

Mark gets £51

5 0
2 years ago
Read 2 more answers
Find the general indefinite integral. (use c for the constant of integration. 4 x 2 + 3 + 8 x2 + 1 dx
ikadub [295]
The answer is 4x^3 + 4x + C

5 0
2 years ago
Find the coordinates of the circumcenter of triangle ABC with vertices A(1,4) B(1,2) and C(6,2)
Ray Of Light [21]
<span>(3.5, 3) is the circumcenter of triangle ABC. The circumcenter of a triangle is the intersection of the perpendicular bisectors of each side. All three of these perpendicular bisectors will intersect at the same point. So you have a nice self check to make sure your math is correct. Now let's calculate the equation for these bisectors. Line segment AB: Slope (4-2)/(1-1) = 2/0 = infinity. This line segment is perfectly vertical. So the bisector will be perfectly horizontal, and will pass through ((1+1)/2, (4+2)/2) = (2/2, 6/2) = (1,3). So the equation for this perpendicular bisector is y = 3. Line segment BC (2-2)/(6-1) = 0/5 = 0 This line segment is perfectly horizontal. So the bisector will be perfectly vertical, and will pass through ((1+6)/2,(2+2)/2) = (7/2, 4/2) = (3.5, 2) So the equation for this perpendicular bisector is x=3.5 So those two bisectors will intersect at point (3.5,3) which is the circumcenter of triangle ABC. Now let's do a cross check to make sure that's correct. Line segment AC Slope = (4-2)/(1-6) = 2/-5 = -2/5 The perpendicular will have slope 5/2 = 2.5. So the equation is of the form y = 2.5*x + b And will pass through the point ((1+6)/2, (4+2)/2) = (7/2, 6/2) = (3.5, 3) Plug in those coordinates and calculate b. y = 2.5x + b 3 = 2.5*3.5 + b 3 = 8.75 + b -5.75 = b So the equation for the 3rd bisector is y = 2.5x - 5.75 Now let's check if the intersection with this line against the other 2 works. Determining intersection between bisector of AC and AB y = 2.5x - 5.75 y = 3 3 = 2.5x - 5.75 8.75 = 2.5x 3.5 = x And we get the correct value. Now to check AC and BC y = 2.5x - 5.75 x = 3.5 y = 2.5*3.5 - 5.75 y = 8.75 - 5.75 y = 3 And we still get the correct intersection.</span>
6 0
3 years ago
Read 2 more answers
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