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3 years ago

0.5 (x-3) = 3x - 2.5 how many solutions

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

4 0

Answer:

There is 1 solution.

Step-by-step explanation:

0.5(x - 3) = 3x - 2.5

0.5x - 1.5 = 3x - 2.5

-2.5x = -1

x = 0.4

There is 1 solution.

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Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour

UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

$C(t) = C(0)e^{rt}$

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So $C(0) = 110$

Husband

Half life of 4 hours. So

$C(4) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{4r}$

$e^{4r} = 0.5$

Applying ln to both sides

$\ln{e^{4r}} = \ln{0.5}$

$4r = \ln{0.5}$

$r = \frac{\ln{0.5}}{4}$

$r = -0.1733$

So for the husband

$C(t) = 110e^{-0.1733t}$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.1733t}$

$C(11) = 110e^{-0.1733*11} = 16.35$

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

$C(10) = 0.5C(0) = 0.5*110 = 55$

$C(t) = C(0)e^{rt}$

$55 = 110e^{10}$

$e^{10r} = 0.5$

Applying ln to both sides

$\ln{e^{10r}} = \ln{0.5}$

$10r = \ln{0.5}$

$r = \frac{\ln{0.5}}{10}$

$r = -0.0693$

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

$C(t) = 110e^{-0.0693t}$

$C(11) = 110e^{-0.0693*11} = 51.33$

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

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3 years ago

Porfavor ayúdame es para hoy

konstantin123 [22]

Answer: 25cm

Es asi: 5cm x 5cm^2

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If the distance between two points (ab) on a circle is 15 cm and the angle between those two cities is 18˚, what is the circumfe

mrs_skeptik [129]

Since 18 is one twentieth of the angle of a full circle, 360, the circumference is 20 times the arc distance of 15, or 300

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Maria has a cube shaped box that measures 9 inches along each edge. Can she fit 1,000 square-inch cubes inside the box?

astra-53 [7]

No, the volume would be 9(9)(9), which is only 729 cubes

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Juan is on his way home and his new car. He has driven 36 miles so far which is 3/4 of the way home. What is the total length of

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Answer:

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Step-by-step explanation:

36/3 = 12 so 4/4 would be 48

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