Which ordered pair is the solution to the system of equations below? 4x+3y=31 2y=22-3x (A) (4,5) (B) (5,4) (C) (6,2) (D) (7,1)

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.

7 0

3 years ago

If you take a number multiply by 7 then takeaway 1. You get the same as if you took the number multiply by 5 then takeaway 8. Wh

muminat

7x - 1 = 5x - 8
Minus 5x on each side
2x -1 = -8
Plus 1 on each side
2x = -7
Divide by 2 on each side
x = -7/2

The number is most likely -7/2

7 0

2 years ago

Read 2 more answers

Find the area of the triangle

Basile [38]

Answer:

Hello! answer: 76

Step-by-step explanation:

Formula to find area is base × height ÷ by 2 12 + 7 = 19 19 × 2 = 152 152 ÷ 2 = 76 HOPE THAT HELPS!

5 0

2 years ago

During the 2007 baseball season, Wade was up to bat 10 more times than

bearhunter [10]

Answer:

The number of times Ellis get to bat is 558.

Step-by-step explanation:

Here, let us assume the number of times Ellis bat = m

So, the number of times Dwight bat = 17 times fewer than Ellis

= m - 17

Also, number of times Wade got to bat = 10 more times than Dwight

= ( m- 17 )+ 10

Total number of bat times = 1650

So, the number of times ( Wade + Dwight + Ellis) bat together = 1650

⇒ ( m- 17 )+ 10 + (m - 17) + m = 1650

or, 3 m - 34 + 10 = 1650

or, 3 m = 1674

⇒ m = 1674/3 = 558 , or m = 558

Hence, the number of times Ellis get to bat = m = 558.

3 0

3 years ago

How to solve this 7/8 n=63

ololo11 [35]

Answer:

It equals n=72

Step-by-step explanation:

7/8 n=63

7n/8=63

8. 7n/8=8. 63

7n=504

7n/7=504/7

n=72

7 0

3 years ago