It is 75 miles from my house to Georgia aquarium on the map it measures one 3/4 inches what is the scale of the map

Ben consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Ben's body decr

Airida [17]

Answer:

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

Step-by-step explanation:

After consuming the energy drink, the amount of caffeine in Ben's body decreases exponentially.

This means that the amount of caffeine after t hours is given by:

$A(t) = A(0)e^{-kt}$

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The 10-hour decay factor for the number of mg of caffeine in Ben's body is 0.2722.

1 - 0.2722 = 0.7278, thus, $A(10) = 0.7278A(0)$ . We use this to find k.

$A(t) = A(0)e^{-kt}$

$0.7278A(0) = A(0)e^{-10k}$

$e^{-10k} = 0.7278$

$\ln{e^{-10k}} = \ln{0.7278}$

$-10k = \ln{0.7278}$

$k = -\frac{\ln{0.7278}}{10}$

$k = 0.03177289938
$

Then

$A(t) = A(0)e^{-0.03177289938t}$

What is the 5-hour growth/decay factor for the number of mg of caffeine in Ben's body?

We have to find find A(5), as a function of A(0). So

$A(5) = A(0)e^{-0.03177289938*5}$

$A(5) = 0.8531$

The decay factor is:

1 - 0.8531 = 0.1469

The 5-hour decay factor for the number of mg of caffeine in Ben's body is of 0.1469.

7 0

3 years ago

What is the measure of CED? O 106° B. 160° O 108° 52 148 O 212

LenKa [72]

Answer:

The answer is D (212 degrees)

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The Cinemania theater showed 108 different movies last year. Of those, 15 movies were action movies. Based on this data, what is

natita [175]

Answer:

A reasonable estimate of the probability is equal to $0.1389$ or $13.89\%$

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

so

Let

x------> size of the event space

y-----> size of the sample space

so

$P=\frac{x}{y}$

In this problem we have

$x=15$

$y=108$

substitute

$P=\frac{15}{108}=0.1389$

Convert to percentage

$0.1389*100=13.89\%$

3 0

3 years ago

Write a slope intercept equation for line with the given characteristics m=-3/5 passes through (4,-4)

Ber [7]

Step-by-step explanation:

Hey there!

Given;

Slope (m) = -3/5

And passes through the point(4,-4).

Now; The equation of a line in slope intercept form is y= mx+b.

So, try to bring it in y= mx+b form.

Firstly let's use one-point formula.

$(y - y1) = m(x - x1)$

Now, keep all values.

$(y + 4) = \frac{ - 3}{5} (x - 4)$

Now, simplify to get answer.

$5(y + 4) = - 3(x - 4)$

$5y + 20 = - 3x + 12$

$5y = - 3x + 12 - 20$

$5y = - 3x - 8$

$y = \frac{ - 3}{5} x - \frac{8}{5}$

Therefore the equation is y = -3/5x - 8/5.

Hope it helps...

3 0

2 years ago

I need the description of how to draw a parallel line and a perpendicular line.

EleoNora [17]

How to Draw Parallel Lines:
1. Draw a straight line any length

2. Draw another straight line any length

(note : ensure the lines will never intersect)

They shall never horizontally or vertically.

How to Draw Perpendicular Lines:
1. Draw a straight line vertically

2. Draw a straight line horizontally

(note : length does not necessarily matter)

The two lines must cross at right angles to each other!!

With the parallel line instructions, simply just draw lines but, when given the slopes of two lines, you must get graphing paper or make your own, and graph it by plotting points and then getting a ruler and tracing it.

With the perpendicular lines it helps with showing a relation between situations along with given slopes. They shall intersect always and meet at a 90° angle. Use the equations and plot them then take a ruler and trace them and notice the intersection. Solve it yourself and see that the intersection and the answers you got are the same.

5 0

2 years ago