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2 years ago

Fill in the space -1•6=(_)•(-1) Commutative or associative

Mathematics

1 answer:

iren [92.7K]2 years ago

6 0

Answer:

Step-by-step explanation:

I am pretty sure this is your correct answer because you just switch the order

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The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.

Mazyrski [523]

Answer:

$a=250 \, mg\\\\b=5\\\\T= 90'$

Step-by-step explanation:

We have that $Q(t) = a\cdot b^{-\frac{t}{T}} \\$

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg. So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when $t=0$ , that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

$Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg$

We have found the constant $a$ ! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

$Q(t+90')=Q(t)/5$

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

$Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}$

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick $T=90'$ and thus we will get:

$b^{-1 }=\frac{1}{5}\\\\\frac{1}{b}= \frac{1}{5}\\\\b=5$

And that is our final result.

3 0

3 years ago

An airport offers 2 shuttles that run on different schedules. If both shuttles leave the airport at 4.00 pm at what time will th

Ksivusya [100]

Answer:

4:18 pm

Step-by-step explanation:

An airport offers 2 shuttles that run on different schedules.If both shuttles leave the airport at 4:00 p.m.,at what time will they next leave theairport together.

Shuttle A leaves every 6 minutes

Shuttle B leaves every 9 minutes

Solution

To solve for when next both shuttles will leave the airport together, find the least common multiples of 6 minutes and 9 minutes

Shuttle A (every 6 minutes) = 6, 12, 18, 24

Shuttle B (every 9 minutes) = 9, 18, 27, 36

The least common multiples of 6 minutes and 9 minutes is 18 minutes

4:00 pm + 18 minutes

= 4:18 pm

The next time both shuttles will leave theairport together is 4:18 pm of the same day

8 0

2 years ago

2.<br>2x2 + 2x - 112 factor

Angelina_Jolie [31]

Answer:

Use order of operation

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Peyton's field hockey team wins 4 games out of every 7 games played. Her team lost 9 games. How many games did Peyton's team pla

andre [41]

Answer:

Games played= 21 games

Step-by-step explanation:

Giving the following information:

Peyton's field hockey team wins 4 games out of every 7 games played.

We know that Peyton's team loses 3 games out of 7.

So if the team lost 9 games, the proportion is completed 3 times.

Games played= 3*7= 21 games

4 0

3 years ago

1. What is the equation of a line that has a slope of ⅔ and a y-intercept of -3?

ArbitrLikvidat [17]

Answer:

1. y = (⅔)x - 3

2. y = 3x + c

3. 1) non-proportional

2) can be proportional if c = 0

Step-by-step explanation:

1. What is the equation of a line that has a slope of ⅔ and a y-intercept of -3?

y = (⅔)x - 3

2. What is the equation of a line that has a slope of 3?

y = 3x + c

3. Lable the 2 equations as proportional or non-proportional and why.

A proportional relation should pass through the origin, i.e the y-intercept should be 0

3 0

3 years ago