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3 years ago

6

The formula for the remaining volume of fuel in a cars tank is I - E • D, where I is the initial volume of fuel, E if the fuel e

fficiency, and D is the distance traveled. Carson drove a distance of 120 kilometres. He initially had 30 litres of fuel, and his car's fuel efficiency is 100 cubic centimetres per kilometer. What calculation will give us the estimated volume of fuel left in Carson's tank by the end of the drive, in litres? a)30-100/1000 • 120 b)30•1000-100•20 c)30/1000 -100•120 d)30-100•1000•120

1 answer:

Y_Kistochka [10]3 years ago

5 0

Answer:

a)30-100/1000 • 120

Step-by-step explanation:

Given:

Remaining volume of fuel in a cars tank = I - E • D

where,

I = initial volume of fuel

E = fuel efficiency

D = distance traveled.

Carson

I = 30

E = 100

D = 120

Estimated volume of fuel in Carson's tank = I - E • D

= 30 - 100/1000 * 120

a)30-100/1000 • 120

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The population of a certain country in 1997 was 288 million people. In addition, the population of the country was growing at a

Crazy boy [7]

Answer:

a) In the year 1998 with 3 days, 2 hours, 44 minutes and 18.1006141 seconds

b) In the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

Step-by-step explanation:

a) To know the time when the population will be 305 million people, we need to isolate the variable t in the equation, $P(t)=288(1.009)^{t-1997}$

So we isolate t with the property of logarithms that allow us go down the exponent, applying in both sides of the equation

For this subsection the value of P is equal to 305 million people

$Ln(305)=Ln[(288)(1.009)]^{t-1997}$

$Ln(305)=(t-1997)*Ln[(288)(1.009)]$

Now, we can isolate the value of t

$\frac{Ln(305)}{Ln[(288)(1.009)]} =t-1997$

$\frac{Ln(305)}{Ln[(288)(1.009)]}-1997 =t$

$t=1998.008531776402$

So to know the exact date we multiply the number after the point, that is 0.008531776402 for the number of days that have 1 year, equal to 365 days

0.008531776402*365= 3.114098387 days

then the number after the point, that is 0.114098387 will be multiply for the number of hours that have 1 day

0.114098387*24= 2.738361282 hours

then the number after the point, that is 0.738361282 will be multiply for the number of minutes that have 1 hour

0.738361282*60= 44.3016769 minutes

Finally, the number after the point, that is 0.3016769 will be multiply for the number of seconds that have 1 minute

0.3016769*60= 18.1006141 seconds

And we obtain that the time, when the population of the country is 305 million people, is in the year 1998 with 3 days, 2 hours, 44 minutes and 25.152 seconds

b) For calculate the time when the population is 395 million people, we do the same process we did in the subsection a)

$Ln(395)=Ln[(288)(1.009)]^{t-1997}$

$Ln(395)=(t-1997)*Ln[(288)(1.009)]$

Now, we can isolate the value of t

$\frac{Ln(395)}{Ln[(288)(1.009)]} =t-1997$

$\frac{Ln(395)}{Ln[(288)(1.009)]}-1997 =t$

$t=1998.05412021527$

0.05412021527*365= 19.75387857 days

0.75387857 *24= 18.09308577 hours

0.09308577*60= 5.585145912 minutes

0.585145912*60= 35.10875472 seconds

And we obtain that the time, when the population of the country is 395 million people, is in the year 1998 with 19 days, 18 hours, 5 minutes and 35.10875472 seconds

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3 years ago

The half-life of a certain tranquilizer in the bloodstream is 47 hours. How long will it take for the drug to decay to 93% of

GaryK [48]

Answer:

It will take 4.84 hours for the drug to decay to 93% of the original dosage.

Step-by-step explanation:

We are given that the half-life of a certain tranquilizer in the bloodstream is 47 hours.

The given exponential model is: $A = A_0 e^{kt}$

Now, we know that A becomes half after 47 hours which means that;

$A = 0.5 A_0$

Using this in the above equation we get;

$A = A_0 e^{kt}$

$0.5 A_0 = A_0 e^{(k\times 47)}$ where t = 47 hours

$\frac{0.5 A_0}{A_0} = e^{(47k)}$

$0.5 = e^{47k}$

Taking log on both sides we get;

$ln(0.5) = ln(e^{47k})$

$ln(0.5) =47k$

$k = \frac{ln(0.5)}{47}$

k = -0.015

Now, the time it will take for the drug to decay to 93% of the original dosage is given by;

$0.93 = e^{kt}$ where t is the required time

$0.93 = e^{(-0.015 \times t)}$

Taking log on both sides we get;

$ln(0.93) = ln(e^{-0.015t})$

$ln(0.93) =-0.015t$

$t = \frac{ln(0.93)}{-0.015}$

t = 4.84 hours

Hence, it will take 4.84 hours for the drug to decay to 93% of the original dosage.

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3 years ago

An electric toothbrush costs $56, including a 40% price markup. What was the cost for the store to purchase the electric toothbr

Anna007 [38]

The cost for the store to purchase the electric toothbrush will be;

⇒ $22.40

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The cost of electric toothbrush = $56

And, The price of markup = 40%

Now,

Since, The cost of electric toothbrush = $56

And, The price of markup = 40%

So, The cost for the store to purchase the electric toothbrush is;

= (40% of $56)

= (40/100 x 56)

= $22.4

Thus, The cost for the store to purchase the electric toothbrush will be;

⇒ $22.40

Learn more about the percent visit:

brainly.com/question/24877689

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1 year ago

Find all of the zeros

noname [10]

Answer:

{-3, -1, 1}

Step-by-step explanation:

Zeros refer to x-intercepts. X-intercepts are x values when y = 0. You can tell where they are by looking at where the line passes the x-axis.

Therefore, {-3, -1, 1} are the zeros.

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4 years ago

3+2(x-6)+5-3(x+4)=6x

Mekhanik [1.2K]

5(x-6)+2(x+4)=6x
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