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denis23 [38]
3 years ago
5

A music store charges $18.50 for a CD plus a 0.5% city tax and a separate 4% state tax

Mathematics
1 answer:
marishachu [46]3 years ago
3 0
<span> The correct answer is $18.50+.83=$19.33. </span>
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An object is heated to 100°. It is left to cool in a room that
stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one.  It involves natural logs and being able to solve equations that require natural logs.  The formula is as follows:

T(t)=T_{1}+(T_{0}-T_{1})e^{kt} where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value.  That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

80=30+(100-30)e^{5k} which simplifies to

50=70e^{5k} Divide both sides by 70 to get

\frac{50}{70}=e^{5k} and take the natural log of both sides:

ln(\frac{5}{7})=ln(e^{5k})

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared).  That gives us:

-.3364722366=5k

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

T(20)=30+(100-30)e^{-.0672944473(20)} which simplifies to

T(20)=30+70e^{-1.345888946}

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

35=30+100-30)e^{-.0672944473t} which simplifies to

5=70e^{-.0672944473t}

Now divide both sides by 70 and take the natural log of both sides:

ln(\frac{5}{70})=ln(e^{-.0672944473t}) which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

3 0
3 years ago
HELP ASAP I NEED HELP LIKE NOW 30 POINTS
padilas [110]

Answer:

25

Step-by-step explanation:

Right angled triangle

Solve for hypotenuse

This is the formula <em>c=√(a^2+b^2)</em> so pug in the numbers a=24 b=7 √(24^2 + 7^2)=c=25

8 0
3 years ago
Read 2 more answers
Reggie surveyed several classmates at his school asking them how many hours they spend doing homework each week. The results of
Neko [114]
Total students 5+16+42+22+5 = 90
0-1's probability is 5 / 90 = 5.5% about
2-3's probability is 16 / 90 = 17.7% about
4-5's probability is 42 / 60 = 46.6% about
6-7's probability is 22 / 90 = 24.4% about
8+'s probability is 5 / 90 = 5.5% about
(percentages not rounded, just cut off at the first decimal)
3 0
3 years ago
A taxi company charges $3 for pick-up plus $0.65 for each mile. Select the expressions that represent the cost in dollars for a
alexira [117]

the equation is y=0.65x+3

8 0
3 years ago
8.7 x 10-4 =<br><br> A) 0.000087 B) 0.00087 C) 8,700 D) 87,000
Gre4nikov [31]
It is B, I promise h gb in h x
3 0
2 years ago
Read 2 more answers
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