Natalie paid $14.99 to join an online music service. If she purchases 9 songs each month at a cost of $0.99 per song, what will
1 answer:
Answer:
Natalie Spent <u>$59.54</u> on songs after 5 months at online music service.
Step-by-step explanation:
Given:
Total membership cost =$14.99
Number of songs purchased in each month = 9
Cost per song = $0.99
We need to find total amount she had spent after 5 months.
Solution:-
So First we will Number of songs purchased in 5 months.
1 month = 9 songs
So in 5 months = Songs purchased in 5 months.
By Using Unitary method we get;
Songs purchased in 5 months =
Now Also Given:
1 song = $0.99
45 songs = Cost for 45 songs.
Again by using Unitary method we get;
Cost for 45 songs =
No Total Amount Natalie spent after 5 months is equal to Total membership cost plus Cost of songs purchased in 5 months.
framing in equation form we get;
Total Amount Natalie spent =
Hence Natalie Spent <u>$59.54</u> on songs after 5 months at online music service.
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The standard deviation is 1.43 below the mean
<h3>How to determine the number of standard deviation?</h3>The given parameters are:
Mean = 98.249
Standard deviation = 0.733
x = 97.2
To calculate the number of standard deviation below the mean, we use
So, we have:
Evaluate the like terms
Divide both sides by -0.733
n =1.43
Hence, the standard deviation is 1.43 below the mean
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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:
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:
which simplifies to
Divide both sides by 70 to get
and take the natural log of both sides:
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:
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):
which simplifies to
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 = ?
which simplifies to
Now divide both sides by 70 and take the natural log of both sides:
which simplifies to
-2.63905733 = -.0672944473t
Divide to get
t = 39.2 minutes