A card is selected at random from a well-shuffled ordinary deck consisting of 13 spades, 13 clubs, 13 hearts, and 13 diamonds. 4
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Answer:
The confidence interval is 6.6<μ<6.8.
Step-by-step explanation:
We have:
Number of observations = 601
Mean = 6.7
Standard deviation σ = 1.5
The z-score for a 95% confidence interval is 1.96.
The limits of the confidence interval can be calculated as
The confidence interval is 6.6<μ<6.8.
We know that the trigonometric identity that uses the adjacent side and the hypotenuse is cosine. We can set this up as:
We need to solve for x, so let's isolate it:
So, x = 10.2 units
We need to solve for x, so let's isolate it:
So, x = 10.2 units
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