Answer:
Step-by-step explanation:
Use Newton's Law of Cooling here:
where T(t) is the temp of something after a certain amount of time, t, has gone by; Ts is the surrounding temp, and T0 is the initial temp. k is the constant of cooling. We need to first solve for this using the information given. Filling in what we know:
which can simplify a bit to
and 
Take the natural log of both sides:
Taking the natural log allows us to pull that exponent down out front:
and now we can divide both sides by ln(38) to get
-35k = .794585 so
k = -.023
Now that have the value for k, we can go on to solve the rest of the problem which is asking us the temp of the soda after 70 minutes. Filling in using the k value and the new time of 70 minutes:
and
and
and
T(t) = 35 F, basically the temp of the fridge, which is not surprising!
Answer:
0.0930
Step-by-step explanation:
Given that one of your friends is testing the effect of drinking coffee on the duration of cold symptoms. The common cold lasts, on average, 6 days.
she tests a one-sided alternative about the population mean cold duration when drinking coffee, H0: μcoffee = 6 Ha: μcoffee < 6 She finds z = −1.68 with one-sided P-value P = 0.0465.
If hypotheses changed to two tailed as:
(Two tailed test)
Since we have mean difference and std error the same, test statistic would remain the same.
p value for two tailed would be = twice the p value for one tail
=
Answer:
The equation has two solutions for x:
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
Step-by-step explanation:
Let's use the quadratic formula for solving for x in the equation:
X^2 - 8X + 41= 0
x² - 8x + 41 = 0
Let's recall that the quadratic formula is:
x = -b +/- (√b² - 4ac)/2a
Replacing with the real values, we have:
x = 8 +/- (√-8² - 4 * 1 * 41)/2 * 1
x = 8 +/- (√64 - 164)/2
x = 8 +/- (√-100)/2
x = 8 +/- (√-1 *100)/2
Let's recall that √-1 = i
x = 8 +/- 10i/2
<u>x₁ = (8 + 10i)/2</u>
<u>x₂ = (8 - 10i)/2</u>
Time taken is equal to distance divided by speed
So time is 50/5 = 10 seconds
