What is the equation in slope-intercept form for the line that passes through the points

A turkey is taken out of the oven with an internal temperature of 169∘F, and is placed on a kitchen counter where the temperatur

Ivanshal [37]

Answer:

47.9758 minutes

Step-by-step explanation:

The temperature difference between the turkey and the room starts at ...

169 °F - 73 °F = 96 °F

and drops to ...

140 °F -73 °F = 67 °F

after 11 minutes. In that time period, the difference becomes 67/96 of what it was initially.

We are asked to find the time it takes for the temperature difference to get to ...

93 °F -73 °F = 20 °F

Then the exponential decay equation we want to solve is ...

20 = 96(67/96)^(t/11) . . . . . t is time in minutes

Dividing by 96 and taking logs, we get ...

20/96 = (67/96)^(t/11)

log(20/96) = (t/11)log(67/96)

Solving for t gives ...

t = 11·log(20/96)/log(67/96) ≈ 47.9758 . . . minutes

After being removed from the oven, it will take the turkey 47.9758 minutes to cool to 93 °F.

_____

Comment on this method of solution

We have dealt exclusively with the temperature difference, and have written the exponential equation in terms of the fractional change in a given time. The form of the equation we wrote is ...

f(t) = (initial value)×(multiplier)^(t/(multiplier's period))

The "multiplier" may also be called a "decay constant" or "growth constant". The exponential term can also be expressed as a power of e, the base of natural logarithms. You will often see that as ...

e^(-kt)

where k is the natural logarithm:

k = -ln(multiplier)/(multiplier's period)

In this problem, the value of k would be ...

k = -ln(67/96)/11 ≈ 0.0326959611

Using this, the temperature decay would be written as ...

temp difference = 96·e^(-0.0326959611t)

and the solution for a temperature difference of 20 degrees would be ...

ln(20/96)/(-0.0326959611) ≈ 47.9758 . . . minutes

You need at least 6 significant figures in the value of k because the answer has 6 significant figures. (Why, we don't know, as neither temperature nor time measurements can be made to that accuracy in this situation. We think it is so the grader can tell if you worked the problem correctly.)

__

You can also write the equation for the turkey temperature (T) as ...

T(t) = 73 +96e^(-0.0326959611t)

This is the room temperature added to the difference from room temperature.

Then you would be seeking the solution to T(t) = 93.

4 0

3 years ago

Find the mode for the data set.

jonny [76]

8.3 ; 8.7 ; 4.5 ; 6.9 ; 4.2 ; 11.7 ; 4

Arrange in order from least to greatest.

4 ; 4.2 ; 4.5 ; 6.9 ; 8.3 ; 8.7 ; 11.7

The mode is the number that appears the most in the data set. Every number only appeared once. So. there is no mode in the data set.

NO MODE.

7 0

4 years ago

1. The matrices show the enrollment of boys and girls on the basketball, lacrosse, and soccer teams in two towns. (a) If we let

alexira [117]

(a). The element being asked is not specified but elements are named according to the number of the row followed by the number of the column. For example, element a₂₁ is the number of boys enrolled in Lacrosse.

(b). The address is a₁₂.

(c). [196 174]
[136 169]
[214 242]

(d). The matrix represents the number of boys and girls from towns A and B enrolled in different sports classes.

(e). 1.125 A = [108 90 ]
[72 99 ]
[117 135]

6 0

3 years ago

14 POINTS PLEASE HELP WILL MARK BRAINLIEST NEED URGENTLY

liraira [26]

Using correlation coefficients, it is found that a coefficient of -1 represents a strong negative correlation.

<h3>What is a correlation coefficient?</h3>

It is an index that measures correlation between two variables, assuming values between -1 and 1.

If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

For this problem, we have a correlation coefficient of -1, hence it means that:

The relation is negative, as -1 is a negative number.

The relation is strong, as the absolute value of the coefficient is of 1, which is greater than 0.6.

More can be learned about correlation coefficients at brainly.com/question/25815006

#SPJ1

7 0

2 years ago

The midpoint of AB is M(3, 3). If the coordinates of A are (2, -1), what are the

Vika [28.1K]

Step-by-step explanation:

Hey there!!

It's so simple.

While finding the coordinates of any point if the midpoint is there it will be much easier. You must remember the midpoint formulae.

Let's simply work with it.

Here, A (2,-1) and midpoint M(3,3) are given.

Let another coordinate be B(x,y).

By midpoint formulae,

$midpoint(x.y) = \frac{x1 + x2}{2} ,\frac{y1 + y2}{2}$