You open a case of Cherry Coke from the garage to put cans in the refrigerator. You put the
85°F cans in the 36°F refrigerator. After 5 minutes, the can temperature has gone down to
71°F. Find the constant "k" using Newton's Law of Cooling.

Answers

Answer 1

9514 1404 393

Answer:

  k ≈ -0.06729

Step-by-step explanation:

The initial temperature difference is 85 -36 = 49 degrees. After 5 minutes, the temperature difference is 71 -36 = 35 degrees. The constant k is the natural log of the ratio of these temperature differences, divided by the time unit.

  k = ln(35/49)/5 ≈ -0.06729

__

The equation for the temperature T of the can in the refrigerator is ...

  T = 49e^(-0.06729t) +36

_____

Additional comment

Be careful with the sign. If you're filling in k in e^(-kt), then the sign of k will be positive. Above, we have taken the form of the exponential term to be e^(kt), so k is negative.


Related Questions

A biker traveled 20 miles in 4 hours. A unit rate to describe this would be 5 miles per hour. What is another unit rate in this situation?
1. 1/5 mile per hour
2. 1/5 hour per mile
3. 1 mile per hour
4. 5 hours per mile

Answers

Answer:

20 miles) / (4 hours) = (20/4) (miles/hours)  =  5 miles per hour

(4 hours) / (20 miles) = (4/20) (hours/miles)  =  0.2 hours per mile =

                                                                            12 minutes per mile

A copy machine makes 84 copies in 3 minutes and 30 seconds, how many copies does it make per minute.

Answers

Answer:

24

Step-by-step explanation:

3 minutes and 30 seconds = 3.5 minutes

84/3.5 = 24copies/minute

24 copies per minute

Put the following equation in slope-intercept form: y−5=7/4(x-1)

Answers

Answer:

y=7/4x+2

Step-by-step explanation:

The linear equation in the slope-intercept form will be y = (7/4)x + 13/4.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equation is given below.

y − 5 = 7/4(x − 1)

Convert the equation into a slope-intercept form. Then we have

y − 5 = 7/4(x − 1)

y − 5 = (7/4)x − (7/4)

y = (7/4)x − (7/4) + 5

y = (7/4)x + 13/4

The linear equation in the slope-intercept form will be y = (7/4)x + 13/4.

More about the linear equation link is given below.

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Beth has a box containing music CDs. Each CD contains songs from only one of these three genres: pop (P), hip-hop (H), and rock (R). She picks one CD from the box, replaces it, and then picks another CD. The sample space for this event is listed.

P-P H-P R-P
P-H H-H R-H
P-R R-R


What is the missing term for this compound event? What is the sample size?

A.
The missing term is H-P, and the sample size is 9.
B.
The missing term is H-R, and the sample size is 9.
C.
The missing term is H-P, and the sample size is 3.
D.
The missing term is H-R, and the sample size is 3.

Answers

Answer:

B). The missing term is H-R, and the sample size is 9.

Step-by-step explanation:

Compound event is characterized as the likelihood of occurring two autonomous events at least one or more than one probable outcome.

As per the details provided, 'the term that is omitted in the given event of the compound would be (H-R) and the size of the sample would be 9(' including this missing one. The eight combination possibilities of the CDs have already been provided and thus, the last one would be 'H-R'(hip-hop and rock music CDs). This is why the total number of possibilities turns 9. Thus, option B is the correct answer.

Answer:  the answer is B :)

Step-by-step explanation:

Help pls might give brainlist also show work if needed!

Answers

Answer:

The mean is 21.

The median is 21

There is no mode here.

Step-by-step explanation:

The graph of - 8x+2y = 8 passes through two points, P(p, 2) and
Q (-4, q). What is the value of pq?

Answers

Answer:

6

Step-by-step explanation:

All the steps are in the photo I attached

what is the approximate volume of the cylinder use 3.14 for π

Answers

Answer:

904.32 cm²

Step-by-step explanation:

V = πr²h

V = 3.14 × (6 cm)² × 8 cm

V = 904.32 cm²

How many degrees Fahrenheit is -20°C?

Answers

answer:

-4°f

step-by-step explanation:

(-20°c × 9/5) + 32

= -4°f

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

PLEASE HELP THIS IS VERY IMPORTANT I WILL GIVE U BRAIN THING IF ITS CORRECT NO LINKS. PLEASE

Answers

Answer:

1. 21 +35

2.5

Step-by-step explanation:

Answer:

1.) 21 + 35

2.) 5

Step by step explanation:

A rectangular prism with a length of 5 centimeters, width of 4 centimeters, and height of 3 centimeters.
What is the volume of the prism?
20 cm3
36 cm3
47 cm3
60 cm3

Answers

Answer:

60 cm3 is the volume of the prism

Step-by-step explanation:

Because the formula for volume is length * width * height!

please mark the brainliest!

Answer:

60

Step-by-step explanation:

Convert radians to degrees.
-i !!!

Answers

Answer:

1 radian = 57.2958 degrees i dont know if thats

what you wanted to know?

What is the volume of an 8-inch by 4-inch by 44-inch rectangular box?​

Answers

Answer:

1408

Step-by-step explanation:

Answer:

1,408 cm³.

Step-by-step explanation:

To find the volume of a rectangular prism, or in this case, a rectangular box, multiply the length, width, and height.

[tex]4*8*44=1,408 in^3.[/tex]

Therefore, the volume of the rectangular box is 1,408 cm³.

Ms. Thomas has a class of 16 students. She can spend 24 on each student to buy math supplies for the year. She first buys all of her students calculators, which costs a total of 79.04 . After buying the calculators, how much does she have left to spend on each student?

Answers

Answer: 19.06

Step-by-step explanation:

Which one is greater?
1.74 × 0.84
OR
1.79 × 0.69
- NO LINKS DOCS OR FILES ETC

Answers

Answer:

1.75 * 0.84

Step-by-step explanation:

1.74 * 0.84 = 1.4616

1.79 * 0.69 = 1.2351

Answer:

1.74 x 0.84 is greater

Step-by-step explanation:

1.74 x 0.84 = 1.4616

while

1.79 x 0.69 = 1.23509

what is the approximate volume for a ice cream cone with a radius of 3 and a diameter of 14

Answers

Answer:

131.95

Step-by-step explanation:

[tex]v = \frac{1}{3} \times \pi \times {r}^{2} \times h[/tex]

[tex]v = \frac{1}{3} \times 3.142 \times {3}^{2} \times 14 \\ v = \frac{1}{3} \times 3.142 \times 9 \times 14 \\ v = 131.964 {cm}^{3} [/tex]

y = (x) = (1/9)^x
Find f(x) when x = (1/2)
Round your answer to the nearest thousandth.

Answers

Answer:

0.333

Step-by-step explanation:

The radius of a circle is 6.1 millimeters. What is the circle's area?

Answers

[tex]area = \pi \times {r}^{2} \\ area = 3.142 \times {6.1}^{2} \\ area = 3.142 \times 37.21 \\ area = 116.91 {mm}^{2} [/tex]

Area of rectangle and trangle
More comeing soo!!

Answers

Answer: Triangle 1 = 30 m2

Triangle 2 = 15 cm2

Step-by-step explanation:

Triangle area formula = 1/2 x base x height

Area1 = 1/2 x 10 x 6

= 30

Area2 = 1/2 x 6 x 5

= 15

Answer:

The area of the triangle is 15 cm and rectangle is 30 or 60

Step-by-step explanation:

SOLVE

ROUND TO THE NEAREST CENT IF NECESSARY

A UNIÓN CONTRACT CALLS FOR 6.9% SALARY INCREASE
FOR ALL EMPLOYEES
DETERMINE THE INCREASE
FOR A WORKER WHO IS CURRENTLY MAKING $32,120


WILL GIVE
BRAINLIST
X
X
X
X

Answers

(32,120 x 6.9)/100=$34,336.28

Use the following dot plot to answer the questions.

What is the mean of the set?

If an additional dot is added to the set in the 3 column, how will the mean change? What will the new mean be?

Answers

Answer:

3.4

Decrease ; 3.375

Step-by-step explanation:

Mean = Σfx / Σf

Σfx = (1 * 2) + (2 * 2) + (3 * 3) + (4 * 9) = 51

Σf = 1 + 2 + 3 + 9 = 15

Mean = 51 / 15 = 3.4

If 1 more dot is added to the 3rd column:

Σfx = (1 * 2) + (2 * 2) + (3 * 4) + (4 * 9) = 54

Σf = 1 + 2 + 4 + 9 = 16

Mean = 54 / 16 = 3.375

17/3 divided by 2/3 help please!:))

Answers

Answer:

0.94444444444

-5 3/4 - 3 1/2 =?

A)2 1/4
B)-9 1/4
C)-2 1/4
D)-8 2/3

Answers

Answer:

-9 1/4

Step-by-step explanation:

-5 3/4 - 3 1/2

Get a common denominator

-5 3/4  - 3 1/2 *2/2

-5 3/4  - 3 2/4

-8  5/4

Rewritng

-8 4/4 - 1/4

-9 1/4

The identity (x2 + y2) = (x2 - y2) + (2xy)? can be used to generate Pythagorean triples. What
Pythagorean triple could be generated using x=8 and y=3

Answers

Answer: 5329, 3025, 2304

Step-by-step explanation:

I just did the test

Pythagorean triple generated is 5329

What is Pythagorean triple?

A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². Such a triple is commonly written, and a well-known example is. If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are coprime

We have,

([tex]x^{2}[/tex]+[tex]y^{2}[/tex] )=( [tex]x^{2}[/tex]-[tex]y^{2}[/tex]) + [tex]2xy[/tex]

Using Points,

x =8, y=3

According to the questions

Taking square in both sides

[tex](x^{2} + y^{2}) ^{2}[/tex] = [tex](x^{2} - y^{2} ) ^{2}[/tex] + [tex](2xy)^{2}[/tex]

when, x = 8, and  y = 3

[tex](8^{2} + 3^{2} )^{2}[/tex] = [tex](8^{2} - 3^{2}) ^{2}[/tex]  + [tex](2.8.3)^{2}[/tex]

               = 3025 + 2304

               = 5329

Hence ,Pythagorean triple is 5329

To learn more about Pythagorean triple from here

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H
45
G
8
F
3
Ε
Find
cos FHE.

Answers

Answer:

no sé pero lo nesesito porfavor

Answer:

Its B. 4/5

Step-by-step explanation:

on edge 2020 :)

100 pts

Read the following email:


Dear Dr. Jones,
Our pharmaceutical company now received 47 complaints about the new pain reliever NoPain, created in your lab. Of the 47 complaints, 24 said their headache got worse, 15 said they had severe cramping after taking the medication, and 8 said they had both problems. We have only been distributing this pain reliever for about 30 days and we are very
concerned. It has cost our company roughly 1.2 million dollars to create the drug and we have recorded sales of $98,600 in the past month at $10 a bottle, so that is 9,860 bottles. Should we be concerned? Do you think we should pull the product and conduct more
research? We may end up losing money on this if we pursue this course of action. Should we keep the product on the shelves and secretly do more research? Or should we just do nothing for the time being, wait it out, and see what happens? Please get back to us as soon as possible with your recommendation.


Thank you,
Jane Smith
Head of Customer Relations



Using your basic mathematical skills, calculate how long it will take the pharmaceutical
company to earn back the amount that it had invested, if it continues to sell the product at the
current selling rate.

Answers

It will be way more than $98,600 because if it’s harmful to people, people will want their money back and if the people know that the company is selling these prescription pills knowing the side effects but not telling anyone, they will get sued as well. Probably we’re talking in the millions they will lose.

Find the surface area of the cone. Round answer to the nearest tenth.*

Answers

Answer:

628.319 rounded= 628.3

Step-by-step

Find the perimeter X(-2,1) Y(4,3) Z(5,-1)

Answers

Answer:

17.728

Step-by-step explanation:

Which values are solutions of the inequality 5 < y -8

8 , 9. , 13. , 15. , 20

Answers

Answer:

5 is greater than y-8 since 5 is positive it + in the begging +5 while - 8 is less than 0 because it has - in the begging

Answer: 15 and 20

Step-by-step explanation:

just did this

Mr. Matthews gives each of his 32 students 15 minutes to
present a book report to the class. How many minutes
will it take for all of his students to present their reports?

Answers

Answer:

480 minutes or 8 hours

Step-by-step explanation:

1 student = 15 minutes

32 students = x

x= 32 students *15 minutes

x=  480 minutes

480 minutes it takes for all of his students to present their reports.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total Students= 32

Each student can take = 15 minutes.

So, time taken by 32 students

= 32 x 15

= 480 minutes.

Hence, students take 480 minutes to complete the report.

Learn more about Unitary Method here:

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A shirt costs $98.
It is 20% off
What is the amount
I will save ?

Answers

Answer:

$19.60 would be saved (off full price)

Step-by-step explanation:

The discount (savings) would be 0.20($98), or $19.60.

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