Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was discovered, the famous detective Hercule Poirot noted that Ratchett had a body temperature of 28 degrees. The body had cooled to a temperature of 27 degrees one hour later. If the normal temperature of a human being is 37 degrees and the air temperature in the train is 22 degrees.

Required:
Estimate the time of Ratchett's death using Newton's Law of Cooling.

Answers

Answer 1

Answer: Mr. Ratchett died approximately at 2AM.

Step-by-step explanation: Newton's Law of Cooling shows the cooling rate between a body and the environment, by stating that the rate is proportional to the difference in temperatures between them.

Mathematically, it is represented as:

[tex]\frac{dQ}{dt}=\alpha.A.(T_{s}-T)[/tex]

This differential equation solved, gives the solution:

[tex]T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}[/tex]

where

[tex]T_{s}[/tex] is temperature of the environment

[tex]T_{0}[/tex] is the initial temperature of the body

k is a parameter dependent of heat transfer coefficient, heat capacity and area of the body

t is time required to change the temperature

For the murder on the Orient Express, first determine parameter k.

In 1 hour, Mr. Ratchett's body decrease 1°:

[tex]27=22+(28-22)e^{-1k}[/tex]

[tex]5=6e^{-k}[/tex]

[tex]e^{-k}=\frac{5}{6}[/tex]

[tex]ln(e^{-k})=ln(0.834)[/tex]

k = 0.1823

Using the parameter, find estimate time:

[tex]28=22+(37-22)e^{-0.1823t}[/tex]

[tex]6=15e^{-0.1823t}[/tex]

[tex]ln(e^{-0.1823t})=ln(0.4)[/tex]

0.1823t = 0.9163

[tex]t=\frac{0.9163}{0.1823}[/tex]

t ≈ 5 hours

The body was found at 7AM. So, it took approximately 5 hours to cool down to 28° at that time. Therefore, Mr. Ratchett died at 2AM.


Related Questions

Brainliest will be givenFor the numbers 2 to 100, including 2 and
100, determine each ratio.

a) the number of even numbers to the

number of odd numbers

b) the number of multiples of 6 to the

number of multiples of 8

c) the number of prime numbers to the

number of composite numbers

Answers

answer: c i believe   hope it helps!!! :D

Order and Operate these please! I will give a lot of points. Please help asap

(x +4) • 9

y + 7 + 8 – 7(x -8)

(4 – 5) + x(6 – 8)

y(4 – 8) – 3y

x + 8y – 16x(1- 3)

82 – x(4 – 8) + √25

53 – 4(y – 7y) - √81

x^2 – 4 – 5y - √36 • √144 + 23(x – 5x)

Answers

Answer:

9x+36y-7x+71-2x-1-7y33x+8y4x+6924y+116x² -92x -5y -76

Step-by-step explanation:

a) (x +4)·9 = 9x +36

__

b) y +7 +8 -7(x -8) = y +7 +8 -7x +56 = y +15 -7x +56 = y -7x +71

__

c) (4 -5) +x(6 -8) = -1 +x(-2) = -2x -1

__

d) y(4 -8) -3y = y(-4) -3y = -4y -3y = -7y

__

e) x +8y -16x(1 -3) = x +8y -16x(-2) = x +8y +32x = 33x +8y

__

f) 8² -x(4 -8) +√25 = 64 -x(4 -8) +5 = 64 -x(-4) +5 = 64 +4x +5 = 4x +69

__

g) 5³ -4(y -7y) -√81 = 125 -4(y -7y) -9 = 125 -4(-6y) -9 = 125 +24y -9 = 24y +116

__

h) x² -4 -5y -√36·√144 +23(x -5x) = x² -4 -5y -6·12 +23(x -5x)

  = x² -4 -5y -6·12 +23(-4x) = x² -4 -5y -72 -92x = x² -92x -5y -76

Nita finds that the expression (a + 1) 2 is sometimes, but
not always, greater in value than (a + 1) 3 when she evaluates both expressions
for the same value of a. How do you explain this finding?

Answers

I guess the expressions are supposed to be (a + 1)² and (a + 1)³.

Consider the inequality,

(a + 1)² > (a + 1)³

Move everything to one side:

(a + 1)² - (a + 1)³ > 0

Factorize the left side:

(a + 1)² (1 - (a + 1)) > 0

-a (a + 1)² > 0

a (a + 1)² < 0

Notice that the left side is exactly 0 if either a = 0 or a = -1.

Now consider the following 3 cases:

• If a < -1, then a is negative, while (a + 1)² is always non-negative, which means a (a + 1)² will always be negative.

• If -1 < a < 0, then again a is negative, so a (a + 1)² is also negative.

• If a > 0, then a (a + 1)² is always positive.

So the inequality is satisfied for all a in the interval (-∞, -1) ∪ (-1, 0). This is to say that (a + 1)² is always greater than (a + 1)³ if a is chosen from this domain.

Another way to look at this: assume a + 1 falls between -1 and 1. Whenever you scale a number between -1 and 1 by another number in the same range, the product will always be smaller than the original number.

More concretely, let's say a + 1 = 1/2. So for instance, 1/2 * 1/2 = (1/2)² = 1/4, and 1/4 is clearly smaller than 1/2. If we multipy again by 1/2, we get 1/2 * 1/2 * 1/2 = (1/2)³ = 1/8, which is smaller than 1/4.


What percent is the same as 3/5
?
O A. 30%
B. 35%
OC. 53%
D. 60%

Answers

Answer:60%

Step-by-step explanation: I got this right on a test

-10 - 6(2v – 8) = -82

Answers

Answer:

v = 10

Step-by-step explanation:

-10 - 6(2v-8) = -82

-10 - 12v + 48 = -82

-12v + 38 = -82

-12v = -120

v = 10

hope this helped, if you need a more in depth answer to how i did it just ask

Answer:

Hello! I hope I’m correct! :)

Step-by-step explanation:

The answer should be V = 10

First, Add 10 to both sides.

-6(2v-8) = -82+10

Next, Simplify

-6(2v-8) = -72

Than, divide both sides by -6

= -72/-6

{Note: two negatives makes a positive}

= 72/6

Simplify.

2v-8=12

Add (+) 8 to both of the sides.

2v= 12+8

Simplify 12+8 to...

2v = 20

Now, divide both sides by 2

V = 20/2

Since we have 20/2, we need to simplify (divide 20 & 2)

20 divided by 2 = 10

V = 10

Therefore the answer is v = 10

Hope this helps! If you have any questions about these steps, feel free to ask! Have a nice day! :)

~by, BrainlyAnime <3

what fraction multiplied by itself is equal to 4/25

Answers

Answer:

2/5

Step-by-step explanation:

we see that 2x2=4

and 5x5is equal to 25

so the answer is 2/5

Answer:

2/5

Step-by-step explanation:

2/5 * 2/5 = 4/25

the number that you can multiply by its self to get 4 is 2 and the number that you can multiply by its self to get 25 is 5

Four out of 32 students in Mr. Lee’s class speak 3 languages. Which decimal represents the number of students who speak 3 languages?

Answers

Answer:

.125

Step-by-step explanation:

4 is one-eighth (1/8) of 32, which would be represented by the decimal .125 or 0.125

what is the slope line ​

Answers

Answer:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m.

Step-by-step explanation:

If 5 is added to one-half of a number, the result is the same as when three-fifths of the number is decreased by 3. Find the number

Answers

Answer:

2.3

Step-by-step explanation:

is your answer

Fraser scores 43% in a spelling test. What percentage did he get wrong?

Answers

Answer:

100-43= 57

Explanation:

So, Frazer did 57% wrong

Answer:

57% incorrect wow he should have studied better lol ;)

Step-by-step explanation:

If he SCORED 43%, than out of 100% the remaining is 57%

The regression equation y = 8.6sin(0.24x – 1.88) + 62.8 models the Fahrenheit temperature in a room x hours after midnight. What is the maximum temperature in the room during the first 24 hours?

Answers

Answer:B (57.0 F°)

Step-by-step explanation:

Answer:

71.4 (D)

Step-by-step explanation:

Edge 2020

I took the test, guessed and got it right

Have a great day everyone

Help I understand but explain the steps and how you got it

Answers

Answer:

7-4 = 3

the change is 3 emails

Step-by-step explanation:

Help me please .........

Answers

Step-by-step explanation:

x ÷ 3 - 7 = -2

x - 7 = -2 × 3

x - 7 = -6

x = -6 + 7

x = 1

Answer:x ÷ 3 - 7 = -2

x - 7 = -2 × 3

x - 7 = -6

x = -6 + 7

x = 1

Step-by-step explanation:

It has generally been believed that it is not feasible for men and women to be just friends (The New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are the days when men worked and women stayed at home and the only way they could get together was for romance. In a recent survey, 186 heterosexual college students were asked if it was feasible for men and women to be just friends. Thirty-two percent of females and 57% of males reported that it was not feasible for men and women to be just friends. Suppose the study consisted of 100 female and 86 male students.
a. Construct a contingency table that shows frequencies for the qualitative variables Gender (men or women) and Feasible (yes or no).
b. Find the probability that a student believes that men and women can be friends.
c. If a student believes that men and women can be friends, what is the probability that this student is a male? Find the corresponding probability that this student is a female.
It has generally been believed that it is not feasible

Answers

Answer:

Step-by-step explanation:

See the attached file .

a companys stock was selling at $30a share a month later it was $33 a share what is the percent gain

Answers

I think it’s 10%
33-30/30x100= 10

What is it? I’m taking a math test and It for a 100 points so could y’all help me out

Answers

Answer:

A.

Step-by-step explanation:

5x100= 500

6x10= 60

7x1= 7

500+60+7= 567

Answer:

The answer is A

Step-by-step explanation:

(5*100)+(6*10)+(7*1)

500+60+7 = 567

GIVING BRAINLIEST TO WHOEVER ANSWERS RIGHT 20pts. stuck between first and second option.

Answers

Answer:

it would be C ;0

Step-by-step explanation:

An airline makes 200 reservations for a flight who holds 185 passengers. The probability that a passenger arrives for the flight is 0.9 and the passengers are assumed to be independent. Use the normal approximation of Binomial distribution to answer the following questions.

a. Approximate the probability that all the passengers who arrives can be seated.
b. Approximate the probability that there are empty seats.
c. Approximate the number of reservations that the airline should make so that the probability that everyone who arrives can be seated is 0.95.

Answers

Answer:

The answer is below

Step-by-step explanation:

given that:

n = sample size = 200, p = probability of a cancelled reservation = 1 - 0.9 = 0.1

The z score is given by:

[tex]z=\frac{x-mean}{standard\ deviation} =\frac{x-np}{\sqrt{np(1-p)} }[/tex]

a) The probability that all the passengers who arrives can be seated can only occur if atleast 15 or more passengers cancelled their reservations.

P(X ≥ 15) = 1 - P(X ≤ 14.5)

[tex]z=\frac{x-np}{\sqrt{np(1-p)} }=\frac{14.5-(200*0.1)}{\sqrt{(200*0.1)(1-0.1)} }=-1.3[/tex]

From the normal distribution table:

P(X ≥ 15) = 1 - P(X ≤ 14.5) = 1 - P(z < -1.3) = 1 - 0.0968 = 0.9

b) The probability that there are empty seat only occur if atleast 16 or more passengers cancelled their reservations.

P(X ≥ 16) = 1 - P(X ≤ 15.5)

[tex]z=\frac{x-np}{\sqrt{np(1-p)} }=\frac{15.5-(200*0.1)}{\sqrt{(200*0.1)(1-0.1)} }=-1.06[/tex]

From the normal distribution table:

P(X ≥ 16) = 1 - P(X ≤ 15.5) = 1 - P(z < -1.06) = 1 - 0.1446 = 0.8554

c)

[tex]0.95=P(X\geq n-185)=1-P(X\leq n-185)\\\\P(X\leq n-185)=1-0.95\\\\P(X\leq n-185)=0.05\\\\0.05=P(Z<\frac{n-185-0.1n}{\sqrt{0.9*0.1*n} } )\\\\0.05 \ correspond\ to \ a\ probability\ of\ -1.64\\\\-1.64=\frac{0.9n-185}{\sqrt{0.9*0.1*n} } \\\\n=198[/tex]

I need help don't know if I did it correctly

Answers

Answer:

You have done it incorrectly It's B (2.333...) not C.

what does it mean to say that a number is a perfect square

Answers

Answer:

A perfect square is the product of a rational number multiplied by itself.

4, 9, and 16 are perfect squares

1, 2, 3, 5, 6, etc. are not perfect squares

Step-by-step explanation:

Answer:

please mark brainliest!

Step-by-step explanation:

NON-DETAILED

A number that is a perfect square is a number that can be square rooted kind of in a perfect match. Example would be 9 because it can be square rooted by 3 for 3 * 3. Another example that would not be a perfect square would be 30 because it can divided by 6 * 5 but neither one of those numbers are perfect squares.

DETAILED

A number called a perfect square means that the number has an exact squared root. In other words, the number has an squared power, which is exact.

Other way to see this, it's taking natural number 1, 2, 3, 4 then, applying the squared power to each one, the results of each squared power is what we call a perfect square. For example, 1, 4, 9, 16, 25, 36, are all perfect square, because they are the result of a squared power:

[tex]1^{2} = 1\\2^2 = 4\\3^2 = 9\\4^2 = 16\\5^2 = 25\\6^2 = 36[/tex]

Find the quotient of 1008 divided by 18

Answers

Answer: 56

Step-by-step explanation: Hopefully this helps!

Answer:

56, I hope this helps

Resuelve estas ecuaciones
1. x I 6 = 14
X=

Answers

Answer:

3 sjshgegegegehsksksjsjsissjs

A car travels along a straight road 100 m east then 50 m west. Find distance and displacement of the car.

Answers

Given parameters:

    First move = 100m east

    Second move  = 50m west

Unknown:

Distance = ?

Displacement  = ?

Solution:

Distance is total path length covered

Displacement is the distance in a specific direction from start to finish.

            -----------------------→

                       100m

                            ←---------

                               50m

So,

        Distance  = first move + second move  = 100 + 50  = 150m

       Displacement  = 100 - 50  = 50m due West

Solve for x.
16 = -2x - 1
x=-7 1/2
x=-8 1/2
x=8 1/2
x=7 1/2

Answers

Answer:

x= -8 1/2

Step-by-step explanation:

PLEASE HELP ILL GIVE BRAINLIEST!!!

Answers

Answer:

[tex]uw = - 4 + 2x = 11 + x - 5 \\ - 4 + 2x = x + 6 \\ 2x - x = 6 + 4 \\ x = 10 \\ \\ uw = - 4 + 2(10) = 16[/tex]

Step-by-step explanation:

ww= - 4 + 2x = 11 + x - 5

- 4 + 2x = x+6

2x - x = 6+4

x=10

ww = -4 +2(10)=16

Covert 52m to kilometers. Explain how you got your answer

Answers

Answer:

0.052 kilometers

Step-by-step explanation:

There are .001 kilometers in 1 meter. So to convert meters to kilometers, multiply the number of meters by .001. 52x.001=.052

I hope you understand...have an awesome day!!! C:

what is the opposite?

Answers

Answer:

like a opposite side of a question

Step-by-step explanation:

opposite (of angle)between opposite side of the intersection of two line

What’s 4.5 rounded to the nearest whole number

Answers

Answer: 5

Step-by-step explanation:

When the number after the point is 5 and above round up

4.5 rounded to the nearest whole number is 5.

When you round a decimal number to the nearest whole number, you are determining which whole number it is closest to.

For 4.5, you can visualize it on the number line.

The decimal number 4.5 lies exactly midway between 4 and 5.

To round to the nearest whole number, we look at the digit immediately to the right of the decimal point, which is 5.

Since 5 is greater than or equal to 5 (the midpoint), we round up to the next whole number, which is 5.

Therefore, 4.5 rounded to the nearest whole number is 5.

To learn more on Number system click:

https://brainly.com/question/1763119

#SPJ6

Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm-too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected.
a. Define the parameter of interest in the context of this study and assign an appropriate symbol to it.
b. State the appropriate null and alternative hypotheses using the symbol defined in (a).
c. Describe what a Type I error would be in this study. Also, describe the consequence of such an error in the context of this study.
d. Describe what a Type II error would be in this study. Also, describe the consequence of such an error in the context of this study. tudy. Jesti- g so, h the in.

Answers

Answer:

a

 True mean diameter[tex][\mu][/tex]

b

    The null hypothesis is  [tex]H_o : \mu = 1.65 \ mm[/tex]

    The alternative hypothesis is  [tex]H_a : \mu \ne 1.65[/tex]

c

Gnerally type I error occurs when the null hypothesis is wrongfully rejected  

The consequence of this is that the wrongfully rejecting a batch of needles because the company do not find strong evidence that its true mean diameter  is 1.65 mm whereas it is  

d

Gnerally type II error occurs when the null hypothesis is wrongfully accepted  

The consequence of this is that the wrongfully accepting  a batch of needles because the company do find strong evidence that its true mean diameter is 1.65 mm whereas it is not    

Step-by-step explanation:

Generally from the question we are told that

    The  needle  needs to have a diameter of  1.65 mm

Now statistically the parameter of interest in the context of this study is the true mean diameter of the needle  and  the symbol is  [tex]\mu[/tex]

    The null hypothesis is  [tex]H_o : \mu = 1.65 \ mm[/tex]

    The alternative hypothesis is  [tex]H_a : \mu \ne 1.65[/tex]

Gnerally type I error occurs when the null hypothesis is wrongfully rejected  

The consequence of this is that the wrongfully rejecting a batch of needles because the company do not find strong evidence that its true mean is 1.65 mm whereas it is  

Gnerally type II error occurs when the null hypothesis is wrongfully accepted  

The consequence of this is that the wrongfully accepting  a batch of needles because the company do find strong evidence that its true mean is 1.65 mm whereas it is not  

Ryan went to the store to buy some apples. The price per pound of the apples is $4.25 per pound and he has a coupon for $2 off the final amount. With the coupon, how much would Ryan have to pay to buy 5 pounds of apples? Also, write an expression for the cost to buy pp pounds of apples, assuming at least one pound is purchased.

Answers

Answer:

x = pp(4.25)-2

Step-by-step explanation:

x is the cost

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