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3 years ago

The mean of four integers is -1. Three of the four integers are 3, -6, and 7 what is the fourth integer?

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

8 0

The fourth integer would be -8. 3-6+7-8=-4. -4/4=-1

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Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was

nasty-shy [4]

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:

$\frac{dQ}{dt}=\alpha.A.(T_{s}-T)$

This differential equation solved, gives the solution:

$T(t)=T_{s}+(T_{0}-T_{s})e^{-kt}$

where

$T_{s}$ is temperature of the environment

$T_{0}$ 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°:

$27=22+(28-22)e^{-1k}$

$5=6e^{-k}$

$e^{-k}=\frac{5}{6}$

$ln(e^{-k})=ln(0.834)$

k = 0.1823

Using the parameter, find estimate time:

$28=22+(37-22)e^{-0.1823t}$

$6=15e^{-0.1823t}$

$ln(e^{-0.1823t})=ln(0.4)$

0.1823t = 0.9163

$t=\frac{0.9163}{0.1823}$

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.

5 0

3 years ago

}

Juliette [100K]

Answer:

the items new price is $60

Step-by-step explanation:

4 0

3 years ago

Suppose you deposit $600 into an account that pays 5% annual interest, compounded continuously. How much will you have in the ac

Sever21 [200]

Answer:

D)$732.84

Step-by-step explanation:

A=p(1+r/n)^nt

P=principal=$600

r=5%=0.05

t=4 years

n=12 months

A=p(1+r/n)^nt

=600(1+0.05/12)^12*4

=600(1+0.0041666666666 )^48

=600(1.0041666666666 )^48

=600( 1.2208953550215 )

=732.53

A=$732.53

Option D)$732.84 is the answer

6 0

3 years ago

The perimeter of a triangle is 150 inches. the width is 12 inches find the length of the base

Anarel [89]

the length for each remaining side is 69 inches

8 0

3 years ago

HELP!!!!!!!!!

wel

Answer:

$y=-\frac{2}{3} x+4$

Step-by-step explanation:

move the variable to the right(-2x) and change the sign(2x now) -3y=-12+2x then change the signs (-3y is 3y , -12 is 12 and then 2x becomes -2x again) then divide both sides of the equation by 3 so 12÷3=4 and -2x÷3= $-\frac{2}{3} x$ then you're going to use the commutative property to reorder the terms . so your answer is $y=-\frac{2}{3} x+4$

3 0

3 years ago