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, estimate the time of Ratchett's death using Newton's Law of Cooling.
Answer:
Time of Death = 2 : 49 : 45 AM
Step-by-step explanation:
The formula for Newton's Law of Cooling is written as follows:
dT/dt = - K(T - Ts)
where,
dT = change in temperature
dt = time interval
K = cooling constant
T = Final Temperature of object
Ts = Surrounding Temperature
First, we will use the data of cooling of body from 28°C to 27°C to find the cooling constant of the body:
dT = 27°C - 28°C = -1°C
dt = 1 hr = 3600 s
K = ?
T = 27°C
Ts = 22°C
Therefore,
-1 °C/3600 s = - K(27 °C - 22 °C)
K = 1 °C/(3600 s)(5 °C)
K = 5.55 x 10⁻⁵ /s
Now, we use data for cooling of body from 37 °C to 28 °C to find the time of death:
dT = 28°C - 37°C = -5°C
dt = ?
K = 5.55 x 10⁻⁵ /s
T = 28°C
Ts = 22°C
Therefore,
- 5 °C/dt = - (5.55 x 10⁻⁵ /s)(28 °C - 22 °C)
dt = 5 °C/(5.55 x 10⁻⁵ /s)(6 °C)
dt = 1.5 x 10⁴ s
dt = 4.17 h = 4 h 10 min 15 s
Therefor,
Time of Death = 7 : 00 : 00 AM - 4 : 10 : 15
Time of Death = 2 : 49 : 45 AM
Adam is scuba diving. He descends 6 feet below sea level. He descends
the same distance 3 more times. What is Adam's final elevation?
Answer:
-24
Step-by-step explanation:
Answer:
-18 feet below sea level
Step-by-step explanation:
Take 6 multiply by 3 then turn into a negative
Each big square below represents one whole.
What percent is represented by the shaded area?
%
Answer:
91%
Step-by-step explanation:
Answer:
91%
Step-by-step explanation:
Count the white blocks: 9
and subtract them from the blue blocks: 100 - 9 = 91%
Two less than seven times a number is the same as ten times the same number increased by 1. What is the
number?
Answer:
x = -1
Step-by-step explanation:
first, create a formula or expression:
7x - 2 = 10x + 1
now, move the 10x, subtract it on the other side
-3x - 2 = 1
add 2
-3x = 3
divide by -3
x = -1
you can substitute it in to check
Evan has 30 trading cards. He put them in stacks that each have 5 cards. Write a division sentence to find the number of stacks
Answer:
6
Step-by-step explanation:
30divided by 5 =6
Answer:
30 divided by 5= 6
Step-by-step explanation:
30 balls in total and 5 groups with 6 in each group
oooooo oooooo
oooooo oooooo
oooooo
Amy, Joan and Kevin each find rock. Amy's rock weighs 20.82 grams. Joan's rock
weighs 20.78 grams. The weight of Kevin's rock is between the weight of Amy's
rock and the weight of Joan's rock. What is a possible weight, in grams. of Kevin's
rock? Explain your thinking.
Answer:
20.80 grams
Step-by-step explanation:
This is a possible answer because 20.80 is directly in between the decimals 20.78 and 20.82
At the beginning of the month Kiran had $24 in his school cafeteria account. Use a variable to
represent the unknown quantity in each transaction below and write an equation to represent it.
Then, represent each transaction on a number line. What is the unknown quantity in each case?
1. In the first week he spent $16 on lunches. How much was in his account then?
Answer:
he has 8$ left
Step-by-step explanation:
if you subtract 24 from 16 you get 8
help please brainliest whoever gives the best answer.
Answer:
the anwser may eather be C or A
Step-by-step explanation:
i know this because if you read this the other two B and D dont entirly make scence and if those are not the correct answer i am sorry
i'm just explaining how i got this answer
The slope (????) of the beam is given by:
θ(x) = dy/dx
Required:
Use a forward divided difference and a step size of h=0.3 to approximate the slope of the beam at x = 1. Calculated the true percent relative error.
Answer:
Step-by-step explanation:
From the given question:
The slope is expressed as;
[tex]\thteta (x) = \dfrac{dy}{dx} - - (1)[/tex]
[tex]\thteta (x) = \dfrac{dy}{dx}\left \{ {{\dfrac{y(x+b)-y(x)}{h} \ \ \to approximate} \atop {\dfrac{1}{100}}(-4+4x-3x^2+2x^3) \ \to \ exact } \right.[/tex]
∴
[tex]\theta (x) _{approximate} = \dfrac{y(1+0.3)-y(1)}{0.3}[/tex]
[tex]\theta (x) _{approximate} = \dfrac{y(1.3)-y(1)}{0.3}[/tex]
[tex]\theta (x) _{approximate} = -2.965 \times 10^{-5}[/tex]
[tex]\theta(x)_{exact} = \dfrac{1}{100}(-4+4-3+2)[/tex]
[tex]\theta(x)_{exact} = -0.01[/tex]
Finally, the true percent relative error TPRE is:
[tex]TPRE= \dfrac{ | \theta(x)_{approximate} -\theta (x)_{exact} }{\theta (x)_{exact} }\times 100\%[/tex]
[tex]TPRE= \dfrac{ 2.965 \times 10^5 --0.01}{-0.01}\times 100\%[/tex]
TPRE = 70..35%
X and Y are supplementary angles. One angle measures 3 times the measure of the
other angle what is the measure of the smaller angle?
Answer:
Step-by-step explanation:
x + y = 180
3x = y
x + 3x = 180
4x = 180
x = 45
3*45 = y
y = 135
The two angles are
45
135
{10, 12, 14, 16, 18, ...} What is the formula ?
Answer:
+2
Step-by-step explanation:
2x-3y=-12 solve for y
Answer:
y intercept is 4
Step-by-step explanation:
Gertrude has 83.21 centimeters of wire. She uses 2 pieces of the wire.
Each piece she uses is 15.12 centimeters long. What is the length of
the remaining wire, rounded to the nearest tenth of a centimeter?
(Only round your final answer.)
Answer:W0t thu Ars £init
Step-by-step explanation:
Answer:
53 centimeters
Step-by-step explanation:
she uses 30.24 wire so subtract that from 83.21 then round that answer which was 52.97 to 53
Please help me urgently
Answer:
184320 Cubic Cenimeters
Step-by-step explanation:
Which of the following ratios is equivalent to 3:4
A: 2/3
B:3/4
C:4/3
Answer: B
hope this helps
sian rounds 103,502 to the nearest thousand and gets 103,000. did sian make a mistake?
Answer:
the answer is 104,000
Step-by-step explanation:
sian needs to use the 5 in the hundreds place holder to round the 3 in the thousands face holder to 4.
hope this helps.
Write an explicit rule for the geometric sequence:
3, -12, 48, -192
please help and thank you!
Answer:
I think you would just multiply by -4
Step-by-step explanation:
3 x -4 = -12
-12 x -4 = 48
48 x -4 = -192
Please let me know if I've done anything wrong!
Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In particular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 189 cases tested in a certain state, 12 were found to be drug-resistant. Suppose also that, of 429 cases tested in another state, 8 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state.) State the null and alternative hypotheses. (Enter != for ≠ as needed.)
H0:
Ha:
Find the value of the test statistic. (Round your answer to two decimal places.)
What is the p-value? (Round your answer to four decimal places.)
p-value =
What is your conclusion?
Reject H0. There is a significant difference in drug resistance between the two states.Do not reject H0. There is a significant difference in drug resistance between the two states. Reject H0. There is not a significant difference in drug resistance between the two states.Do not reject H0. There is not a significant difference in drug resistance between the two states.
Answer:
Reject H₀. There is a significant difference in drug resistance between the two states.
Step-by-step explanation:
In this case we need to determine whether the data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states.
The significance level of the test is, α = 0.02.
(1)
The hypothesis can be defined as follows:
H₀: There is no difference between the proportions of drug-resistant cases in the two states, i.e. [tex]p_{1} - p_{2}= 0[/tex].
Hₐ: There is a statistically significant difference between the proportions of drug-resistant cases in the two states, i.e. [tex]p_{1} - p_{2}\neq 0[/tex].
(2)
Compute the sample proportions and total proportion as follows:
[tex]\hat p_{1}=\frac{12}{189}=0.063\\\\\hat p_{2}=\frac{8}{429}=0.019\\\\\hat p=\frac{12+8}{189+429}=0.032\\[/tex]
Compute the test statistic value as follows:
[tex]Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p(1-\hat p)\times [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]
[tex]=\frac{0.063-0.019}{\sqrt{0.032(1-0.032)\times [\frac{1}{189}+\frac{1}{429}]}}\\\\=2.86[/tex]
The test statistic value is 2.86.
(3)
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=2\cdot P(Z>2.86)=2\times 0.00212=0.00424[/tex]
p-value = 0.00424 < α = 0.02.
The null hypothesis will be rejected at 0.02 significance level.
Reject H₀. There is a significant difference in drug resistance between the two states.
Simplify and divide the following radical expression: √3/ 6√7
Step by step please
Answer:
19
√
5
+
45
Step-by-step explanation:
Multiply:
√
2
⋅
√
6
.
Multiply:
3
√
9
⋅
3
√
6
.
2
√
3
⋅
5
√
2
.
Answer
[tex]21[/tex]/6 write the square root sign with 21 inside /6 (I cant make the sign
[tex]\sqrt{x} 3[/tex]/6 x 7
[tex]\sqrt{x} 3[/tex][tex]\sqrt{x} 7[/tex] /6 TAKE THE X's OUT) ok i cant make the sign alone Draw a line
and put the 6 under the 3 and 7
[tex]3 x 7[/tex] /6 Put the 3x7 under one square root sign /over 6
21/6 Put the 21 inside the square root sign / over 6
Step-by-step explanation:
does that make sense? i cant make the square root symbol so dont put the x's with the numbers
Which quadrant would the point (-5,-3) end up in if it is rotated 180 degrees clockwise?
What is the prime factorization of 23?
Answer: Prime factorization: 23 is prime. The exponent of prime number 23 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 23 has exactly 2 factors.
Step-by-step explanation: Hopefully this helped!
The prime factorization of 23 is 23 × 1. It is already in its simplest form and cannot be expressed as a product of smaller prime factors.
To determine the prime factorization of a number, we check if it is divisible by prime numbers starting from 2. If it is divisible, we continue dividing until we reach the smallest prime factors. However, in the case of 23, it is not divisible by any number other than 1 and 23.
⇒ 23 × 1
The prime factorization of 23 is simply 23 itself. A prime number is a number that is only divisible by 1 and itself, and 23 satisfies this condition. It cannot be further broken down into smaller prime factors.
Therefore, the prime factorization of 23 is 23.
Learn more about Prime Factorization here:
brainly.com/question/4184435
#SPJ6
What is the product of −25 and −0.8? Select all that apply.
Answer:
20
Step-by-step explanation:
comon sence
Answer:
0.32
Step-by-step explanation:
7. All of the following are perfect square trinomials EXCEPT one. Which is it?
A. 4x2 + 12xy + 9y2
C. xy2 - 4x2y2 + 4x2y2
B. 9a? - 36a + 36
D. a²b2 + 4a3b + 4a?
Answer:
All answers EXCEPT answer C. are perfect square trinomials.
Step-by-step explanation:
A perfect square trinomial is polynomial that satisfies the following condition:
[tex](a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}[/tex], [tex]\forall\,a,b\in\mathbb{R}[/tex]
Let prove if each option observe this:
a) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex]
1) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex] Given
2) [tex](2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 2\cdot x[/tex], [tex]b = 3\cdot y[/tex] Definition of perfect square trinomial/Result.
b) [tex]9\cdot a^{2}-36\cdot a + 36[/tex]
1) [tex]9\cdot a^{2}-36\cdot a + 36[/tex] Given.
2) [tex](3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 3\cdot a[/tex], [tex]b = 6[/tex] Definition of perfect square trinomial/Result.
c) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex]
1) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex] Given
2) [tex]x\cdot y\cdot (1-4\cdot x+4\cdot x)[/tex] Distributive property.
3) [tex]x\cdot y \cdot 1[/tex] Existence of the additive inverse/Modulative property.
4) [tex]x\cdot y[/tex] Modulative property/Result.
d) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex]
1) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex] Given
2) [tex](a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = a\cdot b[/tex], [tex]b = 2\cdot a^{2}[/tex] Definition of perfect square trinomial.
All answers EXCEPT answer C. are perfect square trinomials.
holly says 4.131131113... is a rational number . which following best describes whether holly correct and why
Answer:
its d holly is incorrect the decimal part follows a pattern but does not actully reapeat
Step-by-step explanation:
respuesta de x+y+3=0
3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters
Answer:
Since the order of choice matters, we will permute the values. a bit more explanation for this:
If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter
Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters
Since we have 3 slots:
___ ___ ___
Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now
So:
_4_ ___ ___
**Keep in mind that the 4 is the possible number of values this slot can have**
Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with 3 more alphabets
we can put any one of the 3 alphabets in this second slot, Hence:
_4_ _3_ ___
Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3
Therefore:
_4_ _3_ _2_
Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets
Total possible words = 4 * 3 * 2
Total possible words = 24
We could've used the formula for Permutation as well
help me please i’ll give you brainly thingy
Answer:
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
because 8/10 divided by 1/5 equals 4
427 thousand in a scientific notation
Answer:
4.27 x [tex]10^{5}[/tex]
Step-by-step explanation:
The whole digit cannot go past 10 or be less than 1:
1 - 10 is the numbers of its max.
427,000
We would move the decimal point between 4 and 2 making:
4.2700
(Originally the decimal point moved 5 places because 427,000 is a whole number, which means the decimal point would be considered at the end, as shown below)
427,000.
By moving 5 places to the left this will be part of your: scientific notation as
___ x [tex]10^{5}[/tex]
(Then plug in 4.27 in front of your notation)
4.27 x [tex]10^{5}[/tex]
That is your answer!
50 points please help!!
8
I think
Hope this helps
Which equation has the correct sign on the product?
A. 27(-5) = -135
B. (-4)(-4) = -16
C. (-61)(3) = 183
D. 22.4 = -88
Answer:
A
Step-by-step explanation:
27 x -5 = -135
Answer: A
Step-by-step explanation: Hope I helped you.