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
Triangle ABC is transformed to create triangle MNO and triangle PQR as described below.
• MNO represents the translation 2 units left and 2 units down of triangle ABC.
• PQR represents the dilation of triangle ABC by a scale factor of 2
Which of these is correct?
A - The transformation of ABC to PQR preserves both the side lengths and angle measures of the triangle
B - The transformation of ABC to PQR preserves the side lengths but not the angle measures of the angle
C - The transformation of ABC to MNO preserves both side lengths and angle measures of the triangle
D - The transformation of ABC to MNO preserves the angle measures but no the side lengths of the triangle.
Answer: the transformation of ABC to MNO preserves both side lengths and angle measures of the triangle.
Step-by-step explanation:
Answer:
B - The transformation of triangle ABC to triangle MNO preserves both the side lengths and angle measures of the triangle.
A recent study examined hearing loss data for 1628 U.S. teenagers. In this sample, 337 were found to have some level of hearing loss. News of this study spread quickly, with many news articles blaming the prevalence of hearing loss on the higher use of ear buds by teens. At MSNBC (8/17/2010), Carla Johnson summarized the study with the headline: "1 in 5 U.S. teens has hearing loss, study says." To investigate whether this is an appropriate or a misleading headline, you will conduct a test of significance with the following hypotheses:
Null: π = 0.20 Alternative: π ≠ 0.20
A) Describe what the symbol π stands for in this context.
B) Use the Theory-Based Inference applet to determine a p-value.
C) Based on your p-value is there strong evidence that the proportion of all U.S. teens with some hearing loss is different than 1 in 5 (or 20%)?
D) Using the applet, find a 95% confidence interval for the proportion of U.S. teens that have some hearing loss.
E) What is the margin of error for you confidence interval from part (d) of this question?
F) Based on your confidence interval, is 0.20 a plausible value for the proportion of the population that has some hearing loss? Explain why or why not.
G) Based on your p-value, is 0.20 a plausible value for the proportion of the population that has some hearing loss? Explain why or why not.
What is the equation in standard form of the line shown
on the graph?
The equation of the line in standard form is
vbx +
N +
2
-2
2
4
-2
-4
Answer:
Step-by-step explanation:
.
Answer: 3x-4y=12
Step-by-step explanation:
The 3 in 73.084 is _ times the 3 in 65.732.
10x
100x
1/10
Please pick one
PLEASE HELP I AM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100 PTS!!!
The sum and product of two linear functions are shown.
Which statements can be used to describe the original functions f(x) and g(x)? Select two options.
A. When added, the sum of the y-intercepts must be 1.
B. When multiplied, the product of the y-intercepts must be –15.
C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.
Answer:
A and DStep-by-step explanation:
Let the functions be
f(x)= ax + bg(x) = cx + dTheir sum
j(x) = (a+c)x + b+dTheir product
k(x)= (ax + b)(cx + d)The answer optionsA. When added, the sum of the y-intercepts must be 1.
Correct. We see point (0,1) of j(x) on the graph. b+d = 1B. When multiplied, the product of the y-intercepts must be –15.
Incorrect. -15 is the vertex of k(x). The vertex of ax^2 + bx + c is -b/2a. So it has no relation to constants of the functions f(x) and g(x)C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.
Incorrect. It refers to the value of ac. If one of a or c has opposite sign it makes k(x) to open down but it is not as per graph.D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.
Correct. As per above statement, both linear equations could be positive as their sum and product is positive from the graphs of j(x) and k(x)E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.
Incorrect. It should result in decreasing function of j(x) with slope of -4 but it is increasing as per graph.
Someone pls Help me out!!!
Answer:
Gasoline = 10.2 * 3.80= 38.76
Water= 3 * 3.98 = 11.94
Ice- 3 * 1.99 = 5.97
Oranges= 1 * 8.89 = 8.89
Step-by-step explanation:
Como se convierte un entero en fracción
Answer:
aquí es cómo
Step-by-step explanation:
Convertir el número decimal a fracción colocándolo sobre una potencia de diez. Como hay 2 números a la derecha del punto decimal, coloque el número decimal sobre 10 ^ 2 (100). Luego, agregue el número entero a la izquierda del decimal.
espero que esto ayude.
Si puede, no dude en marcarme como Brainliest, sería muy apreciado :D
what is equal to 12.9
(#1) 0.02+12+0.88
(#2) 0.06+12.03
(#3) 11.9+1
(#4) 6.2+3.4+2.3
(#5) 3.01+2.01+7.7
what are all that are equal to 12.9
what is the value of (2^4) ^3 divided by 2^6
Answer:64
Step-by-step explanation:
2*2*2*2=4*4=16. 16*16*16=4,096. 2*2*2*2*2*2=4*4*4=64. 4,096/64=64.
1. The students put together 12 jigsaw puzzles. Each puzzle had 345 pieces. How many puzzle pieces did they put together in all?
Answer:
4140 pieces
Step-by-step explanation:
This is true because we would have to multiply the number of jigsaw puzzles and how many pieces each on of them had to see how many pieces they put together in all.
To set up the equation we would do 345 times 12,
if you calculate it, the answer would be 4140.
Hopes this helps, and good luck!! :)
I need help with that
Answer:
its the 2nd one i think
Universal Claims Processors processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claim with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid $64 per day, and a temporary operator is paid $42 per day. The company wants to determine the number of permanent and temporary operators to hire in order to minimize costs.
Required:
a. Solve the linear programming model using graphical method.
b. Interpret the slack/surplus variables that you obtain based on the optimal values of decision variables in (a).
c. Are there any binding constraints in the model? Explain.
f(x) = (x + 1)2 – 4 g(x) = –4 |x + 1| Which statement compares the ranges of the functions? The ranges of both f(x) and g(x) are limited to y ≥ –1. The ranges of both f(x) and g(x) are limited to y ≤ –1. Since the range of f(x) is limited to y ≤ 0 and the range of g(x) is limited to y ≥ –4, the ranges overlap for the values –4 ≤ y ≤ 0. Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Answer:
Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Step-by-step explanation:
From Function theory we get that range of a function is the set of values of [tex]y[/tex] so that exist a respective value of [tex]x[/tex], whose set is the domain of the function. Let be [tex]f(x) = (x+1)^{2}[/tex] and [tex]g(x) = -4\cdot |x+1|[/tex], the ranges of each function are, respectively:
f(x):
From Real Algebra we know that the square of every number is a non-negative number, which means that:
[tex](x+1)^{2} \geq 0[/tex]
[tex](x+1)^{2}-4 \geq -4[/tex] (Compatibility with addition)
[tex]f(x) \geq -4[/tex] (Definition/Result)
The range of [tex]f(x)[/tex] is: [tex]Ran \{f(x)\} = [-4, +\infty)[/tex]
g(x):
From Real Algebra we know that a absolute value leads to non-negative number, which means that:
[tex]|x+1|\geq 0[/tex]
[tex]-4\cdot |x+1| \leq 0[/tex] ([tex]a> b \longrightarrow a \cdot c < b\cdot c[/tex], if [tex]c < 0[/tex])
[tex]g(x) \leq 0[/tex] (Definition/Result)
The range of [tex]g(x)[/tex] is: [tex]Ran\{g(x)\} = (-\infty, 0][/tex]
If we compare each range, we came into the conclusion that:
[tex]-4 \leq y \leq 0[/tex].
Thus, correct answer is: Since the range of f(x) is limited to y ≥ –4 and the range of g(x) is limited to y ≤ 0, the ranges overlap for the values –4 ≤ y ≤ 0.
Answer:
Its D
Step-by-step explanation:
Got it right on EDGE
Fatima earned an 85 average in her science class. The average is based on 6 tests that she takes over the span of the marking period. On her first four tests she earned an 83, a 78, an 87, and an 80. On her sixth test she scored 8 points more than on her fifth test.
Let x be the score Fatima received on her fifth test. Set up an equation using x that models this scenario. Solve the equation and state what Fatima earned on her fifth and sixth tests.
Answer:
Fifth Score = 87
Sixth Score = 95
Step-by-step explanation:
Given
[tex]Average = 85[/tex]
[tex]Scores = 83, 78, 87, 80[/tex]
[tex]Fifth\ score = x[/tex]
[tex]Sixth\ Score = 8 + x[/tex]
Required
Set up an equation
Solve for the fifth and sixth score
Average is calculated as thus:
[tex]Average = \frac{\sum x}{n}[/tex]
[tex]Average = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}[/tex]
Substitute 85 for Average
[tex]85 = \frac{83 +78 + 87 + 80 + x + 8 + x}{6}[/tex]
[tex]85 = \frac{83 +78 + 87 + 80 + 8+ x + x}{6}[/tex]
[tex]85 = \frac{336+ 2x}{6}[/tex]
Multiply both sides by 6
[tex]85 * 6 = 336 + 2x[/tex]
[tex]510= 336 + 2x[/tex]
Solve for 2x
[tex]2x = 510 - 336[/tex]
[tex]2x = 174[/tex]
Solve for x
[tex]x = 174/2[/tex]
[tex]x = 87[/tex]
Hence:
[tex]Fifth\ Score = 87[/tex]
[tex]Sixth\ Score = 87 + 8[/tex]
[tex]Sixth\ Score = 95[/tex]
Sakura's house is at an elevation between 113 m and 120 m above sea level. Her friend Ted lives about 15 m below he
Part A
Choose the compound inequality that describes the elevation x of Ted's house.
O A 113 s 15 - xs 120
OB. 113 s x + 15 s 120
O C. 113 < x < 120
O D. 113 - x - 15 s 120
Answer:
d
Step-by-step explanation:
All lines that are parallel to AB
Answer:
BA
Step-by-step explanation:
Of three angles of a triangle, one is three times the smallest and the other is five times the smallest. Find the angles
Will mark brainliest
Answer:
20, 60, 100
Step-by-step explanation:
Since the angles in a triangle add up to 180 degrees, we can change the statement by saying x+3x+5x = 180 degrees. That would mean that 9x is equal to 180, and 180/9=20. 20 times 5 is 100, and 20 times 3 is 60.
How do I Invert 6/7? Can you please help me!
Answer:
0. 857142i hope this helps
round 7,883 to nearest thousand
Answer:
8,000
Step-by-step explanation:
the nearest thousand is 8,000 as it is past 7,500.
Hi!
Your answer will be: 8,000.
hope this helps!
a
Positive
b
Negative
c
Undefined
d
Zero
Answer:
B. Negative
Step-by-step explanation:
Because it is sliding down and if it was going up then it would be positive
Select the correct answer which rational number is negative
A.2
B-12/-18
C plus1/plus2
D plus3/-11
Answer: D
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
TABE 11742 Mathematics Practice Test Level M Test 1
Mark to Review Later
Question 8/20
One small box of Quit Smoking Now lozenges holds 36 lozenges. One pack contains 12 small boxes. How many lozenges are in a pack?
O 108 lozenges
O 432 lozenges
O 422 lozenges
0 441 lozenges
me bong recorded
o
BA
Type here to search
a
Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw.
a. Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has a flaw?
b. Assume that the probability that an item has a flaw is 0.10. If an item is passed by both inspectors, what is the probability that it actually has a flaw?
Answer:
a) 0.011
b) 0.0032
Step-by-step explanation:
first lets say A₁ denotes the event that first inspector detects a flaw and A₂ is event that the law will be detected by the second inspector,
also let B denote the event that an item has a flaw.
a)
Given that;
P(B) = 0.1
so
P(A₁ / B ) = 0.9, P(A₂ / B ) = 0.7
using Baye's rule, the probability that an item has a flaw if it was passed by the first inspector is;
P(B / A₁ⁿ ) = [P(A₁ⁿ / B ) P(B)] / [ P(A₁ⁿ / B ) P(B) + P(A₁ⁿ / Bⁿ ) P(Bⁿ) ]
the probability that the first inspector will not detect the flaw if it actually exist is;
P(A₁ⁿ / B ) = 1 - P(A₁ / B )
= 1 - 0.9
= 0.1
Since there are no false detections, the probability that the first inspector will not detect the flaw, given that item does not have flaws is;
P(A₁ⁿ / Bⁿ ) = 1.0
so the probability that the item has flaw if it was passed by the first inspector is;
P(B / A₁ⁿ ) = [(0.1) (0.1)] / [ (0.1 ) (0.1) + (1.0) (1 - 0.1) ]
= 0.01 / ( 0.01 + 0.9)
= 0.01 / 0.91
= 0.011
b)
Also by Bayes rule, the probability that the item has a flaw if it was passed by both inspectors is;
P(B / A₁ⁿ ∩ A₂ⁿ) = [ P(A₁ⁿ ∩ A₂ⁿ / B) P(B)] / [ P(A₁ⁿ ∩ A₂ⁿ / B) P(B) + P(A₁ⁿ ∩ A₂ⁿ / Bⁿ) P(Bⁿ)]
Now since inspectors function independently, the probability that both inspectors will not detect the flaw if it actually exists is;
P(A₁ⁿ ∩ A₂ⁿ / B) = P(A₁ⁿ / B) P(A₂ⁿ / B)
= ( 1 - 0.9 ) ( 1 - 0.7)
= 0.1 * 0.3
= 0.03
since there are no false detections, the probability that both inspectors will not detect the flaw, given that item does not have a flaw is;
P(A₁ⁿ ∩ A₂ⁿ / Bⁿ) = 1.0
therefore
the probability that the item has a flaw if it was passed by both inspectors is;
P(B / A₁ⁿ ∩ A₂ⁿ) = [(0.03)(0.1)] / [(0.03)(0.1) + (1.0)(1-0.1)
= 0.003 / 0.93
= 0.0032
3/4 divided 3/8 what is the quotient of
Answer:2
Step-by-step explanation: Because the answer is 2 :)
A ruby throated humming bird beats its wings 53 times in each second. How many times does the ruby throated humming bird beat its wings 5 second
Answer:
265
Step-by-step explanation:
Answer:
265
Step-by-step explanation:
53*5 (its not that hard man)
11 = -3k - 22 -8k what is the value of k?
Answer:
k = -3
Step-by-step explanation:
Step 1: Write equation
11 = -3k - 22 - 8k
Step 2: Solve for x
Combine like terms: 11 = -11k - 22Add 22 to both sides: 33 = -11kDivide both sides by -11: -3 = kRewrite: k = -3Step 3: Check
Plug in k to verify it's a solution.
11 = -3(-3) - 22 - 8(-3)
11 = 9 - 22 + 24
11 = -13 + 24
11 = 11
Jamie is solving the equation; 4(x-3)=16. Her first step is; 4x - 12 = 16. Which step could be the next step?
Answer:
4x=4
Step-by-step explanation:
What are nutrients?
Suppose you have a 6-face unfair dice with numbers 1,2,3,4,5,6 on each of its faces. If the probability distribution of throwing a number up is as follows:
1 with probability 1/12
2 with probability 1/12
3 with probability 1/12
4 with probability 1/12
5 with probability 1/12
6 with probability 1/2
Which of the following statement is correct?
a. The mathematical expectation of the dice throwing a number up is 3.5
b. The mathematical expectation of the dice throwing a number up is 6
c. The mathematical expectation of the dice throwing a number up is 4.25
d. This is not a proper probability distribution because all the probabilities do not sum up to one
Answer:
D is correct
Step-by-step explanation:
Here, we want to select which of the options is correct.
The correct option is the option D
Since the die is unfair, we expect that the probability of each of the numbers turning up
will not be equal.
However, we should also expect that if we add the chances of all the numbers occurring together, then the total probability should be equal to 1. But this does not work in this case;
In this case, adding all the probabilities together, we have;
1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/2
= 5(1/12) + 1/2 = 5/12 + 1/2 = 11/12
11/12 is not equal to 1 and thus the probability distribution cannot be correct
Brainliest is given to the correct answer!
A high school race track is composed of a rectangle and two semicircles.
a. If the length "l" of the rectangle is twice as long as the diameter of the semicircles, write a formula for "p," the distance around the track, in terms of the radius "r" of the semicircles.
b. Rewrite the formula from a so the radius of the semicircles is given in terms of the distance around the track. Show your work.
Answer:
a. [tex] p = 2\pi r + 8r [/tex]
b. [tex] r = \frac{p}{2\pi + 8} [/tex]
Step-by-step explanation:
a. Radius of semicircle (r) = r
Diameter of semicircle (d) = 2r
Length of rectangle (l) = 2*diameter of semicircle = 2*2r = 4r
Distance around the track (p) = circumference of circle + 2(l)
Note: the two semicircles of the track = 1 full circle
Circumference of full circle = πd = π*2r = 2πr
Distance around the track:
p = 2πr + 2(4r)
p = 2πr + 8r
b. Rewriting the formula to make radius, r, the subject of the formula in terms of distance around the track.
[tex] p = 2\pi r + 8r [/tex]
Factor out r
[tex] p = r(2\pi + 8) [/tex]
Divide both sides by (2π + 8)
[tex] \frac{p}{2\pi + 8} = \frac{r(2\pi + 8)}{2\pi + 8} [/tex]
[tex] \frac{p}{2\pi + 8} = r [/tex]
[tex] r = \frac{p}{2\pi + 8} [/tex]