The temperature of the body after 60 minutes is 60.5° F.
Using the Newton's law of cooling;
T(t) =[tex]Ts + (To - Ts)e^-kt[/tex]
T(t) = temperature at time t
Ts = temperature of the surrounding
To = Temperature of object
t = time taken
k = cooling constant
Now;
[tex]T(t) -Ts=(To - Ts)e^-kt\\45 - 67 = (34 - 67)e^-15k\\-22 = -33e^-15k\\-22/-33 = e^-15k\\0.667 = e^-15k\\ln(0.667) = ln( e^-15k)\\-0.405 = -15k\\k = -0.405/ -15\\k = 0.027[/tex]
At t = 60 min
[tex]T(t) = Ts + (To - Ts)e^-ktT(60) = 67 + (34 - 67)e^-( 0.027*60)\\T(60) = \\67 + (-33)e^-( 0.027 * 60)\\T(60) = \\60.5 F[/tex]
T(60) = 60.5° F
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Answer:
T≈169
Step-by-step explanation:
Enter only the final temperature into the input box.
T_a = 67\hspace{50px}T_0=210
T
a
=67T
0
=210
\text{Write Formula:}
Write Formula:
T=67+(210-67)e^{-kt}
T=67+(210−67)e
−kt
Plug in givens
\color{blue}{T}=67+143e^{-k\color{green}{t}}
T=67+143e
−kt
Simplify
\text{Plug in given time and temperature:}
Plug in given time and temperature:
\color{blue}{193}=67+143e^{-k(\color{green}{1.5})}
193=67+143e
−k(1.5)
Simplify
\text{Solve for }k\text{:}
Solve for k:
193=
193=
\,\,67+143e^{-1.5k}
67+143e
−1.5k
-67\phantom{=}
−67=
\,\,-67
−67
126=
126=
\,\,143e^{-1.5k}
143e
−1.5k
\frac{126}{143}=
143
126
=
\,\,\frac{143e^{-1.5k}}{143}
143
143e
−1.5k
Divide by 143
0.8811189=
0.8811189=
\,\,e^{-1.5k}
e
−1.5k
\ln\left(0.8811189\right)=
ln(0.8811189)=
\,\,\ln\left(e^{-1.5k}\right)
ln(e
−1.5k
)
Take ln of both sides
\ln\left(0.8811189\right)=
ln(0.8811189)=
\,\,-1.5k
−1.5k
\frac{\ln\left(0.8811189\right)}{-1.5}=
−1.5
ln(0.8811189)
=
\,\,\frac{-1.5k}{-1.5}
−1.5
−1.5k
Divide by -1.5
0.0843751=
0.0843751=
\,\,k
k
k\approx
k≈
\,\,\color{blue}{0.084}
0.084
Round k to nearest thousandth
\text{Complete Formula:}
Complete Formula:
T=67+143e^{-\color{blue}{0.084}t}
T=67+143e
−0.084t
Plug in k
\text{Find temperature after }\color{green}{4}\text{ minutes:}
Find temperature after 4 minutes:
T=67+143e^{-0.084(\color{green}{4})}
T=67+143e
−0.084(4)
Plug in time
T=67+143e^{-0.336}
T=67+143e
−0.336
Multiply
T=169.1911041
T=169.1911041
Plug into the calculator
T\approx 169
T≈169
How do you dived a fraction with a number like for an a example:
4/10 divided 2 = ?
Please explain step by step to get marked as brainliest!
Step-by-step explanation:
I assume you mean how do you divide a fraction by a whole number
In order to divide a fraction by a whole number we must use the KFC rule or the "Keep, flip, change" rule
The "Keep" means we keep the first fraction the same.
Next, we "flip" the second fraction (or in this case number; however it can be made into a fraction by putting it over 1). So now we have 4/10 divided by 1/2
Then we "change" the symbol so instead of dividing the fraction, we change the divide to a multiply.
Lastly, you just multiply the fractions as you usually would and you should end up with 4/20 which simplifies to 1/5 if my maths is correct.
Hope this helps.
Answer:
you can use KCF for this answer as well
Step-by-step explanation:
2 as a fraction would be 2/1
you need 4/10 divided by 2/1
applying KCF, you change it to be 4/10 multiplied by 1/2
solve to get 4/20 or simplified 1/5
hope this helped :)
The lengths of the sides of quadrilateral EFGH are as follows: EF = 12 cm, FG = 6 cm, GH = 9 cm, and EH
- 9 cm. If EFGH - MNOP and NO = 7.5 cm, which statement about the side lengths of quadrilateral MNOP
is true?
MN = 12 cm because the scale factor for dilating quadrilateral EFGH is 1.
MP = OP = 7.2 cm because the scale factor for dilating quadrilateral EFGH is
UA
5
HMN = 13.5 cm because the scale factor for dilating quadrilateral EFGH adds 1.5 cm to EF.
MP = OP = 11.25 cm because the scale factor for dilating quadrilateral EFGH is 1.25.
The true statement about the side lengths of quadrilateral MNOP is (d) MP = OP = 11.25 cm because the scale factor for dilating quadrilateral EFGH is 1.25.
The side lengths of EFGH are given as:
[tex]EF = 12\ cm[/tex]
[tex]FG = 6\ cm[/tex]
[tex]GH = 9\ cm[/tex]
[tex]EH = 9\ cm[/tex]
Length NO is also given as:
[tex]NO = 7.5\ cm[/tex]
Because both quadrilaterals are similar, then side NO corresponds to side FG.
The scale factor (k) from EFGH to MNOP is then calculated as:
[tex]k = \frac{NO}{FG}[/tex]
[tex]k = \frac{7.5}{6}[/tex]
[tex]k = 1.25[/tex]
The side lengths of MNOP are then calculated using:
[tex]MN = 12cm \times 1.25[/tex]
[tex]MN = 15\ cm[/tex]
[tex]OP = 9cm \times 1.25[/tex]
[tex]O P = 11. 25 cm[/tex]
Also,
[tex]MP = 11. 25 cm[/tex]
So, the true statement is (d)
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PLEASE HELP ME please please
Answer:
if its before bed time I think it is A
Step-by-step explanation:
Jordan made this design from three pieces of square shaped cloth. What is the total area of design Jordan made? EXPLAIN how u found your answer
Applying the area of a square, the total area of the design is: 116 cm²
Area of SquareA square has equal side lengths, s, this, the area of a square is given as: A = s².
The three pieces of square shaped cloth that Jordan made the design from is shown in the image attached below.
To find the total area of the design, find the area of each square shaped cloth and add all together.
Thus, applying the area of a square, the total area would be:
Total Area = 4² + 6² + 8²
Total Area = 116 cm²
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A complex shape with measurements 6 inches, 5 inches, 4 inches, 3 inches, 4 inches, 2 inches, 6 inches, 10 inches. What is the perimeter of the shape?
Answer: 40
Step-by-step explanation: do 6 add 5 add 4 add 3 add 4 add 2 add 6 add 10
A cruise ship is traveling northwest so that it makes a 45-degree angle with the east-west line. If it has traveled 35 miles from its starting point, what are the components of the vector s formed by the ship's path?
Answer:
Step-by-step explanation:
Answer:
(17.5√2 miles west, 17.5√2 miles north)
Step-by-step explanation:
The distance in the west direction will be ...
35cos(45°) = 17.5√2 . . . . miles west
The distance in the north direction will be ...
35sin(45°) = 17.5√2 . . . . miles north
The vector components are ...
(17.5√2 miles west, 17.5√2 miles north)
_____
Additional comment
When a map with the usual "north is up" orientation is overlaid on an x-y coordinate grid, the (x, y) ordered pair directions correspond to (east, north). Using that coordinate meaning for the vector components here, they would be ...
(-24.7, 24.7) miles
Solve 3-x/2<18.
A. X>-42
B. x > -30
C. X< -30
D. X<42
The solution of the given equation will be C -x< 30
What does it mean to solve an equation?An equation represents the equality of two or more mathematical expressions.
A Solutions to an equation are those values of the variables, involved in that equation for which the equation is true.
We have been given the equation as 3-x/2<18.
Now solving for x
3-x/2<18.
Eliminate 3
-x/2 < 18 - 3
-x/2 < 15
Multiply by 2 on both sides;
-x/2 < 15 (2)
-x< 30
Therefore, the solution of the given equation will be C -x< 30
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Factorize the expressions
px2 + qx
Answer:
SOLUTION
HERE,
=X(P.2+Q)
=X(2P+Q)
Answer:
x(px+q) ( I took x as a common and the remaining are some
-10-9-8-7 -6 -5 -4 -3
-2.1
0
1 2 3 4 5
6
7 8 9 10
3) Which inequality matches the graph?
A) X > .2
B) X <-2
C) x = -2
D) 3.2
Answer:
I think its D
Step-by-step explanation:
The dot starts on -2 and decreases so the answer would = -2 or be less than -2 :)
what is the anser to 9 + 7
[tex] \huge \green{ \boxed{ANSWER}}[/tex]
[tex]9 \: + \: 7 \: = \boxed{16}[/tex]
USE CALCULATOR...
[tex]#CARRYONLEARNING[/tex]
[tex] \mathfrak{JazmineChoi}[/tex]
STAN TREASURE
Does anyone know how to solve this?
Pls confirm if right. Thx!
Answer:
If I am thinking right ya
Step-by-step explanation:
Answer:
Step-by-step explanation:
no mate
your answers for consecutive interior angles are wrong, the answers for that
8 and 13 and 3and 10 should go into the alternate interior angles section
and 2 and 11 should go into the alternate exterior angles section
help me plssssssssssssssssssssss
Answer:
p < 319
Step-by-step explanation:
Find the product of 5 and 539.
Answer:
Step-by-step explanation:
5*539=2695The product of 5 and 539 is 2695
What does it mean to find the product of numbers:Finding the product of numbers simply means multiplying 2 or more numbers.
Therefore, the product of 5 and 539 can be done as follows:
5 × 539Multiplication or product sign is denoted as ×.
Therefore,
5 × 539 = 2695
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Nicole got a prepaid debit card with $25 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the
ribbon was 22 cents per yard. If after that purchase there was $17.52 left on the card, how many yards of ribbon did Nicole buy?
Answer:
34 yards of ribbon
Step-by-step explanation:
If you will subtract the $17.52 to $25 you will get 7.48 then 7.48 divide to .22 you will get 34 as the answer
3.-Las 80 habitaciones de un motel se podrían alquilar todas las noches si el director cobrará
40 € o menos por habitación. Si se cobra (40+x) € por habitación, entonces 2x habitaciones
permanecerán vacantes. Si cada habitación alquilada le cuesta al director 10 € al día y cada
habitación no alquilada 2 € al día, ¿qué precio debería cobrar el director por habitación para
maximizar su beneficio diario?
4.- Un fabricante de automóviles vende 2000 coches al mes, con un beneficio medio de 1000 €
por coche. Las prospectivas de mercado indican que por cada 50 € de descuento que el
fabricante ofrezca a los compradores podría vender 200 coches más al mes.
¿Cuánto descuento debería ofrecer para maximizar el beneficio mensual?
3) Para maximizar su beneficio diario el director debería cobrar cada habitación a €56.
4) El fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.
3- Dado que las 80 habitaciones de un motel se podrían alquilar todas las noches si el director cobrara 40€ o menos por habitación, y si se cobra (40+x) € por habitación, entonces 2x habitaciones permanecerán vacantes, para determinar, si cada habitación alquilada le cuesta al director 10 € al día y cada habitación no alquilada 2 € al día, qué precio debería cobrar el director por habitación para maximizar su beneficio diario, se deben realizar los siguientes cálculos:
80 x 40 - 80 x 2 = 304070 x 50 - 10 x 10 - 70 x 2 = 326060 x 60 - 20 x 10 - 60 x 2 = 328065 x 55 - 15 x 10 - 65 x 2 = 329566 x 54 - 14 x 10 - 66 x 2 = 329264 x 56 - 16 x 10 - 64 x 2 = 329663 x 57 - 17 x 10 - 63 x 2 = 3295Por lo tanto, para maximizar su beneficio diario el director debería cobrar cada habitación a €56.
3) Dado que un fabricante de automóviles vende 2000 coches al mes, con un beneficio medio de 1000 € por coche, y las prospectivas de mercado indican que por cada 50 € de descuento que el fabricante ofrezca a los compradores podría vender 200 coches más al mes, para determinar cuánto descuento debería ofrecer para maximizar el beneficio mensual se debe realizar el siguiente cálculo:
1000 x 2000 = 2.000.000900 x 2400 = 2.160.000800 x 2800 = 2.240.000700 x 3200 = 2.240.000600 x 3600 = 2.160.000850 x 3000 = 2.550.000Por lo tanto, el fabricante debería ofrecer un descuento de 150€ para maximizar su beneficio mensual.
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BINGO cards are $2 for 3 cards. How many BINGO cards can joy get for $12
Answer:
18 cards
Step-by-step explanation:
Because..[tex]12 \div 2 = 6 \times 3 = 18[/tex]yag cuts 75 degrees angle from a paper circle then he cuts out another section measuring 130 degrees ,what is the angle that is left ?
Answer:
155°
Step-by-step explanation:
We know that the sum of the sections must be 360°. So, by removing a section of 75° he leaves the paper circle with a section of 185°, then removes another 130° section, leaving the last section of 155°.
The length of a rectangular garden is 3 feet more than 2 times the width. The perimeter of the garden is 48 feet. Find the length and width of the garden .
Answer:
length 17 feet
width 7 feet
Step-by-step explanation:
Let w represent the width. Then the length is 2w+3, and the perimeter is ...
P = 2(L +W)
48 = 2((2w+3) +w) = 6w +6
42 = 6w
7 = w . . . . . . . . width
(2w+3) = 17 . . . length
The length of the garden is 17 feet; its width is 7 feet.
Select the two pairs of figures that are similar
Help help help math math math
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Sarah opened a savings account with a $725 deposit. This account earns 3.5% annual interest compounded twice each month. How long will it take her account to reach a balance of $2000 if there are no other deposits or withdrawals.
It will take 29 years to reach $725 to $2000 compounded twice in a month.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
The formula for compound interest compounded twice each month is,
A = P(1 +(r/24)/100)²⁴ⁿ.
Given, A = 2000, P = 725, r = 3.5.
∴ 2000 = 725(1 + (3.5/24)/100)²⁴ⁿ.
(1 + (3.5/24)/100)²⁴ⁿ = 2.76.
(1.00146)²⁴ⁿ = 2.76.
24n = [tex]log_{1.00146}2.76[/tex].
24n = 695.87.
n = 29 years.
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Add 8.563 and 4.8292. then times the answer by 9.183 divide it 2 times by 1.192. Add to the answer with this number after your finished: "19.323
Answer:
105.876373581
Step-by-step explanation:
8.563 + 4.8292 = 13.3922
13.3922 × 9.183 = 122.9805726
122.9805726 ÷ 1.192 = 103.171621309
103.171621309 ÷ 1.192 = 86.5533735811
86.5533735811 + 19.323 = 105.876373581
Step-by-step explanation:
8.563+4.8292=A
( A*9.183)÷1.192÷1.192=B
B+19.323=C
Is it possible to arrange 152 books on a shelf so that the first shelf has 7 fewer books than the second shelf and 11 more than the third shelf?
Using a system of equations, it is found that since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.
For the system, we consider that:
x is the number of books on the first shelf.y is the number of books on the second shelf.z is the number of books on the third shelf.In total, there are 152 books, hence:
[tex]x + y + z = 152[/tex]
The first shelf has 7 fewer books than the second shelf, hence:
[tex]x = y - 7[/tex]
Also, it has 11 more books than the third shelf, hence:
[tex]x = z + 11[/tex]
Then:
[tex]y - 7 = z + 11[/tex]
[tex]z = y - 18[/tex]
Then, replacing in the first equation:
[tex]x + y + z = 152[/tex]
[tex]y - 7 + y + y - 18 = 152[/tex]
[tex]3y = 177[/tex]
[tex]y = \frac{177}{3}[/tex]
[tex]y = 59[/tex]
The number of books in each shelf has to be countable, that is, cannot be decimal.
Then, since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.To learn more about system of equations, you can take a look at https://brainly.com/question/14183076
what is 35 divided by 97.3
Answer: 2.78
Step-by-step explanation:
long division
Houa is driving to a concert and needs to pay for parking. There is an
automatic fee of $8 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. How much total money would Houa have to pay for
parking if she left her car in the lot for 3 hours? How much total money would Houa have to pay if she left her car in the lot for 3 hours? How much would Houa have to pay if she left her car in the lot for t hours?
Cost of parking for 3 hours:
I
Cost of parking for t hours:
Step-by-step explanation:
let's create the corresponding equation.
it is linear, because the cost per hour is constant, no matter how many hours the car parks.
t is the variable indicating the amount of hours parking.
every hour costs $2.
and $8 is the starting value (we have to pay that, even if we have 0 hours parking time).
cost(t) = 2t + 8
so, the cost after 3 hours is
cost(3) = 2×3 + 8 = 6 + 8 = $14
Alan needs to mix 3 tablespoons of salt with 5 tablespoons of vinegar to make a cleaning solution. How many tablespoons of salt are needed for each tablespoon of vinegar? (5 points)
Question 3 options:
1)
tablespoons
2)
tablespoon
3)
tablespoon
4)
tablespoon
Answer:
the answer 3/5 lets hop i ace it
Step-by-step explanation:
Describe the location of the polnt having the following coordinates. abscissa and ordinate have the same sign
Quadrant II or Quadrant IV
Quadrant II or Quadrant III
Quadrant or Quadrant IV
Quadrant I or Quadrant III
Answer:
i think its D
Step-by-step explanation:
hope this helps!
Bidmass working out questions
Answer:
2nd one
Step-by-step explanation:
i think(10+2)^2_4*11=100 in my opinion
Which statement is true about the function f(x)= Vx?
O The domain of the graph is all real numbers.
O The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
O The range of the graph is all real numbers greater than or equal to 0.
Answer:
The statement "the range of the graph is all real numbers greater than or equal to 0" is true.
Step-by-step explanation:
As the function is given by
As we know that the domain is the set of all possible input values or all x -values that a function passes through. In other words, domain consists of all the possible input values shown on the x-axis.
Range is the set of all y-values that a function passes through. In other words, range consists of all the possible output values shown on the y-axis.
For the given function
The domain of the given function
The domain of can also be written as: {x | x ≥ 0}
It means the domain of the graph of this function is all real number greater than or equal to 0.
The domain of the graph of this function can not be less than zero, because if we put any negative real number in this function, it would make the the function undefined.
Please check the attached graph as shown in figure a, to visualize the domain and range of
From the graph.
it is visible that the range of the given function
The range of can also be written as: {y | y ≥ 0}
In other words, for every input value in the domain of this function, the range of will be all real numbers greater than or equal to 0. Please see the attached graph as shown in figure a.
So, from the entire discussion, we can safely say that the statement "the range of the graph is all real numbers greater than or equal to 0" is true.