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Complete Question
Maurice takes a roast out of the oven when the internal temperature of the roast is 165°F. After 10 minutes, the temperature of the roast drops to 145°F.
The temperature of the room is 72°F.
How long does it take for the temperature of the roast to drop to 120°F?
Answer:
27.3143 minutes
Step-by-step explanation:
Using the Newton's law of cooling: The formula is given as:
T (t) = T₀ + T₁ e^ (rt)
Where
T₀ = Original temperature of the room (°F) ; 72°F
T₁ = Temperature of the roast (°F)
This is calculated as:
165 - 72 =93°F
r = Rate of cooling (°F/min)
t = time (min)
Substituting the values, we can obtain:
T (t) = 72 + 93 e ^rt
Step 1
We solve for r
From the question, we know that: the temperature dropped to 145°F after 10 minutes,
t =10 mins and T(10) = 145 °F
Substituting
T(10) = 72 +93 e^10r
145 = 72 + 93 e^10r
145 - 72 = 93 e^10r
Divide both sides by 93
(145-72)/93 = e^(10r)
We take the natural logarithm of both the left and right hand sides
In [(145-72)/93 ] = In (e^10r)
In [(145-72)/93 ] = 10r
-0.24214 =10r
r = -0.24214/10
r = -0.02421 °F/min
Substituting into
-0.02421 °F/min for r in the Equation below
T (t) = 72 + 93 e ^rt
T (t) = 72 + 93 e^ (-0.024214t)
To find the time taken to reach 120°F, we substitute into equation
120 = 72 +93 e^(-0.024214 ×t)
(120-72)= 93 e^ (-0.024214t)
Divide bother sides by 93
[(120-72)/93] = e^-0.024214t
We take the natural logarithm of both sides
In[(120-72)/93] = In(e^-0.024214t)
-0.66139 = -0.024214t
Divide both sides by -0.024214t
t = -0.66139/ -0.024214
t =27.3143 minutes
A Large earthworm can travel 25 centimeter in 12 seconds. How many meters does the earthworm travels in1 minute?
We know that it can travel 25 centimetres in 12 seconds. First, we break down the minute into seconds.
60/12= 5
______________________________
Now, multiply 25 by 5.
25x5=125
__________________________________
With this knowledge, we just have to convert the centimetres, to meters.
_______________________________
Your answer is 1.25 meters :)
Jaysen helps his mom in gardening. The produce is sold in the market for $ 17 a bag . This year they sold 25 bags. Jaysen gets 35% of the money that is earned. How much will Jaysen earn
Answer:
Step-by-step explanation:
the money received for 25 bags:
17*25=425
Jaysen get 35%
425*(35/100)=148.75 dollars
Answer:
148,75 $
Step-by-step explanation:
17 × 25 = 425
425 × 0,35 = 148,75
Good night, logging out !
Good night :). Sleep tight!
In the inequality
a> 3x+8 or a>-4x-1, which value of a does the solution consist of numbers greater than -6 and less than 5?
A-16
B-26
C-19
D-23
Answer:
I think it is B correct me if I am wrong
Step-by-step explanation:
in the following figures find the value of angle COD if angle abc is equal to 75 degree and a b is equal to CD
Angle AOB is given as 75 degrees.
O is the center of the circle so AO and CO are the same length. AB and CD are the same length, so angle COD would be the same as AOB
COD = 75 degrees.
Answer:
75°
Step-by-step explanation:
It is given that:
AB and CD are chords of the circle which are equal. Equal chords subtends equal angles at the center of the circle. [tex] \because m\angle AOB = 75\degree [/tex] [tex] \therefore m\angle COD = 75\degree [/tex]Can you help me with these questions pls
Cassandra has a loan of $35,720. This loan has a simple interest rate of 4% per year.
What is the amount of interest Cassandra will pay on this loan at the end of two years?
$2,857.60
$38,577.60
$1,428.80
$5,715.20
solve for x parallel lines
PLZ HELP IM BEING TIMED
Answer:
A
Step-by-step explanation:
Alex helps his father milk cows on their dairy farm. They are paid $2.25
per gallon of milk, that they get from their cows. Together, Alex and his
father are able to milk 12 gallons over a 2-hour period. How much money
could Alex and his father expect to earn if they worked for 10 hours?
А
$22.50
B
$54.00
C
$135.00
D
$270.50
did i do this right if not can you show me how to do it
Answer:
no
Step-by-step explanation:
Order of operations
18/2=9
9/3=3
5-2=3
3/3
1 (simplified)
The outcome is still the same but since you have to show your work.....That's the correct way to do it
Hope this helps. Have a nice day.
How we can differentiate between direct proportion and inverse proportion?
Answer:
Please check explanations for answer
Step-by-step explanation:
Here, we want to differentiate between inverse and direct proportion
Let x and y be two quantities
If they are directly proportional;
x/y = k
x = ky
where k is proportionality constant
If inversely;
xy = k
In verbal terms;
For direct proportionality, when one value increase, the other too does so and vice versa
For inverse, when one value inverse, the other decrease
A rectangular parking lot is surrounded on its perimeter by a fence that is 1,200 feet long. If the length of the rectangular parking lot is 5 times its width, w, which equation can be used to find the width of the parking lot? Ow+ (w+5) = 1,200
Answer:
w+5w=1200
Step-by-step explanation:
what fraction equals to 4
Answer:
confusing wording... read below ( 12/3 )
Step-by-step explanation:
if you meant adding fractions then the other answer, but if i read it right then 12/3. 12 divided by 3 = 4
standard form of 0.000064
Answer:
6.4 × 10^-5
This is the standard form of 0.000064.
f (x) = 2x² - 10x + 13
Find f (-4)
Answer:
85
Step-by-step explanation:
In this question, you would solve by plugging in -4 to x.
Solve:
f(-4) = 2(-4)² - 10(-4) + 13
= 2(16) + 40 + 13
= 32 + 40 + 13
= 72 + 13
= 85
f(-4) = 85
What does 2x + 3x + 4x simlify to?
Answer:
9x does
Step-by-step explanation:
hope it helps
remind me if its wrong
please help angle c angle ahdbdoneoend
Answer:
True
Step-by-step explanation:
The angle that sees the smallest side length has the small angle measurement.
Graph the line that represents this equation:
y=-5z +2
Hello! Could you please help with these? It was due quite a long time ago. I have a D in this class and need to get my grades up.
Answer:
16. [tex]y=7x[/tex]
17. [tex]y=0.5x[/tex]
18. [tex]y=3x[/tex]
19. [tex]y=2x[/tex]
Step-by-step explanation:
Equation is [tex]y=kx[/tex] where k is a constant of proportionality.
16.
[tex]\frac{y}{x}=\frac{10.5}{1.5}=\frac{14}{2}=\frac{24.5}{3.5}=\frac{35}{5}=7[/tex]
So, equation is [tex]y=7x[/tex]
17.
[tex]\frac{y}{x}=\frac{1}{2}=\frac{2}{4}=\frac{2.5}{5}=\frac{3.5}{7}=\frac{1}{2}=0.5[/tex]
Equation is [tex]y=0.5x[/tex]
18.
[tex]\frac{y}{x}=\frac{6}{2}=\frac{9}{3}=\frac{15}{5}=\frac{18}{6}=3[/tex]
Equation is [tex]y=3x[/tex]
19.
[tex]\frac{y}{x}=\frac{4}{2}=\frac{8}{4}=\frac{14}{7}=\frac{18}{9}=2[/tex]
Equation is [tex]y=2x[/tex]
Which dot plot matches the tally chart below?
A 2-column table with 5 rows. Column 1 is labeled Pull-ups Completed in one minute with entries 1, 2, 3, 4, 5. Column 2 is labeled Tally with entries 2, 5, 3, 1, 2.
Answer:
(A) my friend
Step-by-step explanation:
please mark Brainliest because the other answer above me is wrong
Answer:
A
Step-by-step explanation:
What is the value of y = 3x -1 when x is equal to 4?
Answer:
11
Step-by-step explanation:
Y = 11 when x is equal to 4.
y = (3)(4) − 1
Answer:
y = 11
I need to simplify the complex fraction.
Answer:
(15 – 22x)/4x(2x – 5)
Step-by-step explanation:
Let us take the numerator first:
(1/2x – 5) – (7/8x – 20) = (1/(2x – 5)) – (7/4(2x –5)) = (8x – 20 – 7(2x – 5))/(4(2x – 5)(2x – 5)
= (8x – 20 – 14x + 35)/4(2x – 5)² = (15 – 22x)/4(2x – 5)²
The denominator is: x/2x – 5
So we now have:
(15 – 22x)/4(2x – 5)² ÷ x/(2x – 5) = (15 – 22x)/4(2x – 5)² x (2x – 5) /X = (15 – 22x)/4x(2x – 5)
cynthia and amy are customer service representives cynthia earns $13 per hour and amy earns $1.50 more per hour than cynthia. Amy worked 43.5 hours in the last two weeks which equation could she use to find the amount of money she should receive
Answer:
Step-by-step explanation:
Let h bet the # of hours worked
If Cynthia earns $13 per hour then her equation would be:
C = $13h
If Amy makes $1.5 more per hour then her equation would be:
A = $14.5x
Now lets plug in some numbers:)
A = $14.5(43.5)
A = $630.75
Class A has 26 pupils and class B has 15 pupils.
Both classes sit the same maths test.
The mean score for class A is 33.
The mean score for both classes is 39.
What is the mean score (rounded to 1 DP) in the maths test for class B?
Answer:
Concept: Real World Analysis
So we know A has an average of 33We know A+B/2= 39Hence we will solve for b [tex] \frac{33 + x}{2} = 39[/tex][tex]x = 45[/tex]Answer:
It's 49.4
Step-by-step explanation:
((26*33)+(15*x))/41＝39
((858)+(15*x))/41＝39 ‖*41
(858)+(15*x)＝1599 ‖-858
15*x＝741 ‖/15
x＝49.4
Name theorem or postulate?
Answer:
SAS
Step-by-step explanation:
Simplify the expression.
7y+6−1+12y =
Answer:
19+5
Step-by-step explanation:
7y+6-1+12y
Add common variables
19y+5
Can't be simplified any further without an answer to the equation
Hope this helps. Have a great day. May it be filled with joy and happiness
Answer:
24 x y2
Step-by-step explanation:
7+6=13
13-1=12
12+12=24
There is 2 Y's so you do y to the power of 2.
The Blues Festival sold 20% of tickets at a reduced price of $30 and 30% of tickets at $40 and the rest at the door for full price of $50. With 10,000 tickets sold, how much did they earn from ticket sales in dollars?
Answer:
$430,000
Step-by-step explanation:
20% of 10,000 = 2000
therefore, 2000 x $30 = $60,000
30% of 10,000 = 3000
therefore, 3000 x $40 = $120,000
50% of 10,000 = 5000
therefore, 5000 x $50 = $250,000
add all dollar amounts together to get $430,000
14 books in 2 boxes; 20 books in 3 boxes
O Yes, they are proportional
O No, they are not proportional
Answer:
No of course not
Step-by-step explanation:
14x2=24
20x3=60
At the store Brand P potato chips were $19.00 for 5 bags. Brand Q potato chips were $13.17 for 3 bags. Which brand has the cheaper price?
Answer:
Brand P has the cheaper price
Step-by-step explanation:
Brand P: $19.00 / 5 bags = $3.80 per bag
Brand Q: $13.17 / 3 bags = $4.39 per bag