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
Learn more about Newton's law of cooling: https://brainly.com/question/13748261
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
23x25 = please help
Answer:
575
Step-by-step explanation:
23/4 = 5.75 times 100
Answer:
575
Step-by-step explanation:
23×25=575 so 575 would be your answer
❗NEED HELP ASAP PLEASE ❗
The value of -3 xy, for x= 2 and y= 3, is -18.
True False
Please give an explanation, thank you!!!
Answer:
True
Step-by-step explanation:
-3 xy = -18
-3(2)(3) = -18
) f(x) = 4x + 5, g(x) = 2/x;
Find (g • f)(3).
[tex]\text{Given that,}\\\\f(x) = 4x+5,~~~g(x) = \dfrac 2x\\\\\\f(3) = 4(3) +5 = 12 +5 = 17\\\\\\(g\circ f)(3)=g(f(3))=g(17)=\dfrac 2{17}[/tex]
Answer:
The answer is 2/17
Step-by-step explanation: Can I get brainliest again my answer was deletedee
Explain how to use the distributive property to find the product (3) (4 1/5)
Answer:
you didn’t answer my question correctly :(
Step-by-step explanation:
Use the fundamental identities to
Find tan s if sin s=3/4 and s is in quadrant 2
Answer:
Cosine Formula
Thus, the cosine of angle α in a right triangle is equal to the adjacent side's length divided by the hypotenuse. To solve cos, simply enter the length of the adjacent and hypotenuse and solve.
The following graph shows the system of equations?
PLS HELP
A
Hilda has a bank account balance of $1550. Each week, her balance changes by −$82.50. She wants to keep the balance above $395.
How many weeks will Hilda's balance remain above $395?
Select from the drop-down menu to correctly complete the statement.
Hilda's bank balance will remain above $395
Choose...
weeks.
Step-by-step explanation:
1550 - 395 = 1155
1155 / 82.5 = 14
Answer should therefore be 14 weeks.
Not my usual way of doing this sort of question but I'm interested to see if it's right. Alternatively you can subtract $82.50 from $1550 until/before you reach $395. Do not go below $395 though.
Answer:
K12 Answer
Step-by-step explanation:
What expression is equivalent to 8t-18-20t+14
Answer:2(4t-9-10t+7) is answer and for the next it 2(-6t-2)
For shipping the retailer charges a $4.95 flat fee or 5.75% of the total purchase, whichever is greater. If Lucia's total purchase is $78.99, how much shipping will she pay? PLEASE ANSWER ASAP
Find the height of the trapezoid.
7 m
Area = 51 m2
10 m
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $800 per week. How much did she earn last week if she sold $4,700 in electronics merchandise? Round your intermediate calculations and answer to the nearest cent.
Answer:
1164.25
Step-by-step explanation:
How many pennies dose Michael please help please I need your help please please please please help
Answer: He has 91, to figure this out count everything in top row which is 13 and then count everything in left row only which is 7 and 13 x 7 is 91
Step-by-step explanation:
I'm giving out a lot of points for this one!
Answer:
Step-by-step explanation:
AVERAGE rate of change looks only at the endpoints
m = Δy/Δx
m = (1.2 x 10⁶ - 0.35 x 10⁶) / (2640 - 1955)
m = 0.35 x 10⁶/ 685
m = 1241 beings / year
I am doing Khan Academy and I'm stuck on a question that said " What is another way to make 4.65 ? "
I learned it at school but I still need help on that Question.
Answer:
[tex]\frac{465}{100}[/tex] or [tex]\frac{93}{20}[/tex]
Step-by-step explanation:
You can always just multiply the by 100/100 to get any number into a fraction form. I am not sure if this is what you were asking, but here you go. Then you can simplify to get 93/20.
A tiled floor measures 1 ⅔ by 2 ⅔ feet. What is the area of the floor?
let's firstly convert the mixed fractions to improper fractions and then multiply.
[tex]\stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}~\hfill \stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{3}\cdot \cfrac{8}{3}\implies \cfrac{40}{9}\implies 4\frac{4}{9}[/tex]
Use polynomial identities to multiply (5 - 4x3)(5 + 4x3). What identity did you use?
A. Difference of cubes identity
B. Difference of squares identity
C. Binomial Theorem
D. Square of a sum identity
[tex]\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ (5-4x^3)(5+4x^3)\implies [(5)^2-(4x^3)^2]\implies [(5^2)-(4^2x^{3\cdot 2})] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 25-16x^6~\hfill[/tex]
9. Given a scale factor of 3, find the coordinates for the dilation of a triangle with vertices at
(1 point)
(1 4). (4.5), and (2.0).
A 3.7). (7.8). (5.3)
B 3.4) (12,5), (6,0)
C 3.12). (12.15) (6.0)
D (112) (4.15) (2.0)
The coordinates for the dilation of a triangle is (3 12), (12.15), and (6.0).
If the coordinate (x, y) is dilated by a scale factor of k, the resulting coordinate will be at (kx, ky)Given the coordinate of the triangle (1 4). (4.5), and (2.0), if this coordinate is dilated by a factor of 3, the resulting coordinates will be at (3 12), (12.15), and (6.0).
Hence the coordinates for the dilation of a triangle is (3 12), (12.15), and (6.0).
Learn more on dilation here: https://brainly.com/question/10253650
What fraction of one hour (60 minutes) is represented by the following numbers of minutes? Simplify each fraction whenever possible. A sketch of a clock might help you
15 minutes =
20 minutes =
Answer:
[tex] \frac{1}{4} [/tex]
[tex] \frac{1}{3} [/tex]
Suppose a normal distribution has a mean of 79 and a standard deviation of 7. What is P(x ≥ 72)?
A. 0.84
B. 0.975
C. 0.025
D. 0.16
Approximately 65% of the distribution lies within one standard deviation of the mean, which is to say,
P(72 ≤ x ≤ 86) ≈ 0.65
Normal distributions are symmetric, so the percentage of values one standard deviation below the mean is equal to the percentage of values one standard deviation above the mean.
P(72 ≤ x ≤ 79) = P(79 ≤ x ≤ 86)
but since the sum of these make up P(72 ≤ x ≤ 86), we find
P(72 ≤ x ≤ 79) ≈ 0.65/2 = 0.325
Also due to symmetry, exactly half of the distribution lies to either side of the mean; namely,
P(x ≥ 79) = 0.5
It follows that
P(x ≥ 72) = P(72 ≤ x ≤ 79) + P(79 ≤ x)
P(x ≥ 72) = 0.325 + 0.5
P(x ≥ 72) = 0.825 ≈ 0.84
Answer: 0.84
Step-by-step explanation:
in the actual room, the distance between the front and back walls is 8 feet. what is the actual length of the front wall, in feet?
Answer:
8 feet
Step-by-step explanation:
it actually will be 8 feet
hlep me it is easy plssssssssssssss
Answer:
C. (10 - 2) ÷ 4
Step-by-step explanation:
To determine which expression represent a number that is one fourth as great as 10-2 the following logical reasoning has to be made:
Given that a number is raised that is a quarter as large as (10-2), the result of this mathematical operation must be divided by 4.
Thus, since 10 minus 2 is equal to 8 and 8 divided by 4 gives 2, the division is necessary as a mathematical operation.
So, since the only option that raises a division is option C, that's the correct option.
I have a red, blue, green, and yellow ball. If I put them all in a bag and pick one ball at a time (putting it back each time), what chance do I have of never picking a red ball, assuming I pick a color 40 times. Write as a decimal/percentage. (20 points! A good answer would be appreciated)
Answer:
Step-by-step explanation:
You have four balls
A draw of blue, green or yellow (3 balls) means success for NOT drawing a red ball
You have a 3 in 4 chance of not drawing a red ball on the first draw.
With replacement, the 3 in 4 chance occurs on every draw
the odds multiply together for each draw.
Chance of not drawing a red ball in 40 tries is (3/4)⁴⁰
or about 1 in 10⁻⁵ or 0.00001
Help help help math math
Answer:
Slope = 4
Step-by-step explanation:
Change in Y = 4
Change in X = 1
Slope = Δy/Δx = 4/1 = 4
Help help help math math
Answer:
y=-1/2x-3
Step-by-step explanation:
Let's pick two points for slope.
[tex]\frac{-1+3}{-4-0}[/tex]
[tex]\frac{2}{-4}[/tex]
For the y-inctercept, the line intersect at the y-axis at (0,-3)
CHECK:
[tex]y=-\frac{1}{2} (-4)-3[/tex]
[tex]y=2-3[/tex]
[tex]y=-1[/tex]
Kelly base 3328 cookies each year she bakes twice as many cookies in October then in the other much how many cookies does Kelly back in December
Find the value for x
(x+20) (4x-5)
Answer:
I think it x=33
Step-by-step explanation:
[tex]x+20+4x-5=180\\5x+15=180\\-15 -15\\5x = 165\\/5 /5\\x = 33[/tex]
Rewrite the following equation in slope-intercept form. 17x − 4y = 20
Step-by-step explanation:
-4y= -17x+20
4y=17x-20
y= 4.25x-5
Slope intercept form
y=mx+b[tex]\\ \tt\Rrightarrow 17x-4y=20[/tex]
[tex]\\ \tt\Rrightarrow 17x-20=4y[/tex]
[tex]\\ \tt\Rrightarrow y=17/4x-5[/tex]
Today, both the soccer team and the basketball tear
had games. The soccer team plays every 3 days and the
basketball team plays every 5 days. When will both
teams have games on the same day again?
SHOW YOUR WORK PLEASE
Answer:3 to 5
Step-by-step explanation:i took the quiz
What is the distance between points A and B?
A. 1/3
B. 1/2
C. 1 1/3
D. 1 1/2
Answer:
A. 1/3
Step-by-step explanation:
From 1 to ___, ____, and 2 is half and half that would be 2 and a half. the only solution would be 1/3
Answer:
boom
Step-by-step explanation:
24,761 divided by 24
Answer:
1031.70833333
Step-by-step explanation: