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
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]
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
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:
24,761 divided by 24
Answer:
1031.70833333
Step-by-step explanation:
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:
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
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.
❗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
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:
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]
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.
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
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
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
) 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
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]
The following graph shows the system of equations?
PLS HELP
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)
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]
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:
Find the height of the trapezoid.
7 m
Area = 51 m2
10 m
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
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]
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:
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:
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
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
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]
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.