Newton’s law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton’s law of cooling. If the coffee has a temperature of 200◦F when freshly poured, and 1 min later has cooled to 190◦F in a room at 70◦F, determine when the coffee reaches a temperature of 150◦F.
Answers
Answer:
6 mins
Step-by-step explanation:
Given that;
T(t) = Ce^-kt + T(s)
Since T(t) = 200◦F, and T(s) = 70◦F where t = 0
200= Ce^-k(0) + 70
C= 200 - 70
C = 130
Then when T(t) = 190◦F and t= 1s ;
190 = 130e^-(k *1) + 70
190 - 70 = 130e-^(k *1)
120/130 = e^k
0.923 = e^-k
-k = ln(0.923)
k = 0.08
To determine the time taken to reach a temperature of 150◦F
150 = 130e^-(0.08t) + 70
150 - 70/130 = e^-(0.08t)
0.6154 = e^-(0.08t)
-(0.08t) = ln 0.6154
0.08t = 0.4855
t = 0.4855/0.08
t = 6 mins
Related Questions
if (x) = x^2 and g(x) = 2x+1, what expression is equivalent to (f o g)(x)?
Answers
The composite function is defined as:
\((f\circ g)(x)=f(g(x))\)Then in this case we have:
\(\begin{gathered} (f\circ g)(x)=f(2x+1) \\ =(2x+1)^2 \end{gathered}\)Therefore:
\((f\circ g)(x)=(2x+1)^2\)A string of decorative lights has 32 bulbs for every 2 feet of wire.
What is the unit rate of bulbs per yard?
HELP !!!!!
Answers
Answer:
First convert two feet into yards, knowing that:
1 foot = 0.333... yards
So,
2 feet in yards would mean double of 0.333... because one single foot is 0.333... yards.
2(0.333...)
= 0.666..., which we can round to 0.67.
So our new ratio will be 32 bulbs per 0.67 yards.
Now we convert this ratio into a unit rate,
Order your units;
Bulbs 32 47.76
______ ______ = ______, which rounds to about 48.
Yards 0.67 1
So the unit rate is 48 bulbs per yard.
Your house is located at (-4, 3), which is 4 blocks and 3 blocks north of the center of town. To get from your house to the mall, you walk 7 blocks east and 4 blocks south.
a. What ordered pair corresponds to the location of the mall?
b. Is your house or the mall closer to the center of town? Explain.
(NOT A MULTIPLE CHOICE)
Answers
9514 1404 393
Answer:
a) (3, -1)
b) the mall
Step-by-step explanation:
1) We assume the missing word is "west". The walk to the mall represents a change of (7, -4) from your coordinates of (-4, 3). The mall's coordinates are ...
(-4, 3) +(7, -4) = (-4+7, 3-4) = (3, -1) . . . . coordinates of the mall
__
2) One of the orthogonal distances (3) is the same for each location. The location with the least number of blocks in the other direction will be closer to the center of town. (3, -1) is closer to the town center than (-4, 3).
The mall is closer to the center of town.
Complete the coordinate proof of the theorem.
Answers
The coordinate of C( a+c , b) , AC are ((a+c)/2 , b/2) , BD are ((a+c)/2 , b/2)
What are Coordinates ?Coordinates is the value assigned to a point in a x-y graph to determine its location.
The coordinates of parallelogram is
A ( 0,0) B (a,0) , C ( __ , ___) , D ( c , b)
The y coordinate is same as D as b
and the x coordinate will be a+c
C( a+c , b)
The coordinate of the mid point of AC are ((a+c)/2 , b/2)
The coordinate of the mid point of BD are ((a+c)/2 , b/2)
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it’s a -10 btw and a positive 9
Answers
Answer: -1 and -9
Step-by-step explanation:
(- 1) + (-9) = -10
(-1) * (-9) = +9
hope this helps!
Two trains leave the same city at a right angle to each other and continue in straight lines. Train B travels 5 mph faster than train A. After two hours, they are 50 miles apart. Determine the speed of each
train.
Answers
Answer:
Let A have speed 'a.' Remember distance is rate times time, and the Pythagorean theorem. We then have (2a)^2+(2(a+5))^2=50^2. a=15, so the other rate is 20.
Step-by-step explanation:
En la final de un concurso escolar de
matemática participan 6 alumnos de los
cuales 3 son alumnos del colegio A. Si se
premia a los dos primeros con regalos
diferentes, entonces la probabilidad de que
los alumnos del colegio A obtengan los dos
premios (no hay empates), es:
Answers
Usando la distribución hipergeométrica, la probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es: 0.2 = 20%.
¿Qué es la fórmula de distribución hipergeométrica?La fórmula es:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Los parámetros son:
x es el número de éxitos.N es el tamaño de la población.n es el tamaño de la muestra.k es el número total de resultados deseados.Los valores de los parámetros son:
N = 6, k = 3, n = 2.
La probabilidad de que los alumnos del colegio A obtengan los dos premios (no hay empates), es P(X = 2), por eso:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}\)
\(P(X = 2) = h(2,6,2,3) = \frac{C_{3,2}C_{3,0}}{C_{6,2}} = 0.2\)
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what would x equal if 1/2x-2=8
Answers
Answer:
hope this helped you
please mark as the brainliest (ㆁωㆁ)
HELP AS SOON AS POSSIBLE
Answers
The coordinates of polygon A'B'C'D' after the rotation of 180º are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x).90° counterclockwise rotation: (x,y) -> (-y,x).180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y).270° clockwise rotation: (x,y) -> (-y,x).270° counterclockwise rotation: (x,y) -> (y,-x).The original coordinates for this problem are given as follows:
A(0,0), B(5,2), C(5,-5), D(0,-3).
Exchanging the sign of each of the coordinates, the coordinates after the rotation are given as follows:
A'(0,0), B'(-5,-2), C'(-5,5), D'(0,3).
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what are the next terms in the number pattern -11, -8, -5, -2, 1
Answers
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
A bag contains 8 green candies and 4 red candies. You randomly select one candy at a time to eat. If you eat five candies, there are relatively prime positive integers m and n so that m n is the probability that you do not eat a
green candy after you eat a red candy. Find m + n.
Answers
If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.
A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:
GRRRR : \(\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}\)
GGRRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}\)
GGGRR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}\)
GGGGR : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
GGGGG : \(\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}\)
The sum is \(\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}\)
Probability that you do not eat green candy after you eat a red candy =\(\frac{1}{5}\)
so m = 1 and n = 5
m + n =6
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answers
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
PLEASE HELP ME ASAP
Its not that hard im just tired
Answers
Answer:
combine like terms; 15.4z - 12
the difference of x and 22 is equal to 8
Answers
Answer:
Step-by-step explanation:
x - 22 = 8
Lets find variable x.
To isolate the variable, we need to add 22 to both sides.
x = 30
22-14=8
Hope that helped :)
Anne bought a piece of ribbon that is 7 over 9 m long. She used 3 over 18 m of it to tie a birthday present. She then used the remaining ribbon to form squares of sides 1 over 16 m. What was the maximum number of squares she could form?
Answers
Answer:
9 squares
Step-by-step explanation:
Anne bought a piece of ribbon = 7 over 9 m long = 63 m²
she used = 3 over 18 m = 54 m²
left = 9 m²
maximum number of squares she could form of 1 m = 9
Follow the steps and write the equation represented by this graph.
Step 1: Write the general equation.
Step 2: Identify b, the Y intercept (x = 0) b=
Step 3: The second point from graph (x, y) P=
,
Step 4: Define m as ratio of rise / run m = rise /
Step 5: Put coordinates into ratio and get (7 -
) / (
- 0)
Step 6: Perform subtraction; get slope
/ 1
Step 7: Substitute values into y = mx + b
Step 8: Write answer y =
x +
Answers
Answer:
y = 4x + 3
Step-by-step explanation:
Step 1: Write the general equation
y = mx + b
Step 2: Identify b, the Y intercept (x = 0)
b is the value of y when x = 0.
From the graph, when x = 0, y = 3.
Therefore, b = 3
Step 3: The second point from graph (x, y):
P = (1, 7)
Step 4: Define m as ratio of rise / run:
\( m = \frac{y_2 - y_1}{x_2 - x_1} \)
Step 5: Put coordinates into ratio:
Using the two coordinates, (0, 3) and (1, 7), we would have,
\( m = \frac{7 - 3}{1 - 0} \)
Step 6: Perform subtraction to get slope:
\( m = \frac{4}{1} \)
m = 4
Step 7: Substitute values into y = mx + b:
Thus, plug in the values of m and b into the slope-intercept equation.
b = 3, m = 4, therefore:
y = (4)x + (3)
Step 8: Write answer:
y = 4x + 3
Cooper goes miniature golfing. He pays $9.50 for an adult admission ticket and $7.25 for each round he golfs. Write an equation to represent the total cost, c, for any number of rounds, r, cooper plays
Answers
Answer: c = 7.25r + 9.50
Step-by-step explanation:
The total cost depends on how much Cooper goes golfing. That variable, something that can change over the course of time, is r. 7.25 times the amount of rounds, r, is how much he'll be paying without the admission ticket.
The 9.50 is an unchanging amount, because he has to pay to get in. That amount is added to the end result. So:
c = 7.25r + 9.50
PLEASE HELP!! 30 POINTS!!!!
People were asked to choose one of four activities they would prefer to do in hot weather. The table shows data about the responses. Which activity was chosen by most adults over 18 years old?
A
sports
B
movies
C
reading
D
walking
Answers
Answer:
It's D
Step-by-step explanation:
When you add the 19-50 and over 50 then you get the highest answer
A ramp is elevated to a height of 27 inches from the base. The horizontal distance between the lower end of the ramp and the base is 69 inches, as shown in the figure. What is the length of the ramp?
Answers
Answer:
74.09453421...
Step-by-step explanation:
Pythagorean Theorem
Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?
A. a reflection over the x -axis
B. a rotation 90° clockwise about the origin
C. a rotation 180° counterclockwise about the origin
D. a translation 10 units to the left and 10 units down
Answers
A transformation would accomplish this include the following: C. a rotation 180° counterclockwise about the origin.
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Coordinates of point X (0, 4) → Coordinates of point Y = (0, -4)
Coordinates of point X (1, 3) → Coordinates of point Y = (-1, -3)
In conclusion, we can logically deduce that this transformation rule (x, y) → (-x, -y) would map Figure X onto Figure Y.
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Which of the following best describes ABC – DEF?
A. ABC is a dilation of DEF.
B. ABC is similar to DEF.
C. ABC is a reflection of DEF.
D. ABC is congruent to DEF
Please help I will give brainliest.
Answers
Hope it helps!
Answer:
A. ABC is a dialtion of DEF
Can someone help me with this pleaseeeeee
Answers
The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.
What is the solution of the matrix equation?The solution of the matrix equation is calculated by applying Cramer's rule as shown below;
[ 1 1 -1 ] [ 7 ]
[ 2 3 0 ] [ 18 ]
[ -5 -7 -1 ] [ -43 ]
The determinant of the matrix is calculated as follows;
[ 1 1 -1 ]
[ 2 3 0 ]
[ -5 -7 -1 ]
Δ = 1 (-3 - 0) - 1(-2 - 0 ) - 1(-14 + 15)
Δ = -2
The x determinant of the matrix is calculated as follows;
[ 7 1 -1 ]
[ 18 3 0 ]
[ -43 -7 -1 ]
Δx = 7 (-3 - 0) - 1 (-18 - 0 ) - 1(-126 + 129)
Δx = -6
The y determinant of the matrix is calculated as follows;
[ 1 7 -1 ]
[ 2 18 0 ]
[ -5 -43 -1 ]
Δy = 1 (-18 - 0 ) - 7(-2 - 0 ) -1(-86 + 90)
Δy = -8
The z determinant of the matrix is calculated as follows;
[ 1 1 7 ]
[ 2 3 18 ]
[ -5 -7 -43]
Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)
Δz = 0
The values of x, y , and z is calculated as;
x = Δx/Δ = -6/-2 = 3
y = Δy/Δ = -8/-2 = 4
z = Δz/Δ = 0/-2 = 0
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If the vertex of image Q' is located at coordinates (16,8) was dilated by a scale factor of 2, what was the coordinates for the pre-image Q?
Answers
Answer:
(32,16)
Step-by-step explanation:
When you dilate a coordinate by a factor say a, the coordinate of the image are multiplied by this factor to get the coordinate of the pre-image. For example, if the coordinate of the image is (x,y) dilated by a factor of "a", the coordinate of the pre-image will be (ax, ay)
Given the coordinate (16, 8) the coordinate of the pre image of dilated by a factor of 2 is given as;
(2×16, 2×8) = (32, 16)
Hence the coordinates for the pre-image Q is (32,16)
The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm^2/min) is the surface area of the ball increasing when the radius is 9 cm?
Answers
Answer:
51
Step-by-step explanation:
john had 84 apples his friend sam took away 22 of them how many apples does john have left. and what percentage did Sam take away.
Answers
We have the following:
The apples that John has left would be the difference between the ones he initially had minus the ones that Sam took
\(84-22=62\)To calculate the percentage that Sam took, we must divide the amount that Sam took and the total amount, that is, those that John had initially, then multiply by 100 so that it is a percentage.
\(\frac{22}{84}\cdot100=26.19\)Therefore, the percentage is 26.19%
John has left with 62 apples.
Sam takes away 26.19% of the total apples.
Given in the question,
John had 84 apples.
Sam took away 22 apples.
So, to find the number of apples left,
we have to subtract the total number of apples from the number of apples taken by sam,
Remaining apple = 84 - 22
= 62.
Therefore, the number of remaining apples is 62.
Now, we will find the Percentage Of apples taken by Sam,
= \(\frac{22}{84}\) × 100
= 26.19%
Therefore, the percentage taken away is 26.19%
Given a committee of 8 women and 11 men, how many different ways are there to pick a female president, a male treasurer, and a secretary of either gender if one of the men, Pete, says that he cannot be the treasurer? Assume that none can hold more than one office.
Answers
Answer: 1360 ways.
Step-by-step explanation:
Number of men = 11
Number of women = 8
Total members = 8 + 11 = 19
Firstly, the number of ways of selecting 1 woman for female president out of 8 will be:
= 8C1
= 8
Since Pete can not be a treasurer, then the treasurer will then be selected from the remaining 10(11 - 1). The number of ways of selecting 1 treasurer out of 10 will be:
= 10C1
= 10
Thirdly, since none can hold more then one office, in this case, the selection will be done by selecting 1 person out of 7 women and 10 men. Therefore, the number of ways of selecting 1 person out of 17 will be:
= 17C1
= 17
Therefore, the total number of ways will then be:
= 8 × 10 × 17
= 1360
Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−15, 3), (−15, −6), and (25, −6)?
(−6, 25)
(−25, −3)
(6, −25)
(25, 3)
Answers
The missing fourth vertex needed to create a rectangle is (25, 3) option D.
Define the term vertices?Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.
Here, the width of one side of the rectangle;
⇒ +3 - (-6) = 9 unit (left side y-coordinates)
Similarly the length of the rectangle;
⇒ 25 - (-15) = 40 unit (up-side x-coordinates)
Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)
So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:
⇒ (25, -6+9) = (25, 3)
⇒ (-15+40, 3) = (25, 3)
Therefore, the missing fourth vertex is (25, 3)
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IT IS TIMED!!!!!
please help!!!!!!!
Answers
Answer:
b
Step-by-step explanation:
In 2011, Japan experienced an intense earthquake with a magnitude of 9.1 on the Richter scale. In 2003, Japan experienced another intense earthquake that measured 8.3 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.
Answers
Answer:
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Step-by-step explanation:
To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.
Convert the magnitudes to intensities and write them in exponential form.
R=logI
2011 earthquake:
9.1I=logI=109.1
2003 earthquake:
8.3I=logI=108.3
Form a ratio of the intensities.
intensity for 2011intensity for 2003
Substitute in the values and divide by subtracting the exponents to find
109.1108.3100.8≈6.
The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.
Your answer:
The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.
The intensities of the two earthquakes will be 6.3095.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.
The intensity of the earthquake is given as,
㏒ (I₁ / I₂) = M₁ - M₂
㏒ (I₁ / I₂) = 9.1 - 8.3
Simplify the equation, then we have
㏒ (I₁ / I₂) = 9.1 - 8.3
㏒ (I₁ / I₂) = 0.8
Take anti log, then we have
(I₁ / I₂) = 6.3095
The intensities of the two earthquakes will be 6.3095.
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Hurrryy plzzz!!
Which linear inequality is represented by the graph?
y<1/2x+2
y>1/2x+2
y<1/3x+2
y>1/3x+2
Answers
-R