Newton's law of cooling is T = AeW! + C, where is the temperature of the object at time t, and is the constant temperature of the surrounding medium. Supposethat the room temperature is 73, and the temperature of a cup of coffee is 174' when it is placed on the table. How long will it take for the coffee to cool to 131" fork = 0.06889192 Round your answer to two decimal places.
Answers
Solution
We are given the equation
[tex]T=Ae^{-kt}+C[/tex]Room temperature, C = 73 degrees
Temperature at time t = 0, is T = 174 degrees
[tex]\begin{gathered} T=Ae^{-kt}+C \\ 174=Ae^0+73 \\ 174=A+73 \\ A=174-73 \\ A=101 \end{gathered}[/tex]Therefore, the equation becomes
[tex]T=101e^{-kt}+73[/tex]We want to find t = ?, when T = 131 degrees and k = 0.0688919
[tex]\begin{gathered} T=101e^{-0.0688919t}+73 \\ 131=101e^{-0.0688919t}+73 \\ 131-73=101e^{-0.0688919t} \\ 58=101e^{-0.0688919t} \\ e^{-0.0688919t}=\frac{58}{101} \\ e^{-0.0688919t}=\frac{58}{101} \\ -0.0688919t=ln(\frac{58}{101}) \\ t=-\frac{1}{0.0688919}ln(\frac{58}{101}) \\ t=8.051418328 \\ t=8.05minutes\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Therefore, the answer is
[tex]8.05minutes[/tex]Related Questions
A die is rolled 200 times with the following results. Outcome 1 2 3 4 5 6 Frequency 32 36 44 20 30 38 What is the experimental probability of rolling the given result? a number more than 3
Answers
The experimental probability of rolling such that the number is more than 3 is 0.44.
The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
When a dies is rolled 200 times, the results are:
Frequency Outcome
1 32
2 36
3 44
4 20
5 30
6 38
Therefore,
The experimental probability that a number is more than 3 after rolling will be:
= The sum of outcome above 3 / total outcome
= ( 20 + 30 + 38 ) / ( 32 + 36 + 44 + 20 + 30 + 38 )
= 88/ 200
= 0.44
Hence, the probability that the number is more than 3 is 0.44.
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A teacher gives pens and pencils to elementary students at an equal rate.
Pencils Pens
21 63
33 A
45 135
B 153
Determine the missing value for the letter B.
Answers
The missing value for the letter B is 51.
Given,
A teacher gives pens and pencils to elementary students at an equal rate.
Pencil ; 21 33 45 B
Pen ; 63 A 135 153
We have to determine the missing value of B.
Here,
Ratio of pencil to pen for each student.
Student 1; Pencil/pen = 21/63Each student get pencil and pen in the same ratio as 1/3
Then,
Student 2 gets;33/A = 1/3
33 × 3 = A
A = 99
Ratio = 33/99 = 1/3
Student 3 gets;45/135 = 1/3
Student 4 gets;B/153 = 1/3
3B = 153
B = 153/3 = 51
Ratio = 51/153
That is,
The missing value for the letter B is 51.
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The number of tiles needed for a bathroom floor is proportional to the area of the bathroom floor. Five tiles cover an area of 90 square inches. The bathroom floor has a total area of 3,024 square inches. Let n be equal to the total number of tiles needed for the floor. Set up and solve a proportion to find the value of n.( Show your work)
Answers
Given:
5 tiels cover the area 90square inch.
bathroom floor area is 3024
[tex]\begin{gathered} 5\text{ tiles covers the area = 90} \\ 1\text{ tiles cover the area = }\frac{90}{5} \\ \text{ =18} \end{gathered}[/tex]1 tiles cover the area is 18 square inch.
Let n tiles cover 3,024 square inch then:
[tex]\begin{gathered} n\times18=3024 \\ n=\frac{3024}{18} \\ n=168 \end{gathered}[/tex]So 168 tiels required for cover the bathroom floor.
On a coordinate plane, how are the locations of the points (3, -7) and (-3, 7) related?
Answers
A square has a side of length 1.6 yards. What is the area of the square inches? Round to the nearest tenth
Answers
Given that the side of the square is 1.6 yards.
The area of the square is
[tex]A=a^2[/tex]Substitute a=1.6, we get
[tex]A=1.6^2=2.56yards^2[/tex]We need to convert yards to inches.
We know that
[tex]1\text{ yard =36 inches}[/tex]Taking square on both sides, we get
[tex]1^2yard^2=36^2inches^2[/tex][tex]1yard^2=1296inches^2[/tex]Multiplying by 2.56 on both sides, we get
[tex]1\times2.56yard^2=1296\times2.56inches^2[/tex][tex]2.56yards^2=3317.76inches^2[/tex]Rounding to the nearest tenth, we get
[tex]2.56yards^2=3317.8inches^2[/tex]Hence the area of the given square is 3317.8 square inches.
Walmart buys shoes from a factory in China for $8.50. Walmart then marks up the price of the shoes by 65% to sell to their customers. If the shoes aremarked up 65%, how much do they cost at Walmart? *
Answers
Answer
The shoes cost $14.03 at Walmart.
Explanation
The markup, the selling price and the cost price are all related through the relation
[tex]\text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100[/tex]For this question,
Markup percent = 65%
Selling Price = x = ?
Cost Price = $8.50
[tex]\begin{gathered} \text{Markup percent = }\frac{(Selling\text{ Price) - (Cost Price)}}{(Cost\text{ Price)}}\times100 \\ 65=\frac{x-8.5}{8.5}\times100 \\ \text{Divide both sides by 100} \\ 0.65=\frac{x-8.5}{8.5} \\ \text{Cross multiply} \end{gathered}[/tex]x - 8.5 = (0.65) (8.5)
x - 8.5 = 5.525
x = 8.5 + 5.525
x = $14.025
x = $14.03
Hope this Helps!!!
Considering the function
H(x) = -x + 6
which statement is true?
A. The output value of the function is 4 when the input value is -2
B. The output value of the function is 7 when the input value is 1
C. The output value of the function is 6 when the input value is x
D. The output value of the function is 8 when the input value is -2
Answers
The statement which is true is Option(D) The output value of the function is 8 when the input value is -2.
What do mathematical functions mean?An expression, rule, or regulation that establishes a relationship between one variable (the independent variable) and another variable (the dependent variable) is referred to as a function in mathematics.
Given function:
H(x) = -x + 6
In Option A, the input value is -2 so the output of the function will be,
H(x) = -x + 6 = -(-2) +6 = 2+ 6 = 8 ,which is not equal to the given output value 4.
Hence, the statement is false.
Similarly in Option B and C, the input values are 1 and x.
H(x) = -x + 6 = -1 +6 = 5 ≠ 7
H(x) = -x + 6 ≠ 6
The given output values are not equal to the output values calculated.
So both statements are false.
In Option D the input value is -2 and the output value is 8 which is a correct statement as calculated in Option A.
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I would really appreciate if you helped me on all of these
Answers
33. For this problem you have to sole the following system of equations.
x+y=531
5.75x+1.25y=2013.75
After you solve the system of equations you get that
x=300, y=231
Therefore 300 full-price tickets were sold.
34. Since water is not acid, you have to solve the following equation
0*Water + 0.40*50 = 0.30*(Water+50)
After you solve the equation you get
Water = 16.67
So, you have to add 16.67 ML of water.
and that's the solution for 34.
35.
The next problem is very easy, notice that 12/6 = 2 and 4/6 = 0.666666=0.67 , therefore the scale factor would be 6. And that would be it.
help meee pleasee!!!
thank you <3
Answers
Answer:
y = -800x + 294000
286,000
Step-by-step explanation:
To write the equation, you need the slope and the y-intercept.
The slope is -800
You find the slope by the change in y over the change in x
[tex]\frac{288400 - 294000}{7 - 0}[/tex] = [tex]\frac{15600}{7}[/tex] = -800
Now we will find the y -intercept. I will use the slope and the point (0, 294,000) to find this. I could have used the other point given. They will both work.
slope (m) = -800
x = 0
y = 294000
y = mx + b
294000 = -800(0) = b
294000 = b
The equation is
y = mx + b
y = -800x + 294000
2014
y = -800x + 294000
y = -800(10) + 294000
y =-8000 + 294000
y = 286,000
For the polynomial below, 2 is a zero.f(x) = x^3– 8x² + 18x – 124 –Express f (x) as a product of linear factors, F(x)=
Answers
The polynomial can be factorized in linear factors:
[tex]\begin{gathered} f(x)=x^3-8x^2+18x-12 \\ f(x)=(x-2)(\frac{x^3-8x^2+18x-12}{x-2}) \\ f(x)=(x-2)(x^2-6x+6) \end{gathered}[/tex]For (x^2) - 6x - 6 we use the general equation:
[tex]\begin{gathered} x^2-6x+6 \\ x_{1,2}=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\mleft(6\mright)}}{2} \\ x_{1,2}=3\pm\frac{\sqrt[]{8}}{2}=3\pm\frac{\sqrt[]{2^3}}{2}=3\pm2^{\frac{3}{2}-1}=3\pm\sqrt[]{2}^{} \\ x_1=3+\sqrt[]{2} \\ x_2=3-\sqrt[]{2} \end{gathered}[/tex]Then, our factors are:
[tex]f(x)=(x-2)\cdot(x-(3+\sqrt[]{2}))\cdot(x-(3-\sqrt[]{2}))[/tex]Erica and Naomi are both pledging study hours as they prepare for theirAlgebra 1 EOC next week. Erica says that she is going to study fifteen minutesthe first night of this week and then double how much she studies every dayfor the next seven days. Naomi says she is going to study 3 hours the first daythis week and then is going to add on thirty minutes each day for the nextseven days.Part A: Write a recursive and explicit formula for each girl’s study pledge. Erica:Naomi:
Answers
we know that
Erica
The sequence in minute is
15,30,60,120,240,480,960
This is a geometric sequence
where
r=30/15=2 ----> common ratio
the recursive formula For n>1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}*r \\ a_n=a_{(n-1)}*2 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1*r^{(n-1)}[/tex]where
a1=15
r=2
[tex]a_n=15*2^{(n-1)}\text{ ----> explicit formula}[/tex]Naomi
we have the sequence in hours
3 3.5 4 4.5 5 5.5 6
This is an arithmetic sequence
where
d=3.5-3=0.5 ----> the common difference
the recursive formula For n> 1 is equal to
[tex]\begin{gathered} a_n=a_{(n-1)}+d \\ a_n=a_{(n-1)}+0.5 \end{gathered}[/tex]Find out the explicit formula
[tex]a_n=a_1+d(n-1)[/tex]where
a1=3
d=0.5
substitute
[tex]\begin{gathered} a_n=3+0.5(n-1) \\ a_n=3+0.5n-0.5 \\ a_n=0.5n+2.5\text{ ----> explicit formula} \end{gathered}[/tex]An employer pays $450 towards health insurance, while the employer pays $475. what is the ratio of employers contributions to the employees contributions?
Answers
Given :
An employee pays $450 towards health insurance
The second employer pays $475.
So, the ratio of employers contributions to the employees contributions=
[tex]475\colon450=\frac{475}{450}=19\colon18[/tex]
Question 5(Multiple Choice Worth 5 points)
(08.02 MC)
Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 Into the form (x-p)² = q?
Ip and q are integers]
Step 1 x²+ 10x + 24-1-0-1
Step 2
x2²+ 10x+23 = -1
Step 3 (x + 5)2 =-1
Step 1 x²+ 10x+24-2-0-2
Step 2 x²+ 10x+22=-2
Step 3 (x+5)2 = -2
O
Step 1 x²+ 10x+24+2=0+2
Step 2
x²+ 10x + 26 = 2
Step 3
(x + 5)2 = 2
Step 1 x²+ 10x + 24 + 1 = 0+1
Step 2 x²+ 10x + 25 = 1
Step 3 (x + 5)2 = 1
3
Answers
The correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q is a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
What is meant by factorization?Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
a² + b² + 2ab = (a + b)²
Given: x² + 10x + 24 = 0
= x² + 2x × 5 + 24
so b² has to equal 25 = 5²
Now, x² + 10x + 24 = 0
x² + 2x × 5 + 24 + 1 = 0 + 1
simplifying the above equation, we get
x² + 2x × 5 + 25 = 1
(x + 5)² = 1
Therefore, the correct answer is option
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1 and
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
The complete question is:
Which of the following tables shows the correct steps to transform x² + 10x + 24 = 0 into the form (x − p)² = q?[p and q are integers] (5 points)
Select one:
a.
Step 1 x² + 10x + 24 − 1 = 0 − 1
Step 2 x² + 10x + 23 = −1
Step 3 (x + 5)² = −1
b.
Step 1 x² + 10x + 24 − 2 = 0 − 2
Step 2 x² + 10x + 22 = −2
Step 3 (x + 5)² = −2
c.
Step 1 x² + 10x + 24 + 2 = 0 + 2
Step 2 x² + 10x + 26 = 2
Step 3 (x + 5)² = 2
d.
Step 1 x² + 10x + 24 + 1 = 0 + 1
Step 2 x² + 10x + 25 = 1
Step 3 (x + 5)² = 1
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I need the answer for x
Answers
Answer:
x=-1
Step-by-step explanation:
make equation
-2x-3=x
-3=3x
-1=x
Answer:
x=-1
Step-by-step explanation:
-x+-x-1-1-1 = x
-2x-3=x
3x=-3
x=-1
The tallest man living is Sultan Kosen from Turkey. He measures 2510 mm. How many meters tall is he?
Answers
Given:
The height of tallest man is 2510 mm.
Explanation:
The conversion unit for mm to meter is,
[tex]1\text{ mm=}\frac{1}{1000}\text{ meter}[/tex]Determine the height in meters.
[tex]\begin{gathered} 2510\text{ mm=2510 mm}\cdot\frac{1\text{ m}}{1000\text{ mm}} \\ =2.510\text{ m} \end{gathered}[/tex]So height of tallest man Sultan Kosen is 2.510 meters.
Answer: 2.510 meters
three numbers have a sum of 180. the second number is 4 times the smallest number. the third number is 7 times the smallest number. what is the largest number?
Answers
12x=180
X=15
4x=60
7x=105
15+60+105=180
Answer:
105
Step-by-step explanation:
Let x, y and z be the 3 numbers in the order first, second and third
x + y + z = 180
Second number y is 3 times the smallest number and third number z is 7 times the smallest number. So smallest number has to be x
so y = 4x
z = 7x
x + y + z = x + 4x + 7x = 180
12x = 180
x = 15
Largest number = 7 x 15 = 105
A sequence starts Give a rule that the sequence could follow.
Answers
Let's say "n" is the last denominator
A rule that the sequence could follow is
[tex]\frac{1}{2n}[/tex]With 2 as the first value of n, this means that the next term will be 1/2(2)=1/4 and so on.
The next 3 terms in the sequence will be
1/2(8)=1/16
1/2(16)=1/32
1/2(32)=1/64
Consider the function f(x) = 4 - 2x ^ 2 on the interval \ -6,6] Find the average or mean slope of the function on this interval , i.e. (f(6) - f(- 6))/(6 - (- 6)) =
Answers
f(x) = 4 -2x^2
First we need to find f(6)
f(6) = 4 - 2( 6) ^2 = 4 - 2(36) = 4 - 72 = -68
Then we need to find
f(-6) = 4 - 2( -6) ^2 = 4 -2( 36) = 4 - 72 = -68
Now we find the average or mean slope
The mean slope is zero
Now f'(c) must equal 0
The derivative is -4x and evaluated at c
-4c
This must be equal to 0
-4c =0
Solving for c
c=0
g(x)=26÷x-7 how do I find the domain
Answers
The domain of a function, are the values for which the function is defined on the x-axis,
Let the function:
[tex]\frac{26}{x\text{ - 7}}[/tex]denominator can't be
Consider the system of equations.x + 2y = 8-3x – 2y = 12How do you solve the system of equations with Cramer's rule? Drag a value or determinant expression into each box to correctly solve the system using Cramer's rule.
Answers
The solution to the system of equations using Cramer's rule is given by the image at the end of the answer.
How to solve a system of equations using Cramer's rule?The solution of a system of equations using Cramer's rule is based on the use of determinants of matrices.
In the context of this problem, the system is:
x + 2y = 8.-3x - 2y = 12.The matrix for the system is:
M =
[1 2]
[-3 - 2]
The determinant of the matrix M of the system is given as follows:
|M| = -2 + 6 = 4.
(using the standard procedure to obtain the determinant of a 2 x 2 matrix).
To find the matrix for x, the x-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
Mx =
[8 2]
[12 - 2]
Then the determinant is:
|Mx| = 8(-2) - 2(12) = -16 - 24 = -40.
The solution for x is:
x = -40/4 = -10.
To find the matrix for y, the y-coefficients are replaced by the right-side coefficients, that is, the results of the operations, hence:
My =
[1 8]
[-3 12]
The determinant is:
|My| = 12 - (-3)(8) = 12 + 24 = 36.
Hence the solution is:
y = 36/4 = 9.
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Determine whether the graph represents a function.
Answers
x - 0.1x = 54solve for x
Answers
The equation to solve:
[tex]x-0.1x=54[/tex]We can subtract the like terms on the left hand side:
[tex]\begin{gathered} (1-0.1)x=54 \\ 0.9x=54 \end{gathered}[/tex]Now, we can divide both sides by 0.9 and solve for x. Shown below:
[tex]\begin{gathered} \frac{0.9x}{0.9}=\frac{54}{0.9} \\ x=60 \end{gathered}[/tex]The answer is
[tex]x=60[/tex]Answer: x = 60
Step-by-step explanation:
To solve for x, we will isolate the variable with simplifying and reverse operations.
Given:
x - 0.1x = 54
Subtract 0.1 from 1:
0.9x = 54
Divide both sides of the equation by 0.9:
x = 60
All changes saved 5. Harry is purchasing bananas at the grocery store. The table below shows how many he can purchase and the cost. What is Harry's total cost if he wishes to purchase 7 bananas? Note: The table represents a proportional relationship of bananas per dollar. Number of Bananas
Answers
Let's determine the cost of each banana based on the given data.
Number of Bananas Total Cost Price per Banana
4 $2.48 $0.62
8 $4.96 $0.62
12 $7.44 $0.62
lt appears that each banana cost $0.62.
Thus, buying 7 bananas, it'll cost:
7 x 0.62 = $4.34
The answer is letter C.
A bag of marbles contains 6 blue glass marbles, 5 yellow glass marbles, 12 blue stone marbles, and 3 yellow stone marbles. What is the probability of selecting a marble and having that marble be either a blue marble or a stone marble? Express your answer as a decimal rounded to four decimal places. Probability
Answers
The probability of selecting or having a marble to be either a blue marble or a stone marble is 0.8076.
Given, a bag contains 6 blue glass marbles, 5 yellow glass marbles,
12 blue stone marbles and 3 yellow stone marbles.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble = ?
we know that,
Glass marbles:
n(B) = 6 and n(Y)= 5
Stone marbles:
n(B) = 12 and n(Y) = 3
Probability = Number of favorable outcomes/Total number of outcomes.
Probability of selecting a marble and having that marble to be either blue marble or a stone marble:
total number of blue marbles = 18
total number of stone marbles = 15
total number of marbles in the bag = 26
⇒ 18+15-12/26
⇒ 33-12/26
⇒ 21/26
= 0.8076
Hence the probability of selecting a marble and having that marble be either a blue marble or a stone marble is 0.8076.
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a jar contains 100 tickets for a drawing. Among those tickets are 7 winning tickets. what are the odds in favor of winning 7:937:10093:793:100
Answers
From the statement, we know that:
• a jar contains 100 tickets for a drawing,
,• among those tickets are 7 winning tickets.
We must find the odds in favour of winning.
The odds in favour of winning are:
Odds in favour = Number of successes : Number of failures
In this case, we have:
• Number of successes = 7,
,• Number of failures = 100 - 7 = 93.
So we have:
[tex]\text{ Odds in favour }=7:93.[/tex]Answer7:93
Jim's gas tank is 1/3 full. After he buys 9 gallons of gas it is 5/6 full. How many gallons can Jim's tank hold?
Answers
tank is 1/3 full
after he buys 9 gallons of gas it is 5/6
How many gallons can Jim's tank hold?
[tex]\frac{5}{6}-\frac{1}{3}=\frac{1}{2}[/tex]9 gallons = 1/2 tank
18 gallons is the capacity of the tank
A demand function for a certain product is given by the equation q = 1200 - 5p, where p is the price in
dollars, and q is the quantity demanded. Find a function to represent the revenue generated by producing
and selling q items. Use this function to determine the quantity that maximizes revenue. What price
should be charged in order to maximize revenue?
Answers
A function to represent the relation is f = q × p, the quantity that maximizes value could only be when q = p, therefore p = 200 so, q = 200 too according to demand function q = 1200 - 5p.
What is demand function?In mathematics, the relationship between demand and its factors is represented by a demand function. The function demonstrates how elements like a product's own price, buyer income, and the cost of related products affect demand for a given good (substitutes and complements).
We can deduce from the equation how they influence a product's demand, whether positively or negatively, and how much.
A function for generated revenue is simply f = q × p
where f is the generated revenue and
q is the quantity and
p is the price.
The quantity that maximizes value could only be when q = p
Lets substitute the value of q in q = 1200 - 5p,
q + 5p = 1200
But q = p so
p + 5p = 1200
6p = 1200
p = 1200/6
p = 200
So when price is 200 the revenue will be maximized as the quantity is equal to as price.
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Dina pours 16-ounce containers juice into a dispenser with a capacity of 960 ounces. The function y = 16x modeled this situation. What is the range of the function ?
Answers
The range of the function, y = 16x, is 60, where y is 960.
What is the range of a function?The range of the function, y = 16x, are the possible values that x can assume to meet the value of y.
Usually, the range of a function is the output value.
Since the value of y = 960, the range of the function will be 60 (960/16).
The capacity of the dispenser = 960 ounces
The capacity of the juice containers = 16 ounces
The function that models the situation is y = 16x
Where y = 960
x = 60 (960/16)
Thus, the implication is that the range of the function or the number of 16-ounce containers that can fill the dispenser with a capacity of 960 ounces is 60.
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If they had 15 oranges,9 peaches and 18 pears to distribute into the baskets.How many baskets can they make with the SAME number of pieces of fruit in each one?? How many pieces of each type of fruit will be in each basket?
Answers
polynomials: adding and subtracting polynomials find each sum or differenceplease do minimum steps
