The coffee reaches t ≈ 12 minutes a temperature of 150◦F.
(t) = Ts + (T0 - Ts)e-kt, according to Newton's Law of Cooling.
T(t) = temperature of the coffee cup t minutes after being placed in the roomTs is the ambient temperature.T0 indicates the coffee cup's beginning temperature.
(a). Using the given information, we have T(t) = 70 + (160 - 70)e-kt
= 70 + 90e-kt
T(5) = 70 + 90e-k(5) = 112.5
So, 90e-5k = 42.5
e-5k = 0.47222222
-5k = ln(0.47222222)
k = 0.15 Temperature after 10 minutes = T(10) = 70 + 90e-0.15(10)
≈ 90.1
-------------------------------------------------------------------------------------
(b). When will the temperature of the coffee reach 85°?
Find t so that T(t) = 85: 70 + 90e-0.15t = 85
90e-0.15t = 15
e-0.15t = 0.16666666
-0.15t = ln(0.166666666)
t ≈ 12 minutes
what do you mean by newton's law of cooling?According to Newton's law of cooling, a body's rate of heat loss is inversely related to the temperature difference between it and its surroundings. The law is frequently qualified to state that the tiny temperature differential and the consistency of the heat transmission mechanism must exist. As a result, it is the same as asserting that the heat transfer coefficient, which mediates between heat losses and temperature variations, is constant. Due to the fact that the thermal conductivity of the majority of materials very slightly depends on temperature, this requirement is typically satisfied in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is applied in convective heat transfer for forced air or pumped fluid cooling.
To learn more about Newton's Law of cooling, Visit:
https://brainly.com/question/16049511
#SPJ4
without solving determine whether the solution of 1/3x =21 is greater than or less then 21. explain
solution of 1/3x=21 is greater than 21.
What does a linear equation mean in mathematics?A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.
CALCULATIONSolving the linear equation
x/3 = 21
multiplying by 3 on both sides
x/3 * 3 = 21 * 3
x = 63
→63>21,
that is, solution of the linear equation is greater than 21.
learn more about linear equation at :
brainly.com/question/11897796
#SPJ9
1) list out the elements of the set "the letters of the word mississippi" 2) list out the elements of the set "months of the year" 3) write a verbal description of the set {3, 6, 9} 4) write a verbal description of the set {a, i, e, o, u} 5) is {1, 3, 5} a subset of the set of odd integers? 6) is {a, b, c} a subset of the set of letters of the alphabe
1. The elements of the set are {m, I, s, p}
The elements of the set are the letters in Mississippi. Elements cannot repeat themselves.. So the elements of this set would be {m, I, s, p} since all the other letters are just repetitions.
2. Set of months in a year are
{January,February,March,April,May,June,July,August,September,October,November,December}
3. Verbal Descriptions: It is a verbal description of the set is an English sentence to specify a law that allows us to decide the category of objects to be addressed and to determine whether it is in the set for any particular object.
Since, 3, 6 and 9 are divisible by 3 also less than 10.
4. Verbal description of the set {a,e,i,o,u} is vowels
In English these five alphabets{a,e,i,o,u} are known as vowels .
since the given set contains only vowels.
5. Yes (1,3,5) is the subset of odd integers.
The set of odd integers is the superset containing elements :-
Let A = { 1 , 3 , 5 , 7 , 9 ,..... ,( 2n + 1 ) }
And,
B = { 1 , 3 , 5 }
B is a subset of A because all elements of B lie in A .
6. Yes (a,b,c) is the subset of letters of the alphabet.
To learn more about Set theory visit: brainly.com/question/22631070
SPJ4
(-1,3), (-12), (92)
(37), (5,7), (5-3)
(52 73), (96, 73), (94, 1483)
(5-5), (1,4) (4₂2)
Graph and find the 4th point to create a rectangle
The height of 4 cups
is 11.0cm.
8 cups has a height of
16.4cm
What would be
the height of
10 cups ?
Let the height of the cup be h and the extra length be d.
So, when the one cup is placed over another the total height will be h+d.
So, when the one cup is placed over another the total height will be h + d.
When the four cup is placed over each another h + 3d = 11 cm.
So the generalised equation will h +(n-1)d where n is the total number of cups.
When the eight cup is placed over each another = h + 7d = 16.4 cm
h + 3d = 11 cm
h + 7d = 16.4 cm
On solving the above two equation we will get d = 1.35 cm and h = 6.95 cm
So when we put 10 cups on each other = h +9d
6.95 + (9*1.35) = 19.1
Hence, the height of 10 cup will be 19.1cm.
Learn more about height here https://brainly.com/question/12450288
#SPJ9
which way the the graph of g(x) = |x + 3| move
Write an absolute value equation that has the solutions x= -10 and x= -5.
The absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.
According to the question.
We have solutions of a absolute value equation.
As we knoaw that, the non-negative value of a real number x without regard to its sign is known as its absolute value or modulus equation in mathematics and is indicated by the symbol |x|.
To find the absolute value equation whose solution are x = -10 and x = -5 we need to add some previous steps, which make the equation an absolute value equation.
|(x+10)(x+5)|=0,
x=-10 and x=-5
Hence, the absolute value equation for the values of x = -10 and x =-5 will be |( x + 10 )( x + 5 )| =0.
Find out more information about absolute value equation here:
brainly.com/question/28433835
#SPJ1
A fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours?
If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.
DistanceLet d = the distance to the turn around point
Time = Distance/ Speed
Up time + Down time = 2hrs
d/2 +d/8 =2
Multiply by 8
8×d/2 +8×d/8 =8 (2)
4d + d = 16
5d = 16
Divide both side by 5d
d=16/5
d = 3.2 miles to turn around
Hence,
Round trip = (3.2 miles ×2)
Round trip= 6.4 miles
Therefore If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.
Learn more about distance here: https://brainly.com/question/7243416
#SPJ1
a manager of a fast food restaurant wants the drive-thru employee to ask every fifth customer if he or she is satisfied with the service. who makes up the sample?
The population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer as per the concept of statistics.
What are statistics?
A branch of mathematics, statistics is a body of knowledge that deals with the gathering, examination, interpretation, and presentation of data. Instead of being a subfield of mathematics, some people view statistics as a separate mathematical discipline.A population is a total group from which a statistical sample is taken in statistics. Here, the manager only inquires about the fifth customer's pleasure after becoming interested in his drive-through staff. Therefore, those customers who do not use the drive-thru window at this restaurant are not part of the sample population about whom it is possible to inquire.
As a result, the population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer.
Learn more about statistics here:
https://brainly.com/question/12150562
#SPJ4
How many solutions are in the problem two thirds(6j+9)=3j+7
The problem two thirds(6j+9)=3j+7 has one solution.
How many solutions does the problem have?The given problem is 2/3(6j + 9) = 3j + 7
In order to determine the number of solutions, take the following steps:
Expand the bracket on the left:
(2/3 x 6j) + (2/3 x 9)
4j + 6
4j + 6 = 3j + 7
Combine similar terms :
4j - 3j = 7 - 6
Add similar terms
j = 1
To learn more about addition, please check: https://brainly.com/question/19628082
#SPJ1
suppose that $a$ and $b$ are digits, not both nine and not both zero, and the repeating decimal $0.\overline{ab}$ is expressed as a fraction in lowest terms. how many different denominators are possible?
The possible denominators are {3, 9, 11, 33, 99}.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.
We have been given that a and b are digits, not both nine and not both zero, and the repeating decimal.
⇒ 100x = ab⋅abababab
⇒ x = 0.abababab
Subtract the above equation from 100x = ab⋅abababab,
So 99x = ab
The denominator of this fraction will always be a divisor of 99 when represented in the lowest term = 3⋅3⋅11
According to this, we have the options in the set. {1, 3, 9, 11, 33, 99}.
Since a and b both are not both 9 and not both zero the denominator 1 cannot be possible.
Hence, the possible denominators are {3, 9, 11, 33, 99}.
Learn more about the quotient here:
brainly.com/question/27796160
#SPJ4
phytoremediation is the use of plant growth to purify pollutants from soil, water, or air. suppose that a crop of brake ferns can remove 15 milligrams (mg) per square meter of a particular pollutant from the soil in 20 weeks. after 20 weeks, the ferns are harvested and a new crop is planted. if c represents the number of crops of brake ferns needed to phytoremediate soil contaminated with 170mg per square meter of the pollutant down to healthy levels of 5mg per square meter, which equation best models the situation?
Equation that best models the situation is where c = 11
What is phytoremediation?
Living plants are used in phytoremediation technologies to purify contaminated soil, air, and water. According to the definition, it involves "the use of green plants, associated microbes, suitable soil amendments, and agronomic techniques to either contain, remove, or render dangerous environmental toxins harmless." The word is a combination of the Greek words phyto (plant) and remedium (remedy) (restoring balance). Despite being appealing due to its low cost, phytoremediation hasn't been shown to significantly address any environmental issues, at least not to the point where contaminated space has been returned. A cost-effective plant-based method of environmental cleanup called phytoremediation is being proposed. It makes use of plants' capacity to concentrate elements and chemicals from the environment and to detoxify different contaminants. The ability of certain plants, known as hyperaccumulators, to bioaccumulate substances is what causes the concentrating effect. The impact of cleanup is very different. Organic contaminants, which can be destroyed, are typically the main targets for phytoremediation while toxic heavy metals cannot. Several field tests supported the viability of employing plants to clean up the environment.
Let the number of crops needed to remove pollution = c
Since one crop can remove 15 mg of pollution per square meter.
Then, "c" number of crops may remove "15 C" mg of pollutant per square meter.
Now, the total amount of pollution per sq. meter Equals 170 mg
Additionally, it is necessary to reduce pollution to 5 mg per square meter.
Consequently, the equation for the scenario is given by,
Pollutants 'c' crops can remove from the total amount of pollution equal the amount of pollution required, or 170-15c=5.
Upon solving the equation, we get, c= 11.
To know more about phytoremediation, visit:
https://brainly.com/question/23182004
#SPJ4
in the arithmetic sequence 4,11,18 what is the 10th terms
Answer:
67
Step-by-step explanation:
Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.
4+63=67.
The 10th term should be 67
it takes $24$ minutes for jana to walk one mile. at that rate, how far in miles will she walk in $10$ minutes? express your answer as a decimal to the nearest tenth.
This shows that she covered 0.4 miles in 10mins
Rate of changeSpeed is defined as the rate of change of distance.
If it takes 24 minutes for jana to walk one mile, the rate of Jana is expressed as;
Rate= 24/1 mile
Rate = 24min/mile
In order to determine the distance she walk in 10 minutes, we will have;
Distance in 10min = 10/24
Distance in 10 min = 0.4 miles
This shows that she covered 0.4 miles in 10mins
Learn more on rate of change here: https://brainly.com/question/25184007
#SPJ1
tap A fills 260 liters of water in 4 hours
tap B fills 248 liters in 4 hours
how many more liters tap A can fill than tap B in 8 hours
Answer:
Step-by-step explanation:
In a cycle 1 school in Abu Dhabi , the ratio of boys to girls in the 3rd grade is 5 to 8. If there are 72 girls, how many boys will there be?
72/8 = 9,
9x5 = 45 boys
Therefore answer is 45 boys
The polynomial function f(x) has degree 4, a y-intercept of 40, roots of -5 and 4, and a multiplicity 2 root of 1. Enter f(x).
the graph of the equation is shown
The polynomial is:
f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)
How to get the polynomial function?Let's assume the leading coefficient is A, we know that the degree is 4, the y-intercept is 40, and we have the roots (-5, 4, 1, 1)
Then the polynomial is:
f(x) = A*(x + 5)*(x - 4)*(x - 1)*(x - 1)
Now we use the fact that the y-intercept is 40, so we have:
f(0) = 40 = A*(0 + 5)*(0 - 4)*(0 - 1)*(0 - 1)
40 = A*-20
40/-20 = A = -2
Then the polynomial is:
f(x) = -2*(x + 5)*(x - 4)*(x - 1)*(x - 1)
Learn more about polynomials:
https://brainly.com/question/4142886
#SPJ1
Please help as fast as you can!!!!
-2 1/3 - 1 3/4=
4=8/3
I hope this helps, I think thin is the right answer
solve the problem. a basketball player makes approximately 69% of free throws. if she plays in a game in which she shoots 7 free throws, what is the probability the she will make all 7?
If she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
For given question,
a basketball player makes approximately 69% of free throws.
So, the probability of success (p) = 0.69
the probability of failure (q) = 0.31
She plays in a game in which she shoots 7 free throws.
So, n = 7
We need to find the probability that she will make all 7.
Using Binomial probability Distribution,
For x = 7,
[tex]P(x = 7) =~ ^7C_7\times (0.67)^7\times (0.31)^{7-7}\\\\P(x=7)= 1\times 0.0606\times 0.31\\\\P(x=7)=0.0188[/tex]
Therefore, if she plays in a game in which she shoots 7 free throws, the probability that she will make all 7 = 0.0188
Learn more about the Binomial probability Distribution here:
https://brainly.com/question/15902935
#SPJ4
Pls solve this question step by step
Answer:
Step-by-step explanation:
[tex]\frac{-x}{3} + 4 = 20[/tex]
The solution of the linear equation:
-x/3 + 4 = 20
Is x = -48
How to solve the linear equation?Here we have the linear equation:
-x/3 + 4 = 20
And we want to solve it for x. Which means that we need to isolate x in one of the sides of the linear equation.
Remember that we can perform the same operation in both sides of the equation, so we start by subtracting 4 in both sides, then we get:
-x/3 + 4 - 4 = 20 - 4
-x/3 = 16
Now we can multiply both sides of the equation by -3, then we get:
-3*(-x/3)= -3*16
x = -48
The solution of the linear equation is x = -48
If you want to learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
Find the product of -2r² (12r³ − 2r² − 9r + 11) in standard form.
Answer:
-24r⁵ + 4r⁴ + 18r³ - 22r².
Step-by-step explanation:
-2r² (12r³ − 2r² − 9r + 11)
= -24r⁵ + 4r⁴ + 18r³ - 22r²
Answer:
Step-by-step explanation: Refer to attachment.
Evaluate rs + 14s when r = 6 and s = 1/4
Answer:
5
Step-by-step explanation:
rs + 14s
(6)(1/4) + 14(1/4)
[tex]\frac{6}{4}[/tex] + [tex]\frac{14}{4}[/tex] = [tex]\frac{20}{4}[/tex] = 5
Answer:
5
Step-by-step explanation:
rs + 14s
r = 6
s = 1/4
= 6*1/4 + 14*1/4
= 6/4 + 14/4
= (6+14) / 4
= 20/4
= 5
X^2 +7x +12 divided by x + 2
The required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].
To determine the simplified value of x² +7x +12 divided by x + 2.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
As per the given data,
Division of function,
= x² +7x +12/ x + 2
= x² + 7x + 10 + 2 / x +2
= (x + 5)(x + 2) + 2 / x + 2
= (x + 5) (x + 2) / x + 2 + 2 / x + 2
= x + 5 + 2 / (x + 2)
Thus, the required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].
Learn more about simplification here: https://brainly.com/question/12501526
#SPJ1
Maggie Travers works in the town's sanitation department. She is on a group health plan provided by the state for municipal employees. The insurance costs $6700 annually. The state pays 40% of the cost. Maggie is paid semi-monthly. How much should she expect to be deducted from her pay each paycheck for health insurance?
Answer:
$167.50
Step-by-step explanation:
Since the state pays 40% of the health insurance, Maggie will have to pay 100 - 40 = 60% of the insurance amount annually
60% = 0.6 decimal
So Maggie pays 0.6 x 6700 = $4,020
Maggie is paid semi-monthly ie 2 paychecks a month
In a year, there are 12 months so Maggie receives 24 paychecks annually
The total insurance amount of 4020 is split over 24 paychecks
So each paycheck deduction will be 4020/24 = $167.50
determine if the collection is not well defined and therefore is not a set. the collection of current nfl players
The collection of current NFL players is well defined and is a set
Step-by-step explanation:
For a collection to be termed as a set, it is necessary that it has distinct objects that are defined.
For example, a set of first 10 natural numbers is
A= [1,2,3,4,5,6,7,8,9,10]
It is well defined and therefore called as set which has first 10 natural numbers as its elements.
Same is the case with the collection of current NFL players.
The collection contains defined number of players. Therefore, this collection is called a set.
The members of the collection or team will be known as the elements of the set.
You can learn more about a set collection from
https://brainly.com/question/8053622
#SPJ4
What is the most common statistical method of expressing the precision of a series of repetitive measurements?.
The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.
What is a standard deviation?It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.
It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.
Learn more about standard deviation on:
https://brainly.com/question/12402189
#SPJ1
HELP!!!!!! In one serving of trail mix, the ratio of the number of ounces of raisins to the number of ounces of peanuts is 2 to 3. 2). Drag the numbers into the table to show how many ounces of raisins and peanuts are needed for different numbers of serving . tell me the answer you don't have to give me step by step explanation for ratios!!!!!
The ounces of raisins and peanuts needed for different numbers of serving are :
for 4 serving = 8 raisins and 12 peanuts
for 12 serving = 24 raisins and 36 peanuts
According to the question we have been given that in one number of serving the ratio of number of ounces of raisins to the number of ounces of peanuts is given as :
ratio = 2 : 3
We need to find ounces of raisins and peanuts needed for different numbers of serving.
For 4 serving,
Raisins = 4*2 = 8
Peanuts = 4*3 = 12
and we see that their ratio = 8/12 = 2/3
For 12 serving,
Raisins = 12*2 = 24
Peanuts = 12*3 = 36
and we see that their ratio = 24/36 = 2/3
Hence the ounces of raisins and peanuts needed for different numbers of serving are :
for 4 serving = 8 raisins and 12 peanuts
for 12 serving = 24 raisins and 36 peanuts
Learn more about ratio here : https://brainly.com/question/2328454
#SPJ9
the base of a ladder is 10 feet away from the bottom of a building’s wall. if the ladder makes a 35 ◦ angle with the ground, find the length of the ladder to the nearest tenth of a foot.
The length of the ladder to the nearest tenth of a foot as evaluated by trigonometric ratios is; 12.2ft.
What is the length of the ladder as discussed to the nearest of a foot?Since the base of the ladder as indicated in the task content is 10 feet away from the bottom of a building's wall, it follows that the set-up in discuss is analogues to a right triangle whose adjacent is 10ft;
Therefore, the length of the ladder which is the hypothenuse can be evaluated as follows;
cos 35° = 10/L
L = 10/cos 35
L = 12.2ft.
Read more on trigonometric ratios;
https://brainly.com/question/24133971
#SPJ1
For the set {3, 4, 5, 8,x), the
mean, median and mode all
have the same value. What
is the value of x that would
make this true?
Your lunch costs $10.95 at a
Answer:
x = 5
Step-by-step explanation:
Mode: The most frequently occurring data value.
Median: The middle value when all data values are placed in order of size.
Mean: The sum of all data values divided by the total number of data values.
As the mode is the most frequently occurring data value, x must be 3, 4, 5 or 8.
If the mode is 3 or 4, then the data set will be {3, 3, 4, 5, 8} or {3, 4, 4, 5, 8}. Therefore, the median would be 4.
If the mode is 5 or 8, then the data set will be {3, 4, 5, 5, 8} or {3, 4, 5, 8, 8}. Therefore, the median would be 5.
Therefore, the median is 4 or 5.
[tex]\boxed{\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]
If x = 4, the mean would be:
[tex]\sf \implies mean=\dfrac{3+4+5+8+4}{5}=\dfrac{24}{5}=4.8[/tex]
If x = 5, the mean would be:
[tex]\sf \implies =\dfrac{3+4+5+8+5}{5}=\dfrac{25}{5}=5[/tex]
Therefore, the only value of x that allows the mean, median and mode to all have the same value is x = 5.
Which multiplication equation best represents the figure
Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.
What is basic algebra?Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.
Now, firstly refer to the image attached.
Since each large square is one whole, we've been provided with two complete squares, where 4 filled rows and 3 empty rows make up the last entire square row.
According to the third square, the answer is 2.43, i.e., the answer is 2.43 after you multiply to find which of 0.27 and 9 truly equals it, by basic algebra.
The figure is therefore represented by the multiplication equation.
⇒ 0.27 × 9 = 2.43
Hence, Option C uses the multiplication equation to express the figure, 0.27 x 9 = 2.43, by basic algebra.
To learn more about basic algebra, refer to the link: https://brainly.com/question/723406
#SPJ4