Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
[tex]H= f(t)[/tex]
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
[tex]|f(35)'| = 1.5[/tex]
i.e the rate of change of temperature after 35 minutes is 1.5
and
[tex]|f(35)| = 68[/tex]
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the rate of change of the temperature of the cup of coffee is
[tex]R = |f(35)'| * t[/tex]
=> [tex]R = 1.5 * 0.5 [/tex]
=> [tex]R = 0.75 [/tex]
So
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
The units of f'(35) = degC/min.
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Given
The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
1. The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
2. What are the units of f'(35)?
The units of f'(35) = degC/min.
3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
At ║f'(35)║ = 1.5 and f'(35) = 68
|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.
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Serena wants to open a licensed child care center. Her state requires that there be no more than 12 children for each teacher. She would like her child care center to serve
29 children
(a) How many teachers will be needed?
Hats cost $4 each while scarves cost $3 each. John buys 5 items (all hats and scarves) and spends a total of $17. How many hats did he buy?
Answer:
2 hats
Step-by-step explanation:
4+4+3+3+3=17
Each hat costs $4 and each scarf costs $3.
He bought 5 items. Two of those items were hats.
The rest were scarfs.
The number of hats bought by John are 3
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let the hat is represented by x
scarves is denoted by y
Hats cost $4 each while scarves cost $3 each
John buys 5 items and spends a total of $17.
We need to find the number of hats.
3x+4y=17..(1)
x+y=5..(2)
x=5-y
Subtract x value in equation 1
3(5-y)+4y=17
Apply distributive property
15-3y+4y=17
15+y=17
Subtract 15 on both sides
y=2
x+2=5
x=3
Hence, the number of hats bought by John are 3
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Is it carbohydrate, lipid, protein, or nucleic acid?
PLEASE HELP!!! LAST QUESTION AND IM STUCKK.
Answer:
nucleic acid
Step-by-step explanation:
Identify the x- and y- intercept of the graph of the equation -3x + 6y = 24
Answer: x- intercept (0,-8)
Y- intercept (4,0)
Step-by-step explanation:
A parachutist descends 30 feet in 2 seconds.Express the rate of the parachutist’s change in height as a unit rate
Answer:
15
Step-by-step explanation:
30/2= 15 feet per second
given that f (x) x^2 - 3x find f(-4)
Answer:
28
Step-by-step explanation:
If you put -4 into all of the xs, then you should end up with the answer 28.
A taxi driver charges a fee if $4 plus 1.50 per mile. If you total was $13 how manu miles did you take
Answer:
6
Step-by-step explanation:
you need to do this (13-4)/1.50
Can you answer both and tell me the answer please
Answer:
7. 10^2
8. 3x3x3x3x3x3x3x3x3 = 19,683mi^2
What is the inverse of the following statement: “If x is a whole number, then x = 5”?
a) If x is not a whole number, then x ≠ 5.
b) If x = 5, then x is a whole number.
c) If x ≠ 5, then x is not a whole number.
d) If x is not a whole number, then x = 5.
Answer:
It's a
Step-by-step explanation:
Because inverse means opposite so they are asking for the opposite of the statement "If x is a whole number, then x = 5”
Hope this helped ✨
If x is not a whole number, then x ≠ 5 is inverse of the statement if x is a whole number, then x = 5
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given statement is "If x is a whole number, then x = 5". To find its inverse, we need to switch the hypothesis and the conclusion, and negate both parts of the statement.
The hypothesis is "x is a whole number", and its negation is "x is not a whole number".
The conclusion is "x = 5", and its negation is "x ≠ 5".
So, the inverse of the given statement is:
"If x is not a whole number, then x ≠ 5."
Therefore, if x is not a whole number, then x ≠ 5 is correct answer.
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In the following hypothetical scenarios, classify each of the specified numbers as a parameter or a statistic.
a. There have been 44 Presidents of the United States, and 36% of them were Democrats. The 36% here is a:________
b. In a 2015 Gallup poll of 1025 adults living in the United States, 53% said they trust the judicial branch of the federal government. The 53% here is a:________
c. The survey results from 12 local parks show the mean height of 60 ft for mature oak trees. The mean height of 60 ft is a:_________
d. The 72 employees at ABC company have a mean income of $52,317 with a standard deviation of $36,829. The $36,829 is a:______
e. In a random sample of homeowners in the United States, it is found that 34% of the sampled homeowners renew their home warranty. The 34% here is a:______
Answer:
Explained below.
Step-by-step explanation:
A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.
While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.
A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.
(a)
There have been 44 Presidents of the United States, and 36% of them were Democrats. The 36% here is a parameter.
(b)
In a 2015 Gallup poll of 1025 adults living in the United States, 53% said they trust the judicial branch of the federal government. The 53% here is a statistic.
(c)
The survey results from 12 local parks show the mean height of 60 ft for mature oak trees. The mean height of 60 ft is a statistic.
(d)
The 72 employees at ABC company have a mean income of $52,317 with a standard deviation of $36,829. The $36,829 is a parameter.
(e)
In a random sample of homeowners in the United States, it is found that 34% of the sampled homeowners renew their home warranty. The 34% here is a statistic.
Select each transformation that carries a square onto itself.
a reflection over one of the square's sides
3 rotation of 180' clockwise about the square's center
a rotation of 90: clockwise about the squares center
a rotation of 180: clockwise about one of the squares vertices
: reflection over one of the souare s diagonals
Answer:
1. a reflection over one of the square's sides
2. a rotation of 90: clockwise about the squares center
3. a rotation of 180' clockwise about the square's center
Step-by-step explanation:
I did a test :)
what’s the answer bruh? I need help fr fr
Answer:
C.
Step-by-step explanation:
Very simple! First we have to take 4x-y=24 and put it in slope intercept form. We get y=4x-24. After this, we have to find the reciprocal of the slope (4). The reciprocal is 1/4. Which equation has a slope of 1/4? C does!
Answer:
A
Step-by-step explanation:
Rounded to the nearest tenth, what is the perimeter of rectangle ABCD?
A.
48.3 cm
B.
54.6 cm
C.
60.0 cm
D.
173.2 cm
54.6 cm
Step-by-step explanation:Hi there !
T30° => AD = AC/2 = 20cm/2 = 10 cm
T.Phytagoras
CD = √AC² - AD²
= √20² - 10²
= √400-100
= √300
= 10√3
= 10×1.73
= 17.3 cm
P = 2AD + 2CD
= 2×10cm + 2×17.3cm
= 20cm + 34.6cm
= 54.6 cm
Good luck !
I need HELP class is about to start and I don’t know any of this
Answer:
I'm not sure, let me work it out.
Step-by-step explanation:
Brenda has to remote controlled race cars painted red and blue. The red car travel 38 feet in two seconds. The blue car traveled 54 feet in four seconds. Which car was faster and by how much
The value for √10 is approximately between 3 and 4. Approximate further to find the values to the tenths place that √10 is between.
Answer:
A=3.1
B=3.2
Step-by-step explanation:
If there are 12 eggs in a carton, how many are in 5 cartons?
Answer:
60
Step-by-step explanation:
12x5 is equal to 60
On a number line, how are the locations of 9 and -9 related?
A.
The two numbers are opposites in value and lie in opposite direction on the number line.
B.
The two numbers are opposites in value and they lie in the same direction on a number line.
C.
The two numbers are equal in value and lie in opposite direction on the number line.
D.
The two numbers are equal in value and they lie in the same direction on a number line.
Answer:
none.
Step-by-step explanation:
how can you like put a subtract sign next to a number like lol!! how does it make sence!?!? i think the CORRECT answer is apple bobbing. i think this because when you apple bob for 9 apples it like subtracts it from the apple water!! currently crying because your question doesnt make sence like its obv apple bobing
Help me pleaseeeeee!!
Kelly made six batches of cookies his friends asked her to make an extra batch she’s 17 1/4 cups of sugar and needed another 7/8 cups for the extra batch how many cups of sugar will Kelly use all together
Answer:
18 1/8
Step-by-step explanation:
+0
1. Sam has a rope that measures
(5 x 1/10) + (6 x 1/100) + (8 x 1/1000)
How can this measurement be written as a decimal?
Bill is a builder.
On Monday he made mortar mix.
He used 24kg of sand and 5 kg of cement.
On Tuesday Bill will make the same type of mortar mix.
He will use 36 kg of sand.
How much cement does he need to make the same type of mortar mix?
Answer:
7.5 kg
Step-by-step explanation:
24 : 5
36 : x
x = 5 × 36 / 24
= 7.5 kg
Bill needs 7.5 kg of cement
Monday:
Sand = 24 kg
Cement = 5 kg
Tuesday:
Sand = 36 kg
Cement = x kg
Ratio of sand to cement
24 : 5 = 36 : x
24/5 = 36/x
Cross product
24 * x = 5 * 36
24x = 180
x = 180/24
x = 7.5 kg
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a school is having a pizza party. each pizza is cut into 12 slices. which explains whether it is better to estimate a greater or lesser number than the actual number of people that will eat pizza
Answer:
they said each pizza
Step-by-step explanation:
that means it isn't only one pizza but maybe a ton of them
Domain range and function
Melissa is saving $25 that she earned for washing her mom’s car. She earns $19 every week for doing chores, which she also saves. Which equation can be used to find t, the amount of money Melissa will have saved at the end of n weeks of doing chores.
Answer:
25+19x=t At least I think
f
[tex]f(x)2 - 5[/tex]
The linear equation has 5(x + 2) = 5x + 2 A) no solution. B) one solution. C) two solutions. D) infinitely many solutions
it's A it has no solution
I mark as brainliest
Answer:
-2, 0
I think I haven’t done this in 3 years lol
Answer:
-2,0
Step-by-step explanation:
X is -2 and Y is 0.
So X,Y = -2,0.
Write using interval notation
Answer:
(-9,5]
Hope this helps!!!!!
car rental agency charges a base rate plus a certain amount per day (d) and can be modeled using the expression 15+ 18d. What is the meaning of 18d in the expression? *
4 points
It is the base rate to rent a car.
It is the cost of renting a car for a day.
It is the total number of days a car can be rented.
It is the portion of the cost based on renting a car for d days.
Answer:
It is the portion of the cost based on renting a car for d days
Step-by-step explanation:
Given:
Total cost = 15 + 18d
Total cost = fixed cost + variable cost
Fixed cost are cost that do not change.
Fixed cost = base rate = 15
Variable cost changes during production process. The variable cost in the above varies with the number of days (d)
Therefore, 18d is the portion of the cost based on renting a car for d days.
If you rent the car for 1 day
Total cost = 15 + 18d
= 15 + 18(1)
= 15 + 18
= 33