Really need some help understanding this problem?!?!
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT/dt = -k (T-A), where T is the water temperature, A is the room temperature, and k is a positive constant.
If the coffee cools from 180°F to 100°F in 10 minutes at a room temperature of 75°F, how long (to the nearest minute) will it take the water to cool to 80°F?,
Answers
Some of us would rather cut to the chase. We recognize that this is an exponential decay problem in which the initial temperature difference from the 75 °F room temperature is decaying to zero.
In 10 minutes, the temperature difference has decayed from 180-75 = 105 to 100-75 = 25, so we can write the temperature function of time as
.. T(t) = 75 +105*(25/105)^(t/10)
We can solve this for
.. T(t) = 80
using logarithms, but it may be easier to do it graphically.
To the nearest minute, it will take 21 minutes for the coffee to cool to 80 °F.
Related Questions
a cupcake recipe calls for 1/6 cups of milk and you have 5/8 cups of milk in the refrigerator how many cups of milk will you have remaining after baking the cupcakes
Answers
15 - 4 = 11 11/24 cups of milk left
Hope this helps
Answer: 1/8
Step-by-step explanation:
If you worked for 6 days for a total of 67.8 hours. If I worked the same number of hours each day, how many hours did I work in a day?
Answers
To solve this problem, we need to divide 67.8 by 6 to find the amount of hours each day.
67.8 / 6 = 11.3
You worked 11.3 hours each day.
Hope this helps!
Which of the economic goals correlates with the explanation "the ability of people to make choices"?
A. equity
B. innovation
C. efficiency
D. freedom
I got D as my answer, is that correct?,
Answers
which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5
Answers
Answer:
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}}[/tex]
[tex]\sqrt[4]{(\frac{24}{128})\times (\frac{x^{6}}{x^{4}})\times (\frac{y}{y^{5}})}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times {(x)^{6-4}}\times{(y)^{1-5}}}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times x^{2}y^{-4}}[/tex]
= [tex]\sqrt[4]{\frac{3}{(2)^{4}}\times x\times y^{-4}}[/tex]
= [tex]\sqrt[4]{(3\times x^{2)\times (\frac{y^{-1}}{2})^{4}}}[/tex]
= [tex]\frac{y^{-1}}{2}\sqrt[4]{3x^{2}}[/tex]
= [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex] is the correct answer.
Assume that there are 2 trials.
X = 2 where X represents the number of successes.
Which probability matches the probability histogram?
Round the answer to one decimal place.
P(success)=0.3
P(success)=0.4
P(success)=0.6
P(success)=0.7
Answers
Your question is a little unclear, but I believe you are asking about the probability that at least one of the trials in the experiment were successful.
If that is the case, you simply have to add the probability of 1 success with the probability of 2 successes.
That is 0.48 + 0.16 = 0.64
Rounding our answer to one decimal place gives us 0.6.
The correct answer on the test was
P(success)=0.4
Which polynomial is a perfect square trinomial?
A. x^2 +5y + 25
B. x^2 +10y+25
C.x^2+5y+100
D. x^2+10y-25
Answers
When a square of a number (3*3=9) can also add up to another number in the trinomial (3+3=6)
In my example here the equation, in order to be a perfect square trinomial, would be: X^2+6y+9
Now to look at the problem. We can instantly single out C because 10*10 is 100 but 10+10 is not five.
If we look at A we can find the root of 25 (5) but 5+5 is 10 not five. So A is incorrect
Using our previous calculation we know that 5 is our magic number. Leaving us with B and D. If we look at D we can conclude that -5*5 would be -25 but -5+5 is zero. So, it is not D
Using power of elimination we can easily conclude that B is the correct answer. If you wish to check: (5+5=10) (5*5=25)
Answer: B
Hope this helped!
a poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. if 10 voters are selected at random, wht is the probability that exactly five of them will vote in favor of the initiative?,
Answers
Lesson 8: Binomial Distributions
1. a. 91%
2. a. 5.1%
3. c. s^5-25s^4v+250s^3v^2-1250s^2v^3+3125sv^4-3125v^5
4. d. 55.8%
. Classify the triangle according to side length and angle measurement.
(1 point)
isosceles; right
equilateral; obtuse
scalene; acute
scalene; right
Answers
Final answer:
The question requests the classification of a triangle by both its side length and angle measurement. An isosceles triangle has two equal sides, and if it also includes a right angle, it is classified as isosceles; right. This understanding combines the concepts of triangle classification by sides and angles.
Explanation:
The question asks to classify a triangle according to side length and angle measurement. When classifying triangles by side lengths, we have three categories: isosceles, scalene, and equilateral. An isosceles triangle has two sides of equal length, a scalene triangle has all sides of different lengths, and an equilateral triangle has all sides of equal length. In terms of angle measurements, triangles can be classified as right (one 90-degree angle), acute (all angles less than 90 degrees), or obtuse (one angle greater than 90 degrees).
According to the information provided and referencing the 4th Theorem, in an isosceles triangle, the angles opposite to the equal sides are equal. This property helps in classifying a triangle when given its angles or side lengths. Furthermore, for a triangle to be a right triangle, it must include a 90-degree angle. This is crucial when identifying a triangle as isosceles; right, which means it is an isosceles triangle with a right angle, typically resulting in the two equal sides being adjacent to the right angle.
A vacant lot is in the shape of an isosceles triangle. It is between two streets that intersect at an 85.9degree angle. Each of the sides of the lot that face these streets is 150 ft. Long. Find the perimeter of the lot to the nearest foot.
Answers
Sin(α)=Opposite/Hypotenuse
α=89.5°/2=42.95°
Opposite=x
Hypotenuse=105
Sin(42.95°)=x/105
x=(105)(Sin(42.95°))
x=71.54 feet
2. Then the other side of the isosceles triangle (b), is:
b=2x
b=2x71.54 feet
b=143.08 feet
3. The perimeter of the isosceles triangle, is:
P=2a+b
P=2(105 feet)+143.08 feet
P=210 feet+143.08 feet
P=353 feet
PLEASE HELP ME!! 25 points
Anna has a 10-foot long ladder that she is going to rest against a vertical wall along the bottom of a window-sill that is 8.5 feet above the ground. The safety code recommends that the angle the ladder makes with the ground be no greater than 65°. Will the ladder be safe resting on the window sill?
please help with too -->Draw a diagram, and show work to support your answer.
Answers
sin x=opposite/hypotenuse
opposite=8.5 ft
hypotenuse=10 ft
thus
sin x=8.5/10
sin x=0.85
x=arcsin 0.85
x=58.21°
Since 58.21°<65° the we conclude that the ladder is very safe.
Situation: A 15 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1405. N Noe No initial mass (at time 0) N mass at time t k a positive constant that depends on the substance itself and on the units used to measure time t time, in days
Answers
Your welcome
Answer: 4.9
Step-by-step explanation:
Hope this helps
Your friend has prepared his monthly budget and asks you if he has overlooked anything in this planning. Which of the following questions points out his most serious omission?
a. What if your income from stocks is lost? b. What if you need to go to the doctor? c. What if the electric bill increases? d. What if you need to replace the furnace?
Answers
helpppppppppppppppppppppppppppp
Answers
We then have to rewrite:
x*x ^ 2 = 64
Rewriting:
x ^ 3- 64 = 0
x = 4
Answer:
x = 4
option 2
your boss is impressed with your work and gives you a 3% raise.if the inflation rate is 3% you are
A) making more money in today's dollars
B) making about the same amount in today's dollars
C) making less money in today's dollars
D) seeing no change in your paycheck
Answers
Answer: The answer is (B) making about the same amount in today's dollars.
Step-by-step explanation: Given that our boss is impressed with our work and give us a 3% raise.
We are to select the correct statement if there is an inflation of 3%.
Since the raise of 3% and inflation rate of 3% occur simultaneously, so there will not be much change in the amount of money we are making in dollars.
Thus, (B) is the correct option.
simplify 4x+2 - x^2 +x-12 / x-3
a) 3x-2
b)3x+4
c)5x-4
d)5x+4
Answers
Answer:
3x-2
Step-by-step explanation:
on edge
Divide the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of x.
(4x^2 - 10x -24) / (2x + 3)
Answers
Answer:
2x-8
Step-by-step explanation:
A particular computer takes 13 minutes to download a 39-minute TV show. How long will it take the computer to download a 2-hour movie?
Answers
It will take the computer 40 minutes to download a 2-hour movie based on its current download speed, which is 3 minutes of video per minute of download time.
Explanation:To answer this question, we first need to establish the download speed of the computer. This can be done by dividing the length of the TV show by the time it takes to download it. In this case, the computer can download 39 minutes of video in 13 minutes, so its download speed is 39/13 = 3 minutes of video per minute of download time.
To find out how long it will take to download a 2-hour movie, we first need to convert the length of the movie to minutes, because our speed is in minutes of video per minute of download time. Two hours is equal to 2*60 = 120 minutes. Therefore to download a 120-minute video, it will take 120/3 = 40 minutes.
Learn more about Download Time here:https://brainly.com/question/31000914
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sales: Ye has his own business he checks sales receipts three times a day One day his afternoon sales were $50 more than his morning sales and his evening sales were three times this afternoon so if his total sales for the day were $1000 what were his evening service
Answers
This means:
- The afternoon sales are x + 50.
- The evening sales are 3(x + 50) = 3x + 150
Now we can calculate x knowing the total sales:
Total sales = morning + afternoon + evening
1000 = x + x + 50 + 3x + 150
800 = 5x
x = 160
We are asked for evening sales, so let's plug are value for x into the evening expression:
evening = 3x + 150 = 3(160) + 150 = $630
What is the value of x?
x=23
x=35
x=58
x=93
Answers
What is the area of a sector with a central angle of 10pi/7 radians and a radius of 18.4 m? Enter your answer as a decimal.
Answers
.. = (1/2)*(18.4 m)^2*(10π/7)
.. = 759.73 m^2
Refer to Explorations in Literature for a complete version of this passage.
Which quotations from “Here Is New York” develop the author’s viewpoint that commuters do not truly experience New York City?
Select each correct answer.
A "About 400,000 men and women come charging on to the Island each week-day morning, out of the mouths of tubes and tunnels."
B "Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night."
C "The commuter dies with tremendous mileage to his credit, but he is no rover."
D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."
Answers
C "The commuter dies with tremendous mileage to his credit, but he is no rover."
D "Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the sea wall."
Final answer:
The quotations that develop the author's viewpoint about commuters not truly experiencing New York City are highlighted.
Explanation:
The quotations from “Here Is New York” that develop the author’s viewpoint that commuters do not truly experience New York City are:
“Second, there is the New York of the commuter—the city that is devoured by locusts each day and spat out each night.”
“The commuter dies with tremendous mileage to his credit, but he is no rover.”
“Or they may work in a midtown office and may let a whole year swing round without sighting Governors Island from the seawall.”
These quotes highlight the idea that commuters only see a limited and narrow part of the city, and they do not take the time to truly explore and experience all that New York has to offer.
7 is greater than or equal to w, and - 1 is less than w
Answers
Hope this helps!
The population of trout in a certain pond doubles every year. The current population of the pond is 275 trout.
Answers
A tree on a hillside casts a shadow c = 230 ft down the hill. if the angle of inclination of the hillside is b = 19° to the horizontal and the angle of elevation of the sun is a = 49°, find the height of the tree. (round your answer to the nearest foot.)
Answers
let x be the distance from point A to when y intersects the horizonal.
x/230=cos 19
x=230 cos 19=217.5
y/x=tan 19
y=xtan19
y=217.5 tan 19=74.88
(h+y)/x=tan 49
h+y=xtan 49=217.5tan49=250.205
hence
h=250.205-74.88=175.325 ft
the answer is:
height of the tree ~ 175 ft
what triangle congruence theorem is needed?
Answers
**************************************************************
How much will be left after 105 Days?
Answers
Since the half-life is 35 days, to figure out how many half-lives to go through, you diving 105 (the number of days total), by 35 (the number of days in a half-life). This gives us 3.
Now, you divide the base number (816 grams) in half. You do this the number of times we got earlier (in this case, three times.)
And that leaves us with 102 grams.
I hope this helps!
4. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
165units
170units
97units
169 units
is the answer A?
Answers
D=sqrt( (x1-x2)^2 + (y1-y2)^2 )
From T to U
D= sqrt((80-20)^2 + (20-60)^2) = 72.11
Then flying from U to V
D= sqrt((20-110)^2 + (60-85)^2) = 93.4
So T to U to V = 72.11+93.4 = 165.5
BUT checking also T to V to U
From T to V
D= sqrt((80-110)^2 + (20-85)^2) = 71.6
Then from V to U
D= sqrt((110-20)^2 + (85-60)^2) = 93.4
So from T to V to U = 165
Pretty much the same both directions
So yes the answer is A
A research firm conducts a sample survey and discovers that, of all the new watchers of three-dimensional tv, 77% have not reported any side effects such as vertigo, headache, or undue eyestrain compared with watching regular television. if this sample questionnaire had 2,100 respondents, what is the margin of error (me), rounded to the nearest thousandth? hint: me equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over n end fraction end square root comma where p hat is the yes proportion in the sample and n is the sample size. me = ±0.009 me = ±0.017 me = ±0.018 me = ±1.837
Answers
All you have to do is plug the known values into the equation and evaluate it.
First, do the work under the square root sign. 0.77(1-0.77) / 2100 gives you a very small number. If you take the square root of that, you will have 0.0091.
The last step is to just multiply that by 2 and you will have 0.018
What is the area of this figure?
Answers
5 x 5 = 25
4 x 2.5 = 10
25 + 10 = 35.
Hope this helps!:)
A model ship is built to a scale of 1 cm: 4 m. The length of the model is 40 cm. What is the length of the actual ship? a. 160 m c. 40 m b. 50 m d. 15 m Please select the best answer from the choices provided A B C D
Answers
You can get this answer by multiplying the scale by the length of the model