Final answer:
According to Newton's Law of Cooling, it will take approximately 10.76 minutes for the coffee to cool from 210 degrees Fahrenheit to 180 degrees Fahrenheit when placed in a room with a temperature of 68 degrees Fahrenheit.
Explanation:
According to Newton's Law of Cooling, the rate at which an object cools is proportional to the temperature difference between the object and its surroundings. We can use this law to determine how long it will take for the coffee to reach a temperature of 180 degrees Fahrenheit.
First, we need to find the temperature difference between the coffee and its surroundings. The initial temperature of the coffee is 210 degrees Fahrenheit and the room temperature is 68 degrees Fahrenheit. Therefore, the initial temperature difference is 210 - 68 = 142 degrees Fahrenheit.We also know that after 10 minutes, the coffee's temperature has decreased to 200 degrees Fahrenheit. So the new temperature difference is 200 - 68 = 132 degrees Fahrenheit.Now we can set up a proportion to find the time it takes to reach a temperature of 180 degrees Fahrenheit. The ratio between the initial temperature difference and the time it takes for the coffee to cool to 180 degrees Fahrenheit is equal to the ratio between the new temperature difference and the total time it takes for the coffee to cool to 180 degrees Fahrenheit. Let's call the total time T: (142 / T) = (132 / 10). Cross-multiplying, we get 1420 = 132T. Dividing both sides by 132, we find that T = 10.76 minutes.Therefore, it will take approximately 10.76 minutes for the coffee to reach a temperature of 180 degrees Fahrenheit.
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Simplify: ^3√108c^17
My Choics are...
:
a. 6c^8√3c
b. 3^3√4c^17
c. 3c^5 ^3√4c^2
d. 18c^8√3c
Factor y2 + 10z - 10y - yz.
In triangle PQR, C is the centroid.
What is the slope of a line that is perpendicular to the line v= 3/4x-6?
A. 3/4
B. -4/3
C. -3/4
D. 1/6
The slope of line which is given to be perpendicular to the line represented by equation "v = (3/4)x - 6" is : (b) -4/3.
To determine the slope of a line that is perpendicular to the given line v = (3/4)x - 6, we use the property that perpendicular lines have slopes that are "negative-reciprocals" of each other.
The slope of the given line is 3/4. To find the slope of the perpendicular line, we take the negative reciprocal of 3/4.
The negative reciprocal of 3/4 is -4/3. So, the slope of the line that is perpendicular to the given-line v = (3/4)x - 6 is -4/3.
Therefore, the correct answer is (b) -4/3.
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When a meteorologist says that there is a 30% chance of showers, what type of probability is the person using?
The area of a rectangle is 28 ft2 , and the length of the rectangle is 1 ft more than twice the width. find the dimensions of the rectangle.
The length is 8feet and the width of the rectangle is 3.5feet
Let the width of the rectangle be represented by w
Let the length of the rectangle be represented by = 2w + 1
Therefore, based on the information given, the equation to solve the question will be:
w(2w + 1) = 28
2w² + w = 28
2w² + w - 28 = 0
2w² + 8w - 7w - 28 = 0
2w(w + 4) - 7(w + 4) = 0
2w - 7 = 0
2w = 0 + 7
2w = 7
w = 7/2
w = 3.5
The width is 3.5 feet
The length will be:
= 2w + 1
= 2(3.5) + 1
= 7 + 1
= 8
The length is 8feet and the width is 3.5feet
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The altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments measuring 11 centimeters and 5 centimeters. to the nearest tenth, what is the length of the shorter leg of the triangle?
15,000 loses value by 20% each year. What is the value after 3 years
Answer:
Step-by-step explanation: 7680
After losing 20% we have 80% remaining
∴ value after three years = 15,000 × [tex]\frac{80}{100}[/tex] × [tex]\frac{80}{100}[/tex] ×[tex]\frac{80}{100}[/tex]
= 15,000 × [tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex]
= 7680
Help please. Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.
A.5√2 /2
B.5√3
C.5√2
D.5√3 /2
Answer: The value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
Step-by-step explanation: We are given to find the value of the variable 'x' in the figure.
We can see that the figure is a right-angled triangle with the length of the hypotenuse as follows:
h = 5 units.
Now, with respect to the angle of measure 45°, the length of the perpendicular is x units.
That is, p = x units.
From relations between trigonometric ratios, we have
[tex]\sin 45^\circ=\dfrac{\textup{perpendicular}}{\textup{hypotenuse}}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{p}{h}\\\\\\\Rightarrow \dfrac{1}{\sqrt2}=\dfrac{x}{5}\\\\\\\Rightarrow x=\dfrac{5}{\sqrt2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{(\sqrt2)^2}\\\\\\\Rightarrow x=\dfrac{5\sqrt2}{2}.[/tex]
Thus, the value of the variable is [tex]x=\dfrac{5\sqrt2}{2}.[/tex]
(04.01 LC)
Which of the tables represents a function?
Table A
Input
Output
3 1
3 4
2 3
Table B
Input
Output
2 7
5 6
2 9
Table C
Input
Output
1 5
7 2
7 3
Table D
Input
Output
3 4
1 5
8 5
Table A
Table B
Table C
Table D
Answer:
I believe the answer is table D.
Step-by-step explanation:
Each input can only have one output. The other tables have multiple outputs for each input. Therefore they get "cut off," and table D is the answer.
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Find the least common multiple of these two expressions. 14x^2y^4 and 21x^3u^7y^8
A ship traveled for 4 hours heading west and for 5 hours heading north. If the total distance traveled was 119 miles, and the ship traveled 5 miles per hour faster west, at what speed was the ship traveling west
In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ?x - 49
Answer:
0
Step-by-step explanation:
find the center of the circle that can be circumscribed about triangle EFG, E(6,4) F(6,2) and G(10,2)
Final answer:
The center of the circumscribed circle about triangle EFG with given vertices is found by calculating the perpendicular bisectors of the triangle's sides and locating their intersection point, which is the center (8,3).
Explanation:
To find the center of the circumscribed circle about triangle EFG with vertices E(6,4), F(6,2), and G(10,2), we need to determine the perpendicular bisectors of at least two sides of the triangle and then find their intersection point, which will be the center of the circumscribed circle.
First, find the midpoint of side EF, which has the same x-coordinate (since E and F have the same x-coordinate), so the midpoint is (6,3).Next, we need the equation of the perpendicular bisector of EF. Since EF is vertical, its perpendicular bisector is a horizontal line that passes through the midpoint, hence the equation is y = 3.Then, find the midpoint of side FG. As the endpoints have the same y-coordinate, the midpoint will have that y-coordinate (2) and the x-coordinate will be the average of the x-coordinates of F and G, which is (6+10)/2 = 8. So, the midpoint of FG is (8,2).The slope of side FG is 0 (since it's horizontal), so the slope of its perpendicular bisector is undefined, meaning it's a vertical line. Consequently, the equation of this perpendicular bisector is x = 8.Last, by solving the system of equations formed by the two perpendicular bisectors x = 8 and y = 3, we find the intersection point, which is the center of the circumscribed circle: (8,3).The graph of a line goes down and to the right when
simplify
27 2/3
----------
27 4/3
Answer:
It would be 9
Step-by-step explanation:
for edgen 2020
A building is 60 ft tall and another is 80 ft tall. A model of the 60 ft building is made at 1 ft. tall. How tall is the model of the 80 ft tall building?
1 foot = 60 feet
80/60 = 1.333
80 foot building is made 1.33 feet tall (16 inches, 1 foot 4 inches)
A swimming pool is 15 by 30 feet and a consistent 5 feet deep. you are painting the walls and floor of the pool. if a gallon can of paint covers 250 square feet, how many gallon cans would you need to buy
the bottom of the pool is 15 x 30 = 450 sq feet.
you the have 2 walls that are 30 x 5 = 150 x 2 = 300 square feet
then 2 walls that are 15 x 5 = 75 x 2 = 150 square feet
for a total of 450 +300 +150 = 900 square feet
1 can covers 250 sq ft
so 900/250 = 3.6
so you would need 4 cans of paint
Find the 39th term of the arithmetic sequence that starts with 4 and has a common difference of 6.
A. 232
B. 226
C. 238
D. None of these
The x-intercept of the line x = 3.5 is . The y-intercept of the line y = -6.5 is . Enter your answer as an ordered pair such as (1, 1) or (-2, 2).
Two minor league baseball players got a total of 292 292 hits. washington had 18 18 more hits than sanchez. find the number of hits for each player
Write a function max that has two c string parameters and returns the larger of the two.
Final answer:
To determine the larger of two C strings, a function named max uses strcmp to compare them, returning the one considered greater in alphabetical order.
Explanation:
To write a function named max that returns the larger of two C strings, one must compare the two strings alphabetically. Here is an example implementation in C:
#include // Include the header file for string functionsThe strcmp function from the string.h library is used to perform the comparison. If the first string (str1) is greater than or equal to the second string (str2), str1 is returned; otherwise, str2 is returned. Note that the comparison is based on the ASCII values of the characters, effectively ordering them alphabetically.
A student claims that a figure has rotational symmetry and that the angle of rotational symmetry is 360 degrees. Critique the student's statement.
if acircle is inscribed in a hexagon, which of the following must be true ? Check all that apply.
A. The hexagon is circumscribed about the circle.
B. Each vertex of the hexagon lies inside the circle.
C. The circle is congruent to the hexagon.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Answer: A. The hexagon is circumscribed about the circle.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Step-by-step explanation:
Given: A circle is inscribed in a hexagon.
Then the hexagon is circumscribed about the circle.
Each vertex of hexagon lies outside the circle.
As each side of hexagon is just attached to the circle not passing through the circle, thus the circle is tangent to each side of the hexagon.
Since circle is a closed curve and hexagon is regular polygon with 6 sides, they cannot be congruent because they have different shapes.
The screen on Lawrence's new phone is 3.15 centimeters long.What mixed number represent the lenght of the phone screen?
A mosaic is made by having 1 cm square tiles glued onto a photograph. the photograph is a 6 cm by 8 cm rectangular photo. It is enlarged by a scale factor of 1.5. how many tiles are needed to cover the enlarged photo
Bobby knows that the perimeter of the original rectangular is 120 meters he also knows that the perimeter of the reduced rectangular is 30 meters and the reduced length is 9 meters
Answer:36meters
Step-by-step explanation:
two points are collinear
Answer:
1. B
2. C
3. B
4. C
5. A
6. A
7. C
8. A
9. D
10. C
11. B
12. B
The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. what is the temperature of the coldest point in the plane?
which function is equivalent to the inverse of y=sec(x)
a. y=cot^-1(x)
b. y=cos^-1(1/x)
c. y=csc^-1(x)
d. y=sin^-1(1/x)
Answer: B) csc^-1(x)
Step-by-step explanation: EDGE 2021