The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.
K as the temperature in Kelvin,
C as the temperature in Celsius.
We're given that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. So, we can express this relationship as an equation:
[tex]\[ K = C + 237.15 \][/tex]
This equation shows that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature. Similarly, to convert from Kelvin to Celsius, you subtract 237.15.
Here's the equation:
[tex]\[ K = C + 237.15 \][/tex]
1. **Definition of Kelvin and Celsius Scales**:
- Kelvin (K): Kelvin is an absolute temperature scale where 0 Kelvin represents absolute zero, the lowest possible temperature where particles cease to move. One Kelvin is equal in magnitude to one degree Celsius.
- Celsius (C): Celsius is a temperature scale based on the freezing and boiling points of water, where 0 degrees Celsius represents the freezing point of water and 100 degrees Celsius represents the boiling point of water at standard atmospheric pressure
2. **Relationship between Kelvin and Celsius**:
- To convert from Celsius to Kelvin, you add 273.15 to the Celsius temperature. This adjustment is made because the Kelvin scale starts from absolute zero, which is -273.15 degrees Celsius.
3. **Given Relationship**:
- The given information states that a temperature in Kelvin is 237.15 greater than the temperature in degrees Celsius. This means that to convert from Celsius to Kelvin, you add 237.15 to the Celsius temperature.
- We can express this relationship mathematically as [tex]\( K = C + 237.15 \).[/tex]
- Here, [tex]\( K \)[/tex] represents the temperature in Kelvin, and [tex]\( C \)[/tex]represents the temperature in degrees Celsius.
- Adding 237.15 to the Celsius temperature converts it to Kelvin.
- The equation [tex]\( K = C + 237.15 \)[/tex]) provides a way to convert temperatures from degrees Celsius to Kelvin. It reflects the fact that the Kelvin scale starts from absolute zero and is offset from the Celsius scale by 273.15 degrees.
What situation could the
integer - 5 represent?
Answer:
What is the average temperature in degrees Celcius of Alaska in the winter?
The integer -5 can represent a loss or debt of 5 in real-world situations like owing someone 5 dollars, or a temperature drop 5 degrees below zero. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
Explanation:
In Mathematics, an integer can represent various scenarios. The integer -5 could symbiotically stand for a loss or debt of 5 in real-world situations. For example, if you owe someone 5 dollars, your net balance would be -5 dollars. Another example could be temperature. If the temperature drops 5 degrees below zero, it can be represented as -5 degrees.
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Which is the solution to the inequality? y minus 27 greater-than-or-equal-to negative 13
Answer:
y is greater than or equal to 14
Step-by-step explanation:
Answer:
y ≥ 14
Step-by-step explanation:
y - 27 ≥ -13
you manipulate this inequality like it is an equation. Only take care that the inequality swaps if you multiply by a negative. In this case, that is not needed.
y - 27 +27 ≥ -13+27
y ≥ 14
Find the circumference of a circle whose radius is 7 in.
Answer:
43.96
Step-by-step explanation:
you get pi which is 3.14 times 7 and then times 2
Answer:
43.98 inches
Step-by-step explanation:
The circumference of a circle can be found using:
[tex]c=2r\pi[/tex]
We know r, or the radius is 7, so we can substitute that in
[tex]c=2*7(\pi )[/tex]
[tex]c=14\pi[/tex]
c=43.9822972
or, about
43.98 inches
You are ordering a burrito with two main ingredients and three toppings. The menu below shows the possible choices. How many different burritos are possible?
(the number of combinations)
Answer:
840
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
In the menu, there are 6 main ingredients and we take 2 at the same time, so the possible outcomes is:
[tex]C^{6} _{2}[/tex] = [tex]\frac{6!}{(6-2)!*2!}[/tex] = 15
In the menu, there are 8 toppings and we take 3 at the same time, so the possible outcomes is:
[tex]C^{8} _{3}[/tex] = [tex]\frac{8!}{(8-3)!*3!}[/tex] = 56
=> the total number of combinations :
=[tex]C^{6} _{2}[/tex]*[tex]C^{8} _{3}[/tex]
=15 * 56 = 840
The tile backslash will be a mixture of colors of five-inch square tiles. One quarter of the tiles will be "Indian Red" one sixth will be "Tuscan Blue", one fifth will be "Eucalyptus", and the rest will be the color "Sand". What fraction of the tiles will be the color of "Sand"
Answer:
The fraction of tiles that will be the color of "sand" is 23/60
Step-by-step explanation:
we know that
The sum of the fractions of the tiles must be equal to 1
Let
x ----> the fraction of tiles that will be the color of "sand"
we have that
[tex]\frac{1}{4}+\frac{1}{6}+\frac{1}{5}+x=1[/tex]
solve for x
Find the Least Common Multiple of denominators
[tex]LCM=(2^2)((3)(5)=60[/tex]
Multiply both sides by 60
[tex]\frac{60}{4}+\frac{60}{6}+\frac{60}{5}+60x=60[/tex]
simplify
[tex]15+10+12+60x=60[/tex]
[tex]60x=60-37\\60x=23\\x=\frac{23}{60}[/tex]
therefore
The fraction of tiles that will be the color of "sand" is 23/60
What is the value of x in the problem attached?
Answer:
20
Step-by-step explanation:
subtract 5 from 85 then divide by 4
85-5=80
80/4=20
Solve the equation. 8 – 2x = –8x + 14 x = –1 x = x equals negative StartFraction 3 Over 5 EndFraction x = x equals StartFraction 3 Over 5 EndFraction x = 1
Answer:
x =1
Step-by-step explanation:
Solve the equation:
8 - 2x = -8x + 14
Collect like terms
8 - 14 = -8x + 2x
-6 = -6x
x = -6/-6
x = 1
Answer:
x=1
Step-by-step explanation:
i did the quiz
What is 6/ 8 equal to
Answer:
1216 is equivalent to 68 because 12 x 8 = 16 x 6 = 96.
Step-by-step explanation:
You bike 1 mile the first day of your training, 1.5 miles the second day, 2.5 miles the third day, and 4.5 miles the fourth day. If you continue this pattern, how many miles do you bike the seventh day?
Answer:
32.5 miles on the 7th day
Step-by-step explanation:
1, 1.5, 2.5, 4.5
We need to determine the pattern
We are adding .5 + 1/4(2^n)
Lets check
n=1 .5+ 1/4(2) = .5+ .5 =1
n =2 .5 + 1/4*2^2 = .5 +1 = 1.5
n=3 .5 + 1/4 ( 2^3) = .5 + 8/4 = 2.5
n=4 .5 + 1/4 (2^4) = .5 + 16/4 = 4.5
n = 5 .5 + 1/4 (2^5) = .5 +32/4 = 8.5
n = 6 .5 + 1/4 (2^6) = .5 + 64/4 =16.5
n=7 .5 + 1/4(2^7)= .5 + 1/4(128) = 32.5
They bike 32.5 miles
Help meeeeeeeeeeereeee
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
1/2( 4^3 - 6 * 3^2)
PEMDAS says parentheses first
( 4^3 - 6 * 3^2)
Exponents
(64 - 6 * 9)
Multiply and divide from left to right
64 - 54
Add and subtract from left to right
10
Substitute back into the expression
1/2(10)
5
A certain triangle has a 30° angle in a 60° angle. Which must be a true statement about the triangle
Answer:
It is a right triangle.
Step-by-step explanation:
A right triangle is a triangle with at least one angle with 90 degrees.
We know that every triangle has 180 degrees. The other unknown angle is 180 - (30+60) = 180 - 90 = 90. That means that the other angle is 90 degrees. Therefore, it is a right triangle
We also know that in this triangle, that the square of one side plus the square of another is side is equal to the square of the hypotenuse of the triangle. (According to Pythagorean theorem)
Answer:
The second-longest side is the square root of 3 times as long as the shortest side.
I need help on this quick
Answer:
The hypotenuse to the nearest tenth is 8.1
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
Let a be the x leg and b be the y leg
a = 7 units
b= 4 units
7^2 + 4^2 = c^2
49+ 16 = c^2
65 = c^2
Take the square root of each side
sqrt(65) = sqrt(c^2)
8.062257748 =c
To the nearest tenth
8.1 =c
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5617.8 hours and a sample standard deviation of 234.5 hours.
a) Test the hypothesis that the true mean life of a biomedical device is greater than 500 using the P - value approach.
b) Construct a 95% lower confidence bound on the mean.
c) Use the confidence bound found in part (b) to test the hypothesis.
Answer:
a) The evidence suggest the true mean life of a biomedical device > 5500
b) (5487.94, +∞)
c) There is evidence to support that the mean is equal to 5500
Step-by-step explanation:
Here we have
(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500
Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is
H₀: μ = 5500
Therefore, the alternative hypothesis will be
Hₐ: μ > 5500
The test statistic is then found by;
[tex]t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}} =\frac{5617.8-5500 }{\frac{234.5 }{\sqrt{15}}} \approx 1.95[/tex]
The P value from the T table at df = n - 1 = 15 - 1 = 14 is
0.025 < P < 0.05
The P value is given as 0.036 from the T distribution at 14 derees of freedom df
Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ: μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500
(b) The 95% confidence interval is given as
[tex]CI=\bar{x}\pm t_\alpha \frac{s}{\sqrt{n}}[/tex]
Which gives t[tex]_\alpha[/tex] = [tex]\pm[/tex]2.145
[tex]CI=5617.8\pm 2.145 \times \frac{234.5}{\sqrt{15}}[/tex]
The confidence interval of the lower bound on the mean is then
(5487.94, +∞)
c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.
What is the value of 4/15 divided 2/3
Answer:
⅖
Step-by-step explanation:
4/15 ÷ 2/3
4/15 × 3/2
2/5
Answer: 2/5 or 0.4
Step-by-step explanation: When dividing a fraction by another fraction you will always find the reciprocal of the second fraction and then multiply to get your answer.
4/15 divided by 2/3
4/15 multiplied by 3/2
0.4 or 4/10 or 2/5 is the value of 4/15 divided by 2/3
Find the value of 5w-1 given that 3w-4=8
Simplify your answer as much as possible
Answer:
19
Step-by-step explanation:
Solve for the value of w.
3w - 4 = 8
Isolate the variable, w. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 4 to both sides:
3w - 4 (+4) = 8 (+4)
3w = 8 + 4
3w = 12
Divide 3 from both sides to fully isolate the variable, w:
(3w)/3 = (12)/3
w = 12/3
w = 4
Plug in 4 for w in the first expression & solve:
5w - 1
5(4) - 1
20 - 1
19
19 is your value.
~
Answer:
19
Step-by-step explanation:
First, we need to solve for w by isolating it
3w-4=8
Add 4 to both sides
3w=12
Divide both sides by 3
w=4
Now we know w and can plug 4 in for w and solve
5w-1
5(4)-1
20-1
19
Twice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations. Explain how you solved the system.
Answer:
2x+2y=310
x-y=55
multiply seond equation by 2 and adding to first equation
2x-2y=110
add
2x-2y=110
2x+2y=310 +
4x+0y=420
4x=420
divide 4
x=105
sub
x-y=55
105-y=55
minuse 105
-y=-50
mult -1
y=50
the numbers are 105 and 50
The newly elected Chancellor of the Galactic Federation is interested in the opinions of all citizens regarding economic conditions in the galaxy. Unfortunately, she does not have the resources to visit every populated planet or to send delegates to them. Describe how the Chancellor might organize a multi-stage sample to carry out her survey.
The Chancellor can use a multi-stage sampling method to gather citizen opinions by dividing the galaxy into various regions, selecting a sample of these regions, and then selecting a sample of planets within these regions for surveying citizens.
Explanation:The Chancellor could use a multi-stage sampling method to effectively gather data from the galaxy's population. This method involves breaking down the larger population into smaller, manageable subsets in a sequence of levels or 'stages'. Here's an example of how it could work:
First Stage: The Chancellor divides the galaxy into distinct regions (e.g., solar systems, clusters of stars, etc.). This is sometimes called 'clustering'.Second Stage: A random sample of these regions is selected for further study.Third Stage: Within the selected regions, a random sample of planets is chosen.Final Stage: Within the chosen planets, a random sample of citizens is surveyed.This method will make the task feasible and manageable, given the constraint of resources. It also ensures that a diverse range of opinions can be captured from all over the galaxy.
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During the winter months there is a decrease of between 10 and 30 percent in business which of the following could not be the percent winter business is of the normal business
Answer: 30
Step-by-step explanation:
Patricia needs 10 yards of fabric to make curtains for her bedroom she also needs 3 yards of fabric to make a cover for her storage bench Patricia has 15 feet of fabric how many more feet of fabric does she need
Answer:
24 feet
Step-by-step explanation:
According to the question, Patricia needs 10 yards of fabric to make curtains for her bedroom she also needs 3 yards of fabric to make a cover for her storage bench
So, she needs 13 yards
converting into feet
1 yard = 3 feet
13 yards x 3 = 39 feet
Now, she already has 15 feet of fabric.
Finding out the difference : 39 - 15= 24 feet
Therefore, she needs 24 feet more of fabric
Answer:
She needs an additional 24 feet of fabric.
Step-by-step explanation:
In order to solve this problem we first need to calculate how many yards of fabric Patricia needs. This will be given by the sum of the fabric needed for the curtains and the fabric required to cover the storage bench. As seen bellow:
required fabric = 10 + 3 = 13 yards
We need to convert this value to feets, so the units are the same. To do that we multiply by 3.
required fabric = 13*3 = 39 feet
To know how many more fabric she needs we have to subtract the required fabric for the task by the total she already has. This is shown bellow:
needed fabric = 39 - 15 = 24 feet
She needs an additional 24 feet of fabric.
The base of a polyhedron is a square and the lateral faces are triangles. What polyhedron is being described??
9514 1404 393
Answer:
square pyramid
Step-by-step explanation:
The description fits that of a square pyramid.
Consider the circle above. What is the approximate area of the circle?
Answer:
The area of a circle is : π (Pi) times the Radius squared : A = π r 2 or, when you know the Diameter: A = (π /4) × D 2 or, when you know the Circumference: A = C 2 / 4 π
The radius of the base of a cone is decreasing at a rate of 2 22 centimeters per minute. The height of the cone is fixed at 9 99 centimeters. At a certain instant, the radius is 13 1313 centimeters. What is the rate of change of the volume of the cone at that instant (in cubic centimeters per minute)?
Answer:
The Volume is decreasing at a rate of [tex]156\pi[/tex] [tex]cm^3[/tex] per minute.
Step-by-step explanation:
Given a cone of radius r and perpendicular height h
Volume of the cone, [tex]V=\frac{1}{3}\pi r^2 h[/tex]
Since the height of the cone is fixed, the rate of change of the volume of the Cone, [tex]\frac{dV}{dt}[/tex] is given as:
[tex]V=\frac{1}{3}\pi r^2 h \\\frac{dV}{dt}=\frac{h\pi}{3} \frac{d}{dt} r^2\\\frac{dV}{dt}=\frac{2rh\pi}{3} \frac{dr}{dt}[/tex]
We are to determine the rate of change of the Volume, V when:
The radius is decreasing at a rate of 2 cm per minute, [tex]\frac{dr}{dt} = -2 cm/min[/tex]
Height, h=9 cm
Radius = 13cm
[tex]\frac{dV}{dt}=\frac{2rh\pi}{3} \frac{dr}{dt}\\=\frac{2*13*9\pi}{3}* ( -2)\\\frac{dV}{dt}=-156\pi \:cm^3/min[/tex]
The Volume is decreasing at a rate of [tex]156\pi[/tex] [tex]cm^3[/tex] per minute.
Leslie has a rectangular patio. She measures it and finds out it is 2135 feet long by 1115 feet wide. She wants to know how many square feet of tile she will need to completely cover the patio. Draw the patio, and label the measurements. How much tile will Leslie need to cover the patio? If each square foot of tile costs 75 cents, how much will she have to pay to cover her patio?
Answer: (1) Leslie will need 2,380,525 square tiles (1 foot by 1 foot each)
(2) She will have to spend $1,785,393.75 to cover her patio.
Step-by-step explanation: Please refer to the picture attached.
The rectangular patio has been designed and as shown in the diagram has on side measuring 2135 ft and the other side measuring 1115 ft. This means, in order to cover the entire patio, she would have to cover an entire area defined as 2,135 feet into 1,115 feet. If one tile measures 1 foot long by 1 foot wide, the total number of tiles to cover the patio can simply be derived as;
Area = L x W
Where the length is 2135 and the width is 1115,
Area = 2135 x 1115
Area = 2380525
**Having in mind that one tile measures 1 ft by 1 ft, the area of each tile is given as
Area = L x W
Area = 1 x 1
Area = 1 square foot**
(1) The above calculation shows that Leslie would be using up a total of 2,380,525 square tiles to completely cover her patio.
(2) Having been told that each square foot of tile costs 75 cents ($0.75), the total amount spent to cover her patio would be calculated as follows;
Cost = Area x cost per tile
Cost = 2380525 x 0.75
Cost = 1785393.75
The total cost therefore is $1,785,393.75
Leslie needs [tex]\( 2380025 \)[/tex] square feet of tile, and it will cost her [tex]\( \$1785018.75 \)[/tex] to cover her patio.
1. Calculate the area of the patio:
[tex]\[ \text{Area} = 2135 \times 1115 = 2380025 \text{ square feet} \][/tex]
2. Calculate the total cost of tiles:
[tex]\[ \text{Total cost} = 2380025 \text{ square feet} \times \$0.75/\text{sq ft} = \$1785018.75 \][/tex]
Therefore, Leslie needs [tex]\( 2380025 \)[/tex] square feet of tile, and it will cost her [tex]\( \$1785018.75 \)[/tex] to cover her patio.
If a given line has a slope of 2/7, what is the slope of a parallel line?
Answer:
2/7
Step-by-step explanation:
Parallel lines have the same slopes but different y-intercepts. That way they go infinity without touching so are perfectly parallel
Que es la mitad de 5
Answer:
2,5
Step-by-step explanation:
es decimal porque es un numero impar
Answer:
2.5
Step-by-step explanation:
básicamente, dividirías 5 y 2. No hagas 2 y 5. Eso te dará un número completamente diferente y no querrás un decimal de la fracción 2/5. Quieres la mitad de 5. ¡Entonces será 2.5! Lo siento, estoy usando el traductor de Google.
help please! super urgent. simple math problem!! will mark brainliest
Answer:
B
Step-by-step explanation:
Answer:B
Step-by-step explanation:
Can someone please help me on this
Answer:
28.4 miles less
Step-by-step explanation:
1. Find the length of the third side of the triangle with the pythagoream theroum
2. Pythagorean theroum= a^2+b^2=c^2
3. 45^2+ 55^2=c^2
4. 2025+3025=c^2
5. 5050=c^2
6. 71.06=c
7. Instead of driving 100 miles to work, Evelyn will now drive only 71.06 miles to work
7. That is 28.4 miles less than before
Answer:30 miles you save 30 miles
Step-by-step explanation: if you go around its 48+55=103 miles
Do formula a^2+ b^2= c^2
48^2+ 55^2=c^2
2304+3025= c^2
5329=c ^2
Sq rt of 5329 is 73
103-73=30
What percent of 80 is 32?
Answer:
40%
Step-by-step explanation:
multiply 80 by.40 you will get 32 hope this helps god bless
If the rate, in gallons per minute continues, how many gallons of water will flow from the hose in 45 minutes
Answer:
Step-by-step explanation:
45 gallons but your questtion doesnt make sense because you dont give us the number in gallons per minute
What is the slope of the line that passes through the points (5,-2) and (1, 10)
Answer:
-3
Step-by-step explanation:
10 - -2 = 12
1 - 5 = -4
12 / -4 = -3
Answer:
m = -3
Step-by-step explanation:
slope formula [tex]\frac{10-(-2)}{1-5} = -\frac{12}{4}[/tex] = -3