After heating up in a teapot, a cup of hot water is poured at a temperature of 203°F.
The cup sits to cool in a room at a temperature of 72°F. Newton's Law of Cooling
explains that the temperature of the cup of water will decrease proportionally to the
difference between the temperature of the water and the temperature of the room, as
given by the formula below:
T = Ta +(T. -T.)e-kt
To = the temperature surrounding the object
To = the initial temperature of the object
t = the time in minutes
T = the temperature of the object after t minutes
k=decay constant
The
cup of water reaches the temperature of 183°F after 2.5 minutes. Using this
information, find the value of k, to the nearest thousandth. Use the resulting
equation to determine the Fahrenheit temperature of the cup of water, to the
nearest degree, after 5 minutes.

10

Step-by-step explanation:

I think it's 10 my bad if I'm wrong

Answer:

The domain is all the x values and the range is all the y values.

Since there are 6 points on the figure, just find the coordinates (x, y) for all the points. Then get all the x and y values separated in a table.

I'm just going to assume this is scaled by 1 unit per square

Here are all the points on the graph:

(-6, -1)

(-4, 3)

(-4, -6)

(0, 2)

(2, -2)

(5, 7)

Now just split them into their x and y values

The Domain: -6, -4, 0, 1, 5

The Range: -1, 3, -6, 2, -2, 7

Answer:

Interval notation

Step-by-step explanation:

The domain is the x-value on the x-axis. The range is the y-value on the y-axis.

Find the two highest points on opposite sides in the graph.

After this step has been completed, you can write it in different forms, for example in interval notation:

The domain would be [-6, 5]

The range would be [-1, 7]

Note - for interval notation, when the point is a closed circle, the ending parenthesis would be "[ "or "]". However, when it is an open circle, the parenthesis would be "( "or ")".

Answer:

-3/2 or -1 1/2

Step-by-step explanation:

The slope, plugging into the equation (y_2-y_1)/(x_2-x_1) would be -5 + 2 / -1 + 3, or -3/2, which can also be - 1 1/2

Answer:

-3/2

Step-by-step explanation:

slope ('m') formula:  (difference of the y-values) ÷ (difference of the x-values)

m = -2-(-5) ÷ -3-(-1)

m = 3 ÷ -2

slope = -3/2

Answer:8a^7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Conclusion:

Therefore, 8a⁷ is the simplified form of 4a² x 2a⁵.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

oh uhm that is 3,4 <3

Step-by-step explanation:

15% of 850 is 127.5 and therefore the laptop would be reduced by 127.50

The sale price of the laptop is 722.50

Answer:

8/15

Step-by-step explanation:

hope this helps!!! :D

Answer: 8/15

Step-by-step explanation: Tangent is opposite/adjacent

The hypotenuse, the longest side of a triangle which is 17. The adjacent side is the second longest which is 15. And the opposite is the shortest or the base of a triangle which is 8.

For the future, remember these:

Sin = opposite/hypotenuse

Cos = adjacent/hypotenuse

Tan = opposite/adjacent

Therefore, tan is 8/15.

Hope this helps.

Answer:

u= 6, -6

Step-by-step explanation:

simplify the equation. Isolate the variable.

Hey there!

(u + 6)(u − 6) = 0

DISTRIBUTE “u” WITHIN the PARENTHESES

u(u) + (-6) + 6(u) + 6(-6) = 0

u^2 - 6u + 6u - 36 = 0

COMBINE the LIKE TERMS

u^2 - 36 = 0

ADD 36 to BOTH SIDES

u^2 - 36 + 36 = 0 + 36

CANCEL out: -36 + 36 because it gives you 0

KEEP: 0 + 36 because it helps solve for the u-value

NEW EQUATION: u^2 = 0 + 36

SIMPLIFY IT!

0 + 36 = 36

NEW EQUATION: u^2 = 36

TAKE the SQUARE ROOT

u = ± √36

u = -6 or u = 6

Therefore, your answer is: u = 6 or u = -6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer: ≥ without the line on the bottom.

Step-by-step explanation:

I am assuming the expression you are talking about are

[tex]3w^{2} +1[/tex] and [tex]10w+8[/tex].

If we were to replace w with 4 and calculate, we will find the answer:

[tex]3*4^{2} +1=3*16+1=48+1=49[/tex]

[tex]10*4+8=40+8=48[/tex]

Since the first expression, [tex]3w^{2} +1[/tex], is bigger than the second expression, the correct symbol to use is ≥ without the line on the bottom.

Answer:

Ralph's speed is 2 miles in 24 minutes.

(Unit rate, Ralph runs 1 mile in 12 minutes)

Step-by-step explanation:

4 divided by 2 is 2 (miles)

2/5 of an hour is 24 minutes (60/5=12+12=24)

Answer: 120

Step-by-step explanation:

first you distribute 5 to 11 and -17 to get (55 - 85) then you distribute 6 to 14 and -7 to now get (55-85) + (84-42) then you distribute -12 to 2 and 7 to now have (55-85) + (84-42) - ( -24 + -84) to get 120 you multiple when you distruibute for these cause its outside the parenthesis so you multiply the number by everything in the parenthesis

Answer:

x+2y = 5

2x+y=4

->

x+3y = 5

6x-y = 11

->

2x+y=10

x-3y=-2

Step-by-step explanation:

solutions of x and y for each system of equation can be solved by graphing

graph the two equations, and the intercepts of the two equations would be the x and y-values, aka the answers

if there are no intercepts, the equations have no solution

Answer:

the range is 66 to 70 since it can be 2 degrees in either direction

The range of possible temperatures is 66 to 70°F.

It is required to find the range of possible temperatures.

The degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

Given:

The thermostat for a house is set to 68 °F, but the actual temperature may vary by as much as 2 °F.

According to given question we have,

∴The range is 66 to 70 °F since it can be 2 degrees in either direction.

Therefore, the range of possible temperatures is 66 to 70°F.

Learn more about temperature here:

https://brainly.com/question/11464844

#SPJ2

Answer:

Step-by-step explanation:

21 percent of 6600 is 1386.

I'm sorry if I'm wrong.

Using proportions, it is found that it would take 24 minutes if there were 5 people distributing the pamphlets.

The rule of three is:

3 people - 40 minutes

5 people - x minutes

Applying line multiplication:

[tex]5x = 120[/tex]

[tex]x = \frac{120}{5}[/tex]

[tex]x = 24[/tex]

It would take 24 minutes if there were 5 people distributing the pamphlets.

You can learn more about proportions at https://brainly.com/question/24372153

Answer:

15

Step-by-step explanation:

3 times 5 is 15

Answer:

2  Beetle juices and 3 Potion Punch

Step-by-step explanation:

j = Beetle Juice       cost $2.50

p = Potion Punch      Cost $3

         j + p = 5                      Multiply by -3              -3j  - 3p = -15

$2.50j + $3p = $14           Do not change      +   2.50j  -3p = 14      

                                                                                 - .50j      = -1

                                                                                          j = 2   Beetle Juice

   Substitute into the fist equation and solve for y       j + p = 5

                                                                                         2 + p = 5

                                                                                              p = 3   Potion Punch

Answer:

15x/2*4

Step-by-step explanation:

Answer:

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. They may also have been called the input and output of the function.)

Answer:

72

Step-by-step explanation:

I this problem I'm sure you're supposed to multiply: 24 x 3 = 72

hopefully this helped :)

Answer:

  no

Step-by-step explanation:

In terms of area per hour, Bob's works at the rate of ...

  1460 ft²/(4 h) = 365 ft²/h

Rhonda's rate is ...

  753 ft²/(1.5 h) = 502 ft²/h

The rates are different, so they are not proportional.

___

Additional comment

Toni's rate is 803 ft²/(2.2 h) = 365 ft²/h . . . the same as Bob's

Bob's and Toni's rates are proportional.

Answer:

= 59.36

Step-by-step explanation:

S = 207

so, tan(16) = H/S

tan(16°) = 0.28674539

so H = tan(16) * S = 0.28674539 * 207 = 59.35629573

so the tree high = 59.36 foot

Answer:

The answer is C! :) hope that helps haha

Answer:

Try subtracting 9 from 7 to find the value.

Step-by-step explanation:

Answer: 37,007 is greater

Step-by-step explanation:

Can i get a brainliest

Answer:

37,007 is greater than 30,707

Step-by-step explanation:

Thats because as you can see reading the numbers left to right, the first ones on the far left are both 3s. so so far they're the same. then go to the second number, making sure you're moving left to right. 7 is more than 0 therefor 37,007 is greater than 30,707

Answer:

First of all not a math question but wtv

the answer is C since where the story takes place affects what the characters do

Hope This Helps!!!

Answer: Darren got 75% of the questions correct.

Step-by-step explanation:

To find the percentage of questions Darren got correct, we can divide the questions he got correct by the total number of questions.

42 ÷ 56 = 0.75

0.75 X 100 = 75

So, Darren got 75% of the questions correct.

Answer:

[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex]

Step-by-step explanation:

[tex]\frac{a}{b} + \frac{c}{d}[/tex]                          

[tex]\frac{ad}{bd} + \frac{cb}{bd}[/tex]                  Multiply  by the LCD (bd)

[tex](x-4)(x-3) =0\\\\\implies x-4 = 0~~ \text{ or}~~ x - 3 = 0\\\\\implies x = 4~~ \text{or}~~ x = 3[/tex]