At 7:00 A.M., Alicia pours a cup of tea whose temperature is 200°F. The tea starts to cool to room temperature (72°F). At 7:02 A.M. the temperature of the tea is 197°F. At 7:15 A.M. the temperature of the tea is 180°F. Alicia will drink the tea when its temperature is 172°F.
Part A

Which of the following shows an exponential cooling equation that models the temperature of the tea?

A. y = 72(0.989)x + 128

B. y = 128(0.989)x + 72

C. y = 200(0.989)x + 72

D. y = 128(0.989)x + 200

Part B

When can Ella drink the tea?


Ella can drink the tea after
7:22
7:18

Answers

Answer 1

Answer: A) Option B

B) 22.3 minutes.

Step-by-step explanation:

The temperature decreases in an exponential decrease, this means that we can write the equation as:

T(x) = A*r^x + B

Where A is the difference between the initial temperature and the room temperature, B is the room temperature, and r is a positive number smaller than 1, that says "how fast" the temperature decreases (and x is the variable, in units of time)

We know that the initial temperature

A = 200° - 72° = 128°

B = 72°

T(x) = 128°r^x + 72°

The only option with those two values is option B.

T(x) =  128(0.989)^x + 72

We should check that when x = 2m, the temperature must be 197°

T(2m) = 128*(0.989)^2 + 72 = 197.2° (that we can round down to 197°)

So this equation is correct

Now we want to find the time such the temperature is 172°F

then:

172° = 128°(0.989)^x + 72°

100° = 128°(0.989)^x

100/128 = (0.989)^x

x = ln(100/128)/ln(0.989) = 22.3 minutes.

Let's check in our equation:

T(22.3) =  128°(0.989)^22.3 + 72 = 172°


Related Questions

help!!
Mariya was asked to solve StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16 and then graph the solution. Her work is shown below.

Step
Mariya’s work

StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16

Step 1

(Negative 13) StartFraction a over negative 13 EndFraction less-than-or-equal-to negative 16 (negative 13)

Step 2

a greater-than-or-equal-to 208

Step 3
A number line going from 205 to 211. An open circle is at 208. Everything to the right of the circle is shaded.


In which step, if any, did Mariya make a mistake in her work?
Step 1
Step 2
Step 3
No mistake found

Answers

Answer:

Step 3 is the correct answer!

Step-by-step explanation:

Answer:

C- step 3

Step-by-step explanation:

e d g e n u i t y q u i z z

Hope I helped x3

Please need this by the 16th

Answers

Answer:

60

Step-by-step explanation:

12 can be broken into 3*4

15 = 5*3

The least  factors are

3*4*5 = 60

The lowest common denominator is 60

Answer:

7/12= 35/60

7/15= 28/60

PLEASE HELLPPP
what is : -4(3-5)+10-3(7+4)+30​

Answers

Answer:

15

Step-by-step explanation:

Use PEMDAS for this:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

-4(3-5)+10-3(7+4)+30 ​= -4(-2)+10-3(11)+30

-4(-2)+10-3(11)+30 = 8+10-33+30

8+10-33+30 = 18-33+30

18-33+30 = -15+30

-15+30 = 15

Step 1: calculate in parentheses
-4•(-2)+10-3•11+30
Step 2: Multiply
8+10-33+30
Step 3: Calculate
=15

If 400 reduced by two times my present age is 296, how old am I now?

Answers

Answer:

52 years.

Step-by-step explanation:

Represent my current age by c.  Then 400 - 2c = 296, or

104 = 2c

Then c must be 104/2, or 52 years.

On a coordinate plane, a line is drawn from point A to point B. Point A is at (negative 8, negative 13) and point B is at (4, 11). What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is One-third the length of the line segment from A to B? x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1 y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1 (1, 5) (0, 3) (–4, –5) (–5, –7)

Answers

Answer:

c

Step-by-step explanation:

Answer:

It is C

Step-by-step explanation:

Edg 2020

pls help me?????????

Answers

Step-by-step explanation:

Step 1:  Simplify both fractions

[tex]\frac{8}{24}[/tex] → [tex]\frac{8(1)}{8(3)}[/tex] → [tex]\frac{1}{3}[/tex]

[tex]\frac{5}{15}[/tex] → [tex]\frac{5(1)}{5(3)}[/tex] → [tex]\frac{1}{3}[/tex]

Since both of the simplified fractions are equal, that means that they form a proportion.

Answer:  Option A, YES

Simplify x + 3x - 36

Answers

Answer:

4x-36

Step-by-step explanation:

Put together like terms

X plus 3x = 4x


Which equation is NOT an example of a linear function?
A) y = 9 - 2x
B) y = 6/X
C) y = x/2 + 9
D) y = 5/6x - 8

Answers

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

Learn more here: https://brainly.com/question/16459885

Anthony earned the following amount for baby-sitting his brother over winter break: $5, $10, $10, $10, $5, $10, $20, $10, $5, $20, $20, $20, $10, $5, $5. What is the mean and median amount he earned each day?

Answers

Answer:

mean is $11

median is $10

Step-by-step explanation:

Explain the three steps when using distributive property to write an equivalent expression.

Answers

Answer:

Step-by-step explanation:First you apply the distributive property to create equivalent expressions, then you use algebra tiles to write equivalent expressions, and finally you verify that two different values of the variable yield the same value for each expressions, then the expressions are equivalent .

A gardener a coordinate grid to design a new garden. The gardener uses a polygon WXYZ on the grid to represent the garden. The vertical of this polygon are W (3, 3), X (- 3, 3), Y (-3, -3) Z (3, -3). Each grid unit represents one yard. Find the area of the garden.

Answers

Answer:

Find the area of the square using the length of the segment WX as the sides.

s =  |2 |+ | −2 | = 2 + 2 = 4 yards

Then A = s2 = 42 = 16 square yards.

Step-by-step explanation:

I got the same question but with different numbers so you could just use the formula to find you answer.

you do not know how confused i am with this question, please put a little explanation to explain how you did it.

Answers

Answer:

x=2

Step-by-step explanation:

2x = 4  and your multiplying 2 times x so x would have to be equal to 2 time blank which equals 4

Hope it helps!

A square pyramid is sliced parallel to the base and halfway up the pyramid.
Which of these describes the cross section?

A square smaller than the base
A quadrilateral that is not a square
A square the same size as the base
A triangle with a height the same as the pyramid

Answers

Answer:

A square smaller than the base

Explanation:

A square pyramid is a 3 Dimensional image. When you slice a 3 Dimensional image you form is a 2 Dimensional image for example a rectangle, a square, a triangle e.t.c.

The shape of the cross sections formed after slicing a 3 Dimensional image is dependent on the way it was sliced.

This means it can be sliced horizontally or vertically and this would result in different shapes.

If square pyramid is sliced parallel to the base and halfway up the pyramid, the shape of the cross section formed is a square smaller than the base.

Answer:

the first one

Step-by-step explanation:

I need help to find the volume

Answers

Answer:

224ft^3

Step-by-step explanation:

l*w*h= volume

Answer:

The Volume is 224

Step-by-step explanation:

w * h * l

PLEASE help ASAP will give brainliest

Answers

Answer:

1.Understand the problem

2.Gather your resources

3.Come to answer

4.Check your answer and present solution

Step-by-step explanation:

Answer:

Number 1 is gather your resources

Number 2 is understand the problem

Number 3 is come to an answer

and number 4 is check your answer and present the solution

How many solutions are there? 5(6x + 8) = 9x - 10 + 21x

Answers

Answer:

5(6x+8) =9x - 10 + 21x: No solution

Answer: No solution

Steps below

Step-by-step explanation:

1: Groups like terms.

2: Add similar elements 9x+21x=30x

3: Expand 5(6x+8): 30x+40

4: Subtract 40 from both sides

5: Simplify

6: Subtract 30x from both sides

7: Simplify

8: Answer: No solution

Hope this helps.

Answer: none

Step-by-step explanation:

30x+40=30x-10

how to simply this equation

Answers

Answer:

[tex]\sqrt[3]{2}[/tex]

Step-by-step explanation:

     18

 9 .     2

3 3

If a figure is translated 5 units down and 3 units right, how do you represent it algebraically

Answers

Answer

(x+3) -5

Step-by-step explanation:

plug the values into the parent transformation equation to its rightful places

The table shows the estimated number of bees, y, in a hive x days after a pesticide is released near the hive.

A 2-column table with 6 rows. The first column is labeled number of days with entries 0, 10, 20, 30, 40, 50. The second column is labeled estimated number of bees with entries 10,000; 7,500; 5,600; 4,200; 3,200; 2,400.
Which function best models the data?

y = 9,958(0.972)x
y = 0.972(9,958)x
y = 9,219x– 150
y = –150x + 9,219

Answers

Answer:

A

Step-by-step explanation:

y = 9,958(0.972)x

Function which best models the given data is -150x + 9219.

What is the solution of an equation?

A solution is an assignment of values to the unknown variables that makes the equality in the equation true.

According to the given question

y represents the number of bees.

and, x represents the number of days.

Since, we have to find the function to represent the given data.

As, we know the given data are the solution of any function, so they must satisfy the function. For this we will take any value of x and y and check whether it satisfy the given function or not.

From the given data,

Let check for the point (0, 1000).

Substitute (0, 1000) in the given function one by one.

For, y = 9,958(0.972)x

At, x = 0

We get y = 0

⇒ ( 0, 1000) is not the solution of the function 9958(0.72)x

For, y = 0.972(9,958)x

At, x = 0

we get y = 0

⇒ (0, 1000) is not the solution for the function 0.972(9958)x

For, y = 9219x - 150

At x = 0

we get y = -150

⇒ (0, 10000) is not the solution of function, 9219x -150

For, y = -150x + 9219

At x = 0

y = 9219 which is nearly equals to 10000 because y is the estimated number of bees.

⇒ (0, 10000) is the solution of the given function y = -150x + 9219 .

Hence, the function which best models the given data is -150x + 9219.

Learn more about solution of the equation here:

https://brainly.com/question/545403

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Choose the correct symbol.

74 21
>
<
=

Answers

It’s the greater than sign

Explain what the similarities and difference between y=2cosx and y=2cosx-3.

Answers

Answer:

(See explanation for further details)

Step-by-step explanation:

Similarities: Both expression have the same slope for the same values of x.

Difference: The second expression is a translated form of the first function in -3 units.

3. Six less than twice a number is 17. Which equation could be used to determine the
number, n?
A. 6-2n = 17
B. 2n-6 = 17
C. 6 - 7 n = 2n
D. 2n + 6 = 7​

Answers

Answer & Step-by-step explanation:

n represents our number. So, twice a number would be 2n because twice means multiply by two.

When the problem says 6 less, then it means 6 less than 2n. So, it would look like 2n-6.

FInally, the problem says that all of this equals 17 so 17 would be the result.

So, you answer is 2n-6 = 17. This is answer choice B.

Select ALL equations that have a solution of 6.

A
x + 6 = 9
3
B
4x + 15 = 29
C
x + 9 = 5
3
D
2(x + 5) = 18

Answers

None, i checked on photomath and it says none. What are we solving for??

triangle xyz is similar to triangle abc solve for k

Answers

Answer:

k = 13.5

Step-by-step explanation:

We can use ratios to solve

3        4.5

---- = ---------

9          k

Using cross products

3k = 9*4/5

Divide each side by 3

3k/3 = 9*4.5/3

k =13.5

The correct answer is 13.5

Some trapezoids are rectangles true or false

Answers

Answer:

False.

Step-by-step explanation:

A trapezoid is only ONE pair of parallel sides, not two.

One way to show that two triangles are similar is to show that

Answers

Answer:

show that the three sets of corresponding sides are in proportion. If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.

Step-by-step explanation:

Answer:

show that the three sets of corresponding sides are in proportion. If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.

Step-by-step explanation:

What is the area of triangle ABC?
O 2.5 square units
O 3 square units
O 3.5 square units
O4 square units

Answers

Answer:

3 square units

Step-by-step explanation:

Edge 2021

The area of triangle ABC will be 3 square units. Therefore, option B is the correct answer.

Triangle ABC in the figure below, where b= 3 units and h= 4 units.

The area of the triangle ABC= The area of the right triangle ABD - The area of the right triangle ACD

We know that, area of a triangle = 1/2 ×Base×Height

The area of the right triangle ABD

= 1/2 ×3×4

= 6 square units

The area of the right angled triangle ACD

= 1/2 ×3×2

= 3 square units

Now, difference = 6-3 = 3 square units

Therefore, option B is the correct answer.

Learn more about area of triangle here:

brainly.com/question/4075559.

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x sqaure - 3x + x = ? wats the answer

Answers

Answer:

the simplified answer is,

x^2 - 3x + x = x^2 -2x

Faron wants to paint the four walls in his bedroom. The room measures 12 ft long, 10 ft wide and 8 ft high. There are two doors that each measure 3 ft by 7 ft and a window that measures 3 ft by 4 ft. If Faron does not paint the doors and window, what is the total area he will paint?

Answers

Answer:

319 square feet.

Step-by-step explanation:

The walls of the room (the ones on the long side) have an area of 12 x 8 = 96 square feet each one. Thus, their area is 96 x 2= 192 square feet.

The other two walls have an area of 10 x 8 = 80 square feet each one. Thus, their area combined is 80 x 2 = 160 square feet.

Therefore, we have that the total area of the four walls is

192 +160 = 352 square feet

However, we have a door and a window that won't be painted.

The area of the door is: 3 x 7 =21 square feet

The area of the window is 3 x 4 = 12 square feet

Thus, the total amount of area that won't be painted is

21 + 12 = 33 square feet.

So we are going to take the total area minus the area that won't be painted to know the total area that Faron will pain:

352 - 33 = 319 square feet.

Thus, she will paint 319 square feet

Write the standard equation for a circle with center (0,0) and radius 8

Answers

Answer:

Step-by-step explanation:

hello : an equation is :

x²+y²=64

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