Determine what type of model best fits the given situation: The temperature of a cup of coffee decreases by 5 F every 20 minutes.

Answers

Answer 1

Answer:

Final answer:

The situation is best modeled by a linear function, considering the steady and constant rate of temperature decrease. Although this model does not account for other factors, it lays out a fundamental understanding of the time-temperature relationship in the given scenario.

Explanation:

The situation where the temperature of a coffee decreases by 5 F every 20 minutes is best modeled by a linear function. This is because the rate of decrease is steady and constant, meaning it fits the structure of a linear function: y = mx + b, where m is the slope (rate of decrease) and b is the y-intercept (initial temperature). In this case, the slope would be -5/20, as the coffee temperature decreases by 5 F every 20 minutes.

This concept is closely related to Newton's Law of Cooling in Physics, which postulates that the rate of loss of heat from an object is proportional to the difference in temperature between the object and its surroundings, provided the temperature difference is small. However, in this case, since we are dealing with a constant rate of cooling, the linear model is more appropriate.

While this model does not account for factors such as the volume of the coffee, heat transfer to the surroundings or the specific heat capacity of the coffee, it provides a basic understanding of the relationship between time and temperature in this scenario.

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A The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. The interior dimensions of a fish tank are 30 cm, 90 cm, and 70 cm. Each fish requires 27000 cubic centimeters of water. How many tropical fish will this fish tank hold?a. 8
b. 6
c. 9
d. 7

Answers

Answer:

Step-by-step explanation:

We need to first of all find the volume of the fish tank. The most probable shape the ship tank can have is that of a cuboid.

The volume of a cuboid is l * b * h

And this is equals 30cm * 70cm * 90cm = 189,000 cubic centimeters

The number of fish the tank can contain can be obtained by dividing the volume by the volume occupied by a single fish.

This is 189,000/27000 = 7

To make curtains for a living room window for a customer, you will need three pieces of fabric in the following lengths: 3 feet, 3 feet, and 5 feet. What is the total length of fabric you will need? A. 8

Answers

Total length of fabric is: 3 + 3 + 5 = 11 feets

Horce read 160 pages in 4 hours. how many pages can he read in 6hours

Answers

Steps:
1. Do a proportion
160 pages/ 4 hours= x/ 6 hours
2. Do 160 times 6 which equals 960
3. Do 960 divided by 4 which equals 240
4. Your answer is
240 pages

let x be the amount of pages
160/4=x/6
4x=960 (cross multiplied)
x=240 (divided by 4 to both sides)

therefore 240 pages in 6 hours

Crystal said she used the distributive property to evaluate 5(4 + 7). These are the steps she took:5(4 + 7) = 5⋅4 + 7 = 20 + 7 = 27
What mistake did Crystal make? What is the correct answer to 5(4 + 7)?
Type a paragraph

Answers

The value of 5(4 + 7) is 55.

It is required to find the correct answer.

What is simplification?

Simplification means simplifying processes involved in work towards consistency of efforts, costs and time. It eliminates useless and disadvantageous (or unnecessary) diversity and variety.

Given that:

By the Distributive Property

If a, b, c are real numbers, then

a*(b+c)=a*b+a*c

Crystal's did mistake was that she distributed the 5 only to the 4, not to the 5 to 7 as well.

First distribute and then multiply, we get

The correct step should have been

= 5(4 + 7)

= 5⋅4 + 5⋅7.

= 20 + 35.

= 55

Therefore, the value of 5(4 + 7) is 55.

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Answer:

Crystal's mistake was that she distributed the 5 only to the 4, not to the 7 as well.

The correct step should have been 5(4 + 7) = 5⋅4 + 5⋅7.

Using the distributive property correctly would give the sum of the two products, 20 + 35. The value of 5(4 + 7) is 55.

A sample with which of these variances has a standard deviation that is greater than the variance?A. 2.25
B. 1.75
C. 0.75
D. 1.25

Answers

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

What is standard deviation?

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value

Here we have to find a sample with standard deviation greater than the variance.

We know that Standard deviation is the square root of the variance so if we want a sample with greater Standard deviation than the variance then it's variance should be less than one as we know that if

$0 < x < 1 \Rightarrow \sqrt x > x$

And here given variances are

2.25, 1.75,0.75 and 1.25

Hence 0.75 is correct answer

By using relation between standard deviation and variance we got that sample with 0.75 variance has a standard deviation that is greater than the variance

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Standard deviation is the square root of the variance. For the square root of a number to be greater than the number, the number must be between 0 and 1.
Hence, for the standard variation to be greater than the variance, the variance must be between 0 and 1.

Answer: C [0.75]

What is one extensive and one intensive property of marker ink?

Answers

One extensive property of marker ink is volume, whereas one intensive property of marker ink is color.

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