MATHEMATICS HIGH SCHOOL

The table represents the temperature of a cup of coffee over time. Which model best represents the data set?

exponential, because there is a relatively consistent multiplicative rate of change

exponential, because there is a relatively consistent additive rate of change

linear, because there is a relatively consistent multiplicative rate of change

linear, because there is a relatively consistent additive rate of change

Answers

Answer 1

Answer:

Answer: first choice, exponential, because there is a relatively consistent multiplicative rate of change.

Explanation:

1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.

These are the data:

Time (min) ------ Temperature (°F)

0 ----------------------- 200

10 ---------------------- 180

20 --------------------- 163

30 --------------------- 146

40 ---------------------131

50 -------------------- 118

60 -------------------- 107

2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.

3) The other two options involve exponential models.

The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.

4) You can prove it:

i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:

y₁ = A [r]¹

y₂ = A[r]²

y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.

ii) Test some data:

180 / 200 = 0.9

163 / 180 ≈ 0.906 ≈ 0.9

146 / 163 ≈ 0.896 ≈ 0.9

131 / 146 ≈ 0.897 ≈ 0.9

118 / 131 ≈ 0.901 ≈ 0.9

107 / 118 ≈ 0.907 ≈ 0.9

As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.

Answer 2

Answer:

A. exponential, because there is a relatively consistent multiplicative rate of change

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What type of number is 3.75i+7

Answers

Answer:

Step-by-step explanation:

In my day they called them imaginary numbers.

I think the answer you want is a complex number.

Which point is an x-intercept of the quadratic functionf(x) = (x – 8)(x + 9)?

(0,8)
(0,–8)
(9,0)
(–9,0)

Answers

If you would like to find the x-intercept of the quadratic function f(x) = (x - 8) * (x + 9), you can do this using the following steps:

f(x) = (x - 8) * (x + 9)

(-9, 0): f(-9) = (-9 - 8) * (-9 + 9) = (-17) * 0 = 0
x = -9 and y = 0

The correct result would be (-9, 0).

Answer:

C: on edge.

Step-by-step explanation:

The area of a circle of radius r is given by A=\pi r^2A=πr 2 and its circumference is given by C=2\pi rC=2πr. At a certain point in time, the radius of the circle is r=8r=8 inches and the area of the circle is changing at a rate of \frac{dY}{dt}=\pi\sqrt{2} dt dA =π 2 square inches per second. How fast is the radius of the circle changing at this time

Answers

Answer:

Step-by-step explanation:

If I'm understanding this correctly, your problem is as follows:

The area of a circle is given by the formula

$A=\pi r^2$

The area of the circle is changing at a rate of $(dA)/(dt)=√(2)\pi$ . Find the rate of change of the radius, $(dr)/(dt)$ , when r = 8.

Assuming that is what you are asking, we will begin by finding the derivative of the area of a circle using implicit differentiation.

$(dA)/(dt)=\pi2r(dr)/(dt)$

Filling in what we have:

$√(2)\pi=\pi(2)(8)(dr)/(dt)$ which simplifies a bit to

$√(2)\pi=16\pi(dr)/(dt)$

Divide both sides by 16π to get:

$(√(2)\pi )/(16\pi)=(dr)/(dt)$

The π's cancel leaving the rate of change of the radius as

$(dr)/(dt)=.0883883476$ inches per second

What fraction is equivalent to 1/8??

Answers

Answer:

2/16

5/40

Step-by-step explanation:

Li needs 15 pieces of string each one half of an inch long. she cut a 6 inch piece of string into pieces that are one half of an inch long. how many more piece of string does she need?

Answers

6 times 2 is 12 and 15 minus 12 is 3 so three more pieces are needed.

About 7/10 of the human body is water. If a person weighs 130 pounds about how many pounds are water?

Answers

Amount of water=(7/10) * Weiht of the person
Amount of water=0.7 * 130 pounds=91 pounds.

answer: 91 pounds of water.

Final answer:

Given that the human body is about 70% water, a person who weighs 130 pounds would carry about 91 pounds of water weight.

Explanation:

The question is asking us to calculate the amount of water by weight in a human body. We can solve this by using a percentage (or a decimal equivalent) and multiplying that by the person's total weight. Given that 7/10 (or 70%) of the human body is water and the person weighs 130 pounds, we simply multiply 130 by 0.7 (the decimal equivalent of 7/10).

To calculate: 130 pounds * 0.7 = 91 pounds. Therefore, about 91 pounds of a person who weighs 130 pounds is water.

Learn more about Percentage Calculation here:

brainly.com/question/329987

#SPJ2

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