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2 years ago

3.2.4 practice modeling slope-intercept Equation of a line

Mathematics

1 answer:

UNO [17]2 years ago

3 0

Answer:

this is from apex

Step-by-step explanation:

1. Which option did you choose? Discuss with another student why you made the choice you made. (1 point)

Troposphere (above the surface) because it looks simpler.

what do you know? the upper crust of the Earth is the layer extending 10 to 40 km beneath the surface. The surface temperature averages 15 degrees Celsius and increases 25 degrees Celsius with each kilometer of depth

what do you want to find out? The range of temperatures I would expect to encounter while traveling within the boundaries of the upper crust.

what answers do you expect to find? a range of temperatures (duh).

Writing an Equation

2. Define the variables you will use in your equation. (1 point)

Let one variable be the distance away from the surface and the other variable be the temperature.

D for distance and T for temperature.

The y-intercept is the starting position at Earth's surface. The coordinates of the y-intercept are (0, the temperature at Earth's surface).

3. What is the b-value of the y-intercept for your equation? (1 point)

15, I finally figured it out after 2 days lol.

The slope is the rate of change for temperature.

If the temperature increases (gets hotter) as the distance from the surface increases, then the slope is positive.

If the temperature decreases (gets colder) as the distance from the surface increases, then the slope is negative.

4. What is the slope of your equation? (1 point)

the slope of my equation is... positive!

5. Write an equation that models the relationship between your variables. (1 point)

umm, let's see... y= 25x+15 with x being each kilometer down from the surface temp. (15).

or if you just need the "equation" equation, then its y=mx+b

Interpreting the Equation

6. Identify and explain what each term represents in the temperature model.

a) The slope (1 point)

b) The y-intercept (1 point)

Graph the line

7. Identify three points on your line. (1 point)

(10,265) (11,290) (12,315)

8. Using the coordinates from question 7, calculate the slope of your line. Does it match the slope from your model? (2 points)

the slope of my line is 25, just like in my model. (wow magical)

Graph the Equation

9. On the graph below, plot the points and sketch your line. (4 points: 1 for each graphed point, 1 for the line)

see attachment.

Find the Temperature Range

10. Complete the sentence for your layer. (1 point)

The upper crust is the region that starts at Earth's surface and ends between 10 km and 40 km below the Earth's surface.

Use the temperature equation to find the temperature range for your layer.

range: between 265 degrees Celsius and 1015 degrees Celsius. (10km - 40 km)

11. What is the temperature at the end of your layer that is farthest from the surface? (1 point)

1015 degrees celsius.

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2 years ago

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Lonzell said the function shown in the graph is positive on the interval (−,) and negative on the interval (−,−)open negative 5

Nezavi [6.7K]

Answer:

The positive graph is on the points (-5,-4) and (2,5)

And, negative would be (-4,2)

Step-by-step explanation:

As it seems that fgraph shows positive in the case when it is over x-axis, and negative when it is below y-axis

As on the interval (-1,5)

The graph is below x-axis i.e. on (-1,2)

And, over x-axis i.e. on (2,5)

At this point Lonzell’s is not correct

As on the interval (-5,-1)

The graph is below x-axis i.e. on (-4,-1)

And, over x-axis i.e. on (-5,4)

At this point Lonzell’s is not correct

So,

The positive graph is on the points (-5,-4) and (2,5)

And, negative would be (-4,2)

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2 years ago

Riko wants to find the distance between the points (−2, −3) and (2, −5). His work is shown. Riko correct? Explain why or why not

nadya68 [22]

Answer:

I'm guessing you want to know the distance I think so the distance is √20

Step-by-step explanation:

Distance formula

√(x2-x1)^2+(y2-y1)^2

√(2-(-2)^2+(-5-(-3)^2

√16+4= 20

√20

finding the square root gives you a long decimal which is 4.472135954999 and so on

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2 years ago

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In your sock drawer you have 5 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them

pentagon [3]

The question is incomplete! The complete question along with answers and explanation is provided below!

In your sock drawer you have 5 blue, 7 gray, and 2 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing the following socks. (Round your answers to four decimal places.)

a) 2 blue socks

b) no gray socks

c) at least 1 black sock

d) a green sock

e) matching socks

Answer:

a) P(2 blue socks) = 0.1099 = 10.99%

b) P(no gray socks) = 0.2307 = 23.07%

c) P(at least 1 Black sock) = 0.2748 = 27.48%

d) P(green sock) = 0%

e) P(Matching socks) = 0.3516 = 35.16%

Step-by-step explanation:

Given Information:

5 Blue socks

7 Gray socks

2 black socks

Total socks = 5 + 7 + 2 = 14

a) The probability of wearing 2 blue socks

P(2 blue socks) = P(B1 and B2)

P(B1) = no. of blue socks/total no. of socks

P(B1) = 5/14 = 0.3571

Now there are 4 blue socks remaining and total 13 socks remaining

P(B2|B1) = 4/13 = 0.3077

P(B1 and B2) = 0.3571*0.3077 = 0.1099 = 10.99%

b) The probability of wearing no gray socks

5 Blue socks + 2 black socks = 7 socks are not gray

P(no gray socks) = P(Not G1 and Not G2)

P(Not G1) = no. socks that are not grey/ total no. of socks

P(Not G1) = 7/14 = 0.5

Now there are 6 socks remaining that are not gray and total 13 socks remaining

P(Not G2 | Not G1) = 6/13 = 0.4615

P(Not G1 and Not G2) = 0.5*0.4615 = 0.2307 = 23.07%

c) The probability of wearing at least 1 black sock

5 Blue socks + 7 Gray socks = 12 socks are not black

P(at least 1 Black) = 1 - P(Not B1 and Not B2)

P(Not B1) = no. socks that are not black/ total no. of socks

P(Not B1) = 12/14 = 0.8571

Now there are 11 socks remaining that are not black and total 13 socks remaining

P(Not B2 | Not B1) = 11/13 = 0.8461

P( Not B1 and Not B2) = 0.8571*0.8461 = 0.7252

P(at least 1 Black) = 1 - P( Not B1 and Not B2)

P(at least 1 Black) = 1 - 0.7252 = 0.2748 = 27.48%

d) The probability of wearing a green sock

There are 0 green socks, therefore

P(Green) = 0/14 = 0%

e) The probability of wearing matching socks

P(Matching socks) = P(2 Blue socks) + P(2 Gray socks) + P(2 Black socks)

P(2 Blue socks) already calculated in part a

P(2 Blue socks) = P(B1 and B2) = 0.1099

For Gray socks

P(G1) = no. of gray socks/ total no. of socks

P(G1) = 7/14 = 0.5

Now there are 6 gray socks remaining and total 13 socks remaining

P(G2 | G1) = 6/13 = 0.4615

P(2 Gray socks) = P(G1 and G2) = 0.5*0.4615 = 0.2307

For Black socks

P(B1) = no. of black socks/ total no. of socks

P(B1) = 2/14 = 0.1428

Now there is 1 black sock remaining and total 13 socks remaining

P(B2 | B1) = 1/13 = 0.0769

P(2 Black socks) = P(B1 and B2) = 0.1428*0.0769 = 0.0110

P(Matching socks) = P(2 Blue socks) + P(2 Gray socks) + P(2 Black socks)

P(Matching socks) = 0.1099 + 0.2307 + 0.0110 = 0.3516 = 35.16%

7 0

1 year ago

A hollow cylindrical iron pipe with external and internal radii 8cm and 6cm respectively and length 35cm is melted and recast in

marusya05 [52]

Answer: length of wire = 500cm

Step-by-step explanation:

We would determine the volume of material used in making the hollow cylindrical iron pipe by subtracting the volume of the inner pipe from the volume of the outer pipe.

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Volume of inner pipe = π × 6² × 35 = 1260π

Volume of outer pipe = π × 8² × 35 = 2240π

Volume of material used in making the hollow cylindrical iron pipe is

2240π - 1260π = 980πcm³

The solid wire made is cylindrical and has a thickness of 2.8cm. This is the diameter. It means that the radius of the wire is 2.8/2 = 1.4cm

Volume of wire = 980πcm³

Applying the volume of cylinder formula, it becomes

980π = π × 1.4² × h

where h = length of wire

h = 980/1.4² = 500cm

3 0

1 year ago