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tia_tia [17]
3 years ago
13

Jack plotted the graph below to show the relationship between the temperature of his city and the number of ice cream cones he s

old daily:
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points)

Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)

Mathematics
2 answers:
Inessa05 [86]3 years ago
8 0

#1 There is a positive correlation between the temperature and the amount of ice cream sold. This means that as the temperature increases the amount of ice cream also increases.

 #2 For the best fit you must calculate the slope between two points that are more-or-less representative of the entire graph.  In this case it seems to have already done this with certain points so if you take the points (15,35) and (0,5) you can calculate the slope between these two points which is m=(35-5)/(15-0)=30/15=2.  So the best fit slope for this particular case would be two and you would just draw a line through the graph at approximately the middle of the dots to best represent all of the data.

fredd [130]3 years ago
5 0

A) As the temperature rises more ice cream cones are bought.

B) To make a line of best fit, you need to have a line that best represents the data so it should go through as many points as possible. Let's find the slope. First, I need to pick to points I will pick 5,15 and  10,25 so let's subtract the x and we get 5 and if we subtract the y we get 10. So now we have 5,10 we need to find the y-intercept.

It is 5 so the equation is y= 10/5 + 5

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Kala, Deandre, and Eric have a total of $119 in their wallets, Kala has $6 more than Deandre. Eric has 3 times what kala has. Ho
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Eric = 3(x+6)
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4 0
2 years ago
What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

A_s=\frac{\theta}{360}*\pi r^2 where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

A_s=\frac{60}{360}*\pi (\sqrt{3})^2 which simplifies a bit to

A_s=\frac{1}{6}*\pi(3) which simplifies a bit further to

A_s=\frac{1}{2}\pi which of course is the same as

A_s=\frac{\pi}{2}

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \frac{\sqrt{3} }{2}. Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

A=\frac{1}{2}bh. There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2 which simplifies to

3=h^2+\frac{3}{4} and

3-\frac{3}{4}=h^2 and

\frac{12}{4} -\frac{3}{4} =h^2 and

\frac{9}{4} =h^2

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

A=\frac{1}{2}(\sqrt{3})(\frac{3}{2}) which simplifies to

A=\frac{3\sqrt{3} }{4}

Therefore, the area in terms of pi for that little segment is

A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}, choice A.

8 0
3 years ago
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