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lesya [120]
4 years ago
6

You are told that a 95% confidence interval for a population proportion is (0.3775, 0.6225) What was the sample proportion that

lead to this confidence interval?. Also, what is the size of the sample used.
Mathematics
1 answer:
Maru [420]4 years ago
6 0
The mean of the confidence interval is (0.3775 + 0.6225) / 2 = 0.5. Therefore, the standard deviation of the proportion would have been sqrt[0.5*(1 - 0.5) / n], where n is the sample size. This expression simplifies to sqrt(0.25/n).

A 95% CI has a corresponding z = 1.96, so since the distance from 0.5 to 0.3775 (or 0.6225 to 0.5) is equal to 0.1225. Therefore, if we divide 0.1225 / 1.96 = 0.0625, we get the value of the SD, and this should be equal to sqrt(0.25/n).

0.0625 = sqrt(0.25/n)
n = 64
This means that the proportion was 0.5 and the sample size was 64.
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A cube-shaped hole is cut in a rectangular prism as shown below.
IgorC [24]
Surface area of the prism is 2xy+2xz+2yz 
I think, we can cut hole on the face of the prisma 40x30, and size of the whole will be 5X5X5
hole increases surface area. If side of the cube is "a", then a^2 is the area of the one face of the cube.  
when we are doing the hole, we remove 2 faces and add 4 more faces, so 
 2xy+2xz+2yz-2a^2+4a^2=  2xy+2xz+2yz+2a^2
So, 2*5*40+2*5*30+2*40*30+2*5^2=3150 cm^2
 i hope it helps, it is what i can come up with now



6 0
4 years ago
Read 2 more answers
Can somebody help me
choli [55]
Is it post to be a fraction?

7 0
3 years ago
Read 2 more answers
2-6&gt;-3<br> is this correct
romanna [79]

Answer:

im gonna say no and sorry if my answer is wrong

Step-by-step explanation:

subtract 2-6 = -4

now when you work with negative numbers or integers the bigger number will be the closest to the 0 so it's not correct -3 is bigger than -4

4 0
3 years ago
21. Water that is sprayed upward from a
sleet_krkn [62]

Answer:

  • 2 seconds to maximum height
  • 20 meters maximum height
  • 4 seconds to reach the ground

Step-by-step explanation:

The function can be graphed using a graphing calculator, geometry app, or spreadsheet. One such graph is attached. Often, these tools are capable of identifying extrema and intercepts.

__

<h3>extreme</h3>

The vertex of the graph is reported as (x, y) = (2, 20). This means the maximum height is reached after 2 seconds. That maximum height is 20 meters.

__

<h3>intercept</h3>

The drop is launched from ground level at x = 0 seconds. It returns to ground level at x = 4 seconds.

3 0
2 years ago
If the shaded area is 23cm^2, then what is the smallest possible value of the inner area?
bagirrra123 [75]

Answer:

I suspect it can = 0 when the roots are solved for.

x = 10.44 which is the only positive root. There is another one, but I think it gives a minus number for the white area.

Step-by-step explanation:

There are two areas that are possible given the dimensions of the two rectangles. The trick is to find both of them. and compare.


Step One  

Find the area of the inside rectangle (unshaded area)


Area = (2x - 1)*x Use the distributive property to find the area


Area = 2x^2 - x  


Step Two


Find the area of the outside of the frame


Area = (x + 5)(x + 3) Remove the brackets using FOIL


Area = x^2 + 5x + 3x + 15


Area = x^2 + 8x + 15


Step Three

Find the area of the shaded region


Area shaded = x^2 + 8x + 15 – (2x^2 – x)                  Remove the brackets


Area shaded = x^2 + 8x + 15 – 2x^2 + x                    Combine like terms  


Area shaded = x^2 + 9x + 15 - 2x^2


Area shaded = -x^2 + 9x + 15

Step Four


Find the roots of the quadratic.

a = -1

b = 9

c = 15

Using the quadratic formula, and substituting for a b and c, we get

\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a}  

\text{x = }\dfrac{ -9 \pm \sqrt{9^{2} - 4*(-1)(15 } }{2(-1)}  

\text{x = }\dfrac{ -9 \pm \sqrt{81  + 4*(1)(15 } }{2(-1)}

There  is only 1 value that works for this problem and that is when x = 10.44

4 0
4 years ago
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