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3 years ago

THE CYLINDRICAL CAN CONTAINS 1500 CM3 OF COCUNUT MILK. THE HEIGHT OF THE CAN IS 15 CM. CALCULATE THE RADIUS OF THE CAN.

1 answer:

8 0

The equation for the volume of a cylinder is pir^2h or 3.14*radius squared* height.
We can switch the equation around to find r^2=v/3.14*h
Now insert the known values.
R^2=1500/3.14*15
Solve
R^2=1500/47.1
R^2=31.8
R=5.6
Hope this helps!

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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 w

irina1246 [14]

Answer:

A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students who eat cauliflower

n = sample of students

p = population proportion of students who eat cauliflower

<em>Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.</em>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;

$n = n + Z^{2}__(\frac{_\alpha}{2})$

n = $24 + 1.96^{2}$ = 27.842

$\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}$ = $\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}$ = 0.141

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ , $0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ ]

= [0.012, 0.270]

Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.

7 0

3 years ago

If x is an even integer and y is an odd integer than x + y is a rational number. A) Always True B) Sometimes True C) Usually Tru

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A) Always TRue
Both integers are rational, so the sum must be rational

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3 years ago

When John bought his new computer he purchased an online computer help service. The help service has a yearly fee of 25.50 and a

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First you need to find out how much he spends each session which would be___?

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3 years ago

Becky is planning a 2 100-mile trip to St. Louis to visit a college. Her car averages 30 miles per gallon

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Answer:

Step-by-step explanation:

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2 years ago

In this polygon, all angles are right angles. What is the area of this polygon? Enter your answer in the box. ft² Polygon in the

Serga [27]

The area of the L shaped figure is 258 ft²

Area is the amount of space occupied by a two dimensional figure.

The area of a rectangle is given by:

Area = length * breadth

From the diagram, the area is:

Area = [18 * (21 - 12)] + (12 * 8) = 258 ft²

The area of the L shaped figure is 258 ft²

Find out more on Area at: brainly.com/question/25292087

5 0

2 years ago

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