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Lena [83]
2 years ago
14

Determine the point estimate of the population proportion, the margin of error

Mathematics
1 answer:
ahrayia [7]2 years ago
8 0

Answer:

\hat p=0.645\\\\ME=0.233\\\\x=645 \ individuals

Step-by-step explanation:

-Given the boundaries as 0.412 and 0.878

-\hat p is the point estimate for the population proportion and is calculated as follows:

\hat p=\frac{Upper \ Bound+Lower \ Bound}{2}\\\\=\frac{0.878+0.412}{2}\\\\=0.645\\\\

#The margin of error, ME can be calculated for the confidence intervals using the formula:

ME=\frac{Upper \ Bound-Lower \ Bound}{2}\\\\=\frac{0.878-0.412}{2}\\\\=0.233

#The number of individuals in the sample is the product of the point estimate and population size:

\hat p=\frac{x}{n}\\\\x=\hat pn\\\\=0.645\times 1000\\\\=645

Hence, there are 645 individuals in the sample.

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Give triangle ABC is a right triangle, and angle A is the right angle. If sin(B)=3/5, find the cos(B).
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Cos B = 4/5

Step-by-step explanation:

From the question given above, the following data were obtained:

Sine B = 3/5

Cos B =?

Recall:

Sine B = Opposite / Hypothenus

Sine B = 3/5

Therefore,

Opposite = 3

Hypothenus = 5

Next, we shall determine the Adjacent. This can be obtained as follow:

Opposite = 3

Hypothenus = 5

Adjacent =?

Hypo² = Adj² + Opp²

5² = Adj² + 3²

25 = Adj² + 9

Collect like terms

Adj² = 25 – 9

Adj² = 16

Take the square root of both side

Adj = √16

Adjacent = 4

Finally, we shall determine Cos B. This can be obtained as follow:

Hypothenus = 5

Adjacent = 4

Cos B =?

Cos B = Adjacent / Hypothenus

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2 years ago
Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nea
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ANHL player's labor negotiating committee is to be selected from 8 player representatives from the Eastern Conference and 7 play
cestrela7 [59]

Answer:

21 / 143

Step-by-step explanation:

Given that:

Number of Eastern conference reps = 8

Number of western conference rep = 7

Probability of selecting 3 from Eastern reps and 2 from western reps

Probability = required outcome / Total possible outcomes

Total possible outcomes:

selection to be made = 3+ 2 = 5

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Total possible outcomes

Using combination formula :

nCr = n! / (n-r)!r!

15C5 = 15! / 10!5! = (15 * 14 * 13 * 12 * 11) / (5*4'3*2*1) = 360360 / 120 = 3003

Total possible outcomes = 3003

Required outcome :

8C3 * 7C2

8C3 = 56 ; 7C2 = 21

8C3 * 7C2 = 56 * 21 = 1176

required outcome / Total possible outcomes

= 1176 / 3003

= 21 / 143

6 0
3 years ago
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