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Elza [17]
2 years ago
7

Determine whether the underlined value is a parameter or a statistic. In a national survey on substance abuse comma Modifying 66

.4 % with underline of respondents who were full dash time college students aged 18 to 22 reported using alcohol within the past month.
Mathematics
1 answer:
Iteru [2.4K]2 years ago
4 0

Answer:

Parameter                                                                                

Step-by-step explanation:

Parameter and statistic:

  • Parameter is a numerical value that describes a population.
  • A sample is a part of the population and always smaller than the population.
  • The statistic is a numerical value that describes a sample.

Population of interest:

College students aged 18 to 22

Parameter:

66.4% reported using alcohol within the past month

Thus, the given is a parameter as it describes a population proportion.

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Find the area of the region that lies inside the first curve and outside the second curve.
marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = \dfrac{1}{2}

\theta = -\dfrac{\pi}{3}, \ \  \dfrac{\pi}{3}

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \  \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \  5^2 d \theta

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \  \theta  d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \   d \theta

A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  \dfrac{cos \ 2 \theta +1}{2}  \end {pmatrix} \ \ d \theta - \dfrac{25}{2}  \begin {bmatrix} \theta   \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}

A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  {cos \ 2 \theta +1}  \end {pmatrix} \ \    d \theta - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}}    \ \ - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{2 \pi}{3} \end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3})  \end {bmatrix} - \dfrac{25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} +   \dfrac{\pi}{3}  \end {bmatrix}- \dfrac{ 25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3}   \end {bmatrix}- \dfrac{ 25 \pi}{3}

A =    \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx
7 0
2 years ago
Which statement is true?<br> GRAPHA<br> GRAPH B
WARRIOR [948]

Answer:

Graph B is correct

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Lacey decides to take her five year old son to the history museum. The price for the child's ticket is 2.75 dollars less than th
Andrei [34K]
If the price for the adult ticket is $2.75 more than the child ticket, the adult ticket would be x + $2.75
3 0
3 years ago
38) The length of a rectangle is 15.6 cm correct to 1 decimal place.
Ede4ka [16]

Answer:

38.75

Step-by-step explanation:

perimeter = 2(15.6+3.8) =38.8

lower bound = the smallest value that would round up to the estimated value =38.75

6 0
3 years ago
What is the value of b2 - 4ac for the following equation? 5x2 + 7x = 6
shtirl [24]
B²-4ac? 

<span>5x²+7x-6 = 0 </span>
<span>the form is ax²+bx+c = 0 </span>

<span>a=5, b=7, c=-6 </span>


<span>The discriminant D = b²-4ac </span>
<span>= 7² - 4(5)(-6) = 49 + 120 </span>
<span>= 169 </span>
5 0
3 years ago
Read 2 more answers
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