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Elis [28]
3 years ago
7

A pizzeria owner wants to know which pizza topping is least liked by her customers so she can take it off the menu. She used fou

r different methods to find this information.
Method 1: The owner asked every third customer to rate all the pizza toppings in order of preference.
Method 2: The owner gave all customers a toll-free telephone number and asked them to phone in their topping preferences.
Method 3: The owner asked the preferences of every other teenager who entered the pizzeria.
Method 4: The owner reviewed the pizzeria’s complaint cards and assessed all complaints related to pizza toppings.

Which method is most likely to give a valid generalization?
Mathematics
1 answer:
Kaylis [27]3 years ago
8 0

Answer:

I suggest method 1 because it is unbiased and systematic.  

The second method requires a lot on the initiatives of customers, and likely to have extreme cases only (liked very much or disliked very much).  

The third is biased towards teenagers, which may not be the only category of customers who ordered pizzas.

Again, the fourth requires initiative from the customer, so biased towards customers who had something to say.

Step-by-step explanation:

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XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3
nataly862011 [7]
<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = \frac{1}{2} x b x h      -------------(i)

Where;

A = 18\sqrt{3}

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18\sqrt{3} =  \frac{1}{2} x b x 6

18\sqrt{3} =  3b

<em>Divide through by 3</em>

6\sqrt{3} =  b

Therefore, b = XZ = 6\sqrt{3}

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}

\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}

\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}

\frac{1}{12}  = \frac{1}{2|OZ|}

\frac{1}{6} = \frac{1}{|OZ|}

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

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