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erma4kov [3.2K]
4 years ago
9

A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not i

dentify the celebrities. readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly?
Mathematics
2 answers:
ipn [44]4 years ago
7 0
There are 3 options for the celebrities and 3 options for the babies. There is a 1 in 3 chance that a reader guessing at random will guess correctly. You compute the probability by dividing 100 by 3. 100 divided by 3 is 33.33%. Thus, there is a 1 in 3 chance or 33.33% that a reader guessing at random will answer correctly.
Anna35 [415]4 years ago
5 0

The probability of matching the first one correctly is  1/3 .
Then there are only two baby-pix left, so ...
The probability of matching the second one correctly is  1/2 .
Then there's only one baby-pic left, so ...
The probability of matching the third one correctly is  1 .

So the probability of matching all three correctly is

                (1/3) x (1/2) x (1)  =  1/6  =  (16 and 2/3) percent .
 
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An industry demand curve faced by firms in a duopoly is P = 69 - Q, where Q = Q1 + Q2. MC for each firm is 0. How many units sho
emmasim [6.3K]

You first need to establish the benefits function B. For each firm it is equal to the amount produced (q1 for firm 1 and q2 for firm 2) multiplied by the price P, minus cost C. It is

B1 = P.q1 - C1 = (69 - q1 - q2)q1 - C1

B2= P.q2 - C2 = (69 - q1 - q2)q2 - C2

As firma Will maximize benefits we need the derivative in q1 and q2 for firms 1 and 2 respectively. This will give us

69 - 2q1 - q2 = 0

69 - q1 - 2q2 = 0

Note that the derivative of cost is null as marginal cost is null.

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q2= 69 - 2q1

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69- q1 - 138 + 4q1 = 0

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Replacing in the q2 equation:

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7 0
3 years ago
Solve the proportion 15/6 = 10/p
V125BC [204]

Answer:

  p = 4

Step-by-step explanation:

The usually recommended procedure for solving a proportion is to "cross multiply", then divide by the coefficient of the variable. (Solve the remaining one-step equation.)

<h3>Cross multiply</h3>

This means multiply both sides of the equation by the product of the denominators:

  (15/6)(6p) = (10/p)(6p) . . . . "cross multiply"

  15p = 60 . . . . . . simplify

<h3>Second step</h3>

Now, divide by the coefficient of the variable.

  15p/15 = 60/15

  p = 4

The solution is p = 4.

__

<em>Additional comment</em>

If the variable is in the <em>numerator</em> of the proportion, using cross multiplication, you will find that you end up multiplying and dividing by the other denominator. To solve it in that case, you only need to multiply by the denominator under the variable.

__

For example, to solve ...

  2/5 = p/10

you only need to multiply by 10. You don't need to multiply by 50, then divide by 5.

__

Any proportion can be written 4 ways:

  \dfrac{a}{b}=\dfrac{c}{d}\ \Leftrightarrow\ \dfrac{a}{c}=\dfrac{b}{d}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{d}{c}\ \Leftrightarrow\ \dfrac{c}{a}=\dfrac{d}{b}

This suggests another strategy: invert the whole proportion, then solve it as one with p in the numerator:

  6/15 = p/10   ⇒   p = 10(6/15) = 4

4 0
2 years ago
Read 2 more answers
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