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geniusboy [140]

2 years ago

15

Carly purchased 9 and 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pints of ice cream. What is t

he greatest number of guests that Carly can serve?

1 answer:

aksik [14]2 years ago

4 0

Answer: The greatest amount of guest you can serve is 15

Step-by-step explanation: .60=3/5 .60 x 15 = 9 If you do another 3/5 it will be over how much icecream she has

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2 years ago

A fried chicken franchise finds that the demand equation for its new roast chicken product, "Roasted Rooster," is given by p = 4

LUCKY_DIMON [66]

Answer:

1. $q=(\dfrac{45}{p})^{\frac{2}{3}}$

2. $E_d=-\dfrac{2}{3}$

Step-by-step explanation:

The given demand equation is

$p=\dfrac{45}{q^{1.5}}$

where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.

Part 1 :

We need to Express q as a function of p.

The given equation can be rewritten as

$q^{1.5}=\dfrac{45}{p}$

Using the properties of exponent, we get

$q=(\dfrac{45}{p})^{\frac{1}{1.5}}$ $[\because x^n=a\Rightarrow x=a^{\frac{1}{n}}]$

$q=(\dfrac{45}{p})^{\frac{2}{3}}$

Therefore, the required equation is $q=(\dfrac{45}{p})^{\frac{2}{3}}$ .

Part 2 :

$q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}$

Differentiate q with respect to p.

$\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})$

$\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})$

$\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})$

Formula for price elasticity of demand is

$E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}$

$E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}$

Cancel out common factors.

$E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}$

Using the properties of exponents we get

$E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})$

$E_d=-\dfrac{2}{3}(p^{0})$

$E_d=-\dfrac{2}{3}$

Therefore, the price elasticity of demand is -2/3.

3 0

2 years ago