a grocery store sells a bag of 4 lemons for $0.79. Which pricing option would result in the same unit price for each lemon

Suppose the Sunglasses Hut Company has a profit function given by P ( q ) = − 0.02 q 2 + 5 q − 30 , where q is the number of tho

Andrew [12]

Answer:

A) Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) The actual maximum profits that can be expected is 180 thousands dollars.

Step-by-step explanation:

Given : Suppose the Sunglasses Hut Company has a profit function given by $P(q)=-0.02q^2+4q-20$

where, q is the number of thousands of pairs of sunglasses sold and produced and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses.

To find :

A) How many pairs of sunglasses (in thousands) should be sold to maximize profits?

Profit is $P(q)=-0.02q^2+4q-20$

Compare with general quadratic equation $ax^2+bx+c$

a=-0.02, b=4, c=-20

The maximum value of quadratic function is at $x=-\frac{b}{2a}$

So, maximum profit occur at q is given by,

$q=-\frac{4}{2(-0.02)}$

$q=\frac{4}{0.04}$

$q=100$

i.e. 100 thousand pair of sunglasses.

Pairs of sunglasses should be sold to maximize profits is 100 thousand.

B) What are the actual maximum profits (in thousands) that can be expected?

Maximum profit occurs at q=100 thousand pairs is given by,

$P(100)=-0.02(100)^2+4(100)-20$

$P(100)=-0.02\times 10000+400-20$

$P(100)=180$

The actual maximum profits that can be expected is 180 thousands dollars.

7 0

2 years ago

Which measure is the largest? 1.2 km, 120,600 cm, 1,220,000 mm, 120 meters

Margarita [4]

The first thing you should know to answer this question is the following conversions:
1Km = 1000m
1m = 1000mm
1Km = 1000000mm
1m = 100cm
By making the conversions to the same unit, we can know what measure is greater:
1.2Km = 1200m
120600cm = 1206.00m
1220000mm = 1220m
120m = 120m
Answer
The biggest measure is
1220000mm = 1220m

6 0

2 years ago

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were m

aalyn [17]

This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

Answer: The initial deposit is $10,001

Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

Pv = present value

i = the interest rate

t = the time in years

e = a mathematical constant that is usually approximated by 2.7183

In this case, the Fv = 13,231.30

i = 3.5% or 0.035

t = 8 years

e = 2.7183

Pv = ? (The unknown variable).

13,231.30 = Pv × [2.7183^(0.035 × 8)]

13,231.30 = Pv × [2.7183^(0.28)]

13,231.30 = Pv × 1.323

Pv = 13,231.30/1.323

Pv = $10000.98

= $10,001

Therefore the initial deposit is $10,001

8 0

2 years ago

Which function shows a fabric with a price of $1.25 per square yard? A table showing Price of Fleece with five columns and two r

morpeh [17]

Answer:

Answer D is correct

Step-by-step explanation:

1: (1, 1.25) (2, 2)

So you have your first problem, your first number is x1 while your next number in the first set of parenthesis is y1. Your next set of parenthesis will be x2 and y2 like this:

x1 y1 x2 y2

(1, 1.25) (2, 2)

Then you set up a equation like this!

x2-x1

-------Divided

y2-y1

so we now plug in the numbers and get this

2-1.25 = 0.75

--------- ---- or 0.75 BUT not 1.25 like we need!

2-1 = 1

8 0

2 years ago