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4 years ago

Express the interval

1 answer:

6 0

Using inequality for the give interval which states that :
A function lies in an open interval from -2 to 6.
Hence,we can rewrite it as :

-2 < x < 6

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When the admission price for a baseball game was $5 per ticket, 35,000 tickets were sold. When the price was raised to $6, only

zysi [14]

The profit function is P(x) = ( - x² / 5000 ) + 11.9x - 95000.

35,000 baseball game tickets were sold at $5 per ticket.

When the price is raised to $6, then 30,000 tickets were sold.

The variable and fixed costs for the ballpark owners are $0.10 and $95,000 respectively.

Let's say x is the number of tickets sold, and P is the profit.

Then,

P = ax + b

At P = 5,

5 = (35000)a + b ---------(1)

At P = 6,

6 = (30000)a + b --------(2)

Subtracting (2) from (1),

5 - 6 = (35000)a + b - (30000)a - b

- 1 = 5000(a)

a = ( - 1/5000)

So if a = ( - 1/5000),

Then,

5 = (35000)a + b

5 = (35000)( - 1 / 5000 ) + b

5 = - 7 + b

b = 12

Therefore,

P(x) = ( - x /5000) + 12

Now, the profit function is:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Now, R(x) = xp(x)

R(x) = x[ ( - x/5000) + 12]

R(x) = ( - x² / 5000 ) + 12x

The fixed cost is F(x) = $95000

Hence, the costs will be:

C(x) = 95000 + (0.10)x

Therefore the profit function is:

P(x) = R(x) - C(x)

P(x) = ( - x² / 5000 ) + 12x - 95000 - (0.10)x

P(x) = ( - x² / 5000 ) + 11.9x - 95000

Learn more about profit function here:

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7 0

1 year ago

A chef uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors

Westkost [7]

Answer:

The chef uses 5452.8 grams of butter each day.

Step-by-step explanation:

Given:

Chef use 12 pounds of butter each day.

To find the amount of butter in grams used by chef each day.

Conversion units:

1 pound = 16 ounces

1 ounce = 28.4 grams

Solution:

We need to convert 12 pounds of butter in grams of butter.

We will apply unitary method to carry out the conversion.

If 1 pound = 16 ounces

Then, 12 pounds = $12\ pounds\times\frac{16\ ounces}{1\ pound}= 192\ ounces$

If 1 ounce = 28.4 grams

Then, 192 ounces = $192\ ounces \times \frac{28.4\ grams}{1\ ounce} = 5452.8\ grams$

Thus, the chef uses 5452.8 grams of butter each day.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=f%28x%29%3D%281-0.08%29%5E%7B%5Cfrac%7B1%7D%7B12%7D%20%7D%20%5E%7B%2812t%29%7D" id="TexFormula

oksano4ka [1.4K]

Answer:

See Below.

Step-by-step explanation:

We have:

$\displaystyle f(x)=(1-0.08)^{\frac{1}{12}(12t)}$

First, we can subtract within the parentheses:

$f(x)=(0.92)^{\frac{1}{12}(12t)}$

By the properties of exponents:

$f(x)=((0.92)^\frac{1}{12})^{12t}$

Approximate. Use a calculator:

$f(x)\approx (0.993)^{12t}$

Notes:

0.993 is only an approximation, hence the approximately equal sign.

I'm not given the context of the problem, but it's simpler to just simplify in the exponent like so (the fractions cancel):

$\displaystyle f(x)=(1-0.08)^{\frac{1}{12}(12t)}=(0.92)^t$

Full Problem:

The value of Sara's car decreases at a rate of 8% per year.

We will use the exponential decay formula with a set time, given by:

$f(x)=a(r)^{x/d}$

Where a is the initial value, r is the rate, x is the time that has passed (dependent on d), and d is the amount of time for one decrease.

For this problem, we can ignore the initial value.

And since the value decreases at a rate of 8% per year, r = 0.92 (we acquire this from 1 - 0.08).

Part 1) Per Month:

Since it decreases per month, d = 12.

$f(x)=(0.92)^{x/12}$

Approximate:

$f(x)=((0.92)^{1/12})^x\approx(.993)^x$

In this case, x is measured in months.

Part 2) Per Week:

Since it decreases per week, d = 52.

$f(x)=(0.92)^{x/52}$

Approximate:

$f(x)=((0.92)^1/52)^x\approx (.998)^x$

In this case, x is measured in weeks.

Part 3) Per Day:

So, d = 365.

$f(x)=(0.92)^{x/365}$

Simplify:

$f(x)=((0.92)^{1/365})^x\approx(.999)^x$

In this case, x is measured in days.

Part 4)

So, as d increases, our r increases as well.

Therefore, the smaller the time interval (from months to weeks to days), the higher our rate of decrease is.

8 0

3 years ago

The given figure has been reflected over the line y = x. Which picture shows the figure before it was reflected?

NikAS [45]

Can you show the pictures

7 0

3 years ago

Read 2 more answers

Write an equation of the line that passes<br> through (4, 1) and has a slope of -2.

DanielleElmas [232]

Answer:5

Step-by-step explanation:

3 0

3 years ago