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3 years ago

12

Twenty-five teenagers were surveyed about food. Five more preferred pizza than steak. Write and solve system of equations to fin

d out how many preferred pizza.

1 answer:

viktelen [127]3 years ago

6 0

Hope this helps! I can resubmit if my hand writing is too bad.

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An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let

Advocard [28]

Answer:

$P(t)=3,000,000-3,000,000e^{0.0138t}$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

<em>P(0) = 0 and P(50) = 1,500,000 </em>

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The <em>integrating factor </em>is

$e^{Kt}$

Multiplying both sides of the equation by the integrating factor

$e^{Kt}P'(t)+e^{Kt}KP(t)= e^{Kt}3,000,000*K$

Hence

$(e^{Kt}P(t))'=3,000,000Ke^{Kt}$

Integrating both sides

$e^{Kt}P(t)=3,000,000K \int e^{Kt}dt +C$

$e^{Kt}P(t)=3,000,000K(\frac{e^{Kt}}{K})+C$

$P(t)=3,000,000+Ce^{-Kt}$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

so

$e^{-50K}=\frac{1}{2}\Rightarrow K=-\frac{log(0.5)}{50}=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^{0.0138t}$

5 0

2 years ago

Of the following options, what could be a possible first step in solving the equation 3x − 1 = 2x + 4? Combining like terms, 3x

faust18 [17]

<span>Subtracting 2x from both sides of the equation would be a reasonable first step in solving this equation as it properly combines like terms to the left side of the equation. It quickly shows that the next step would be adding 1 to both sides of the equation, which would have us arrive at the answer of x = 5.</span>

8 0

2 years ago

Read 2 more answers

What is 6 divied 192 please show work

suter [353]

The problem presented with the word used as "divied" is very tricky and misleading to the point that it might create an understanding.

So we will approach this is in two ways.

If this was meant to be "divided by" then it would look like this:
6 / 192

If this was meant to be "divided to" then it would look like this:
192 / 6

Let us first solve for the first possible problem:
6 / 192 = ?
0.0312

0.0312 would be the answer.

Let us then solve for the second possible problem:
192 / 6 = ?
32 = ?

32 would be the answer.

So 0.0312 and 32 would be two possible answers to this problem.

4 0

2 years ago

Read 2 more answers

Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three

icang [17]

Answer: No

Step-by-step explanation:

According to triangle inequality theorem which state that: the sum of any 2 sides of a triangle must be greater than the measure of the third side.

Now let's test the given parameters if they obey this theorem

4 inches, 5 inches and 1 inch

4 + 5 = 9

9 > 1 correct

5 + 1 = 6

6 > 4 correct

4 + 1 = 5

5 not > 5 wrong

Therefore he won't be able to create the triangular component with these toothpicks without modifying any of the lengths

3 0

2 years ago

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Find the area, a rectangle with a length of 4 cm and a width of 2.5 cm

Brums [2.3K]

Answer:

10

Step-by-step explanation:

4x2.5=10CM2

the area of a rectangular =width multiply its length

5 0

7 months ago

Read 2 more answers