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The profit a company makes from producing x tabletops is modeled by the equation P(x) = 480x – 2x^2. For what number of tabletops does the company make a profit of $0? A. 100 B. 120 C. 240 D. 480

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# Tag: modeled

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The minimum and maximum temperature on a cold day in Lollypop Town can be modeled by the equation below:2|x − 6| + 14 = 38What are the minimum and maximum temperatures for this day? A:x= -9,x=21 B:X= -6,X=18 C:X=6,X= -18 D:no solution

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assume she want to find for what value of x, her function reaches the value, 3, or 8.2, or any value a (larger than 0)

so she shants to solve (“for what value of x, is 12 to the power of x equal to a?”)

this expression is equivalent to ,

(so 12 to the power of x is a, for x=)

we can generalize this result by creating a function f.

In this function we enter x, the specific value we want to reach. f will calculate the exponent needed, in the following way:

(example: we want to calculate at which value is equal to 5?

answer: f(x)= ,

check:, which is true, by properties of logarithms)

Answer: log_1_2(x) (B)

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The given function is:

P = 120 i / (i^2 + i + 9)

or

P = 120 i (i^2 + i + 9)^-1

The maxima point is obtained by taking the 1st

derivative of the function then equating dP / di = 0:

dP / di = 120 (i^2

+ i + 9)^-1 + (-1) 120 i (i^2 + i + 9)^-2 (2i + 1)

setting dP / di =0 and multiplying whole equation by (i^2

+ i + 9)^2:

0 = 120 (i^2 + i + 9) – 120i (2i + 1)

Dividing further by 120 will yield:

i^2 + i + 9 – 2i^2 – i = 0

-i^2 + 9 =0

i^2 = 9

**i = 3 (ANSWER)**

Therefore P is a maximum when i = 3

Checking:

P = 120 * 3 / (3^2 + 3 + 9)

P = 17.14

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**Answer:**

C. Yes, because the population values appear to be normally distributed.

**Step-by-step explanation:**

Given is a graph which shows the distribution of values of a population

The graph has the following characteristics

i) Bell shaped

ii) symmerical about mid vertical line

iii) Unimodal with mode = median =mean

iv) As x deviates more from the mean probability is decreasing and also curve approaches asymptotically the x axis

Hence we find that the curve is a distribution of normal

Option C is right

C. Yes, because the population values appear to be normally distributed.

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**Answer:**

A. y=sec x

D. y= csc x

**Step-by-step explanation:**

We have that,

Range of the functions is the set of all real numbers greater than or equal to 1 or less than or equal to -1.

As, we know that,

Range of the functions, y = tanx and y = cotx is i.e. the set of all real numbers.

So, options B and C are discarded.

Since, and .

Thus, their range will be greater than the the range of y = sinx and y = cosx.

Now, as it is known that the range of the functions y = sinx and y = cosx is [-1,1].

**Then, the range of y=sec x and y= csc x is the set of all real numbers greater than or equal to 1 or less than or equal to -1.**

Hence, options A and D are correct.

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Assuming the growth is of 1st order, we can

start using the formula for rate of 1st order reaction:

dN / dt = k * N

Rearranging,

dN / N = k dt

Where N = amount of sample, k = growth factor, t = time

Integrating the equation from N = Ni to Nf and t = ti to

tf will result in:

ln (Nf / Ni) = k (tf – ti)

Finding for the growth factor k:

k = ln (Nf / Ni) / (tf – ti)

k = ln (1.022 Ni / Ni) / 1 year

k = 0.02176 / year

The population in 2011 is:

ln (Nf / Ni) = k (tf – ti)

ln (Nf / 25000) = (0.02176 / year) * (2011 – 2006)

**Nf = 27,873.7 = 27,874**

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**Answer:**

Here, **c** represents the **cost of one greeting cards**,

Since, each card costs same,

Thus, the cost of 3 greeting cards = 3 × the cost of one greeting cards

= 3 × c

= 3c

According to the question,

The cost of 3 greeting cards = $ 12.69

⇒** 3c = 12.69**

**Which is the required equation **that represents the given situation,

After solving this,

We get,

**c = 4.32**,

Thus, the cost of one card is $ 4.32.

**Which is the required solution**.

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**Answer: The correct option is (C) **

**Step-by-step explanation: **We are given to** write a rule for the linear function given in the graph.**

Since the graph is a straight line, so we are to find** the equation of the line to find the rule.**

**From the graph, we note that**

the **points (3, -1) and (4, 3) lie on the straight line.**

So, **the slope of the line will be**

Since the line passes through the point (4, 3),** so the equation of the line is given by**

**Thus, the required rule for the linear function is**

**Option (C) is correct.**

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**Answer: **The answer is** (B), (C) and (E).**

**Step-by-step explanation: **We are given five options out of which we are to select all those which can be modelled by exponential functions.

We can see that the options (A) and (D) cannot be modelled by exponential functions, because the rate of increasing or decreasing are not calculating compoundly.

But, in options (B), (C) and (E), the rate is increasing or decreasing each year.So, these three can be modelled by exponential functions.

In fact, the options (B) and (E) will show exponential growth because the number is increasing and option (C) will show exponential decay as the number is decreasing.

**Thus, (B), (C) and (E) are the correct options.**

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