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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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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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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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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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If Denise wanted to create a function that modeled an exponential function with base of 12 and what exponents were needed to reach specific values, how would she set up her function? f(x) = x12 f(x) = log12x f(x) = 12x f(x) = logx12

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Denise creates the exponential function g(x)=12 ^{x}

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 12 ^{x}=a   (“for what value of x, is 12 to the power of x equal to a?”)

this expression is equivalent to x=log_1_2(a)

(so 12 to the power of x is a, for x=log_1_2_(a))

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:

f(x)=log_1_2(x)  

(example: we want to calculate at which value is  12^{x} equal to 5?
answer: f(x)= log_1_2(5),

check: 12^{log_1_2(5)} =5, which is true, by properties of logarithms)

Answer: log_1_2(x)       (B)

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The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function p = 120i i2 + i + 9 where i is the light intensity (measured in thousands of foot-candles). for what light intensity is p a maximum?

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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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Marissa researched the cost to have custom T-shirts printed by several local and online vendors. She found that each store’s charge for the job could be modeled by a linear function that combined a flat charge for artwork with a per T-shirt rate. Marissa plotted the functions on a coordinate grid and found that two of the functions produced lines that had the same y-intercept. How should Marissa interpret this result? A:Those two vendors charge the same rate per shirt. B:Those two vendors charge the same flat rate for artwork. C:Those two vendors will have the same total cost to produce one shirt. D:Those two vendors will charge the same total cost for any size job.

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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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The long jump record, in feet, at a particular school can be modeled by f(x)= 18.1 + 2.2ln (x+1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 14 years after record started being kept? Round your answer to nearest tenth.

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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 (-infty,infty) i.e. the set of all real numbers.

So, options B and C are discarded.

Since, csc x=frac{1}{sin x} and sec x=frac{1}{cos x}.

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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The height h, in feet, of a projectile t seconds after launch is modeled by the equation h = 32t- 16t^2. How long after does the projectile return to the ground?

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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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Bakersfield, California was founded in 1859 when Colonel Thomas Baker planted ten acres of alfalfa for travelers going from Visalia to Los Angeles to feed their animals. The city’s population can be modeled by the equation 450488-1.jpg, where t is the number of years since 1950. Find the projected population of Bakersfield in 2010. a. 13,415,334 c. 361,931 b. 3087 d. 73,965,796

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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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Write a real world problem that can be modeled 1/2x –2=8

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Answer:  The correct option is (C) y=4x-13.

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

m=dfrac{3-(-1)}{4-3}\\\Rightarrow m=4.

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

y-3=m(x-4)\\Rightarrow y-3=4(x-4)\\Rightarrow y=4x-16+3\\Rightarrow y=4x-13.

Thus, the required rule for the linear function is

y=4x-13.

Option (C) is correct.

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Which of the following can be modeled with an exponential function? Select all that apply. A. Height over time that a football is thrown across the field. B. The cost to attend Universal Studios increases by 1% each year. C. An endangered species population is decreasing by 12% each year. D. The distance a bicyclist travels when cycling a constant speed of 25 mph. E. The population of a town that is growing by 5% each year.

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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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