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2 years ago

A caricature artist works 5 days a week, draws 18 portraits per day on

Mathematics

2 answers:

IgorC [24]2 years ago

5 0

Answer:

The answer is 6.

Step-by-step explanation:

APEX APEX APEX!!!!!!

aivan3 [116]2 years ago

3 0

Answer:

Thus our artist now has to draw 24 Portraits a day (hence 6 more portraits per day) if he wants to lower the price from $16 to $12 per portrait and still make the same profit of $1440.

Step-by-step explanation:

Lets analyse the information given in the question for our caricature arist.

18 Portraits per Day Drawn
$16 Per Portait Charged
5 days work in a week

This can tells us the Profit the arist makes in 5 days of work selling 18 portraits for $16 per portrait by multiplying all three values together as:

$Profit = 18_{portraits}*16_{dollars}*5_{days}=1440$ Eqn(1)

Now the question tells us that the artist lowered the price from $16 to $12 dollars and he needs to know the number of portraits he must make now to still make the same profit of $1440 as in Eqn(1). In the first part our uknown was the Profit. In this part our known is the Portraits number (lets call it $p$ ) so Eqn(1) can now be expressed as follow, to obtain $p$ that will still gives as $1440 Profit:

$12_{dollars}*5_{days}*p=1440\\\\60p=1440\\\\p=\frac{1440}{60} \\p=24$

Thus our artist now has to draw 24 Portraits a day (hence 6 more portraits per day) if he wants to lower the price from $16 to $12 per portrait and still make the same profit of $1440.

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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to

nikklg [1K]

Answer:

Part 1)

See Below.

Part 2)

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

Step-by-step explanation:

Part 1)

The linear approximation L for a function f at the point x = a is given by:

$\displaystyle L \approx f'(a)(x-a) + f(a)$

We want to verify that the expression:

$1-36x$

Is the linear approximation for the function:

$\displaystyle f(x) = \frac{1}{(1+9x)^4}$

At x = 0.

So, find f'(x). We can use the chain rule:

$\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)$

Simplify. Hence:

$\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}$

Then the slope of the linear approximation at x = 0 will be:

$\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36$

And the value of the function at x = 0 is:

$\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1$

Thus, the linear approximation will be:

$\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x$

Hence verified.

Part B)

We want to determine the values of x for which the linear approximation L is accurate to within 0.1.

In other words:

$\displaystyle \left| f(x) - L(x) \right | \leq 0.1$

By definition:

$\displaystyle -0.1\leq f(x) - L(x) \leq 0.1$

Therefore:

$\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1$

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between y = 0.1 and y = -0.1) for x values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

$\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)$

4 0

2 years ago

Jenny bought a new car for $25,995. The value of the car depreciates by 16 percent each year. Which type of function could model

motikmotik

Answer: The answer is expensive the car is expensive. JK the answer is c. you can eliminate a and d because the 16 % a year increase so your left with c and b it's not b because of the price so your best answer would have to be c

hoped this helped lol have a good day

6 0

2 years ago

Read 2 more answers

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers have maintained careful records

madreJ [45]

Answer:

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

3 0

2 years ago

A multiple choice question has 18 possible answers, only one of which is correct. Is it "significant" to answer a question cor

yan [13]

Answer:

It is not ''significant''

Step-by-step explanation:

Let's call the event

A : ''Answer a question correctly if a random guess is made''

Now we calculate the probability for the event A

$P(A)=\frac{cases where A occurs}{total cases}$

In the exercise A occurs in only one way and the total cases are the number of possible answers

$Total cases = 18$

$P(A)=\frac{1}{18} =0.0555555$

An event B is ''significant'' if $P(B)\leq 0.05$

$P(A)=0.0555555$

⇒A it is not a ''significant'' event

8 0

2 years ago

Ethel Meyer sells wheelchairs. SHE EARNS AN 11 PERCENT COMMISSION ON THEE FIRST $5,000 AN 14 PERCENT ON ALL SALES OVER $5000.HOW

sergeinik [125]

Ok so Ethel starts off with 11% of $5,000 that is $550 of commission
and 14% on sales above 5,000 for 14,000 all of her commission would be 14% that means she would get $1,000 because 14% of 14,000 is 1,000
hope this helped.

4 0

2 years ago