The top three prices for works of art sold at auction in 2013 totaled $306.7 million. These three works of art were a sculpture, a painting, and a photograph. The
selling price of the painting was $50.5 million more than that of the photograph. Together, the painting and the photograph sold for $17.1 million more than the
sculpture. What was the selling price of each work?

Answer:

A. 2(2e + 4f + 10g)

Step-by-step explanation:

Answer:

Part 1)

See Below.

Part 2)

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Step-by-step explanation:

Part 1)

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

[tex]\displaystyle L \approx f'(a)(x-a) + f(a)[/tex]

We want to verify that the expression:

[tex]1-36x[/tex]

Is the linear approximation for the function:

[tex]\displaystyle f(x) = \frac{1}{(1+9x)^4}[/tex]

At x = 0.

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

[tex]\displaystyle f'(x) = -4(1+9x)^{-4-1}\cdot (9)[/tex]

Simplify. Hence:

[tex]\displaystyle f'(x) = -\frac{36}{(1+9x)^{5}}[/tex]

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

[tex]\displaystyle f'(1) = -\frac{36}{(1+9(0))^5} = -36[/tex]

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

[tex]\displaystyle f(0) = \frac{1}{(1+9(0))^4} = 1[/tex]

Thus, the linear approximation will be:

[tex]\displaystyle L = (-36)(x-(0)) + 1 = 1 - 36x[/tex]

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:

[tex]\displaystyle \left| f(x) - L(x) \right | \leq 0.1[/tex]

By definition:

[tex]\displaystyle -0.1\leq f(x) - L(x) \leq 0.1[/tex]

Therefore:

[tex]\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1[/tex]

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:

[tex]\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)[/tex]

Answer:

[tex]x = 12[/tex]

Step-by-step explanation:

Given

[tex]\angle D = 9x + 5[/tex]

[tex]\angle F = 13x -43[/tex]

Required

Find x

To find x, we make use of:

[tex]\angle D =\angle F[/tex] --- opposite angles of a parallelogram

So, we have:

[tex]9x + 5 =13x -43[/tex]

Collect like terms

[tex]9x - 13x = -5-43[/tex]

[tex]-4x = -48[/tex]

Divide by -4

[tex]x = 12[/tex]

Answer:

Option C is correct

Step-by-step explanation:

[tex]log( {10}^{3} )[/tex]

[tex]3 \: log \: (10)[/tex]

[tex]3×1[/tex]

[tex]3[/tex]

Answer:

i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one

and there you go thats your graph

Step-by-step explanation:

Answer:

I have no clue my bad bro.

Answer:

a) 0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.

b) 0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

Question a:

Event A: Jumbo

Event B: Business

60% of its capacity is provided on jumbo jets.

This means that [tex]P(A) = 0.6[/tex]

On jumbo jets, 30% of the passengers are on business

This means that [tex]P(B|A) = 0.3[/tex]

Desired probability:

We want to find [tex]P(A \cap B)[/tex], so:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.6*0.3 = 0.18[/tex]

0.18 = 18% probability a randomly chosen business customer flying with Global is on a jumbo jet.

b) What is the probability a randomly chosen non-business customer flying with Global is on an ordinary jet?

Event A: Ordinary

Event B: Non-business

60% of its capacity is provided on jumbo jets.

So 100 - 60 = 40% are ordinary, which means that [tex]P(A) = 0.4[/tex]

On ordinary jets 25% of the passengers are on business.

So 100 - 25 = 75% are non-business, that is [tex]P(B|A) = 0.75[/tex]

Desired probability:

We want to find [tex]P(A \cap B)[/tex], so:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.75*0.4 = 0.3[/tex]

0.3 = 30% probability a randomly chosen non-business customer flying with Global is on an ordinary jet.

Answer:

Expression: 7+7+9.5+6+9.5

Evaluation: 39 cm

Step-by-step explanation:

Let's write the numerical expression for the figure to the right. The perimeter is the addition of all sides of the figure. Therefore, we write 7+7+9.5+6+9.5 for our expression.

Now, to evaluate the expression, we just add them together. 7+7+9.5+6+9.5=39 cm.

Answer: 18/25 chapters / hour

Step-by-step explanation:

Concept:

Here, we need to know the idea of unit rate.

A unit rate is a rate with 1 in the denominator.

In simple words, the unit rate is something per one thing. For example, when you go to a store, you bought a book that is priced at $10. In actually meaning, it is $10 per book, or $10/book.

Solve:

Given formula

Unit rate = Number of chapters / Hours

Substitute the value into the formula

Unit rate = (3/5) / (5/6)

Convert to multiplication by taking the reciprocal of the divisor

Unit rate = (3/5) · (6/5)

Numerator times numerator / denominator times denominator

Unit rate = (3 × 6) / (5 × 5)

Unit rate = 18 / 25 chapter / hour

Hope this helps!! :)

Please let me know if you have any questions

The unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.

To calculate the unit rate, we're trying to find out how much of something (in this case, chapters) happens in a single unit of another thing (time, in hours).

In this scenario, Maria reads 3 out of 5 chapters in 5 out of 6 hours. To find the unit rate, we divide the chapters read (3/5) by the time taken (5/6 hours):

Unit Rate = Chapters Read / Time Taken

= (3/5) / (5/6)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

Unit Rate = (3/5) * (6/5)

= (3 * 6) / (5 * 5)

= 18 / 25

So, the unit rate is 18/25 chapters per hour. This means Maria is reading at a rate of 18/25 chapters in one hour.

Learn more about unit rate at https://brainly.com/question/19493296

#SPJ3

Answer: 12%

Step-by-step explanation:

95,000-83,600=11,400

(11,400/95000)(100) = 12%

The percentage reduction in the price of the car is 12%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here: Original price of car=95000 and Selling price=83600

Thus the reduction in price= 95000-83600

                                            =11400

Thus percentage reduction in the price of the car is

= 11400/95000 × 100

=12%

Hence, The percentage reduction in the price of the car is 12%

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ2

Answer: 15328

Step-by-step explanation:

The following can be deduced from the information given:

N = 20000

μ = 80

σ = 11

P(X>72) = 1 - P (X<72)

= 1 - P(Z < 72-80/11)

= 1 - P(Z < -8/11)

= 1 - P(Z < 0.7272)

= 1 - 0.2336 = 0.7664

Therefore, the number of students that were better than Lingard n(X > 72) will be:

= 20000 × 0.7664

= 15328

Answer:

Can you select multiple answers to this question? then option A, B and C all three applies, if only one the go for option C, since that's the major change happens to the parent function

Answer:

u^2- 18u +81 = (u-9)^2

Step-by-step explanation:

u^2- 18u +

Take the u coefficient

-18

Divide by 2

-18/2 = -9

Square it

(-9)^2 = 81

u^2- 18u +81 = (u-9)^2

Answer:

The blank should contain 81

Step-by-step explanation:

E = u^2 - 18u + (-18/2)^2

E = (u^2 - 18u + 9^2)

E = (u - 9)^2

To be perfectly correct what you have there is a perfect square, but you need to subtract out (9/2)^2 to make it a valid statement.

E = (u - 9)^2 - 81

Answer:

The butter for one portion cost $ 0.375.

Step-by-step explanation:

Given that you buy butter for $ 3 a pound, and one portion of onion compote requires 2 oz of butter, to determine how much does the butter for one portion cost, the following calculation must be performed:

2 oz = 0.125 lb

1 = 3

0.125 = X

3 x 0.125 = X

0.375 = X

Therefore, the butter for one portion cost $ 0.375.

Answer:

∡A =41°

~~~~~~~~~~~~

BC=21

~~~~~~~~~~~~~~

sin(24)/AC=sin(41)/21

AC=13

~~~~~~~~~~~~~~

sin(115)/AB=sin(41)/21

AB=29

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

i donno  

Step-by-step explanation:

i

Step-by-step explanation:

X= - 1

X=0

X=4/3

X=3

We solve for x by simplifying both sides of the equation, then isolate the variable.

Answer :

C (x=4/3)

Answer:

d. the current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

Step-by-step explanation:

Mean was of 8 hours, test if it has changed:

At the null hypothesis, we test if it has not changed, that is, the mean is still of 8, so:

[tex]H_0: \mu = 8[/tex]

At the alternative hypothesis, we test if it has changed, that is, the mean is different of 8, so:

[tex]H_1: \mu \neq 8[/tex]

Using a 95% confidence interval of (7.7, 9.3), our conclusion is that:

8 is part of the confidence interval, which means that the study does not provide evidence that the mean has changed, and the correct answer is given by option d.

Step-by-step explanation:

jlejej

are u using chrome os

Answer:

Step-by-step explanation:

I think you got it correct. The reciprical of this function is y = x.

Answer:

The Cost Price of the Almirah Is 4000

Answer:

The answer is "Option D"

Step-by-step explanation:

In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.

Answer:

Step-by-step explanation:

I answered this question in question #24285520

Answer:

Step-by-step explanation:

Total number of chocolate boxes that can be produced: x+y Answer

≤

Answer

800

Restrictions based on demand of each: y Answer

≤

Answer

1/2

x

Maximum amount of white chocolate production: y Answer

≤

Answer

200

Minimum amount of milk chocolate production: x Answer

≥

Answer

0

Minimum amount of white chocolate production: y Answer

≥

Answer

0

Vertices of the feasible region: (0,0)(400, Answer

200

)( Answer

600

, Answer

200

)( Answer

800

,0)

Optimization equation: Profit = Answer

2.25

x+ Answer

2.5

y

Your maximum profit is $ Answer

1850

. You should produce Answer

600

boxes of milk chocolate and Answer

200

boxes of white chocolate.

Answer:

This variation is a source of

response error.

Step-by-step explanation:

A response error shows the lack of accuracy in the customer responses to the survey questions.  A response error can be caused by a questionnaire that requires framing improvements, misinterpretation of questions by interviewers or respondents, and errors in respondents' statements.  Some responses are influenced by the answers provided to previous questions, which introduces response bias.

(-1;2;-3)

а, b, c

~~~~~~

Answer:

300

Step-by-step explanation:

A significant figure is the most important (largest) number you can round it to.

As it wants 1 significant figure, you count 1 to the left and round the 4 down.

Hope this helps :)

Answer:

Z = 1

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

[tex]\mu = 100, \sigma = 18[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{106 - 100}{6}[/tex]

[tex]Z = 1[/tex]

So Z = 1 is the answer.

Solution :

Here the probability that exactly 28 out of 304 students will not graduate on time. That is

P (x = 28)

By using the normal approximation of binomial probability,

[tex]$P(x=a) = P(a-1/2 \leq x \leq a+1/2)$[/tex]

∴ [tex]$P(x=28) = P(28-1/2 \leq x \leq 28+1/2)$[/tex]

                   [tex]$=P(27.5 \leq x \leq 28.5)$[/tex]

That is the area between 27.5 and 28.5

Therefore, the correct option is (e). Area between 27.5 and 28.5

Answer:

D. 77

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The population standard deviation is estimated to be $300

This means that [tex]\sigma = 300[/tex]

If a 98% confidence interval is used and the maximum allowable error is $80, how many cardholders should be sampled?

This is n for which M = 80. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]80 = 2.327\frac{300}{\sqrt{n}}[/tex]

[tex]80\sqrt{n} = 2.327*300[/tex]

[tex]\sqrt{n} = \frac{2.327*300}{80}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*300}{80})^2[/tex]

[tex]n = 76.15[/tex]

Rounding up:

77 cardholders should be sampled, and the correct answer is given by option d.