The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set.

Final answer:

When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.

Explanation:

The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.

In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.

Answer:

31%

Step-by-step explanation:

Answer:

31%

Step-by-step explanation:

Answer:

28.27

Step-by-step explanation:

gl on test

Answer:

The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]

Step-by-step explanation:

Given : Complex number [tex]-2+2\sqrt{3}i[/tex]

To find : Express the complex number in trigonometric form?

Solution :

The complex number [tex]a+ib[/tex] trigonometric form is [tex]r(\cos\theta+i\sin\theta)[/tex]                      

Where, [tex]r=\sqrt{a^2+b^2}[/tex]

and [tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]

On comparing with given complex number  [tex]-2+2\sqrt{3}i[/tex]

a=-2 and [tex]b=2\sqrt{3}[/tex]

Substitute the value,

[tex]r=\sqrt{a^2+b^2}[/tex]

[tex]r=\sqrt{(-2)^2+(2\sqrt{3})^2}[/tex]

[tex]r=\sqrt{4+12}[/tex]

[tex]r=\sqrt{16}[/tex]

[tex]r=4[/tex]

[tex]\theta=\tan^{-1}(\frac{b}{a})[/tex]

[tex]\theta=\tan^{-1}(\frac{2\sqrt3}{-2})[/tex]

[tex]\theta=\tan^{-1}(-sqrt3)[/tex]

[tex]\theta=\tan^{-1}(\tan(-60))[/tex]

[tex]\theta=-60[/tex]

Substituting all values in the formula,

[tex]r(\cos\theta+i\sin\theta)[/tex]

[tex]4(\cos(-60)+i\sin(-60))[/tex]

[tex]4(\cos(60)-i\sin(60))[/tex]

Therefore, The required trigonometric form is [tex]4(\cos(60)-i\sin(60))[/tex]

Answer:

D. log base 5 of 56

Step-by-step explanation:

Since, by the multiplication law of logarithm,

[tex]log_a(m)+log_a(n) = log_a(mn)[/tex]

Given expression is,

log base 5(4*7 )+log base 5 of 2

[tex]=log_5(4\times 7)+log_5(2)[/tex]

[tex]=log_5(28)+log_5(2)[/tex]

By the above property,

[tex]=log_5(28\times 2)[/tex]

[tex]=log_5(56)[/tex]

= log base 5 of 56

Hence, Option D is correct.

Answer:

13946

Step-by-step explanation:

Answer: [tex]144^{\circ}[/tex]

Step-by-step explanation:

In the given figure , we have given a parallelogram .

We know that the opposite sides and angles of a parallelogram are equal.

Thus from the given parallelogram PORS  we have

[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]

Also, the value of angle p is given by :-

[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]

Answer:

B. 27.

Step-by-step explanation:

We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.

We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.

Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:

[tex]60=k*20[/tex]

[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]

[tex]3=k[/tex]

The equation [tex]y=3x[/tex] represents our given direct proportional relation.

Now, we will substitute [tex]x=9[/tex] to solve for y as:

[tex]y=3*9[/tex]

[tex]y=27[/tex]

Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.

To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.

Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.

The initial cost for the first 1/5 mile is given as $1.75.

We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:

[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]

To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:

[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]

Thus, there are 28 additional 1/5 mile increments.

Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:

[tex]\[ 28 \times 0.25 = 7.00 \][/tex]

The total cost is the initial cost plus the cost for the additional distance:

[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]

Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.

A - all defective

B - none defective

[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]

Answer: The correct option is d.

Explanation:

From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).

The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.

The point (1,1) represents that the first term is 1. Similarly from  (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.

The sequence is 1,2,4,8.

It can be written as,

[tex]2^0,2^1,2^2,2^3[/tex]

Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,

[tex]a_n=2^{n-1}[/tex]

Therefore, the correct option is d.

The median number of pretzels is 54.

The lower and upper quartiles are represented by the left and right sides of the box in a box and whisker plot. The box encompasses the interquartile interval, which contains 50% of the data. The median is the vertical line that divides the box in half. On the box plot, the mean is sometimes shown by a dot or a cross.

From the given box plot we can have the following information:

Minimum = 45

Lower Quartile = 47

Median= 54

Upper Quartile= 61

Maximum = 68

Thus, the Required median is 54.

Learn more about Box- whisker plot here:

https://brainly.com/question/22812839

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The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.

To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.

For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad

Thus, the radian measure of a 150° angle is (5/6) π rad.

Answer:

40 cm or 2/5 of a meter.

Step-by-step explanation:

A short-sighted person, at a positive diopter, will take an estimation of about 2.5 and make it the denominator by 1 as the numerator to find out the distance (in meters) that they can see clearly.

We can find the value of f, given the value for P:

P = +2.50

f = 1 / p = 1 / 2.50

(changing the units, it will be)  ---> 100 / 2.50 which is equal to 40 cm.

Therefore, 40 cm which is 2/5 of a meter is the distance a person with glasses +2.5d can see clearly.