10. Unlocked for sale The "sold" listings on a popular auction website included 20 sales of used "unlocked" phones of one popular model. Here are the sales prices. 450 415 495 300 325 430 370 400 325 400 235 330 304 415 405 449 355 425 299 355 (a) Find the percentile of the phone that sold for $330. (b) What was the sales price of the phone that was at the 75th percentile?​

Answer:

4

Step-by-step explanation:

Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have

population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as

(original population)*1.011ˣ

Therefore, to get from 7 billion to 7.31 billion, we have

7 billion * 1.011ˣ = 7.31 billion

divide both sides by 7 billion to relatively isolate the x

1.011ˣ = 7.31/7

Another way of writing this is

log (base 1.011) (7.31/7) = x

≈ 3.96

Rounding to the nearest whole number, we get 4 as our answer

The number of years it takes for the population to grow from 7 billion to 7.31 billion is;

n = 4 years.

We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.

Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;

P_1 = 1.011¹ × P

After 2 years, it will be;

P_2 = 1.011² × P

Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;

P_n = 1.011ⁿ × P

Now, we are told that the population grew from 7 billion to 7.31 billion.

Thus;

P = 7 billion

P = 7 billion P_n = 7.31 billion

Thus;

7 billion × 1.011ⁿ = 7.31 billion

divide both sides by 7 billion to get;

1.011ⁿ = 7.31/7

1.011ⁿ = 1.044285

n log 1.011 = log 1.044285

n = 0.018819/0.004751156

n ≈ 4 years

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Considering Justin's serve, it is found that:

a) The ball traveled 21.4 feet, which means that Justin's estimate is correct.

b) An assumption regarding the angle of Justin's serve was made.

c) The Pythagorean Theorem was used to solve this mathematical problem.

The Pythagorean Theorem relates the length of the legs \(l_1\) and \(l_2\) of a right triangle(triangle which has an angle of 90º between the two legs) with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following rule:

\(h^2 = l_1^2 + l_2^2\)

Assuming that the ball was served at an angle of 90º, the situation can be summarized as follows:

Hence the Pythagorean Theorem is applied and the distance is calculated as follows:

d² = 7.5² + 20²

d = sqrt(7.5² + 20²)

d = 21.4 feet.

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Answer: 48.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

Draw a horizontal line from the top corner of the left wall to the right wall. Now you have a rectangle on the bottom 8’x10’ (80 square feet) and a triangle on the top with a height of 5’ and a base of 8’. 1/2 base times height =20. You need to paint 100 sq feet so you need 2 gallons.

Considering the factors of time and cost, strategic alliances generally emerge as the quickest and cheapest way to develop a global strategy. (option c)

Strategic alliances involve partnerships or collaborations between companies from different countries, with the goal of leveraging each other's strengths to achieve mutual benefits.

By sharing resources, knowledge, and networks, companies can expand their global presence more efficiently and cost-effectively. Strategic alliances can enable faster market entry and access to new markets by leveraging the partner's existing infrastructure, distribution channels, and customer base.

Moreover, pooling resources can help reduce costs and risks associated with global expansion.

Therefore, strategic alliances can be a relatively quicker and cheaper way to develop a global strategy, as they provide an opportunity to tap into existing capabilities and market presence of the alliance partner.

Hence the correct option is (c).

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Answer:

B. For every increase in three hours of usage, Jimmy had to use two more batteries.

Step-by-step explanation:

Jimmy is using gadget for many hours. He has to replace the batteries after the usage of 5 hours continuously. The scatter plot represents the fact that Jimmy has to use two more batteries for every hour increase in the usage of gadget. The relationship between the batteries usage and the hours used is linear as it is same for all the day.

Answer:

B. For every increase in three hours of usage, Jimmy had to use two more batteries.

Step-by-step explanation:

Answer:

£40

Step-by-step explanation:

sum the parts of the ratio, 2 + 5 = 7 parts

divide the amount by 7 to find the value of one part of the ratio.

£56 ÷ 7 = £8 , then

5 parts = 5 × £8 = £40 ← amount Georgia gets

Out of £56, the money received by Georgia is equivalent to $40.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given is Gary and Georgia who split £56 in the ratio 2:5.

There are total of 7 parts. This means that £56 is divided equally among the seven parts. Assume that the one part is equivalent to x. Then the cost of 7 parts = 7x. From the question, we can write -

7x = 56

x = 8

Georgia has 5 parts, therefore the money received by Georgia will be = 5 x 8 = 40

Therefore, out of £56, the money received by Georgia is equivalent to $40.

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Answer:

D. -8√70 + 7√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

√7(-8√10 + √14)

Step 2: Simplify

=======================================================

Explanation:

The box says 10 & 2/3 cups of mix will make 24 pancakes.

Carrie only wants to make half that and only wants 12 pancakes.

So we'll divide the mixed number in half.

This means we divide each piece of the mixed number in half like so

Overall, the mixed number 10 & 2/3 divides in half to get 5 & 1/3 which is the final answer.

------------

To check the result, notice that

Meaning that doubling 5 & 1/3 lands us on 10 & 2/3.

The answer has been confirmed.

Therefore, based on the analysis, the sample result of 110 grams is considered unusually low compared to the expected population mean of 118 grams.

To determine if the sample result of 110 grams is unusually low, we can use statistical analysis by comparing the sample mean to the population mean and considering the standard deviation.

Population mean (μ) = 118 grams

Standard deviation (σ) = 14 grams

Sample size (n) = 50

Sample mean (x) = 110 grams

First, we can calculate the standard error of the sample mean using the formula:

Standard Error (SE) = σ / √(n)

SE = 14 / √(50)

≈ 1.98 grams

Next, we can calculate the z-score, which measures the number of standard deviations the sample mean is away from the population mean. The formula for the z-score is:

z = (x - μ) / SE

z = (110 - 118) / 1.98

≈ -4.04

The z-score tells us how many standard deviations the sample mean is below the population mean. In this case, the z-score is approximately -4.04. To determine if the sample result is unusually low, we need to compare the z-score to a critical value. Typically, a z-score beyond a certain threshold (usually 2 or -2) is considered unusual. Using a threshold of 2 standard deviations, if the z-score falls beyond -2, it would indicate that the sample mean is unusually low. In this case, the z-score of -4.04 is significantly below -2, which suggests that the sample mean of 110 grams is indeed unusually low.

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For every mile the car is driven, the cost increases by 0.52 units.

Consider a line that passes through the origin at a distance 'a' from the Y-axis and has a slope of m. In this situation, the distance an is the definition of the line's y-intercept. At this moment, the line will cross the y-axis (0, a). The equation for the line will then be y = mx + a. The same goes for a line that crosses the X-axis at a position b from the origin and has a slope of m. (b,0). The distance b is the line's x-intercept. The equation for the line will be y = m* (x-b)

Given, the equation that relates cost of renting and miles driven is
y = 0.52 x + 186
Therefore, for a car travelling one mile, cost is y₁ = 0.52*1 + 186 = 186.52
For a car travelling two miles, cost is y₂ = (0.52*2) + 186 = 187.04
Thus, for every next mile the cost increases by = y₂ - y₁ = 187.04 - 186.52 = 0.52 units

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If the sum of two vectors is equal to the sum of their absolute values, it means they are orthogonal and equal in magnitude.

The amount of two vectors addresses the consolidated impact of the two vectors. At the point when the amount of two vectors is equivalent to the amount of their outright qualities, it implies that the two vectors are opposite to one another and their extents are equivalent. All in all, the two vectors are symmetrical and they have a similar length.

This relationship can be shown mathematically utilizing the Pythagorean hypothesis. In the event that we have two vectors An and B, their total C can be addressed as the hypotenuse of a right triangle, where An and B are the other different sides. In the event that An and B are opposite to one another, the Pythagorean hypothesis can be utilized to show that the size of C is equivalent to the square foundation of the amount of the squares of An and B, which is equivalent to the amount of their outright qualities.

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Answer:

A

Step-by-step explanation:

I used Desmos (highly suggest using it if you have questions like this)

Answer:

AAAAAAAAAAAAAAAA

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

LB of d = 186.5

UB of d = 187.5

LB of p = 27.5

UB of p = 28.5

186.5/28.5 = 6.54

187.5/27.5 = 8.81

The answer is 7 since both bounds round up to 7.

The value of c for the David journey is 7.

Since David drove a distance (d) of 187 km

So here the 3 significant figures should be

LB of d = 186.5

UB of d = 187.5

And,

LB of p = 27.5

UB of p = 28.5

Now the average should be

\(186.5\div 28.5\) = 6.54

And,

\(187.5\div 27.5\) = 8.81

So, The value of c for the David journey is 7.

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To plot the given fractions and decimals on a number line, let's arrange them in ascending order:

0.125, 0.4, 0.7, 1/3, 5/6, 7/8

Now, let's represent each value on the number line:

markdown

Copy code

          |      |      |       |        |         |

          0.125  0.4    0.7    1/3      5/6       7/8

Please note that due to the limitations of the text-based format, the number line may not be perfectly to scale. However, it provides a visual representation of the relative positions of the given fractions and decimals.

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It is reasonable for Stacy to use a normal model for the sampling distribution of the sample proportion. This is because, according to the Central Limit Theorem,

when the sample size is large enough (typically considered to be at least 30), the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution.

In Stacy's case, she plans on surveying a random sample of students, which implies that she will have a sufficiently large sample size. Therefore, the conditions for using a normal model are satisfied.

In conclusion, Stacy can use a normal model for the sampling distribution of the sample proportion in her survey for the final project.

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Option-C is correct that is the algebraic expression of the function F = (x +y +z').(x +y' +z').(x' +y +z) from the circuit in the picture.

Given that,

We have to find what is the algebraic expression of the function F.

In the picture we can see the diagram by using the circuit we solve the function F.

We know that,

From the circuit for 3 - to - 8 decoder,

D₀ = \(\bar{x}\bar{y}\bar{z}\)

D₁ = \(\bar{x}\bar{y}{z}\)

D₂ = \(\bar{x}{y}\bar{z}\)

D₃ = \(\bar{x}{y}{z}\)

D₄ = \({x}\bar{y}\bar{z}\)

D₅ = \({x}\bar{y}{z}\)

D₆ = \({x}{y}\bar{z}\)

D₇ = xyz

We can see bubble after D₀ to D₇ in the circuit,

So, Let A = \(\bar{D_1}\) = \(\overline{ \bar{x}\bar{y}{z} }\) = x + y + \(\bar{z}\)

Now, Let B = \(\bar{D_3}\) = \(\overline{ \bar{x}{y}{z} }\) = x + \(\bar{y}\) + \(\bar{z}\)

Let C = \(\bar{D_4}\) = \(\overline{ {x}\bar{y}\bar{z} }\) = \(\bar{x}\) + y + z

Now, Output F = A.B.C

F = (x + y + \(\bar{z}\)).(x + \(\bar{y}\) + \(\bar{z}\)).(\(\bar{x}\) + y + z)

F = (x +y +z').(x +y' +z').(x' +y +z)

Therefore, The algebraic expression of the function F = (x +y +z').(x +y' +z').(x' +y +z).

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The question is incomplete the complete question is -

What is the algebraic expression of the function F.

Option-

a. F = (x+y+z)(x+y'+z)(x'+y+z')(x'+y'+z)(x'+y'+z')

b. F = (x'+y'+z')(x'+y+z)(x+y+z')(x'+y+z)(x+y+z)

c. F = (x +y +z').(x +y' +z').(x' +y +z)

d. F = (x' +y' +z').(x +y +z').(x +y +z)

Answer: the greater mean is Store A, the greater median is Store A, the greater range is Store B

Step-by-step explanation:

Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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The function f(x,y) = x^2/2 + 5y^3 + 6y^2 − 7x has a global maximum at (7,-4/5) and no global minimum.

To determine if the function has a global maximum or minimum, we need to check its critical points and boundary points.

Taking partial derivatives with respect to x and y and setting them equal to 0, we have:

∂f/∂x = x - 7 = 0

∂f/∂y = 15y^2 + 12y = 0

From the first equation, we get x = 7. Substituting this into the second equation, we get:

15y^2 + 12y = 0

3y(5y + 4) = 0

This gives us two critical points: (7, 0) and (7, -4/5).

To check if these critical points are local maxima or minima, we need to use the second partial derivative test. Taking second partial derivatives, we have:

∂^2f/∂x^2 = 1, ∂^2f/∂y^2 = 30y + 12

∂^2f/∂x∂y = 0 = ∂^2f/∂y∂x

At (7,0), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = 0, which indicates a saddle point.

At (7,-4/5), we have ∂^2f/∂x^2 = 1 and ∂^2f/∂y^2 = -12, which indicates a local maximum.

To check for global extrema, we also need to consider the boundary of the domain. However, the function is defined for all values of x and y, so there is no boundary to consider.

Therefore, the function has a global maximum at (7,-4/5) and no global minimum.

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Step-by-step explanation:

The area of the polygon is 51cm².

Answer:

To find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem . Here is what it means: Perimeter = the sum of the lengths of all the sides Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side

Step-by-step explanation:

i thingk i help u

Answer: plot points (0,-2) (1.-5) (2.-8) (-1.1) (-2.1) makes a upside down V

-3|0+2|+4=-2

-3|1 +2|+4= -5

-3|2+2|+4= -8

-3|-1+2|+4=1

+3|-2+2|+4=1

Step-by-step explanation:

To determine the magnification values of the proportional controller (P), the integral proportional controller (PI), and proportional controller of integral derivatives (PID) using the Ziegler-Nichols method, we need to follow a few steps. I'll guide you through the process:

Step 1: Determine the open-loop transfer function (Gm(s)) of the process. Given:

Gp(s) = 10/((s + 2)(2s + 1))

To obtain the open-loop transfer function, we need to set the controller gain to 1. Therefore, Gm(s) = Gp(s).

Step 2: Find the frequency at which the magnitude of Gm(s) crosses 0 dB (decibels). This frequency is called the ultimate frequency (fu). We can determine fu by finding the frequency at which the phase angle of Gm(s) is -180 degrees.

Step 3: Calculate the ultimate gain (Ku) at the ultimate frequency (fu). Ku is the magnitude of Gm(s) at fu.

Step 4: Use the values of fu and Ku to determine the appropriate controller gains based on the Ziegler-Nichols method.

Now, let's calculate these values.

Step 1: Open-loop transfer function (Gm(s)) is the same as Gp(s):

Gm(s) = 10/((s + 2)(2s + 1))

Step 2: To find the ultimate frequency (fu), we need to find the frequency at which the phase angle of Gm(s) is -180 degrees.

At s = jω (where j is the imaginary unit), the magnitude of Gm(s) is given by:

|Gm(jω)| = 10/|((jω + 2)(2jω + 1))|

To find the frequency at which the phase angle is -180 degrees, we need to solve the following equation:

arg(Gm(jω)) = -180 degrees

Step 3: Once we determine the ultimate frequency (fu), we can find the ultimate gain (Ku) at that frequency by substituting ω = 2πfu into |Gm(jω)|.

Step 4: Based on the Ziegler-Nichols method, we can determine the controller gains as follows:

Proportional Controller (P):

Gain (Kp) = 0.5 * Ku

Integral Proportional Controller (PI):

Gain (Kp) = 0.45 * Ku

Integral Time (Ti) = Tu/1.2

Proportional Controller of Integral Derivatives (PID):

Gain (Kp) = 0.6 * Ku

Integral Time (Ti) = Tu/2

Derivative Time (Td) = Tu/8

Now that we have the steps and formulas, let's calculate the values for the given process.

Step 2 (cont.): Solving the equation arg(Gm(jω)) = -180 degrees, we find:

10/|((jω + 2)(2jω + 1))| = -180 degrees

By evaluating the expression above for various ω values, we find that ω = 3.16 rad/s is the frequency at which the phase angle is -180 degrees.

Step 3 (cont.): Substituting ω = 2πfu = 2π * 3.16 rad/s into |Gm(jω)|, we get:

|Gm(jω)| = 10/|((j * 3.16 + 2)(2j * 3.16 + 1))|

Calculating the magnitude, we find that Ku = 2.53.

Step 4 (cont.): Now, using the Ku value, we can calculate the appropriate controller gains:

Proportional Controller (P):

Kp = 0.5 * Ku = 0.5 * 2.53 = 1.265

Integral Proportional Controller (PI):

Kp = 0.45 * Ku = 0.45 * 2.53 = 1.1385

Ti = Tu/1.2 = 3.16/1.2 = 2.6333

Proportional Controller of Integral Derivatives (PID):

Kp = 0.6 * Ku = 0.6 * 2.53 = 1.518

Ti = Tu/2 = 3.16/2 = 1.58

Td = Tu/8 = 3.16/8 = 0.395

To summarize, the magnification values for the Ziegler-Nichols method are as follows:

Proportional Controller (P):

Gain (Kp) = 1.265

Integral Proportional Controller (PI):

Gain (Kp) = 1.1385

Integral Time (Ti) = 2.6333

Proportional Controller of Integral Derivatives (PID):

Gain (Kp) = 1.518

Integral Time (Ti) = 1.58

Derivative Time (Td) = 0.395

These values can be used to configure the respective controllers for the given process.

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Answer:

1.5

Step-by-step explanation:

we calculate the circumference of this circle.

circumference of a circle=2πr

data:

r=8 mm

circumference=2(8 mm)π=16π mm

2)we calculate the measure, in radians of the angle.

We know that:

circumference of a circle=2π radians

therefore:

16π mm=2π radians.

16 π mm--------------------------2π radians

12 mm-----------------------------  x

x=(12 mm  *  2π radians) / 16π mm=1.5 radians.

Based on the given information, it can be inferred that the graduation budget has a deficit of $125.

What is a budget deficit?

The scenario where spending exceeds revenue is referred to as a budgetary deficit. It is a symptom of financial health.

Given, total revenue = $2,500 per month

total expenses = $2,625 per month

Remaining amount = $2,500 - $2,625 = -$125

The negative (-) sign represents a deficit of amount $125.

Hence, the graduation budget has a deficit of $125.

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The dendrogram represents the hierarchical clustering of the eight utility companies based on their similarity in terms of the eight numerical variables. The vertical axis represents the distance between the clusters, while the horizontal axis represents the eight utility companies.

To determine the most appropriate number of clusters to organize the utility companies, we need to look for the level at which the dendrogram cuts through the branches such that each cluster is homogeneous and well-separated from the other clusters.

In this dendrogram, there are several possible levels at which we could cut the dendrogram to form clusters. However, we need to choose the level that results in the most meaningful and interpretable clusters.

One possible approach is to look for the longest vertical line that does not intersect any of the horizontal lines. This line corresponds to a distance of around 3.5. Cutting the dendrogram at this level would result in three clusters: one cluster containing companies 1, 2, and 3, another cluster containing companies 4, 5, and 6, and a third cluster containing companies 7 and 8.

Another approach is to look for the largest vertical gap between the horizontal lines that intersects the dendrogram. This corresponds to a distance of around 2.5, which would result in two clusters: one cluster containing companies 1, 2, 3, 4, 5, and 6, and another cluster containing companies 7 and 8.

Ultimately, the choice of the number of clusters will depend on the purpose of the analysis and the desired level of granularity in the clusters. In this case, either two or three clusters could be reasonable choices depending on the specific objectives of the analysis.

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The equation of the linear function is f(x) = 20x - 150.

To find the equation of the linear function, we need to find the slope and the y-intercept.

Using the given points, we can find the slope:

slope = (f(9) - f(6)) / (9 - 6) = (30 - (-30)) / 3 = 20

Now, to find the y-intercept, we can use one of the points. Let's use (6, -30):

y - y1 = m(x - x1)

y - (-30) = 20(x - 6)

y + 30 = 20x - 120

y = 20x - 150

Therefore, the equation of the linear function is f(x) = 20x - 150.

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