create a box and whisker plot for the following set of data

It should be noted that to prove that G is connected, we can use proof by contradiction. Suppose that G is not connected, which means that there exist two vertices u and v that are not connected by any path in G. Since every vertex in G has degree at least 1, both u and v must have at least one neighbor each.

Let w be a neighbor of u, and x be a neighbor of v. Since u and v are not connected, there is no edge between w and x. But then, the vertices u, w, x, and v form a cycle of length 4, which contradicts the fact that G has minimum degree 1.

Therefore, G must be connected. To show that every pair of vertices is of distance at most 2, let u and v be any two vertices in G. If u and v are adjacent, then they are clearly at distance 1 from each other. Otherwise, let w be a neighbor of u. Since G is connected, there exists a path from w to v, and so the vertices u, w, and v form a path of length 2 from u to v.

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Answer:1111

Step-by-step explanation:

We know that the angle bisector theorem and the specified requirements are satisfied if BC = 16, CZ = 8, and BZ = 24. The angle bisector theorem is also satisfied if BC = 8, which also makes CZ = 16/3 and BZ = 112/9.

The opposite side of a triangle is divided into two portions that are proportional to the sides they are on if the angle is bisected by a line, according to the angle bisector theorem.

The angle bisector theorem, which asserts that if a line bisects a triangle's angle, it divides the opposite side into two segments that are next sides to each other, can be used to solve this problem.

Let BC and BZ both equal x. The angle bisector theorem provides us with:

AC/AB = CZ/BZ

16/(16+x) = 16/y

We solve y in terms of x, and as a result,

y = 16(16+x)/16 = x+16

Upon substitution, we discover—

16/(16+x) = 16/(x+16)

If we cross-multiply, we obtain:

16(x+16) = 16(16+x)

Simplifying, we get:

16x + 256 = 256 + 16x

In light of the fact that 16x cancels on both sides, we are left with:

256 = 256

As a result, there exist an endless number of BC and BZ values that could satisfy the requirements.

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Answer:

1/6 of flowers were blue

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

Answer:

Step-by-step explanation:

-9

Answer:

166.666666.......

Step-by-step explanation:

30÷5=6

1000÷6=166.6666.......

the 6 is a repeating decimal

the average low temperature in Norwood for February was 35°F.

If the average low temperature in Norwood for January was 50°F, then the average low temperature in February was:

50°F - 30% of 50°F

To find 30% of 50°F, we can multiply 50°F by 0.3:

30% of 50°F = 0.3 x 50°F = 15°F

Substituting this value back into the original equation, we get:

50°F - 15°F = 35°F

Therefore, the average low temperature in Norwood for February was 35°F.

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Answer:

After 5 half-lives, the remaining mass of the radioactive isotope will be 155 * (1/2)^5 = 4.84375 grams. Rounded to the nearest gram, the answer is 5 grams.

Step-by-step explanation:

The probability that a person who tests positive actually has the disease is ≈0.0158.

        Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. 1 is the probability of every event in a sample space.

    For instance, when we flip a coin, there are just two possible results: Head OR Tail. (H, T). However, if two coins are tossed, there are four possible results: (H, H), (H, T), (T, H), and (T, T).

we solve the given question using BAYE's theorem:

Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

P(disease/positive)= [tex]\frac{P(disease)P(positive/disease)}{P(disease)P(positive/disease)+P(no disease)P(positive/disease)}[/tex]

P(disease/positive)= [tex]\frac{(0.008)(0.04)}{(0.008)(0.04)+(0.992)(0.02)}[/tex]  ≈ 0.0158

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Answer:

To solve this problem, we can use the equations of motion for a particle moving in the vertical direction with constant acceleration g. The equation for the height (h) of the particle as a function of time (t) is:

h = ut - 1/2 gt^2

The particle will reach its maximum height when it has zero velocity, which occurs at the peak of its trajectory. The time taken to reach the peak can be found by setting the velocity equal to zero:

0 = u - gt

t = u/g

Substituting this value of t into the equation for h, we get:

h = u(u/g) - 1/2 g(u/g)^2

h = u^2/2g - u^2/2g

h = 0

This tells us that the particle reaches a height of zero at the end of its trajectory, which is not the maximum height. To find the maximum height, we need to consider the distance s between the point of projection and the wall.

Let t1 be the time taken by the particle to reach the wall, and t2 be the time taken to return to the ground. These times can be found by solving the quadratic equation:

s = ut1 + 1/2 gt1^2

0 = ut2 - 1/2 gt2^2

Using the quadratic formula, we get:

t1 = (u + sqrt(u^2 + 2gs))/g

t2 = (u - sqrt(u^2 + 2gs))/g

The maximum height is reached halfway between t1 and t2, which occurs at:

t = (t1 + t2)/2

t = (u/g)

Substituting this value of t into the equation for h, we get:

h = u(u/g) - 1/2 g(u/g)^2 - s

h = u^2/2g - gs/2

Therefore, the greatest height that a particle with initial velocity u can reach on a vertical wall at a distance s from the point of projection is u²/2g - gs²/2u².

Step-by-step explanation:

VOLUME of a SPHERE

   4/3 pi r^3 = volume

                   r =     cubrt ( volume / (4/3 pi)   )   Plug in the numbers

                  r = cubrt ( 65.45/ ( 4/3 * pi)  = 2.5 inches

The correct answer is: Both the mean and median are appropriate measures of center.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and computational tools to summarize and analyze large sets of data, with the goal of extracting meaningful insights and identifying patterns or trends.

Here,

The mean is the sum of all salaries divided by the number of salaries. In this case, the sum is:

37,000 + 38,500 + 35,000 + 37,000 + 45,000 + 40,000 + 75,000 = 307,500

And there are seven salaries. Therefore, the mean is:

307,500 / 7 = 43,928.57

The median is the middle value when the salaries are arranged in order from lowest to highest. First, we need to arrange the salaries in order:

35,000, 37,000, 37,000, 38,500, 40,000, 45,000, 75,000

The median is the middle value, which is 40,000.

The mode is the value that appears most frequently in the set of salaries. In this case, both 37,000 and 40,000 appear twice, so there is no unique mode.

Since the salaries are not symmetrically distributed, the mean is not a perfect measure of central tendency. However, it can still provide useful information about the "average" salary. On the other hand, the median is resistant to extreme values and may be a better measure of central tendency for this dataset. Therefore, both the mean and median are appropriate measures of center for this dataset.

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The probability of all six numbers matching is:

1/311875200 * 1/28 = 1/8764976 ≈ 0.0000114

The correct option is  A 311875200.

The probability  of choosing a matched number are 1/52 on the first draw, 1/51 on the second, 1/50 on the third, 1/49 on the fourth, and 1/48 on the fifth.

The likelihood that all five digits will match is as follows:

1/52 * 1/51 * 1/50 * 1/49 * 1/48 = 1/311875200

The probability of matching the sixth number is 1 in 28, as it is chosen at random and might match any of the 28 potential numbers.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Predict:

Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).

If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.

If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.

Calculate:

See the table below.

Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)

100 20 2,000 2,000 0

120 18 2,160 1,800 360

140 16 2,240 1,600 640

160 14 2,240 1,400 840

180 12 2,160 1,200 960

200 10 2,000 1,000 1,000

Analyze:

Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.

As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.

The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.

Quadratic Regression:

a) Using the provided calculator link, we obtain the following values:

a = 0.05

b = -10

c = 500

r2 = 0.9

b) The standard form of the equation that represents the data is:

f(x) = 0.05x2 - 10x + 500

c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.

d) See graph below.

Graph of quadratic equation

Evaluate:

Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these

Answer:

20

Step by step explanation

17+8+36+32+9+11+20+18+29+13+16+31

12

=240

12

=20

Step-by-step explanation:

From a z-score table

   z-score = 1 corresponds to  .8413   or  84.13 percentile

     meaning 84 .13 % have a lesser score than you

Answer:

B

Step-by-step explanation:

i looked it up...............................................

Answer:

Step-by-step explanation:

The distance formula is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

x1 is a,

x2 is 0,

y1 is 0 and

y2 is b. Fitting those into the formula where they belong:

[tex]d=\sqrt{(0-a)^2+(b-0)^2}[/tex] and

[tex]d=\sqrt{(-a)^2+(b)^2}[/tex]

Since a negative squared is a positive, then

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

which is the second choice down.

For the given graph:

A. f(x) > 0 at x = x₁, x₂, x₃, x₄ and x₅

B. f'(x) > 0 at x = x₃, x₄

C. f(x) is increasing at x = x₃, x₄

D. f'(x) is increasing at x = x₁, x₂,

E. The slope of f(x) is negative at x = x₁, x₂ and x₅

F. The slope of f'(x) is negative at x = x₃, x₄ and x₅

The steepness of the hill is called slope. The same applies to the steepness of the line. Slope is defined as the ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two points.

The slope of a straight line is usually expressed in m.

m = (y₂ - y₁)/(x₂ - x₁)

It's important to keep the x and y coordinates in the same order in both the numerator and denominator. Otherwise you will get the wrong gradient.

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Answer:

We can use the Law of Cosines to find the distance between points a and b.

Using the angles given, we can find the angle between points a and b:

Angle C = 180 - (76 + 32) = 72 degrees

Next, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the distance between points a and b, a is the distance between point c and point a (210 ft), b is the distance between point c and point b (150 ft), and C is the angle between points a and b (72 degrees).

Plugging in the values:

c^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

c^2 ≈ 21069.27

Therefore, the distance between points a and b is approximately:

c ≈ 145.2 ft

The distance between points A and B is approximately 170.4 ft.

To solve the problem, we can use the law of cosines. Let's call the angle between points A and B "x". Then we have:

cos(x) = (150^2 + 210^2 - 2(150)(210)cos(180°-76°-32°))/ (2(150)(210))

Simplifying this expression, we get:

cos(x) = 1/2

To solve for x, we take the inverse cosine of both sides:

x = cos^(-1)(1/2)

Using a calculator, we find that:

x ≈ 60°

Now we can use the law of sines to find the distance between points A and B:

sin(76°) / 210 = sin(60°) / d

where d is the distance between points A and B.

Simplifying this expression, we get:

d = 210sin(60°) / sin(76°)

Using a calculator, we find that:

d ≈ 170.4 ft

Therefore, the distance between points A and B is approximately 170.4 ft.

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Answer: 4

Step-by-step explanation:

To find the unit rate, we can cross-multiply the fractions.

Multiplying the numerator of the first fraction by the denominator of the second fraction, we get 1/5.

Multiplying the numerator of the second fraction by the denominator of the first fraction, we get 1/20.

Now we have the equation 1/5 = 1/20.

To solve for the unknown, we can cross-multiply again, which gives us 20 * 1/5 = 4.

Therefore, the unit rate is 4.

To respond to the question, we must identify the m-values for which V(m)  equation decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months),

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

We must identify the values of m for which the function V(m) is dropping in order to estimate the time span during which the value of the card was declining.

The function V(m)'s derivative is provided by:

V'(m) = 500m - 3,500

By setting V'(m) = 0 and solving for m, we may determine the crucial point(s):

500m - 3,500 = 0

m = 7

V''(m) = 500

To respond to the question, we must identify the m-values for which V(m) decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months), as we know that V(m) is falling for m 7.

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Answer:  1st one

Step-by-step explanation:

We can estimate that there are approximately 134 glass beads in the bin.

What is probability?

Probability is a measure of the likelihood of an event occurring.

To estimate the number of glass beads in the bin, we can use the proportion of glass beads in the handful that Jasper selected.

There are 15 beads in the handful, and 4 of them are glass. So, the proportion of glass beads in the handful is:

4/15 ≈ 0.267

We can assume that the proportion of glass beads in the bin is similar to the proportion in the handful. Therefore, we can estimate the number of glass beads in the bin as

0.267 x 500 ≈ 134

Therefore, we can estimate that there are approximately 134 glass beads in the bin.

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Answer: ∡1 = 153°

∡2 = 27°

Step-by-step explanation:

Answer:

angle 2=27°

angle 1= 153°

Step-by-step explanation:

6x-9+x=180

7x-9=180

7x=189

x=27

angle 2=27°

angle 1= 27×6-9=153°

angle 1= 153°

Answer:

x = √17

y = 10.1

Step-by-step explanation:

x² + 8² =  9²

x² = 81 - 64 = 17

x = √17

sin∅ = √17/9

∅ = 27.27°

9/y = cos(27.27)

y = 9/cos(27.27) = 10.13

y = 10.1