The diameter, d, of the circle below is 77 cm.
What is the circumference of the circle?
Give your answer to 1 d.p.
77 cm
circumference = nd

The number of ways we can paint is g(nk)=1/n ∑d | n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))

Given,

Whether your circle has named sectors (i.e., is fixed) or lacks labels will determine this (i.e. is free).

In the first scenario, inclusion-exclusion can be used to create sets Ai,j of colorings with adjacent sectors I and j having the same color. Next, generally

|Ai1,j1∩⋯∩Air,jr|={(k^n − r r<n) ( k r=n)

And inclusion-exclusion yields f(n, k), the number of sectors that are colored with k colors that are not related to any of Ai, j (i.e., do not have similar adjacent colors):

f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n - r + (−1)^n (n, n)k

And the result of adding and subtracting (1) is:

⟹f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n−r + (−1)^n (n, n)k = (k−1)^n + (−1)^n (k−1)

That is your response to the fixed circle.

Burnside's Lemma, which generates the cycle index of a combinatorial necklace, must be applied if you want the solution for a free circle (assuming the symmetries involved are merely rotations):

Z(Cn) = 1n∑d∣nϕ(d)an/dd

Then, n/d cycles with dN sectors in each cycle, an/dd permutations representing rotations of sectors, and (d) is the Euler Totient Function[4] are used.

Since each cycle must contain a single color from the n available options, we must swap out an/dd with f(n/d, k), resulting in a total of g(n, k) free colorings for n>1*:

g(n, k)=1/n ∑d∣n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))

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Dividing the class by using Coin flip , The instructor has created minimal group

Researchers employ a technique called the minimal group paradigm to instigate new social groups in the lab. The objective is to classify people into groups using minimal, meaningless, or arbitrary criteria.

A minimal group is a a group lacking interdependence, group cohesion, structure, and other characteristics typically found in social groups.

An example is a group of people disembarking from a bus.

According to the question ,

The instructor is dividing the class by means of coin

Here, the flipping of coin is an arbitrary criteria . Also , the group formed will be anonymous

Hence , the formed group will be minimal group

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The example that represents a proportional relationship is A. y = -x

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form of y = kx.

In the proportional relationship, the constant of proportionality k is equal to the slope m and the line passes through the origin

It should be noted that y = -x is a linear equation that passes through the origin.

In conclusion, the correct option is A.

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Answer:

−3 < −1

−3 ≤ −1

Step-by-step explanation:

Symbol explanation

A negative number is any number that is less than zero.

On the number line the negative numbers are to the left of the zero.

-3 is less than -1 because -3 lies to the left of -1 on the number line.

Therefore, the only given inequalities that are true statements are:

There is sufficient data to back up the assertion that salespeople with college degrees generate much higher average sales than salespeople without.

Given,

This is a test of the hypothesis that the means of the two populations differ.

The assertion is that salespeople with college degrees generate much higher average sales than salespeople without.

The alternative and null hypothesis are then:

H₀ ; μ₁ - μ₂ = 0

Hₐ ;  μ₁ - μ₂ > 0

The level of significance is 0.05.

The mean and standard deviation for sample 1 (college degree), with n1=14, are 3542 and 468, respectively.

The mean and standard deviation of sample 2 (non-college degree), with n2=17, are 3301 and 642, respectively.

Now,

Md = M₁ - M₂ = 3542 - 3301 = 241

Md=241 is the difference between the sample means.

The following formula is used to calculate the estimated standard error of the difference between means:

S Md = √(σ₁²/n₁ + σ₂²/n₂) = √(468²/14 + 642²/17) = √(15644.6 + 24244.94) = 199.72

Then, we can calculate the t-statistic as:

t = (Md - (μ₁ - μ₂) / S Md = 241 - 0 / 199.72 = 241/199.72  = 1.21

The degrees of freedom for this test are:

Df = n₁ + n₂ - 2 = 14 + 17 - 2 = 29

Right-tailed tests have 29 degrees of freedom and t=1.21, so the following formula is used to determine the P-value for this test:

P Value = P(t > 1.21) = 0.118025

The effect is significant since the P-value (0.118025) is less than the 0.05 standard of significance.

The null hypothesis is rejected.

Therefore,

The idea that salespeople with college degrees generate much higher average sales than those without is supported by sufficient data.

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The measures of central tendency from the given stem-and-leaf plot are given as follows:

The stem-and-leaf plot shows the measures of the data-set, in which:

For example:

4|7 = 47.

Hence all the measures of the data-set are given as follows:

47, 51, 56, 57, 62, 63, 63, 66, 66, 68, 68, 70, 71, 73, 73, 73, 73, 76, 76, 77, 77, 79, 80, 81, 82, 83, 86, 88, 88, 90, 91, 93, 93, 97.

The mean is given by the sum of all scores divided by the number of scores, hence it is given as follows:

Mean = 74.62.

The median is the middle value of the data-set. The data-set has 34 elements, which is an even cardinality, hence the median is given by the mean of the 17th and of the 18th element, as follows:

Median = (73 + 76)/2 = 74.5.

The mode is the value that appears the most times in the data-set, which is of 73, as it is the only score to appear four times in the data-set.

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Answer:

if the first equation 3x - 3y = -2 is multiplication by 3

therefore, 3x - 3y = -2

multiplied by 3

:9x - 9y = -6

then the equations are added,

9x - 9y = -2 + 10x + 710x + 118x + 7

9x + 10x + 710x + 118x + 9y + 7

947x + 9y = 7

If Diandre completed 15 drills in 2 hours, the unit rate will be 7.5 drills per hour.

It is defined as the change in values of a dependent variable with respect to the independent variables.

It is given that, Diandre completed 15 drills in 2 hours. The rate is 15/2

A unit rate is a cost for just one of something. This is expressed as a ratio with a denominator of 1. For instance, it is useful in large applications like finding the average speed.

Thus, if Diandre completed 15 drills in 2 hours, the unit rate will be 7.5 drills per hour.

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Answer:33%

Step-by-step explanation: take 1 divided by 3 which equals 0.33 multiply that by 100 to get a percentage of 33 percent

you don't need to give me anything

Answer:

33%

Step-by-step explanation:

I want your chocolate.

In general, there are n>3 lines in the plane. Show that at least n - 2 triangles are formed by these lines.

Let's consider the following diagram, where each line is labelled with a letter:

A-B-C-D-E

Since each line intersects with at least one other line, there are at least n-2 triangles that can be formed. For example, triangle ABC, triangle ABD, triangle ABE, triangle BCD, triangle BDE, and triangle CDE are all triangles that can be formed from our five lines.

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The Coefficient of determination is the proportion of variability of the dependent and independent variable this statement is true.

The primary result of the regression analysis is the coefficient of determination because it indicates the percentage of variations in the dependent variable that can be accounted for by the independent variable.

The effectiveness of a statistical model in forecasting a result is indicated by the coefficient of determination [tex]R^2[/tex]. The dependent variable in the model is a representation of the result. [tex]R^2[/tex] can have a minimum value of 0 and a maximum value of 1.

Researchers frequently rely on coefficient, also referred to as R-squared (or [tex]R^2[/tex]), when performing trend analysis to determine how strong the linear relationship is between two variables.

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Answer:

if he can run 1.5 miles in 12 min he can run 4 miles in 0.5

Answer:

The total length of the tree in the total of 19 years (including the first year) would be 210 inches.

Answer: 210in

Step-by-step explanation:

One sample mean t test is used to to check whether the true average is 59k.

Average:

In statistics, average means a mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Given,

Here we need to find in what test can you use to check whether the true average is 59k.

While we looking into the given question we have identified the following details,

Number of students = 49

True average = 59k

Sample average = 44k

In this given situation, the perfectly suitable test is one sample t test,

Why we used this because of a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value.

Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k.

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Answer:

c) Multiplicative Identity

Step-by-step explanation:

Given equation,

→ c × 1 = c

Then the given equation shows,

→ Multiplicative Identity

(number × 1 = number)

Hence, the option (c) is correct.

The equation that doesn't belong is (c) 12(p + 8) = 3(20 - 2p)

From the question, we have the following parameters that can be used in our computation:

Options A to D

Looking through the options, we can see that:

However, three of the equations have their variables on one side

While the last has its variable on both sides

Hence, the one that does not belong is (c) 12(p + 8) = 3(20 - 2p)

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Answer:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70

o

=

length of ladder

maximum safe height of wall

= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70

o

=

16 ft

h

= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70

o

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.

Here is the Correct asnwer.

Answer:

1 1/3 or 4/3

Step-by-step explanation:

1/6 + 1/6 = 2/6

simplified, it would be 1/3 then you add the one, and you get 1 1/3 or (written as a mixed number,) 4/3

Answer:

2

Step-by-step explanation:

Since the denominator is the same, we can add the numerators.

11/6  +  1/6  =  12/6

We can simplify this to 2.

So, the answer is 2.

Answer:

Step-by-step explanation:

Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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Answer:

r = 0

Step-by-step explanation:

the first thing you can do to solve this equation is to remove the parenthesis

2r + 4 = r + 4

now subtract 4 from both sides

2r = r

subtract 4 from both sides

r = 0

that is your answer

Answer:

Step-by-step explanation:

The equation of the line in slope intercept form is y = 4/5 x.

For the stated question-

The given points are-

(x1, y1) = (5,4)

(x2, y2) = (10,8)

Slope m = (y2 -y1)/ (x2 - x1)

m = (8 - 4)/(10 - 5)

m = 4/5

Equation of the line;

y - y1 = m(x - x1)

y - 4 = 4/5 (x - 5)

y = 4/5 x - 4 + 4

y = 4/5 x

Thus, the equation of the line in slope intercept form is y = 4/5 x.

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The thermometer relates with the rectangular coordinate system in the sense that both have

The idea behind how a thermometer works is that solids and liquids tend to expand as a function of temperature.

Mercury starts to rise when a thermometer lamp is submerged in a particular solution or material. On a temperature scale, this increase in mercury is investigated.

The mercury in the tube is similar to the y coordinate which gives the output while the object being measured  is similar to the x coordinate which is the input

The graduation in thermometers into units that rises and falls is a similar feature in the rectangular coordinate system

The functions from thermometer can be plotted on a graph in a rectangular coordinate system

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240 people can seat in a row without restriction in an arrangement.

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory.

According to the question:

Consider A and B being the people sitting next to each other, as one entity AB or BA.

There are now 5 entities (one of two persons A and B and five of one single person) that have to be placed in a row.

With AB, there are thus 5! possibilities. With BA, there are also 6! possibilities.

Considering both, there are thus 2× 5! = 240 ways to seat 6 people in a row of six seats if two people insist on sitting next to each other.

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The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters

From the question, we have

Fencing available, Perimeter = 1600 meters

Number of sections, n = 3

Represent the dimensions with x and y

So, we have:

Area = Number of sections* x * y = 3xy

Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y

Recall that

Perimeter = 1600 meters

So, we have

6x + 4y = 1600

A = 3xy

Divide 6x + 4y = 1600 by 2

3x + 2y = 800

Make y the subject

y = (800 - 3x)/2

Substitute y = (800 - 3x)/2 in A = 3xy

A = 3x(800 - 3x)/2

So, we have

A = 1200x - 4.5x²

Differentiate and set to 0

1200 - 9x = 0

So, we have

9x = 1200

Divide by 9

x = 400/3

Recall that y = (800 - 3x)/2

So, we have

y = (800 - 3 x 400/3)/2

Evaluate

y = 200

Hence, the dimensions are 200 by 400/3

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Answer:

Ava is running faster than Maura.

Step-by-step explanation:

We are finding the speed in miles/minute.

6/75=0.08miles/minute

5/45=0.(1)miles/minute

0.(1)is greater than 0/08

Ava is running faster than Maura.