The harmonic mean of two real numbers x and y equals 2xy/(x + y). By computing the harmonic and geometric means of different pairs of positive real numbers, formulate a conjecture about their relative sizes and prove your conjecture.

Answers:

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Explanations:

Part (a)

There is only one disc labeled "3" out of 10 total. So we end up with the probability 1/10.

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Part (b)

The list of numbers less than 4 are {1,2,3} which are 3 items out of 10 discs. We end up with 3/10.

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Part (c)

A square number, aka a perfect square, smaller than 10 is the list {1,4,9}

Since 1 = 1^2, 4 = 2^2 and 9 = 3^2

Like part (b), we end up with the same result of 3/10.

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Part (d)

The list of primes smaller than 10 is {2, 3, 5, 7}. Notice that 1 is not prime.

So we end up with 4/10 = 2/5.

Answer:

y=3^(x-2) + 1

Step-by-step explanation:

When dealing with graphs I always use a graphing calculator or Desmos to graph and double check my answers especially when doing translations!

Answer:

Step-by-step explanation:

Lines with undefined slopes are perfectly vertical, of the form "x = ". A line with "the same x-intercept" as the given line that has an undefined slope will be the line that we want. I know that sounds confusing; we'll work through it then I'll explain it better. In order to find the x-intercep of the given line, solving it for y will make it a bit easier to "see". Therefore,

-y = -x + 1 and

y = x - 1. The x-intercept exists when y = 0, so setting y equal to 0 and solving for x:

0 = x - 1 and

1 = x. That's the x-intercept. It's also the line that we want that has an undefined slope, because "x = " lines are lines vertical lines and vertical lines have undefined slopes.

x = 1 is the line you want.

Answer:

there are 4 aces in the deck of 52 cards

so the probability to draw one ace is 4/52

if we draw an ace, there are 3 left in 51 cards.

so the next probability will be 3/51

we need to multiply probabilities to know how likely it is that this happens in a row.

for three in a row that's

[tex] \frac{4}{52} \times \frac{3}{51} \times \frac{2}{50} [/tex]

rewritten its:

[tex] \frac{4 \times 3 \times 2}{52 \times 51 \times 50} [/tex]

we'll see soon why this is easier to write.

we also have to account for the two cards that are no aces. it doesn't matter if the first two cards are no aces, the last two, or any rodney. just the ammount of non-aces is important.

there are 48 non-aces in the deck.

so the probability to draw one of them in the first step is 48/52.

wich each draw the number of cards left in the deck decreases by 1. and depending what we draw, that ammount also decreases.

we draw 5 cards, so we know what the denominators will be. the numerator will be the rest-ammounts of each event, like shown in the complicated fraction above.

let's write it most easily as this:

[tex] \frac{4 \times 3 \times 2 \times 48 \times 47}{52 \times 51 \times 50 \times 49 \times 48} [/tex]

this scenario looks like it only describes 3 aces, then two non-aces, but the order of multiplication isn't important. you could put the 48 and 47 to the left, same solution. so this expression represents all permutations of "3 aces when drawing 5 cards", including the two cards that are not aces.

that's why writing it as one convoluted fraction is indeed better and simpler than many fraction multiplied in row.

time to grap a calculator.

our probability for the event is

54144 possible valid outcomes out of

311875200 possible combinations.

luckily the calculator can reduce that to a simpler form of

[tex] \frac{47}{270725} [/tex]

(reduced with 2^6*3^, big number, but tried it out by hand stacking up prime factors until hittinga prime in the numerator)

written as a readable kind of number you probably know and like it's

0.0001736079047

in decimal form. now rounded as asked for:

0.00017

(as percentage: 0.017%)

hope the way how we got here is somewhat clear. feel free to ask any questions.

kind regards

Alex

Answer:

D

Step-by-step explanation:

Answer:0

Step-by-step explanation:

because 3x+1 is 0

The 3x+1 Conjecture asserts that, starting from any positive integer n, repeated iteration of this function eventually produces the value 1.

Answer:

[tex] \frac{8}{?100} \times 25000[/tex]

=2000

365×10=3650

2000×3650=7300000

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$25000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A=25000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=25000(1.08)^{10}\implies A\approx 53973.12[/tex]

Answer:

A. The null hypothesis is [tex]H_0: \mu = 130[/tex].

The alternative hypothesis is [tex]H_a: \mu > 130[/tex]

B. The value of the test statistic is [tex]t = 1[/tex]

C. The p-value is of 0.1636.

D. The critical value is [tex]t_c = 1.711[/tex]

Step-by-step explanation:

Question a:

Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco's rivals would like to determine whether its customers spend more per trip.

At the null hypothesis, we test if the mean is the same as Costco's, that is:

[tex]H_0: \mu = 130[/tex]

At the alternative hypothesis, we test if the mean is more than 130, that is:

[tex]H_a: \mu > 130[/tex]

B. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

130 is tested at the null hypothesis:

This means that [tex]\mu = 130[/tex]

A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population standard deviation is $10.50 and that spending follows a normal distribution.

This means that [tex]n = 25, X = 135.25, s = 10.50[/tex]

Then

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{135.25 - 130}{\frac{10.50}{\sqrt{25}}}[/tex]

[tex]t = 1[/tex]

The value of the test statistic is [tex]t = 1[/tex]

C. Calculate the p-value.

Test if the mean is more than a value, so a right-tailed test.

Sample of 25, so 25 - 1 = 24 degrees of freedom.

Test statistic of t = 1.

Using a t-distribution calculator, the p-value is of 0.1636.

D. Calculate the critical value

24 df, using the standard 0.05 significance level.

Using a critical value calculator, the critical value is [tex]t_c = 1.711[/tex]

Answer:

see image

Step-by-step explanation:

one by one, move each point

Answer:

no se guey..... pero gudluc

Answer:

-12

Step-by-step explanation:

cause from the rule

we should always solve from bracket so -3×8= -24

and -24/4= -6

and -6-6

= -12

Answer:

10 degrees C

Step-by-step explanation:

the difference between both temperatures is expressed by a subtraction

7 - -3 = 7 + 3 = 10

you could also do the subtraction the other way around :

-3 - 7 = -10

but the negative sign has no meaning for a distance between two points (a distance itself has no direction).

so, we are always using the absolute value of such difference calculations (when it is about lengths, distances, and so on, where the direction had no meaning).

and so, also the -10 is actually simply 10 for our problem here.

the temperature fell by 10 degrees.

The correct answer is A. Figure A.

A mathematical statement is a declarative sentence that expresses a truth or falsehood using mathematical symbols. It is usually made up of two terms that are related by an operator, such as an equals sign. Mathematical statements can be used to prove results, solve equations, and make predictions about the behavior of systems.

This diagram represents the statement "If it is a tree, then it has leaves" because the top box is labeled "tree" and the bottom box is labeled "has leaves". The arrow running between them indicates that if the condition of the top box is true, then the bottom box is also true. This is an example of a conditional statement.

To know more about mathematical statement click-
https://brainly.com/question/27839142
#SPJ1

Answer:

Yes the samples can be drawn from a population with the same mean and standard deviation 10 hours

Step-by-step explanation:

We are given;

Sample mean for male employees; x1¯ = 63

Sample mean for female employees; x2¯ = 66

Sample size = 50

Standard deviation; σ = 10

First,let's define the hypotheses of the question;

Null hypothesis; H0: μ1 = μ2

Alternative hypothesis; Ha: μ1 ≠ μ2

Now, let's find the test statistic from the formula;

z = (x1¯ - x2¯)/(σ√(2/n))

Thus;

z = (63 - 66)/(10√(2/50))

z = -3/2 = - 1.5

Now, we are not given the significance value but usually when it is not given, we can adopt α = 0.05.

Thus, from online p-value from z-score calculator using; z = -1.5; α = 0.05; two tailed test; we have;

p-value = 0.13364

The p-value is greater than the significance value and thus we will fial to reject the null hypothesis and conclude that these samples can be drawn from a population with the same mean and standard deviation

Answer:

2 staff members

Step-by-step explanation:

Given

See attachment for missing details

Let

[tex]s \to staff\ member[/tex]

[tex]p \to participant[/tex]

[tex]e \to puzzle[/tex]

Required

Staff members for 18 participants

From the attachment, we have:

[tex]1s \to 8p[/tex] ---- 1 staff member to 8 participants

[tex]s \to 8p[/tex]

Multiply both sides by 1

[tex]s * 2 \to 8p * 2[/tex]

[tex]2s \to 16p[/tex]

This means that 2 staff members are required for 16 participants

Answer:

The answer is A

Step-by-step explanation:

Starting from -3 in the Y values of option A. If you subtract three from each value, you will get the next value to the right.

Answer:

Someone already answered it but I won't let 50 points go to waste. !!!!!

Step-by-step explanation:

Step-by-step explanation:

there is your answer in attachment

Answer:

ccccccc is bebebebebebebeebebbeebebeb

Answer:

Cost for 50 songs: $64

Cost for s songs: s + 14

Step-by-step explanation:

Since it is $1 per song, if he downloaded 50 songs, it would be $50 extra dollars.

Add this to the monthly charge of 14:

50 + 14

= 64

So, the cost of 50 songs would be $64.

Now, find the cost for downloading s songs.

Each song is $1, so the cost can be represented by s + 14.

The answer is:

Cost for 50 songs: $64

Cost for s songs: s + 14

Answer:

1.d. None of these measures  (do not exist interpreted as all of these exist)

2.The mean is increased from 346.8 to 361.32

Step-by-step explanation:

After calculations we find that all the measures of central tendency exist for this data. The mean , median and mode can be easily calculated .

The mean is 346.8

The mode is 281

The median is 316

Suppose that the measurement 806 (the largest measurement in the data set) were replaced by 1169.  The mean would be affected by the change.

The mean is 361.32

The mode is 281

The median is 316

The mean is increased from 346.8 to 361.32

Answer: x=52

Step-by-step explanation:

x+72=34+90

x+72=124

124-72=x

x=52

Answer:

Step-by-step explanation:

yeah

Answer: 1/125 or 0.008 (simplify 1.125 or should I do it?)

Step-by-step explanation:

Well, when there is a negative sign in the exponent you only move the negative exponents. Moving only negative exponents is recommended because using this rule, you multiply two exponents with the same base and add their powers.

Answer:

What is a Combination? A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

#happylearning

Answer:

B'(4, 0)

Step-by-step explanation:

B (1, 5)

it translated right 3 units => x'=x+3

down 5 units => y'= y-5

Answer:

17.

Step-by-step explanation:

The differences form an arithmetic sequence 3, 5, 7, 9,,11.

The missing number  is 10 + 7 = 17.

This is a quadratic sequence.

The nth term = n^2 + 1.

Thus the 4th term = 4^2 + 1 = 17.

Answer as an improper fraction = 16/5

Answer as a mixed number = 3 & 1/5

Answer in decimal form = 3.2

All of those values represent the same thing, but written in a different way.

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Explanation:

I'm assuming HM stands for Harmonic Mean in this case.

If so, then we apply the reciprocal operation to each value to get 1/2 and 1/8 (from 2 and 8 respectively).

Add up those fractions:

1/2 + 1/8 = 4/8 + 1/8 = 5/8

Now we'll divide n = 2 over that result. The n = 2 refers to the number of items in the original set.

n divide over (5/8) = 2*(8/5) = 16/5 which is the answer as an improper fraction

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To convert to a mixed number, we can do the following:

16/5 = (15+1)/5

16/5 = 15/5 + 1/5

16/5 = 3 + 1/5

16/5 = 3 & 1/5

Or if you need the answer in decimal form, then using a calculator would get you 16/5 = 3.2

You always get a unit rate from dividing. You always have two ways to do it, and get two unit rates, but one of them is more helpful.

2000 meters/4 minutes = 500 meters per minute

4 minutes/2000 meters = 0.002 minute per meter

(By the way ... Franklin is "jogging" a 3:13.12 mile. The world record is 3:43.13 .)

Answer:

The playable area has a width of 9 inches and a height of 6 inches.

Step-by-step explanation:

There are a number of ways you can get there.

1. Check the answers to see which have the right area and aspect ratio.

A: area = 24 in² — does not match 54 in²

B: area = 54 in², aspect ratio 6:9 = 2:3 — does not match 3:2 aspect ratio

C: area = 54 in², aspect ratio 9:6 = 3:2 — matches problem statement

D: area = 121.5 in² — does not match 54 in²

2. If the screen were 3:2 (inches), its area would be 6 in². The area of 54 in² is 9 times that value, so the actual screen dimensions are √9 = 3 times 3:2. That is, they are width:height = 9:6 inches — matches selection C.

3. You can write equations for width and height and solve.

w/h = 3/2

wh = 54

Substituting w=3/2·h into the second equation gives

... (3/2)h·h = 54

... h² = 36 . . . . . multiply by 2/3

... h = √36 = 6 . . . . square root, result in inches

Answer:

D. The playable area has a width of 9 inches and a height of 6 inches.

Step-by-step explanation:

if the playable area is 54 and that such ratio of dimensions is 3:2

Then we are basically being asked to find the factor of ratios below that also multiply to get 54

54 = 9 x 6 and this is also a ratio of 3:2

As 3(3 + 2) = 54

and as width was asked first when ratio was given 3:2

The width therefore is 9 and the height is 6

So answer is D