if 12 people at a party shake Hands once and only once with everyone else how many handshakes occur

Write a general formula to describe each variation.

The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Few things to note:

i. direct variation: When a variable x varies directly with another variable y, we write it in this form;

x ∝ y.

This can then be written as;

x = ky

Where;

k = constant of proportionality variation.

ii. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;

x ∝ [tex]\frac{1}{y}[/tex]

This can then be written as;

x = k([tex]\frac{1}{y}[/tex])

Where;

k = constant of proportionality or variation

iii. combined variation: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;

x ∝ ([tex]\frac{y}{z}[/tex])

This can then be written as;

x = k ([tex]\frac{y}{z}[/tex])

Where;

k = constant of proportionality or variation

From the question;

The square of T varies directly with the cube of a and inversely with the square of d.

Note that

square of T = T²

cube of a = a³

square of d = d²

Therefore, we can write;

T² ∝ [tex]\frac{a^3}{d^2}[/tex]

=> T² =  k ([tex]\frac{a^3}{d^2}[/tex])        -------------------(i)

Since;

T = 4 when a = 2 and d = 3

We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;

(4)² =  k ([tex]\frac{2^3}{3^2}[/tex])

16 =  k ([tex]\frac{8}{9}[/tex])

8k = 16 x 9

8k = 144

k = [tex]\frac{144}{8}[/tex]

k = 18

Now substitute the value of k back into equation (i);

T² =  18 ([tex]\frac{a^3}{d^2}[/tex])

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Therefore, the general formula that describes the variation is;

T² =  [tex]\frac{18a^3}{d^2}[/tex]

Answer:

Hello There!!

Step-by-step explanation:

The answer is that=>Yes It is a rational number.

hope this helps,have a great day!!

~Pinky~

Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be written as a fraction. These include whole numbers, fractions, decimals that end, and decimals that repeat. Positive and negative do not affect rationality.

Answer:

I think the answer is option B

Answer:

I think it is (b

Step-by-step explanation:

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

Explanation:

There are 4 ways to select 3 aces where order doesn't matter. It's basically the same as saying there are 4 ways to leave out one ace.

Then we have 2 slots left to fill. There are (48*47)/2 = 1128 ways to do this where order doesn't matter. The 48 is from the fact there are 52-4 = 48 cards that aren't aces. We step down to 47 after picking the first non-ace card. The 2 in the denominator is to correct for double counting.

We found there were 4 ways to pick the three aces, and 1128 ways to pick the other two non-ace cards. Overall, there are 4*1128 = 4512 ways to pick all five cards where we have exactly 3 aces.

This is out of 52C5 = 2,598,960 ways to select any five cards from a 52 card deck. I'm using the nCr formula which is

[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]

Use n = 52 and r = 5 to get the value mentioned. The exclamation marks indicate factorial.

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

To recap, there are

Dividing the two values gets us the final answer

4512/(2,598,960) = 0.001736079047

This value rounds to 0.00174

The probability that exactly 3 of these cards are Aces is 0.004%.

Given that five cards are drawn randomly from a standard deck of 52 cards, to determine the probability that exactly 3 of these cards are Aces the following calculation must be performed:

Therefore, the probability that exactly 3 of these cards are Aces is 0.004%.

Learn more in https://brainly.com/question/821892

Answer:

A) 0.7696

B) 0.0474

C) Yes it's unusual

D) 0.05746

E) No, it is not unusual

F) No, it is not unusual

Step-by-step explanation:

This is a binomial probability distribution question.

We are told that 92.4% of those admitted graduated.

Thus; p = 92.4% = 0.924

From binomial probability distribution, q = 1 - p

Thus;

q = 1 - 0.924

q = 0.076

Formula for binomial probability distribution is;

P(x) = nCx × p^(x) × q^(n - x)

A) At least 11 graduated out of 12.

P(x ≥ 11) = P(11) + P(12)

P(11) = 12C11 × 0.924^(11) × 0.076^(12 - 11)

P(11) = 0.3823

P(12) = 12C12 × 0.924^(12) × 0.076^(12 - 12)

P(12) = 0.3873

P(x ≥ 11) = 0.3823 + 0.3873

P(x ≥ 11) = 0.7696

B) that exactly 9 of them graduated out of 12. This is;

P(9) = 12C9 × 0.924^(9) × 0.076^(12 - 9)

P(9) = 0.0474

C) We are not given significance level here but generally when not given we adopt a significance level of α = 0.05.

Now, exactly 9 out of 12 that graduated which is P(9) = 0.0474.

We see that 0.0474 is less than the significance level of 0.05. Thus, we can say that it is unusual to randomly select 12 students from the special programs and get exactly 9 that graduate

D) that at most 9 of them out of 12 graduated.

P(x ≤ 9) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8) + P(9)

This is going to be very long so I will make use of an online probability calculator to get the values of P(0) to P(8) since I already have P(9) as 0.0474.

Thus, we have;

P(0) = 0

P(1) = 0

P(2) = 0

P(3) = 0.00000001468

P(4) = 0.00000040161

P(5) = 0.00000781232

P(6) = 0.00011081163

P(7) = 0.00115477385

P(8) = 0.00877476184

Thus;

P(x ≤ 9) = 0 + 0 + 0 + 0.00000001468 + 0.00000040161 + 0.00000781232 + 0.00011081163 + 0.00115477385 + 0.00877476184 + 0.04741450256

P(x ≤ 9) = 0.05746

E) P(x ≤ 9) = 0.05746 is more than the significance level of 0.05, thus we will say it is not unusual.

F) from online binomial probability calculator, probability of getting only 9 out of 12 is more than the significance value of 0.05. Thus, we will say it is not unusual

Answer:

MN = 50

Step-by-step explanation:

Given:

PQ = 49 – 8x

MN = 41 + 3x

Required:

Measure of MN

Solution:

PQ = ½(MN) => Mid-segment theorem of a triangle

Substitute

49 - 8x = ½(41 + 3x)

Multiply both sides by 2

2(49 - 8x) = 41 + 3x

98 - 16x = 41 + 3x

Collect like terms

98 - 41 = 16x + 3x

57 = 19x

57/19 = 19x/19

3 = x

x = 3

Find MN:

MN = 41 + 3x

Plug in the value of x

MN = 41 + 3(3) = 41 + 9

MN = 50

Answer:

Step-by-step explanation:

the pidgeon is flying east

Answer:

D

Step-by-step explanation:

Answer:

D....................

coz 100 has 0 so the number should at least have 0 in it

Answer:

Step-by-step explanation:

Answer:

Will take 8hrs.

Step-by-step explanation:

if pipe 1 takes 6 hrs then the 2nd pipe drains it 3x slower

Which means pipe 1 will take 1 hr slower every 3 hrs taken

and will be at ratio 3:2 for when pipe 2 is used

6 + 2 = 8 (hrs)

Will take 8hrs.

Step-by-step explanation:

pool = 1600 sq.cm

1600 sq.sm = 50cm × 32cm

AB = 50cm

the area of the park of A'B' :

50cm×4=200 sq.cm

Answer:

.6

Step-by-step explanation:

BUA= A+B-A∩B

.5+.3-.2= .6

Answer:

A. 25 < (x – 1)² + y² and 16 > x² + (y + 4)²

Step-by-step explanation:

the solutions are in the outside of the bigger circle, but inside of the smaller circle

The inequality is 25 < (x – 1)² + y² and 16 > x² + (y + 4)². Option A is correct.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to, > ‘greater than, or < ‘less than.

The solutions are on the outside of the bigger circle, but inside of the smaller circle.

The radius of the bigger circle is 5 and the radius of the smaller circle is 4. The graph of the inequality is attached with the answer below.

To know more about inequality follow

https://brainly.com/question/24372553

#SPJ5

Answer:

1496 cubic inches

Step-by-step explanation:

Answer:

the y-coordinate will be at (0, 2.4)

the x-coordinate will be at (6, 0)

Step-by-step explanation:

y coordinate of the graph is the point where the curve cuts the y axis

According to the graph, the curve cuts the y axis at y = 2.4. Hence the y-coordinate will be at (0, 2.4)

Similarly, the x-coordinate of the graph is the point where the curve cuts the x-axis

According to the graph, the curve cuts the x-axis at x = 6. Hence the x-coordinate will be at (6, 0)

Answer:

Arc GH = 78°

Step-by-step explanation:

Inscribed angle = m<GIH = 39°

Measure of arc related to inscribed angle = arc GH = ?

Thus:

m<GIH = ½(arc GH) => Inscribed angles theorem

Substitute

39° = ½(arc GH)

Multiply both sides by 2

2*39° = arc GH

78° = arc GH

Arc GH = 78°

Answer:

28

Step-by-step explanation:

it is missing where ?

based on the answer options I guess it is missing between 20 and 36.

if that is true, then the answer is 28.

the difference between 36 and 44 is 8.

the difference between 20 and 36 is 16.

the right answer should cut the interval of 16 into 2 parts (first logical approach to cut it in 2 halves of 8) and be related to the next interval between 36 and 44 (8).

the solution covering both considerations is the middle of the large interval = 20 + 8 = 28.

Answer: With that assumption, we have a square, whose area is given by the formula Asquare=a2, and two semicircles. The distance D is simply the square's diagonal. The area of each semicircle is given by the formula Asemicircle=π*r2/2. then you will get your answer!

9514 1404 393

Answer:

  A)  3.2

Step-by-step explanation:

In this geometry, all of the right triangles are similar. This means side lengths are proportional:

  short side/hypotenuse = x/8 = 8/20

  x = 8×8/20 = 64/20

  x = 3.2

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

Explanation:

Ignoring the slashes, there are 8 digits here. If we could tell those '1's and '2's apart, then we'd have 8! = 40,320 different codes. The exclamation mark indicates a factorial.

However, the '1's and '2's are indistinguishable. We have to divide by a!*b! = 3!*3! = 6*6 = 36 to account for this.

The a! = 3! = 6 is from the fact we have 3 copies of '1'.

The b! = 3! = 6 is from the fact we have 3 copies of '2'

Dividing by 36 gets us (40,320)/36 = 1120

Answer:

616

Step-by-step explanation:

A fraction that is equivalent to 38 is 616

Answer:

8

Step-by-step explanation:

8 is the correct answer

Answer:

12 2/3

Step-by-step explanation:

Answer:

a) The probability distribution is [tex]f(x) = \frac{1}{8}[/tex]

b) 0.5 = 50% probability that X will take on a value between 21 and 25.

c) 0.25 = 25% probability that X will take on a value of at least 26.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{a - x}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

Uniform distribution over the interval from 20 to 28.

This means that [tex]a = 20, b = 28[/tex]

a. What’s the probability density function?

The probability density function of the uniform distribution is:

[tex]f(x) = \frac{1}{b - a}[/tex]

In this question:

[tex]f(x) = \frac{1}{28 - 20} = \frac{1}{8}[/tex]

b. What’s the probability that X will take on a value between 21 and 25?

[tex]P(21 \leq X \leq 25) = \frac{25 - 21}{28 - 20} = \frac{4}{8} = 0.5[/tex]

0.5 = 50% probability that X will take on a value between 21 and 25.

c. What’s the probability that X will take on a value of at least 26?

[tex]P(X > 26) = \frac{28 - 26}{28 - 20} = \frac{2}{8} = 0.25[/tex]

0.25 = 25% probability that X will take on a value of at least 26.