What’s the answer for 18 and 19?

Short answer (I write nPr = P(n, r) and nCr = C(n, r) ):

P (6, 4) = 6! / (6 - 4)! = 6! / 2! = 720 / 2 = 360

C (6, 4) = P (6, 4) / 4! = 6! / (4! (6 - 4)!) = 360 / 24 = 15

Long answer:

P(n, r) counts the number of permutations of n objects taken r at a time, given by

P(n, r) = n ! / (n - r )!

A permutation is a unique arrangement of objects such that the order in which they are arranged is taken into account. For example, if the objects in question are the numbers in the set {1, 2, 3}, then

• there are 3! = 6 total possible permutations if we take all 3 numbers at once:

123, 132, 213, 231, 312, 321

• there are 3!/(3-2)! = 3!/1! = 6 total permutations if we only take 2 numbers at once:

12, 13, 21, 23, 31, 32

• there are 3!/(3-1)! = 3!/2! = 3 total permutations if we take only 1 number at a time:

1, 2, 3

• and there is 3!/(3-0)! = 3!/3! = 1 way of permuting the 3 numbers without taking any of them:

(the permutation itself is just empty space)

By contrast, C(n, r) counts the combinations of n items taken r at a time, given by

C(n, r) = P(n, r) / r !

A combination is like a permutation, but the order of the objects doesn't matter. Continuing with the previous example of arrangements of the numbers from {1, 2, 3}, we have

• 3! / (3! (3-3)!) = 1 combination taking all 3 numbers at once:

123

(the other 5 permutations listed earlier are made up of the same numbers, so we consider them duplicates)

• 3! / (2! (3-2)!) = 3 combinations taking only 2 numbers at once:

12, 13, 23

• 3! / (1! (3-1)!) = 3 combinations taking only 1 number:

1, 2, 3

• 3! / (0! (3-0)!) = 1 combination taking none of them:

(again, empty space)

The main point is that the order of objects is considered across permutations, while it's ignored across combinations.

Answer:

O A).

Step-by-step explanation:

Answer:

(-9) + 9 = 0

The integer that should be added is nine

Step-by-step explanation:

when you have a negative integer and you added it by itself but it's a positive instead of a negative the positive takes over the negatives and makes it zero. I hope that made sense

Answer:

It does not restate the thesis.

Answer:

Step-by-step explanation:

Do 51360-48000= (A)

Then do

Difference (A) / 48000

All times by 100

Answer:

A,b I’m pretty sure

Step-by-step explanation:

Answer:

b=3/4

Step-by-step explanation:

((3/4)x)/2=9/32

The length of the base will be 3/4. The length of the base from formula of area of triangle.

The area of the triangle is half of the length and base of the triangle.Area of triangle is found as;

[tex]\rm A= \frac{1}{2} \times L \times B\\\\ A=\frac{9}{32} \\\\ \frac{9}{32} =\frac{1}{2} \times \frac{3}{4} \times B \\\\ B=\frac{3}{4}[/tex]

Hence,the length of the base will be 3/4.

To learn more about area of triangle refer;

https://brainly.com/question/19305981

#SPJ2

Answer:

Step-by-step explanation:

Standard equation of a circle is given by,

(x - h)² + (y - k)² = r²

Here, (h, k) is the center of the circle.

From the graph given in the picture,

Center of the circle → (-1, 1)

Radius of the circle = 3 units

Therefore, standard equation of the circle will be,

(x + 1)² + (y - 1)² = 3²

(x + 1)² + (y - 1)² = 9

General equation of the circle is the expanded form of the standard equation.

x² + 2x + 1 + y² + 1 - 2y = 9

x² + y² + 2x - 2y + 2 = 9

x² + y² + 2x - 2y - 7 = 0

Therefore, general equation of the given circle is,

x² + y² + 2x - 2y - 7 = 0

Answer:

[tex]x=-9[/tex]

Step-by-step explanation:

[tex]36^{x-3}=1296^{x+3}\\(6^2)^{x-3}=(6^4)^{x+3}\\2(x-3)=4(x+3)\\x-3=2x+6\\x+6=-3\\x=-9[/tex]

Answer:

The required confidence inteval = 94.9%.

Step-by-step explanation:

Confidence interval: Mean ± Margin of error

Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).

i.e.  Mean + Margin of error = 42.969               (i)

Mean - Margin of error = 36.191                    (ii)

Adding (i) and (ii), we get

[tex]2Mean =79.16\\\\\Rightarrow\ Mean= 39.58[/tex]

Margin of error = 42.969-39.58             [from (i)]

= 3.389

Margin of error = [tex]t^* \dfrac{\sigma}{\sqrt{n}}[/tex]

here n= 25 [tex], \ \sigma=8.25[/tex]

i.e.

[tex]3.389=t^*\dfrac{8.25}{5}\\\\\Rightarrow\ t^* = \dfrac{3.389}{1.65}\\\\\Rightarrow\ t^* =2.0539 \[/tex]

Using  excel function 1-TDIST.2T(2.054,24)

The required confidence inteval = 94.9%.

Answer:

So, we know that the speed of the aircraft is 600 miles /per hour/. The question is, how many miles does it travel over 6 hours?

Since “per hour” means it travels that far in 1 hour, we need to take that speed (600mph) and multiply it by 6, since we were asked about the distance in 6 hours.

So:

600*6=3600

And we get a total of 3600 miles traveled in 6 hours, as opposed to 600 miles in 1 hour.

Answer:D

Did it on khan academy

Answer:

the mean is 7

Step-by-step explanation:

used a mean calculator

Answer:

14.1 ft

Step-by-step explanation:

A = 200 ft^2

s = √A

s = √(200ft^2)

s = 14.1 ft

Please mark brainliest if this helped!

Please mark brainliest if this helped!

The length of each side of his patio is S = 14.1ft.

Given that,

Chip has enough concrete to pave a square area of 200ft^2 for a backyard patio,

Use the formula S=√A.

We have to determine,

The length of each side of his patio.

According to the question,

Chip has enough concrete to pave a square area of 200ft^2 for a backyard patio,

To obtain the length of each side of patio using the given formula.

Formula; [tex]S= \sqrt{A}[/tex]

Where, [tex]A = 200ft^2[/tex]

Substitute the value of A in the given formula,

[tex]S = \sqrt{A}\\\\S = \sqrt{100 (ft)^2}\\\\S = 14.1ft[/tex]

Hence, The length of each side of his patio is S = 14.1ft.

To know more about Surface Area click the link given below.

https://brainly.com/question/11777802

Answer:

A = (-6, 4)

B = (2,2)

C =  (-2, 2)

Step-by-step explanation:

If a coordinate (x, y) is dilated by a factor of k, the resulting coordinate will be expressed as (kx, ky). Note that each coordinate is multiplied by the scale factor

Given the coordinates (-3,2),(1,1)(-1,-1), if they are dilated by a factor of 2, the resulting coordinate will be;

A = (2(-3), 2(2)) = (-6, 4)

B = (2(1),2(1)) =(2,2)

C = (2(-1), 2(-1)) = (-2, 2)

Answer:

Alia has 11 jelly beans.

Step-by-step explanation:

4^2= 163^3= 2727-16=11

Answer:

Explanation:

7 - 1 = 6

2/3 = 4/6

so

5 - r = 4

r = 5 - 4

r = 1

(1, 1) (7, 5)

Answer:

a = 14

Step-by-step explanation:

28[-14]=14;

-14

Answer:

A= -14

Step-by-step explanation:

a + 28 = 14

28-14=14

make 14 an negative then add

-14 + 28 = 14

*pls give brainlist*

Answer:

1\9

Step-by-step explanation:

probability of picking 6 once is 1/3

then picking 6 again would be 1/9

Answer:

4/6 or 2/3.

Step-by-step explanation:

You need to multiply 1/2 by 3/3 so you can can the denominater having a 6.

Answer:

-7

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

5 out of 25 reduces to 1 out of 5

Answer:

(-3/8)/(-1/3)

=(-3/8) x (-3)

=9/8

=11/8

Step-by-step explanation:

Answer:

2.5 Grams

Step-by-step explanation:

You divide 25 by 10 giving you 2.5 Grams.

Answer:

$420

Step-by-step explanation:

In the figure, the living room is 5 cm by 3.5 cm.

We use the scale to convert to the real measurements.

1 cm = 4 ft

5 cm * 4 ft/cm = 20 ft

3.5 cm * 4 ft/cm = 14 ft

The actual dimensions of the room are 20 ft by 14 ft.

actual area = 20 ft * 14 ft = 280 ft²

carpet cost = $1.50/ft²

cost of carpet = 280 ft² * $1.50/ft²

cost of carpet = $420

Answer: $420