Divide. Give the Quotient and Remainder. 520 / 22

The probability that m balls is P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n).

The total number of possible arrangements of distributing n balls into n compartments is given by n^n. Each ball has n choices for which compartment to fall into, and since there are n balls, we multiply n by itself n times.

Now, let's consider the number of ways m balls can fall into the first compartment. We can choose m balls out of the n balls to go into the first compartment in nCm ways, which is the binomial coefficient.

The remaining (n-m) balls can go into any of the remaining (n-1) compartments in (n-1)^(n-m) ways. Therefore, the probability that m balls will fall into the first compartment is given by:

P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n)

This formula calculates the ratio of favorable outcomes (m balls in the first compartment) to the total number of possible outcomes (all possible arrangements of distributing n balls into n compartments).

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The series ∑n=1∞8n+19−n∑n=1∞​−n8n+19​ is convergent, but the sum does not exist (divergent).

To determine whether the series ∑n=1∞8n+19−n∑n=1∞​−n8n+19​ is convergent or divergent, we can analyze its behavior.

By observing the terms of the series, we can see that the general term 8n+19−n−n8n+19​ can be simplified to −8−19n−8−n19​. As nn approaches infinity, the term tends towards −8−8.

To further confirm this, we can evaluate the limit of the general term as nn approaches infinity:

lim⁡n→∞(−8−19n)=−8−0=−8limn→∞​(−8−n19​)=−8−0=−8

Since the limit of the general term is a finite value (-8), the series is convergent.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S=a1−rS=1−ra​

where aa is the first term and rr is the common ratio. In this case, the first term is −8−8 and the common ratio is 11. Plugging in these values, we get:

S=−81−1=−80S=1−1−8​=0−8​

The denominator is zero, which means the sum does not exist. Therefore, the series diverges.

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Answer:

y = 4x + 5.5

Step-by-step explanation:

We put 2y in the y spot, obviously

2y = mx + b

Then we put 8x in the x spot

2y = 8x + b

Then we put 11 in the b spot

2y = 8x + 11

Then, to simplify, we divided by equation by two (it still gives the same results)

y = 4x + 5.5

Answer:

6

Step-by-step explanation:

The perimeter of a rectangle with a length of 9x - 4 and a width of (5x + 2) will be 18x - 4.

Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be given as,

Perimeter of the rectangle = 2(L + W) units

The dimension of the rectangle is given as,

L = 9x - 4
W = 5x + 2

Then the perimeter of the rectangle is given as,

P = 2(L + W)

P = 2(9x - 4 + 5x + 2)

P = 2(14x - 2)

P = 18x - 4

The perimeter of a rectangle with a length of 9x - 4 and a width of (5x + 2) will be 18x - 4.

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Step-by-step explanation:

25 1/2 = 51/2

1 1/2 = 3/2

51/2 / 3/2 = 17

therefore,

b >15

The distance of chord GH is \(x = 10$.\)

What is meant by chord?

In geometry, a chord is a line segment that joins two points on the circumference of a circle. The two endpoints of a chord lie on the circle, and the chord itself may or may not pass through the center of the circle.

Since G, H, J, K are collinear, we can use the power of a point theorem to set up an equation:

\($$(GH)(HJ) = (KJ)(MJ)$$\)

Substituting the given values, we get:

\($$(x+8)(8) = (6)(18+6)$$\)

Expanding and simplifying, we get:

\($$8x + 64 = 144$$\)

Subtracting 64 from both sides, we get:

\($$8x = 80$$\)

Dividing both sides by 8, we get:

\($$x = 10$$\)

Therefore, the distance between G and H is \(x = 10$.\)

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Answer:

A.

Step-by-step explanation:

Potential energy is energy that is collected when it has the most intention. In this case, the ball is on top of the hill, and has the potential to roll down. Ball D has the least potential because it is on the lowest part of the hill.

----------

Answer:

I'm not as sure about this one, but I THINK it's B...?

Step-by-step explanation:

You might want to double check with someone else about that one, but I think it's ball B because kinetic energy is energy in motion. If you think about it, when you roll a ball down a hill the first "dip" is where it goes fastest, thus more kinetic energy.

The potential energy of the ball at point {A} will be maximum.

The gravitational potential energy is the energy of a body due to its position with respect to earths surface. Mathematically, we can write the formula for potential energy as -

E{p} = mgh

Given is a graph that shows a ball rolling.

The heights of various points can be arranged as -

H{A} - Maximum height

H{D} - Minimum height

E{p} \($\alpha\) H

We can arrange the potential energies of various points can be arranged as -

H{A} - Maximum Potential energy

H{D} - Minimum Potential energy

Therefore, the potential energy of the ball at point {A} will be maximum.

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The probability that the two pets selected are of the same species  is 0.2426   .

In the question ,

it is given that ,

the number of puppies in the pet store = 6

the number of kittens in the pet store = 9

the number of lizards in the pet store = 4

the number of snakes in the pet store = 5

total animals = 24

the probability of selecting 2 puppies = ⁶C₂/²⁴C₂

the probability of selecting 2 kittens = ⁹C₂/²⁴C₂

the probability of selecting 2 lizards = ⁴C₂/²⁴C₂

the probability of selecting 2 snakes = ⁵C₂/²⁴C₂

So , the required probability is

= ⁶C₂/²⁴C₂  + ⁹C₂/²⁴C₂ + ⁴C₂/²⁴C₂  + ⁵C₂/²⁴C₂  

Simplifying further ,

we get ,

= 5/92 + 3/23 + 1/46 + 5/138

= 0.0543 + 0.1304 + 0.0217 + 0.0362

= 0.2426

Therefore , the required probability is 0.2426   .

The given question is incomplete , the complete question is

The pet store has 6 puppies , 9 kittens , 4 lizards and 5 snakes . if you select two pets from the store randomly, what is the probability that they are both the same species ?

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Answer: It would be 29.01

Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.

In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.

When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;

f(x) = 3 - x²

f(x) = 3 - (-2)²

f(x) = 3 - 4

f(x) = -1

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Answer:

4

Step-by-step explanation:

combine the ones with the x first: 16/4x+1/4x = 17/4x

combine the ones with the n: -1/5n+1/3n = -3/15n+5/15n = 2/15n

combine: 17/4x+2/15n (17/4 is also equal to 4 1/4)

4

Answer: good luck

Step-by-step explanation:Step 1) Because the first equation is already solved for

y

we can substitute

3

x

+

8

for

y

in the second equation and solve for

x

:

8

x

+

4

y

=

12

becomes:

8

x

+

4

(

3

x

+

8

)

=

12

8

x

+

(

4

⋅

3

x

)

+

(

4

⋅

8

)

=

12

8

x

+

12

x

+

32

=

12

(

8

+

12

)

x

+

32

=

12

20

x

+

32

=

12

20

x

+

32

−

32

=

12

−

32

20

x

+

0

=

−

20

20

x

=

−

20

20

x

20

=

−

20

20

20

x

20

=

−

1

x

=

−

1

Step 2) Substitute

−

1

for

x

in the first equation and calculate

y

:

y

=

3

x

+

8

becomes:

y

=

(

3

⋅

−

1

)

+

8

y

=

−

3

+

8

y

=

5

The solution is:

x

=

−

1

and

y

=

5

or

(

−

1

,

5

)

Answer:

6=28 1=125

Step-by-step explanation:

65+59=124 180-124=56/2 equals 28 and if the question is correctly written

then both sides that you don't yet know should be 28

The answer for one if I'm correct is 125 since you add 204+31=235 then you do 360-235=125

If I'm wrong at all I'm sorry but with that how are you in math honors when I'm just in algebra 1 T_T

Answer:

15/100*1800=15*1800/100=15*18=270

Step-by-step explanation:

1800-270=1530 therefore answer is 1530

The area of the region cut from the first quadrant by the cardioid is 3π/8 +1

A cardioid is a two-dimensional plane figure that has a heart-shaped curve. The equation of cardioid is r = a(1 ± sinθ) .

The area of the polar function can be calculated if the boundary condition that form the reason is given or can be found from the given information now we use the formula using the polar formula of the area as:

\(A = \int\limits^b_a {\frac{r^{2}}{2}} d\theta\)

The Area of the region cut from the first quadrant by cardioid,

\(A = \int\limits^\frac{\pi}{2}_0 {\frac{r^{2}}{2}} d\theta\)

Substituting r = 1 + sin ∅

\(A = \int\limits^\frac{\pi}{2}_0 {\frac{(1+ sin\theta)^{2}}{2}} d\theta\)

Opening square ,

\(A = \frac{1}{2}\int\limits^\frac{\pi}{2}_0 {1 +2sin\theta + sin^{2}\theta d\theta\)

=> \(A = [ \frac{1}{2} (\theta - 2cos\theta + \frac{1}{2} (\theta - \frac{1}{2}sin2\theta))]^\frac{1}{2}_{0}\)

=> 3π / 8 - (-1)

=> 3π/8 +1

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The equivalent inequality of -v >  -4 is v < 4

How to find the equivalent of -v > -4

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"

while solving inequalities and have to divide the both sides of the inequality by a negative number the inequality sign changes and this gives the equivalent

solving the equation

= -v >  -4

dividing through by -1

= v < 4

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Answer:

for wat its worth i dont know realy

Answer:

False because of the way your trionomial is setup

given 2 variables and you only have one

Step-by-step explanation:

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let x be the cοst οf οne apple pie, and y be the cοst οf οne lemοn meringue pie.

\(6x+8y=208\)

\(6x+ 2y= 88\)

\(-24x - 8y = - 352\)

\(6x + 8y = 208\)

\(-18x =-144\)

\(X = 8\)

\(6(8) +8y =208\)

\(48+8y=208\)

\(8y =160\)

\(Y= 20\)

Therefοre, the cοst οf οne apple pie is $8, and the cοst οf οne lemοn meringue pie is $20.

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To find the probability of at least one head when the fair coin is tossed 5 times is 0.9688.

Here, the total number of possible outcomes is 2 (since the coin is fair)

The possible outcomes of throwing the fair coin 5 times are:

From the above possible outcomes, we can see that there is at least one head in each case except for the outcome TTTTT.

Therefore, the probability of at least one head when the fair coin is tossed 5 times is 0.9688 (approx) .

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Answer:

D.

Step-by-step explanation:

Your answer is D which is 10 because when you calculate 110/11 you would get 10 therefor When you calculate 110/11 you would get 10. Hope it helps you!

                             -Hope you have a great day ahead

Answer:

13/13= Slope = 1

Step-by-step explanation:

M=rise/run, So that means 13 down then 13 to the left.

So 13/13 is the slope, but if it is simplified it is slope=1

The maximum area of the pen is the highest area the pen can have

The maximum area is 16200 square yards

Let the dimension be x and y.

So, the perimeter is given as:

\(\mathbf{P = 360}\)

Because it has one additional fence, the perimeter is calculated as:

\(\mathbf{2x + y = 360}\)

Make y the subject

\(\mathbf{y = 360 - 2x}\)

The area is calculated as:

\(\mathbf{A = xy}\)

Substitute \(\mathbf{y = 360 - 2x}\)

\(\mathbf{A = x(360 -2x)}\)

Expand

\(\mathbf{A = 360x -2x^2}\)

Differentiate

\(\mathbf{A' = 360 -4x}\)

Set to 0

\(\mathbf{360 -4x = 0}\)

Rewrite as:

\(\mathbf{4x = 360}\)

Divide both sides by 4

\(\mathbf{x = 90}\)

Substitute 90 for x in \(\mathbf{A = 360x -2x^2}\)

\(\mathbf{A = 360 \times 90 - 2 \times 90^2}\)

\(\mathbf{A = 16200}\)

Hence, the maximum area is 16200 square yards

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Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

Given,

What is the weight at birth?

Birth weight is the term used to describe a newborn's body weight. Typically, newborns of European heritage weigh between 2.5 and 4.5 kilos, on average 3.5 kilograms, at delivery. Babies from South Asia and China typically weigh 3.26 kg.

Here,

Babies of nonsmokers frequently ranged in weight from 1,000 to 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

The usual ranges of birth weights between the two groups do show some notable differences, though. Nearly half of neonates among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grams since there are fewer babies in the lower weight ranges. Fewer babies are in the bigger weight groups, with 40 of 74, or 54%, of the newborns delivered to smokers having birth weights between 2,000 and 3,000 grams.

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If the high temperature on Friday is equal to this week's average daily high temperature, the option that could be Friday's high temperature is: C. -12°.

Using this formula to find the high temperature

High temperature= Last week average daily high temperature + ( -This week average daily high temperature)

Let plug in the formula

High temperature = 12° + (-24°)

High temperature= -12°

Therefore the correct option is C.

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Answer:

For the first question it would be New Haven and it would be 4.7 degrees warmer. As for the second question it would be 3 hours after midnight the temperature is -2.5°C. Hope this helps!

Step-by-step explanation:

The equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

To find the formula for the tangent line to f(x)=ln(x) at x=2, we first need to take the derivative of the function:

f'(x) = 1/x

At x=2, the derivative is:

f'(2) = 1/2

The equation of the tangent line at x=2 is given by:

y - f(2) = f'(2)(x - 2)

Substituting the values of f(2) and f'(2) gives:

y - ln(2) = 1/2(x - 2)

Simplifying this equation gives us the equation of the tangent line:

y = 1/2x - ln(2) + ln(2)

Therefore, the equation of the tangent line to f(x)=ln(x) at x=2 is given by y = 1/2x - ln(2).

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