What is the slope of the line with equation y-3=-1/2(x-2)

Answer:

Converges to -25.

Step-by-step explanation:

[tex]\sum_{k=1}^{\infty} -5 \cdot (\frac{4}{5})^{k-1}[/tex] converges since [tex]r=\frac{4}{5}<1[/tex].

The sum is given by [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is -5.

[tex]\frac{-5}{1-\frac{4}{5}}=\frac{-5}{\frac{1}{5}}=-5(5)=-25[/tex].

Answer:

1. reflection across x-axis

2. translation 6 units to the right and 3 units up (x+6,y+3)

Step-by-step explanation:

The trapezoid ABCD has it vertices at points A(-5,2), B(-3,4), C(-2,4) and D(-1,2).

First transformation is the reflection across the x-axis with the rule

(x,y)→(x,-y)

so,

Second transformation is translation 6 units to the right and 3 units up with the rule

(x,y)→(x+6,y+3)

so,

Answer:

  D.)  AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′

Step-by-step explanation:

Option A identifies two sides and the angle not between them. The two triangles will be congruent in that case only if the angle is opposite the longest side, which is not true in general.

Option B: same deal as Option A.

Option C identifies three congruent angles, which will prove the triangles similar, but not necessarily congruent.

Option D identifies two angles (sufficient for similarity) and one side, sufficient (with similarity) for congruence. The applicable congruence theorem is AAS.

The statements that could be used to prove that ΔABC and ΔA′B′C′ are congruent are: A.) ∠A≅∠A′, AC≅A′C′, and BC≅B′C′; C.) ∠A≅∠A′, ∠B≅∠B′, and ∠C≅∠C′; and D.) AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′.

The statements that could be used to prove that ΔABC and ΔA′B′C′ are congruent are:

A.) ∠A≅∠A′, AC≅A′C′, and BC≅B′C′

C.) ∠A≅∠A′, ∠B≅∠B′, and ∠C≅∠C′

D.) AB≅A′B′, ∠A≅∠A′, and ∠C≅∠C′

In order for two triangles to be congruent, their corresponding angles and sides need to be congruent. In this case, option A states that ∠A≅∠A′, AC≅A′C′, and BC≅B′C′, which satisfies the conditions for congruence. Option C has congruent angles but does not mention congruent sides, so it does not prove congruence. Option D mentions congruent sides but does not mention congruent angles, so it also does not prove congruence.

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Answer:

[tex]8\frac{19}{20}[/tex] in.

Step-by-step explanation:

To find your answer, subtract.

[tex]12\frac{3}{4}[/tex] may be rewritten as [tex]\frac{51}{4}[/tex] and [tex]3\frac{4}{5}[/tex] may be rewritten as [tex]\frac{19}{5}[/tex]

Establish a common denominator, which would be the lowest common multiple of 4 and 5, which is 20. Multiply both parts of your first fraction by 5 to get a denominator of 20, and both parts of your second fraction by 4 to get a denominator of 20.

[tex]\frac{51}{4} *\frac{5}{5} =\frac{255}{20}[/tex]

and

[tex]\frac{19}{5} *\frac{4}{4} =\frac{76}{20}[/tex]

Subtract.

[tex]\frac{255}{20} -\frac{76}{20} =\frac{179}{20}[/tex]

This fraction may be rewritten as [tex]8\frac{19}{20}[/tex].

Answer:

[tex]8\frac{19}{20}[/tex] inches.

Step-by-step explanation:

Average rainfall of Tucson = [tex]12\frac{3}{4}[/tex] inches

                                              or  [tex]\frac{51}{4}[/tex] inches

Average rainfall of Yuma =  [tex3\frac{4}{5}[/tex] inches

                                              or  [tex]\frac{19}{5}[/tex] inches

Now we have to find the fifference of average rainfall in Tucson as compared to Yuma.

Difference =  [tex]\frac{51}{4}[/tex] -  [tex]\frac{19}{5}[/tex]

                  =  [tex]\frac{255-76}{20}[/tex]

                  =  [tex]\frac{179}{20}[/tex]

                  =  [tex]8\frac{19}{20}[/tex] inches.

Answer:

let the equal sides of the triangle be of length "a"  . let the angle between these two sides be " x  ". Then drop a perpendicular from the vertex to the base.  now u have 2 similar triangles  .the angle between the perpendicular and one of the equal sides is now (x/2)  . length of perpendicular = a cos(x/2)  length of base = 2a sin(x/2)  . area of triangle = (1/2) 2sin(x/2) cos(x/2) a-square  

= (1/2) (sin x) a-square

Answer:

  3/10

Step-by-step explanation:

Bonnie has completed 0.5 + 0.2 = 0.7 of her art project. 1 - 0.7 = 0.3 of her art project remains to be completed.

_____

1/2 = 5/10 = 0.5

1/5 = 2/10 = 0.2

Answer:

Approximately 5.19 hours.

Step-by-step explanation:

The question is asking that you solve for T (the amount of time spent with patients in a day). To do so, simply input the values which it has given you for your variables. We can substitute 16 for I as that is the doctor's preferred interval time and we can substitute 21 for N as that is the amount of appointments the doctors wishes to have per day.

[tex]16=1.08(\frac{T}{21} )[/tex]

To solve, start by multiplying both sides by 21.

[tex]336=1.08T[/tex]

Next, divide both sides by 1.08.

[tex]311.11=T[/tex]

Your answer comes out to 311.11 minutes. The question is asking for this to be translated into hours per day, which equates to approximately 5.19 hours.

The required hours per day is 5.19 hours a day needed by doctors to spend with patients.

Given that,

The interval​ time, I, in​ minutes, between appointments is related to the total number of minutes T that a doctor spends with patients in a​ day, and the number of appointments​ N, by the​ formula: I = 1.08 ​(T/N).
I = 16 minutes, N = 21.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
I = 1.08 (T / N)
16 = 1.08 * T / 21
T = 16 * 21 / 1.08
T = 311.11 minutes
T = 311.11 / 60 hours
T = 5.19 hours

Thus, the required hours per day is 5.19 hours a day needed for doctors to spend with patients.

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Answer:

A statistics class with 36 students is arranged so that there are 6 rows with 6 students in each row, and the rows are numbered from 1 through 6. A die is rolled and a sample consists of all students in the row corresponding to the outcome of the die. This is not a simple random sample. It is a random sample only.

For the same class described in part (a), the 36 student names are written on 36 individual index cards. The cards are shuffled and six names are drawn from the top. This is a simple random sample. It is also a random sample.

For the same class described in part (a), the six youngest students are selected. This is not a simple random sample. It is also not a random sample.

Answer:

The first option:

Vertices: A, B, C, D, E, F, G, H;

Edges: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG;

Bases: rectangle ABEH and rectangle DCFG

Hope this helps C:

The correct option is option A:

    rectangular prism

The point where 2 or more side intersects is called vertices.

The individual flat surface of the solid object is the face.

The line segment where 2 faces intersect each other.

The prism whose bases are rectangular and are connected by line segment is called a rectangular prism.

As Rectangular prism has 2 rectangular bases at top and bottom position of the prism, 8 vertices, 6 faces, and 12 sides.

From the definition, It is clear that,

This figure is a rectangular prism whose

8 vertices are: A, B, C, D, E, F, H, G.

12 edges are: AB, BC, CD, DA, BE, EF, FG, GH, HE, AH, CF, and DG

2 rectangular bases are: ABEH and DCFG

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For this case we have the following expression:

[tex]\sqrt [3] {5x-2} - \sqrt [3] {4x} = 0[/tex]

If we add to both sides of the equation [tex]\sqrt [3] {4x}[/tex] we have:

[tex]\sqrt [3] {5x-2} = \sqrt [3] {4x}[/tex]

To eliminate the roots we must raise both sides to the cube:

[tex](\sqrt [3] {5x-2}) ^ 3 = (\sqrt [3] {4x}) ^ 3\\5x-2 = 4x[/tex]

So, the correct option is the option c

Answer:

Option C

Answer:

C

Step-by-step explanation:

Final answer:

The answer explains how to calculate the probability of not receiving one's own ID card using the inclusion-exclusion principle and provides the limit of this probability as n approaches infinity.

Explanation:

Inclusion-Exclusion Principle:

(a) To calculate the probability that no one receives their own ID card back, we use the principle of inclusion-exclusion. The probability is given by 1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n * 1/n!.

(b) As n approaches infinity, the probability approaches e-1 which is approximately 0.3679.

Answer:

option 4 ⇒ 236 lb.

Step-by-step explanation:

Best explanation of the question is as shown in the attached figure.

we will use the parallelogram method to calculate resultant force.

to get the length of the resultant force ⇒ use the cosines law

The cosine law is a² = b² + c² - 2 * b * c * cos (∠A)

Applying at the question where b = F₁  , c = F₂  and  ∠A = ∠x

Given that F₁ = 100 pounds  , F₂ = 150 pounds  and  ∠x = 180° - 40° = 140°

∴ (Resultant force)² = 100² + 150² - 2 * 100 * 150 * cos (∠140) = 55481

∴ Resultant force = √55481 = 235.54 ≅ 236 pounds

The answer is option 4 ⇒ 236 lb.

Answer:

30 and 150

Step-by-step explanation:

Whether these are same side interior or same side exterior, the sum of them is 180 when they are on the same side of a transversal that cuts 2 parellel lines.  If angle A is 5 times smaller than angle B, then angle B is 5 times larger.  So angle A is "x" and angle B is "5x".  The sum of them is 180, so

x + 5x = 180 and

6x = 180 so

x = 30 and 5x is 5(30) = 150

Answer:

30 and 150

Step-by-step explanation:

YOUR WELCOME!

[tex]

A(4,-2) \\

B(0, 10) \\

AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\

AB=\sqrt{(0-4)^2+(10-(-2))^2} \\

AB=\sqrt{16+144} \\

AB=\sqrt{160}\approx\boxed{12.65} \\

[/tex]

The answer is D.

Hope this helps.

r3t40

Answer:

Step-by-step explanation:

In all of these problems, the key is to remember that you can undo a trig function by taking the inverse of that function.  Watch and see.

a.  [tex]sin2\theta =-\frac{\sqrt{3} }{2}[/tex]

Take the inverse sin of both sides.  When you do that, you are left with just 2theta on the left.  That's why you do this.

[tex]sin^{-1}(sin2\theta)=sin^{-1}(-\frac{\sqrt{3} }{2} )[/tex]

This simplifies to

[tex]2\theta=sin^{-1}(-\frac{\sqrt{3} }{2} )[/tex]

We look to the unit circle to see which values of theta give us a sin of -square root of 3 over 2.  Those are:

[tex]2\theta =\frac{5\pi }{6}[/tex] and

[tex]2\theta=\frac{7\pi }{6}[/tex]

Divide both sides by 2 in both of those equations to get that values of theta are:

[tex]\theta=\frac{5\pi }{12},\frac{7\pi }{12}[/tex]

b.  [tex]tan(7a)=1[/tex]

Take the inverse tangent of both sides:

[tex]tan^{-1}(tan(7a))=tan^{-1}(1)[/tex]

Taking the inverse tangent of the tangent on the left leaves us with just 7a.  This simplifies to

[tex]7a=tan^{-1}(1)[/tex]

We look to the unit circle to find which values of a give us a tangent of 1.  They are:

[tex]7\alpha =\frac{5\pi }{4},7\alpha =\frac{\pi }{4}[/tex]

Dibide each of those equations by 7 to find that the values of alpha are:

[tex]\alpha =\frac{5\pi}{28},\frac{\pi}{28}[/tex]

c.  [tex]cos(3\beta)=\frac{1}{2}[/tex]

Take the inverse cosine of each side.  The inverse cosine and cosine undo each other, leaving us with just 3beta on the left, just like in the previous problems.  That simplifies to:

[tex]3\beta=cos^{-1}(\frac{1}{2})[/tex]

We look to the unit circle to find the values of beta that give us the cosine of 1/2 and those are:

[tex]3\beta =\frac{\pi}{6},3\beta  =\frac{5\pi}{6}[/tex]

Divide each of those by 3 to find the values of beta are:

[tex]\beta =\frac{\pi }{18} ,\frac{5\pi}{18}[/tex]

d.  [tex]sec3\alpha =-2[/tex]

Let's rewrite this in terms of a trig ratio that we are a bit more familiar with:

[tex]\frac{1}{cos(3\alpha) } =\frac{-2}{1}[/tex]

We are going to simplify this even further by flipping both fraction upside down to make it easier to solve:

[tex]cos(3\alpha)=-\frac{1}{2}[/tex]

Now we will take the inverse cos of each side (same as above):

[tex]3\alpha =cos^{-1}(-\frac{1}{2} )[/tex]

We look to the unit circle one last time to find the values of alpha that give us a cosine of -1/2:

[tex]3\alpha =\frac{7\pi}{6},3\alpha  =\frac{11\pi}{6}[/tex]

Dividing both of those equations by 3 gives us

[tex]\alpha =\frac{7\pi}{18},\frac{11\pi}{18}[/tex]

And we're done!!!

Answer:

  (x +8)^2 +(y -15)^2 = 289

Step-by-step explanation:

The numbers 8, 15, 17 are a Pythagorean Triple, so we know the radius of the circle is 17. Filling in the given information in the standard equation of a circle, we get ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . circle with center (h, k) and radius r

  (x +8)^2 +(y -15)^2 = 289 . . . . . circle with center (-8, 15) and radius 17

_____

Once you have identified the center (h, k)=(-8, 15) and a point you want the circle to go through (x, y)=(0, 0), evaluate the equation for the circle to find the square of the radius:

  (0 +8)^2 +(0 -15)^2 = r^2 = 64+225 = 289

Final answer:

The equation of the circle with center at (-8, 15) that passes through the origin is (x + 8)² + (y - 15)² = 289.

Explanation:

The equation of a circle is given in the form (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is at (-8, 15). Since the circle passes through the origin (0,0), we can find the radius by calculating the distance between the origin and the center using the distance formula: √[(-8 - 0)² + (15 - 0)²] = [tex]\sqrt{(64 + 225)}[/tex] = [tex]\sqrt{289}[/tex] = 17.

Now that we have the radius, we can substitute our values into the circle's equation. The equation becomes (x + 8)² + (y - 15)² = 17² or (x + 8)² + (y - 15)² = 289.

Answer:

4, 10

Step-by-step explanation:

The value for the third side of the triangle is given by

b-a < n < b+a where a and b are the two other sides of the triangle and b>a

7-4 < n < 7+4

3 < n < 11

Since n is an integer

4 would be the smallest value and 10 would be the largest

Answer:

Smallest value of n = 4

Largest value of n = 10

Step-by-step explanation:

The sum of the shortest sides of a triangle must be greater than the longest side.

If 7 is the longest side, then:

n + 4 > 7

n > 3

n is an integer, so the smallest n can be is 4.

If n is the longest side, then:

4 + 7 > n

11 > n

n is an integer, so the largest n can be is 10.

Answer:

750

Step-by-step explanation:

If we go up 1000 feet from sea level and then come down 250 from that, then we are being asked to compute the difference of 1000 and 250.

1000

-  250

---------

   750

We are 750 feet above sea level.

Answer:

1,250

Step-by-step explanation:

The answer would be 1,250 because you would add 1,000 and 250 to get the total elevation of the air craft.

Answer:

1.5

2.11

3.4

4.10

Step-by-step explanation:

We are given that store the following vectors of 15 values as an object in your workspace :

6,9,7,3,6,7,9,6,3,6,6,7,1,9,1

We have to find the number of elements

1.equal to  6

2. equal  or greater than 6

3.less than 6

4.not equal to 6

The 15 vectors are arrange in increasing order then we get

1,1,3,3,6,6,6,6,6,7,7,7,9,9,9

1.6,6,6,6,6

There are five elements which is equal to 6.

2.Number of elements equal or greater than 6=6,6,6,6,6,7,7,7,9,9,9=11

There are eleven elements which is equal or greater than 6.

3. Number of elements which is less than 6=1,1,3,3=4

There are four elements which is less than 6.

4.Number of elements which is not equal to 6=1,1,3,3,7,7,7,9,9,9=10

There are ten elements which is less than 6.

Answer:

a) The probability of being dealt a blackjack hand

[tex]= \frac{64}{1326}[/tex]

b) Approximate percentage of hands winning blackjack​ hands

[tex]4.827%[/tex]

Step-by-step explanation:

It is given that -

Winning Black Jack means -  getting 1 of the 4 aces and 1 of 16 other cards worth 10 points

Thus, in order to win a "black jack" , one is required to pull 1 ace and 1 of 16 other cards

Number of ways in which an ace card can be drawn from a set of 4 ace card is [tex]C^4_1[/tex]

Number of ways in which one card can be drawn from a set of other 16 card is [tex]C^16_1[/tex]

Number of ways in which two cards are drawn from a set of 52 cards is [tex]C^52_2[/tex]

probability of being dealt a blackjack hand

[tex]= \frac{C^4_1* C^16_1}{C^52_2} \\= \frac{4*16}{\frac{51*52}{2} }\\ = \frac{64}{1326} \\[/tex]

Approximate percentage of hands  winning blackjack​ hands

[tex]= \frac{64}{1326} * 100\\= 4.827[/tex]%

After completing this question, I got the calculation that the probability of being dealt a blackjack hand is 32/663. The percentage is 4.83%, or as a decimal ~0.0483

Answer:

A. f(x) = 6x + 9

Step-by-step explanation:

The given equation is:

y - 6x - 9 = 0

We have to write this equation in function notation with x as the independent variable. This means that y will be replaced by f(x) and all other terms will be carried to the other side of the equation to get the desired function notation.

y - 6x - 9 = 0

y = 6x + 9

f(x) = 6x + 9

Therefore, option A gives the correct answer.

Answer:

[tex]x^{2} \sqrt{x} \neq \sqrt[n]{x} \pi \alpha \frac{x}{y} x_{123}[/tex]

Step-by-step explanation:

Answer:

736 Newtons

Step-by-step explanation:

Given

Pressure = [tex]\frac{Force}{Area}[/tex]

Multiply both sides by Area

Area × Pressure = Force

Area = 2.3 × 1.6 = 3.68 m², hence

Force = 3.68 × 200 = 736 Newtons

Answer:

Let X be the event of feeling secure after saving $50,000,

Given,

The probability of feeling secure after saving $50,000, p = 40 % = 0.4,

So, the probability of not  feeling secure after saving $50,000, q = 1 - p = 0.6,

Since, the binomial distribution formula,

[tex]P(x=r)=^nC_r p^r q^{n-r}[/tex]

Where, [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

If 8 households choose randomly,

That is, n = 8

(a) the probability of the number that say they would feel secure is exactly 5

[tex]P(X=5)=^8C_5 (0.4)^5 (0.6)^{8-5}[/tex]

[tex]=56(0.4)^5 (0.6)^3[/tex]

[tex]=0.12386304[/tex]

(b) the probability of the number that say they would feel secure is more than five

[tex]P(X>5) = P(X=6)+ P(X=7) + P(X=8)[/tex]

[tex]=^8C_6 (0.4)^6 (0.6)^{8-6}+^8C_7 (0.4)^7 (0.6)^{8-7}+^8C_8 (0.4)^8 (0.6)^{8-8}[/tex]

[tex]=28(0.4)^6 (0.6)^2 +8(0.4)^7(0.6)+(0.4)^8[/tex]

[tex]=0.04980736[/tex]

(c) the probability of the number that say they would feel secure is at most five

[tex]P(X\leq 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)[/tex]

[tex]=^8C_0 (0.4)^0(0.6)^{8-0}+^8C_1(0.4)^1(0.6)^{8-1}+^8C_2 (0.4)^2 (0.6)^{8-2}+8C_3 (0.4)^3 (0.6)^{8-3}+8C_4 (0.4)^4 (0.6)^{8-4}+8C_5(0.4)^5 (0.6)^{8-5}[/tex]

[tex]=0.6^8+8(0.4)(0.6)^7+28(0.4)^2(0.6)^6+56(0.4)^3(0.6)^5+70(0.4)^4(0.6)^4+56(0.4)^5(0.6)^3[/tex]

[tex]=0.95019264[/tex]

Answer:

11.8 feet

Step-by-step explanation:

The given situation is represented in the figure attached below. Note that a Right Angled Triangle is being formed.

We have an angle which measures 28 degrees, a side opposite to the angle which measure 6.3 feet and we need to calculate the side adjacent to the angle. Tan ratio establishes the relation between opposite and adjacent by following formula:

[tex]tan(\theta)=\frac{Opposite}{Adjacent}[/tex]

Using the given values, we get:

[tex]tan(28)=\frac{6.3}{x}\\\\ x=\frac{6.3}{28}\\\\x=11.8[/tex]

Thus, the distance from the pole is 11.8 feet

Step-by-step explanation:

You are close.  When calculating the radius and angle, you use the magnitudes of the real and imaginary terms.  In other words, you leave out the i in the calculation.

r = √((-8)² + (√3)²)

r = √(64 + 3)

r = √67

θ = π + atan((√3) / (-8))

θ ≈ 2.928

Answer:True

Step-by-step explanation:

Given Fran earn [tex]\$ 225[/tex] per week working 15 hr

i.e. in 7 days he earn [tex]\$ 225[/tex]

in 1 day [tex]\frac{225}{7}[/tex]

i.e. in 15 hr he earns [tex]\frac{225}{7}[/tex]

in 1 hr  [tex]\$ \frac{15}{7}[/tex]

he has to earn [tex]\$600 [/tex]extra to make [tex]\$1400[/tex]

i.e. he needs to work [tex]\frac{600\times 7}{15}[/tex]hr extra

For 20 weeks he needs to work 2 hr extra

i.e. total 17 hr per day to save [tex]\$ 1400[/tex]

she needs to work atleast 17 hr

Answer:

B on edgenuity

Step-by-step explanation:

Answer:

  8184 vocalists sang in total

Step-by-step explanation:

The number needed is ...

  8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096

You can add these up to get a total of 8184, or you can use the formula for the sum of a geometric series:

  Sn = a1(r^n -1)/(r -1) . . . . where a1 is the first term and r is the common ratio

  S10 = 8(2^10 -1)/(2 -1) = 8(1024 -1)/1 = 8184

Answer:

6,138

Step-by-step explanation:

Number of vocalist needed on the first day = 6

Each day after that, the number of vocalists needed doubles

To Find:

The total number of vocalist found on the 10th day = ?

Solution:

By using the geometric series

Where

a is the first term

r is the ratio

n is the number of terms

On substituting the values

That is

The first day = 6 vocalist

Second day = 12 vocalist

third day =24 vocalist

Fourth day   =48 vocal list

Fifth day = 96 vocalist

Sixth day = 192 vocalist

Seventh day = 384 vocalist

eight day = 768 vocalist

Ninth day = 1536 vocalist

Tenth day = 3072 vocalist

So

6+12+24+48+96+192+384+768+1536+3072 = 6138 vocalist sang in total on the  end of tenth day.

Answer:

7

Step-by-step explanation:

I am assuming that the division problem looks like this:

-2|  1   2   -3   1

Going off that assumption, we will work this problem.  The first thing you always do in the execution of synthetic division is to bring down the first number.  Then multiply that number by the one "outside", which is -2, then put that number up under the next number in the line:

-2|  1   2   -3   1

         -2

     1

Now add the 2 and -2 and bring that down as a 0 and multiply the -2 times the 0:

-2|   1   2   -3   1

          -2    0

      1    0

Now add -3 and 0 to get -3 and multiply that -3 times the -2 and put the product up under the next numbe in line;

-2|   1   2   -3   1

           -2   0  6

      1     0   -3

Now add the 1 and the 6 to get the remainder:

7

Answer: 7

Step-by-step explanation:

A

P

E

X

By the conditional property we have:

If A and B are two events then A and B are independent if:

                  [tex]P(A|B)=P(A)[/tex]

                               or

                 [tex]P(B|A)=P(B)[/tex]

( since,

if two events A and B are independent then,

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

Now we know that:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Hence,

[tex]P(A|B)=\dfrac{P(A)\times P(B)}{P(B)}\\\\i.e.\\\\P(A|B)=P(A)[/tex] )

Based on the diagram that is given to us we observe that:

Region A covers two parts of the total area.

Hence, Area of Region A= 72/2=36

Hence, we have:

[tex]P(A)=\dfrac{36}{72}\\\\i.e.\\\\P(A)=\dfrac{1}{2}[/tex]

Also,

Region B covers two parts of the total area.

Hence, Area of Region B= 72/2=36

Hence, we have:

[tex]P(B)=\dfrac{36}{72}\\\\i.e.\\\\P(B)=\dfrac{1}{2}[/tex]

and A∩B covers one part of the total area.

i.e.

Area of A∩B=74/4=18

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{18}{72}\\\\i.e.\\\\P(A\bigcap B)=\dfrac{1}{4}[/tex]

Hence, we have:

[tex]P(A|B)=\dfrac{\dfrac{1}{4}}{\dfrac{1}{2}}\\\\i.e.\\\\P(A|B)=\dfrac{2}{4}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}[/tex]

Hence, we have:

[tex]P(A|B)=P(A)[/tex]

         Similarly we will have:

[tex]P(B|A)=P(B)[/tex]

The only thing you can do with this expression is to factor a 5 out of the two terms: we have

[tex]15n-20 = 5(3n-4)[/tex]

Answer:

5(3n-4)

Step-by-step explanation:

because(5*3n)-(5*4)=15n-20