How is Pascal's triangle used in binomial theorem?.

The words in the image is translated from Russian language to English language  as "Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly,  I don't know"

To translate this paragraph to English, if you're not a native Russian speaker or fully understand the language to read and write, we can easily  apply an online free tool for this type of text. This tool can translate texts as well as words in an image.

Using that here, the paragraph can roughly be translated as

"Don't you really think you can learn something for yourself? - Ilya. She spoke with that goal that she hated in herself, i don't believe it. For example, here Vekshina! Exactly,  I don't know"

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16 student volunteers and 5 faculty volunteers will make up the four-person student-faculty government committee. the probability of the likelihood that the following members will be on the committee:

A) All academic staff

Probability is equal to 5C4 / 21C4 or 5/5985.

The likelihood that the committee will be made up of only academics is 0.000835.

b) Two pupils and two professors equal (16C2 x 5C2) / 21C4.

There is a 0.40100 chance that the committee will be made up of two students and two faculty members.

b) All pupils = 16C4 / 21C4 = 1820 / 5985

The likelihood that every student will be represented on the committee is 0.30409

d) Three students and one professor equal 5c1 * 16c3 / 21c4 or 5 * 560 / 5985.

There is a 0.46783 percent chance that the committee will be made up of one professor member and three students.

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Sampling variation will have more impact on confidence interval, but is not accounted for by the margin of error.

What is Sampling variation?

What factors lead to sampling variation?

Sample Sizes and Variability

What does the sample variation reveal?

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a) Number of elements in the union of all three sets when the sets are pairwise disjoint is 300

b) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and no elements in all three sets  is 150

c) Number of elements in the union of all three sets when there are 50 common elements in each pair of sets and 25 elements in all three sets  is 175

d) Number of elements in the union of all three sets when the sets are equal is 100

What do you mean by relation and function?

(INPUT, OUTPUT) is a representation of an ordered pair.

The relationship between INPUT and OUTPUT is demonstrated by the relation. A function, on the other hand, is a relation that yields one OUTPUT for each given INPUT. Although all relations are functions, not all functions are relations. A function is a relationship that states that there should only be one output for each input, or we could refer to it as a particular category of relationship (a collection of ordered pairs) that adheres to a rule.

Given are three distinct sets, A1, A2, and A3, each with 100 members. The number of elements in the uninon set, A1 U A2 U A3, are as follows, according to the circumstances.

First off, if we remember the formula, it will be really simple to determine how many components make up the union set;

n(A1 U A2 U A3) = n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 ),

a) This states that we dont have any common elemets in  any pair of these sets,

n( A1 ∩ A2 ) = 0, n( A2 ∩ A3 ) = 0 , n( A1 ∩ A3 )  = 0 and also  n( A1 ∩ A2 ∩ A3 ) = 0 and as given n( A1 ) = n( A2 ) = n( A3 ) = 100 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 0 - 0 - 0 + 0

= 300      

b)  We have

n( A1 ) = n( A2 ) = n( A3 ) = 100

n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and n( A1 ∩ A2 ∩ A3 ) = 0 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 50 - 50 - 50 + 0

= 150      

c) We have

n( A1 ) = n( A2 ) = n( A3 ) = 100

n( A1 ∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = 50 and

n( A1 ∩ A2 ∩ A3 ) = 25 .

Hence the no of elements in the union set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 50 - 50 - 50 + 25

= 175      

d) This states that all the common elemets are present in the three sets, so

n( A1 ) = n( A2 ) = n( A3 ) = 100 as well as n( A1∩ A2 ) = n( A2 ∩ A3 ) = n( A1 ∩ A3 ) = n( A1 ∩ A2 ∩ A3 ) = 100

Hence the no of elements in the unino set A1 U A2 U A3 will be

n(A1 U A2 U A3)

= n( A1 ) + n( A2 ) + n( A3 ) - n( A1 ∩ A2 ) - n( A2 ∩ A3 ) - n( A1 ∩ A3 ) + n( A1 ∩ A2 ∩ A3 )

= 100 + 100 + 100 - 100 - 100 - 100 + 100

= 100    

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The amount of time it will take 16000 gallons to fill the pool 3/4 full is 320 minutes.

Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.

To calculate the amount of time it takes to fill 3/4 of the pool , we  use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1 and solve for t

Hence, the time it will take is to fill the pool 3/4 full 320 minutes.

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Sadie didn't simplify the expression properly and made mistakes during the simplification. The correct answer after simplification will be [tex]3a^{3} b\sqrt{6ab }[/tex]

Whenever we are about to simplify an expression, we should do it till the most simplified answer we got and follows the maths rules properly.
Sadie simplified the expression [tex]\sqrt{54a^{7}b^{3} }[/tex].

He first made an error during the simplification step at
[tex]\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex] where it should be [tex]3^{2}[/tex] not [tex]3^{3}[/tex].
Secondly, he came to the answer [tex]3a b \sqrt{6 a^5 b}[/tex] but we can simplify it more by simplifying [tex]a^{5}[/tex].

We can find the correct answer by simplifying the expression [tex]\sqrt{54a^{7}b^{3} }[/tex] by the following:

[tex]\sqrt{54a^{7}b^{3} }[/tex] = [tex]\sqrt{3^2 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}[/tex]

=  [tex]3 \cdot a \cdot|b| \sqrt{6 \cdot a^5 \cdot b}[/tex]

= [tex]3 a b \sqrt{6.a^4.a.b}$[/tex]
= [tex]3.a.b.a^{2} \sqrt{6ab}[/tex]
[tex]= 3a^{3}b\sqrt{6ab}[/tex]

So the most simplified answer to the expression  [tex]\sqrt{54a^{7}b^{3} }[/tex]  is  [tex]3a^{3}b\sqrt{6ab}[/tex].

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Your question is incomplete, but most probably your full question is:

Sadie simplified the expression [tex]\sqrt{54 a^7 b^3}[/tex], , where [tex]$a \geq 0$[/tex] as shown:

[tex]\sqrt{54 a^7 b^3}=\sqrt{3^3 \cdot 6 \cdot a^2 \cdot a^5 \cdot b^2 \cdot b}=3 a b \sqrt{6 a^5 b}[/tex]

Describe the error Sadie made, and explain how to find the correct answer.

The best description of the graph of the proportional relationship is: D.  A line from (0, 0) going through (43, 36.55) where the x-axis is labeled Weight (in pounds) while the y-axis is labeled Cost (in dollars).

The graph that represents a proportional relationship is a straight line graph that passes through the origin (0, 0) and has a constant of proportionality, k, which is y/x.

Thus, given that the relationship between total cost for laundry service (y) is proportional to the weight of laundry (x), it means that the graph that will pass represent this would have the following features:

Therefore, the best description in words is: option D (last option).

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Answer:

Its A i did the practice exam test

Step-by-step explanation:

the guy above was wrong and didn't even make sense so here you go ;)

A list of 6 one digit whole numbers with an average of 5, a median of 6, a range of 9, and no mode is

since the numbers will have no mode so they are all different

Assuming the numbers are: a, b. c. d. e. and f

The average is 5

(a + b + c + d + e + f ) / 6 = 5

a + b + c + d + e + f = 30

The median is 6

(c + d)/2 = 6

c + d = 12  (assume c = 5 and d = 7)

range is 9

f - a = 9, since it is a one digit number a range of 9 is possible for 9 - 0

hence a = 0 and f = 9

substituting assumed values to the average

0 + b + 5 + 7 + e + 9 = 30

b + e + 21 = 30

b + e = 9 (let b = 8and e = 1)

hence the numbers are

0, 1, 5, 7, 8, and 9

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For the circle , AC and CB are orthogonal

According to the question ,

AB is the diameter of a circle with center O and the C is a point on one

of the two arcs joining A and B

Let AO = -u and OB = u and CO = v

To prove that AC and AB is orthogonal .

We have to show their dot product is zero i.e.  CA . CB = 0

=> CO + CA = -u

=> CA = -v -u

=> CO + CB = -v

=> CB = -v + u

So, the dot product,

CA . CB = (-v -u ) . ( -v +u)

=> v .v + u . v - v . u - u .u

=> |v|² +u . v - u . v - |u|²

=> |v|² - |u|² = 0

Hence , the length of v is same as the length of u

Therefore , AC and AB are orthogonal

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Answer:

1 11/20

Step-by-step explanation:

3 3/4 - 2 1/5 = 3 15/20 - 2 4/20 = 1 11/20

The doubles Plus 1 is a strategy to learn addition and subtraction faster and make it easy to do.

we know that adding the same number twice is easier than adding two different numbers

like: 8+8 = 16  this is easier to remember and do

       8+9 = 17  here we might make mistakes

so if we use the double plus one strategy to solve 8+9

we write it as 8+9 = (8+8)+1 = 16+1 = 17

hence this makes is easier for us to understand and do it faster.

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The center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

The equation of the circle is given as x² + y² - 32x+24y +396 = 0.

Comparing the given equation with general equation of circle, x² + y² + 2gx + 2fy + c = 0.

The center of circle is C = (-g, -f)

The radius of circle is r = √g² + f² - c

Therefore, from the given equation,

2g = -32

g = -16

2f = 24

f = 12

C( -16, 12)

And the radius is

r = √(-16)² + (12)² - 396

= √256 + 144 -396

=√4

= 2

Hence, the center and the radius by completing the square of the given equation of circle is x² + y² - 32x+24y +396 = 0 is C( -16, 12) and radius is 2.

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The sample standard deviation of 12,7,6,4 and 11 will be 3.4.

According to the question,

We have the following set of data:

12,7,6,4 and 11

Now, we know that the following formula is used to find the sample standard deviation for a set of data:

Sample standard deviation = [tex]\sqrt[]{\frac{sum of (xi - mean)^{2} }{n-1} }[/tex]

whereas n is the number of data set and xi is the different numbers of the data set

Number of scores in data set = 5

So, we have the mean:

(12+7+6+4+11)/5

40/5

8

Now, subtracting each number from the mean:

12-8 = 4

7-8 = -1

6-8 = -2

4-8 = -4

11-8 = 3

Now, we will square these numbers:

4*4 = 16

-1*-1 = 1

-2*-2 = 4

-4*-4 = 16

3*3 = 9

Now, we have the following step for sample standard deviation:

(16+1+4+16+9)/(5-1)

46/4

11.5

Now, the square root of this number will be final answer:

[tex]\sqrt{11.5}[/tex]

3.4

Hence, the correct option is A.

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The two quantities x and y, are directly proportional. If x is doubled, then value of y will also be doubled.

If two quantities become directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.

For the given situation;

x and y are in the direct proportional relation.

Thus,

x ∝ y

Thus,

x = k y

k = proportionality constant.

Thus,

multiplying both side by 2

2 x = 2 k y

Y also becomes twice .

If x is multiplied by 4 then,

4 x = 4 k y

y also get 4 times.

Thus, if x is doubled, then value of y will also be doubled and if x get 4 timed y also become 4 times.

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By using SAS congruence theorem we have proved that ΔABC≅ΔCDE.

Two triangles are congruent if any two sides and the angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle included between the sides of the second triangle.

Triangle SAS-Congruence

Example: AB= PQ, AC=PR, and the angle between AC and AB equals the angle between PR and PQ, i.e. A = P.

That is specifically stated in the SAS rule. When two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent. An included angle is one that is formed by the intersection of two given sides.

In the illustration,

∠B≅∠D

By using SAS congruence,

If the two triangles are congruent then their sides are equal.

Therefore,

[tex]\bar{AB}[/tex]=[tex]\bar{CD}[/tex]

And [tex]\bar{AC}[/tex]=[tex]\bar{CE}[/tex]

[tex]\bar{BC}[/tex]=[tex]\bar{DE}[/tex]

ΔABC≅ΔCDE

Hence, Δ ABC ≅ Δ PQR.

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If the leading coefficient is positive, bigger inputs only make the leading term more and more positive

How do you tell if a graph has a positive or negative coefficient?

If the leading coefficient is positive, bigger inputs only make the leading term more and more positive. The graph will rise to the right. If the leading coefficient is negative, bigger inputs only make the leading term more and more negative. The graph will descend to the right.

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A line passes through (0, 2) and has a slope of 13. What is the equation of the line in slope-intercept form?

y = 1/3x + 2 (y equals 1 third x plus 2)

y = 1/3x − 2 (y equals 1 third x minus 2)

y = −1/3x + 2 (y equals negative 1 third x plus 2)

y-intercept is : (0 , 2)

slope = 13 or 13/1 (this is positive so slope will be positive)

slope = rise/run = y/x

The scatterplot that represents Bryson's data is the scatterplot that is downward sloping.(Check the graph attached)

What is negative correlation?

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By calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.

It is given to us that -

Eighty percent of seniors at the local high school graduate each year

There are in total 750 seniors this year

We have to find out the number of seniors who will graduate.

Since it is mentioned that Eighty percent of seniors at the local high school graduate each year and there are in total 750 seniors this year, then the number of seniors who will graduate this year will be equal to -

80% of 750

= (80/100) * 750

= 600

Therefore by calculating the percentage of seniors that graduate each year, it can be concluded that this year 600 seniors will graduate.

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The total cost "C" for the construction as a function of h is C = 5h/√2 + 10h   .

In the question ,

it is given that ,

the shape of the triangle is = isosceles triangle

length of the legs of the triangle = x ft ,

length of the hypotnuse of the triangle = f ft ,

the cost of fencing for legs = $5 per feet ,

the cost of fencing for hypotnuse = $0 per feet .

The pen is in shape of an isosceles right angle. This means one of angle is 90 degrees and 2 sides of triangle are equal and base angles are equal too.

So , By Pythagoras Theorem ,

x² [tex]+[/tex] x² [tex]=[/tex] h²

2x² = h²

x² = h² / 2

x = √h²/ √2 = h/√2

the cost will be written as  ,

Cost = 5×(x) + 10×(h)

Cost = 5×(h/√2) + 10h

C = 5h/√2 + 10h

Therefore , The cost function is C = 5h/√2 + 10h .

The given question is incomplete , the complete question is

A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. if fencing costs $5/ft for the legs and $10/ft for the hypotenuse, write the total cost c of construction as a function of h.

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The total cost of 44 people in the class party will be $631

The total cost in dollars of a class party is 59 + 13n

Where n = number of people attending in the class party

Let F(n) be the function representing the total cost in dollars of a class party

Such as, F(n) = 59 + 13n

As per the question, the total cost of attending the 44 people will be:

For 44 people we have n = 44

As we had, F(n) = 59 + 13n

Here, F(n) will be treated as a function in which n will be its domain while F(n) will give the output as a range.

F(44) = 59 + 13(44)

     = 59 + 572

    = 631

Total cost will be $631

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Total number of games for 9 teams so that each team will play 12 games in the baseball league will be 432

Total number of teams in the baseball league is 9

Total number of games that each team will play is 12

Since, each team will have option of 8 teams to play with since no team can play with itself

Therefore, number of games that each team will play after playing 12 games will be 8 x 12 = 96

Since there are 9 teams, therefore total number of games that two teams will play = 96 x 9 = 864

Now, as it takes two teams to play a game therefore the required number of games for the 9 teams = 864/2 = 432

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A graph that correctly displays the solution of the system of inequalities is graph D.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality plotted on a graph and these include the following:

Additionally, the y-value for these system of inequalities intersects the x-axis at 5 and the boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be represented with the greater than (>) inequality symbol.

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Answer:

should be that graph, picture below!

Step-by-step explanation:

taking test!

The probability of heads and tail on coin flipped can be determined using Pascal's Triangle

Probability for flipping coin can be determined using Pascal's Triangle, here's how it's works:

1st level of Pascal's Triangle is 1, it means only 1 possibility when the coin not flipped

2nd level of Pascal's Triangle is 1 1, it means there's 2 possibility when the coin flipped 1 times, 1 heads and 1 tail

3rd level of Pascal's Triangle is 1 2 1, it means there's 3 possibility when the coin flipped 2 times, 2 heads (1 probability), 1 head 1 tail (2 probability), and 2 tails (1 probability)

4th level of Pascal's Triangle is 1 3 3 1, it means there's 4 possibility when the coin flipped 3 times, 3 heads (1 probability), 2 heads 1 tail (3 probability), 1 head 2 tails (3 probability) and 3 tails (1 probability)

And the list will go on depends how many the coins flipped

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The given statement is False . That is regression sum of squares (ssr) can be greater than the total sum of squares (sst).

Regression sum of squares (ssr)

The sum of squares regression is the sum of the differences between the predicted value and the mean of the dependent variable.

SSR = ∑( yᵢ-cap - y-bar)² and i = 1 to N

Total Sum of Squares (SST) :

Total Sum of Squares is the deviation of the value of the dependent variable from the sample mean of the dependent variable. Essentially, the total sum of squares quantifies the total sample variation. It can be found using the formula:

SST = ∑(yᵢ - y-bar )²

The first is that the regression sum of squares cannot be computed as a total sum of squares. Let's find an explanation for this. We know that the sum of squares can be divided. There's the dualism of squares, some of the squares and regressions, sums of squares, dead food. A regression sum of squares is not formed, it is a total sum of squares. This means the statement is false. The next processing is the value, which is always positive, but we know that the value the confession of the adjustment, in the range -1 to 1.

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The correct option is,

There is no relationship between attending training and the preferred source of auto parts.

What is Null Hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to estimate the probability that the null hypothesis is correct using statistical testing.

Null hypothesis always states that there is no significant difference between given observations. This also means that there is no such relationship between the two sets. That is, there is no effect of value in one set increases on value of another set will increase or decrease.

Hence the Null Hypothesis for given statement , "the relationship between attending training and preferred source of ordering parts " is :

H0 : There is no relationship between attending training and the preferred source of auto parts.

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When two rays intersect an angle is created, As different classification of angles are there on the basis of measurement of angles and on the basis of properties of angles.

When two rays or straight lines intersect at one of their ends, an angle is created. Vertex of an angle refers to the point at which two points meet. The Latin word "angulus," which means "corner," is the origin of the English term "angle."

Symbol of Angle

The symbol ∠ represents an angle. Angles are measured in the form of degrees (°) using a protractor.

For example, 45 degrees is represented as 45°

Sections of Angles

Types of Angles

Based on their measurements, here are the many types of angles:

Interior and Exterior Angles:

Interior angles: Interior Angles are angle formed inside the shape.

Exterior angles: Exterior angles are to be angles that is formed outside a shape, between any side of  shape and to an extended adjacent side.

Complementary and Supplementary Angles:

Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles.

Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles.

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The correlation coefficients that indicate that an increase in one variable results in a decrease in the other;

B. r=-0.5776

C.r=0.2361

Correlation coefficient is a measure of how similar two datasets are acting.

When the correlation coefficient comes out as -1, it means that both the datasets are negatively oppositely correlated. One data increases, other data starts decreases in the opposite direction.

When the correlation coefficient comes out below 0, then values are negatively correlated. SO,

All of the given option are negatively correlated.

If the correlation coefficient comes out as 0, that means both the data sets are uncorrelated.

Therefore, the correlation coefficients that indicate that an increase in one variable results in a decrease in the other;

B. r=-0.5776

C.r=0.2361

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Answer:

R = 1

Step-by-step explanation:

R = y/x

Substitute the x and y values, for example, the first row

5.8/5.8 = 1

Therefore the answer is 1