Identify the GCF of the following terms; 18a^4b^9c^2 and 34a^6b^5 and 22a^8bc^7

Using the probability concept, it is found that:

a) The tree diagram is given by the image at the end of the answer.

b) The probability is of 0.18 = 18%.

c) The probability is of 0.72 = 72%.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a in this problem, we have two independent events, hence the tree diagram will contain two nodes, one with each event and it's probabilities.

For item b, since the events are independent, to find the probability of both, we multiply the probability of each, hence:

0.3 x 0.6 = 0.18.

For item c, first we find the probability of none being completed, hence:

(1 - 0.3) x (1 - 0.6) = 0.7 x 0.4 = 0.28.

At least one is complementary to none, hence the probability is given as follows:

p = 1 - 0.28 = 0.72 = 72%.

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Step-by-step explanation:

22. 7 + x

24. 5x

26. f/10

28. 3x + 16

30. k² - 11

32. x + 10

34. 18q

23. x - 35

25. x/3

27. 45/r

29. 18 - 3d

31. 20/t⁵

(although, if being superficial, it could mean (20/t)⁵)

33. (k + 2) - 15

35. 2m + 6

The mathematical statement of the expression t - 3 is the difference between t and 3

Expressions are mathematical statements that are represented by variables, coefficients and operators

The algebraic expression is given as

t - 3

The above mathematical representation is an algebraic expression that is already in its most simplified form

This means that the algebraic expression cannot be further simplified

However, the algebraic expression can be rewritten as a mathematical statement

Recall that, we have

t - 3

The pronunciation of the above expression is:

t minus 3

In expressions, minus represents difference

So, we have

t minus 3 can be represented as the difference between t and 3

Hence, the representation of the algebraic expression given as t - 3 is the difference between t and 3

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Step-by-step explanation:

you can ask questions for clarification

The fraction of straight section of motor racing circuit is 3/14 miles.

To find the fraction of circuit which is straight, we will perform division. The fraction will be found as - Fraction = length of straight section ÷ total length of motor racing circuit

Keep the values in mentioned relation to find the fraction of circuit which is straight.

Converting the mentioned lengths from mixed fraction to fraction.

Length of motor racing circuit = (6×5 + 5)/6

Length of motor racing circuit = 35/6

Length of straight section of circuit = (4×1 + 1)/4

Length of straight section of circuit = 5/4

Fraction of straight circuit = (5/4)/(35/6)

Simplifying the fraction

Fraction of straight circuit = (5×6)/(35×4)

Performing multiplication in numerator and denominator

Fraction of straight circuit = 30/140

Performing division

Fraction of straight circuit = 3/14 miles

Thus, the straight section is 3/14 miles.

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Answer:

x = 3y

y + x = 4y = 180

y = 45

x = 135

Answer:

–37

Step-by-step explanation:

–42 – 19 – (–24)

–42 – 19 + 24

–61 + 24

= –37

The angles that are supplementary angles are: ∠SRT and ∠SRO

Angles that are supplementary will give us a sum of 180 degrees when we add the two angles together. One is the supplement of the other.

Some examples of angles that are supplementary angles that are formed when two parallel lines are intersected by a transversal include:

Angle SRT and angle SRO are angles that are adjacent to each other because they share a common side SR and a common vertex R. They line on the straight line OT.

Therefore, angle SRT and angle SRO are two angles that are supplementary angles as shown in the diagram attached below where lines NP and QS are parallel lines. The supplementary angles are therefore angle SRT and angle SRO.

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The given equations (5b - 2)² + 4 = 25b²– 20b and (2x² + y²)(2x² - y²) = 4x² – y have been found not to be true identities

A) We want to check if (5b - 2)² + 4 = 25b²– 20b is a true identity.

A true identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions. By definition, the two sides of an identity are interchangeable, so we can replace one with the other at any time.

(5b - 2)² + 4 when expanded gives;

25b² - 20b + 4 + 4 = 25b² - 20b + 8

That is not equal to the right hand side and as such, we can say that both equations are not true identities

B) (2x² + y²)(2x² - y²) = 4x² – y

Expand the left side to get;

4x⁴ - y⁴

This result is not equal to the right hand side and as such, we can say that both equations are not true identities.

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Correct question is;

Which of the equations are true identities?

A. (5b - 2)² + 4 = 25b²– 20b

B. (2x² + y²)(2x² - y²) = 4x² – y

Line m passes through the points (6, 10) and (1, 6) & line n passes through the points (2, -1) and (8, 5) , both the lines are neither parallel nor perpendicular.

As given in the question,

Given two lines 'm' and 'n'

Line m passes through the points

(x₁ ,y₁) =(6,10)

(x₂ ,y₂)=(1,6)

Slope of the line m 'm₁'

= (y₂ -y₁)/ (x₂ -x₁)

= (6 -10) / (1 - 6)

=-4 / -5

=4 / 5

Line n passes through the points 'm₂'

(x₁ ,y₁) =(2,-1)

(x₂ ,y₂)=(8 ,5)

Slope of the line m

= (y₂ -y₁)/ (x₂ -x₁)

= (5 - (-1)) / (8 - 2)

= 6 / 6

= 1

m₁ ≠ m₂

m₁ × m₂ ≠-1

Therefore, line m passes through the points (6, 10) and (1, 6) & line n passes through the points (2, -1) and (8, 5) , both the lines are neither parallel nor perpendicular.

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The coordinates of the image of polygon A'B'C'D' would be A' (-1, 1), B' (-1, -2), C' (3, -2), D' (3, 2).

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the pre-image of polygon ABCD is translated (shifted) vertically downward by 4 units and right 5 units, the coordinates of the image of polygon A'B'C'D' would be given by:

(x, y)                    →            (x + 5, y - 4)

Coordinate A = (-6, 5)   →    Coordinate A' (-6 + 5, 5 - 4) = (-1, 1)

Coordinate B = (-6, 2)   →    Coordinate B' = (-6 + 5, 2 - 4) = (-1, -2)

Coordinate C = (-2, 2)   →     Coordinate C' = (-2 + 5, 2 - 4) = (3, -2)

Coordinate D = (-2, 6)   →     Coordinate D' = (-2 + 5, 6 - 4) = (3, 2)

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Answer:

x=mp-n

so that leaves us with the answer

Step-by-step explanation:

m=n+x/p

first you want to move the P over to the left side by x P

so:

mp=n+x

the P on the right side cancels out

now you want to move the n to the left side by subtracting it form both sides

Answer

Step 1:         6,3

Step 2:       x1  -1                     y2- 2

Step 3:           1, 7

Step-by-step explanation:

56 small cubes can be placed in the given cuboid that has the given dimensions.

A cuboid's volume can be calculated using the formula below:

Volume of a cuboid = (length)(width)(height).

A cube has equal height, length, and width. Therefore, the volume of a cube is calculated as:

Volume of a cube = (side length)³.

The number of small cubes that can be placed in the given cuboid = volume of the cuboid/volume of one small cube.

Find the volume of the cuboid:

Length = 60 cm

Height = 54 cm

Width = 30 cm

Volume of the cuboid = (60)(54)(30)

Volume of the cuboid = 97,200 cm³

Find the volume of one cube:

Side length of one small cube = 12 cm

Volume of one small cube = (12)³

Volume of one small cube = 1,728 cm³.

Number of small cubes that will be placed in the cuboid = 97,200/1,728 ≈ 56 cubes.

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The measurement deviates from the mean by more than 100 standard deviations.

It's a way to gauge how widely apart each data point is from the mean. The standard deviation formula comes in two different forms: Standard deviation for the population When you can measure the entire population or the entire collection of data, you use the population version of the formula. Experts in statistics have determined that measurements that fall within a 2 SD range of the true value are more accurate than those that do not..

based on the facts provided;

the average population, =100

The standard deviation for the population

σ=10

Z score:

Z=X−μσ

X:The measurement.

The number of standard deviations the measurement is from the mean:

We are not given the measurement. So, assuming the measurement is equal to 139.

When

X=139

Z=139−100/10

=3.9

It implies that the measurement of

139 is 3.9

standard deviation above the mean of 100;

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Answer:

it's S:21

i had this same question lol

Answer:

1/3

Step-by-step explanation:

0.3333...=1/3

The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.

Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.

Where P exists at the origin and line segment is a horizontal one.

The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).

The segment exists not a horizontal or vertical line:

The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].

Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).

where neither P nor Q exists at the origin.

Use the end points of the segment PQ to estimate the components of the directed segment.

[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle \\[/tex]

= (6, -4)

The components of the segment PX where X exists a point on the segment 1/3 of the way from P to Q are

[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle[/tex]= (2, -1.25)

To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.

Therefore, the coordinates of the point X exists (1 + 2, 6 - 1.25) = (3,4.75).

The segments, PX and XQ, have lengths in a ratio of 1: 2.

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a.

[tex] {3}^{2} \times {3}^{x} = {3}^{7 \\ } \\ \\ {3}^{2 + x} = {3}^{7} \\ 2 + x = 7 \\ x = 7 - 2 \\ x = 5[/tex]

b.

[tex] {7}^{8} \div {7}^{y} = {7}^{6} \\ {7}^{8 - y} = {7}^{6} \\ 8 - y = 6 \\ y = 8 - 6 \\ y = 2[/tex]

c.

[tex]( {q}^{4} )^{z} = q ^{12} \\ q^{4 \times z} = q^{12} \\4 z = 12 \\ \frac{4z}{4} = \frac{12}{4} \\ z = 3[/tex]

I used the laws of exponents.

The y intercept of the function f(x) = 2^2−4 is 0

The x intercept of the function f(x) = 2^2−4 is 0 or 2

The zeros of the function f(x) = 2^2−4 is 0 or 2

When f(x) = f(-4) then the function f(-4) = 48

When f(x) = 2 then x = -0.4142 or 2.142

given data

f(x) = 2^2 − 4

The y intercept

f(x) = 2^2−4

y = 2^2−4

at x = 0

y = 2 ( 0 ) ^2 - 4 ( 0 )

y = 0 - 0

y = 0

The x intercept

f(x) = 2^2 − 4

y = 2^2− 4

at y = 0

0 = 2^2− 4

0 = 2x( x - 2 )

2x = 0    OR     x - 2 = 0

x = 0      OR     x = 2

The zeros

This same as the x intercept

f(-4)

f(x) = 2^2− 4

f(-4) = 2 (-4)^2 - 4 * -4

f(-4) = 2 * 16 + 16

f(-4) = 48

f(x) = 2 when x =

f(x) = 2^2− 4

2 = 2x( x - 2 )

1 = x^2 - 2x

0 = x^2 - 2x - 1

x = -0.4142 or 2.142

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The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

If x= -12 and y=8 then the value of 2/x-3/ - /2y/ over /x+y/ is: 7/2. See the explanation below.

First, recall that the numbers enclosed in |   | are absolute values. That is they remain in the positive domain regardless of their polarity. Recall that the absolute value is the distance between a number and Zero.

Since we know:

x = -12; and

y = 8

Hence,

[2|x-3| - |2y|] / |x+y|

= [2|-12-3| - |2 * 8| ]/ (|-12+8|)
= [2|-15| - | 16|] / |-4|

= ((2*15) - (16))/4    [Using the absolute values]

= (30 -16)/4

= 14/4

= 7/2

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The complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

In this question, we have been given some information about lines a, b, k and m.

We need use this information and determine which lines in the figure are parallel.

We have been given angle 2 is supplementary to angle 3.

We know that, the sum of the angles on the same side of the transversal which are inside the two parallel lines is always 180°

Also, supplementary angles are the angles whose sum is 180°

i.e., ∠2 + ∠3 = 180°

From above we conclude that, the lines and b are parallel and line k would be the transversal.

Therefore, the complete statement would be 'Because it is given that ∠2 is supplementary to ∠3, lines a and b are parallel by Same-Side Interior Angles Postulate'

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Using vertical angles, Maggie made her mistake when combining the like terms of x, which has a result of -3x and not 3x, hence the correct result is of x = 9.

Vertical angles are two angles that are opposite by the same vertex when two lines cross each other, and they are congruent, that is, they have the same measure.

For this problem, the vertical angles are given as follows:

Since they are congruent, we can solve for the variable x as follows:

4x + 2 = 7x - 25.

Moving all the terms with x to the left side of the equality and all the constant terms to the right side, with opposite signal, we have that:

4x - 7x = -25 - 2

Combining the like terms, it is found that:

-3x = -27.

Here happened Maggie's mistake, as 4x - 7x = -3x, hence the correct solution is given by:

3x = 27

x = 27/3

x = 9.

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We need to calculate the 10% of 20. By definition, a% is:

Where a can be any positive number. In this case a = 10, then:

In mathematics, the word "of" is reserved for the product. Then 10% of 20 is just:

Solving this leads to 2.

Answer:

50 percent.

Step-by-step explanation:

10 of 20 as a fraction is

10/20

- divide top and bottom by 10 and this simplifies to

1/2.

To convert to a percentage we multiply by 100:

= 1/2 * 100

= 50%.

The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is; 2.9698

From the complete question written below, we are given that;

Mean Number; M = 103.4

Standard deviation; σ = 21

Sample size; n = 50

Now, in statistics, the formula for the standard error of mean is;

σM = σ/√n

Plugging in the relevant values gives us;

σM = 21/√50

σM = 2.9698

The z score typical average difference between the mean number of seats is;

z = (103.4 - 99.2)/( 2.9698 )

z = 1.41

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Complete Question is;

There are 559 full-service restaurants in Delaware. The mean number of seats per restaurant is 99.2. [Source: Data based on the 2002 Economic Census from U.S. Census Bureau.]

Suppose that the true population mean mu = 99.2 and standard deviation sigma = 21 are unknown to the Delaware tourism board. They select a simple random sample of 50 full-service restaurants located within the state to estimate mu. The mean number of seats per restaurant in the sample is M = 103.4, with a sample standard deviation of s = 18.2. The standard deviation of the distribution of sample means (that is, the standard error, sigma_m) is_.

Answer:

Step-by-step explanation:

To find the unit rate, we divide the price by the number of items bought.

In this question:

Price: $99

Items: 9 books

Unit rate: $99/9 = $11

The unit rate is of $11 per book.

Answer:

2000

Step-by-step explanation:

Number of shares after split is 5/2 times the pre split value =800*5/2 = 2000