10 people always get on a bus in the same order and sit on the same places. what is the probability that, if the 1st person has randomly changed his/her seat, the 10th will be able to sit on his/her original seat?

The dimensions of the corral of maximum area 80 x 160 feet

What is Area?

Area is a quantity that describes the extent of an area on a plane or curved surface. The area of ​​a planar region or planar region refers to the area of ​​a shape or planar layer, while surface area refers to the area of ​​an open surface or boundary of a three-dimensional object

Set each side perpendicular to the wall x

Parallel to the wall would be 320-2x

the area would be:

A(x) = x (320-2x)

A(x) = 320x-2x ^ 2

It is quadratic with a = -2 and b = 320

The largest area will happen when x = -b / 2a

= -320 / (- 2 * 2)

= 80 feet

so the width will be 80 feet and the length will be:

length = 320-2 * 80

           = 160 feet

Hence, The dimensions of the corral of maximum is 80 x 160 feet

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The double number line that represents the distance and time of the bird shows the equivalent in the given values which is further illustrated in the attached diagram.

Number line is defined as the representation of numbers in suc a way that numbers at the right side of the line are positive and larger than the numbers at the left which are negative.

The double number line is defined as the type of number line that contains two labelled parallel lines that contains figures that are marked at equal increments.

From the attached diagram, the first line is labelled the distance covered by the bird which is measured in meters.

The second line is labelled the time used by the bird to cover the given distance.

The given values of both the distance and time is shown to have an equivalent ratio which appears vertically on the double number line.

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Answer:

F and D are whole numbers

Mr. and Mrs. Crone needs to deposit $2164.31 to have $20000 in 10 years.

Finalize the compound growth formula using the amounts. Then equate for the unknown digit.

A = P[tex](\frac{1+r}{n} )^{nt}[/tex]

where A is the account balance, P is the investment amount that needs to be figured out, r is the annual interest rate which is 1.25%, t is the year which is 10 years, and n is the number of annual interest rates which is 52,

Filling in the given values, we have

20000 = P[tex](\frac{1 +.0125}{52} )^{520}[/tex]

20000 = P(0.092403)

P = 20000 ÷ 0.092403

P ≈ 2164.31

Therefore, $2164.31 is required to have $20000 in 10 years.

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Answer:

2.  See below.

4.  Domain = {57, 68, 93, 99}

Step-by-step explanation:

Given relation:

[tex]\{ (1,5),(2,3),(3,2),(4,1),(5,0)\}[/tex]

The given relation is a set of ordered pairs (x, y), where the first element is x and the second element is y.

To express the given relation as a table, enter the x-value of each ordered pair in the left column, and the corresponding y-value of each ordered pair in the right column:

[tex]\begin{array}{|c|c|}\cline{1-2} x & y\\\cline{1-2}1&5\\\cline{1-2}2&3\\\cline{1-2}3&2\\\cline{1-2}4&1\\\cline{1-2}5&0\\\cline{1-2}\end{array}[/tex]

An ordered pair is used to represent the position of a point on the coordinate plane.  Therefore, to represent the given relation as a graph, plot each ordered pair on the given coordinate plane.  

(See attachment 1).

To represent the given relation as a mapping diagram:

(See attachment 2)

The domain is the set of all x-coordinates.

Therefore, the domain of the given mapping diagram is {57, 68, 93, 99}.

Answer:

Step-by-step explanation:

C. Explanation: 100+20=120

X=100

There is an infinite number of values that are in both the domain and range.

Here, we are given a function f(x) = m, where m is a real number greater than 0.

For a function, domain is all the input values that the function can take and range is all the output value that the function can take.

Here, all the x values are the domain and the set of all the values that m can take is the range of the function.

Here m can take all values except 0. Whereas there is no constraint on the x values.

Since the range can never have the value 0, options 1 and 2 are eliminated.

Clearly, there can be many values that are both in the domain and range of the given function.

Thus, there is an infinite number of values that are in both the domain and range.

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Answer:

no

Step-by-step explanation:

12+16+12+16=56

48 is smaller than 56

Answer:

33 1/3 %increase

Step-by-step explanation:

You take the difference of 60 and 45 which is 15 and divide that by 45

[tex]\frac{15}{45}[/tex] i s.3333333  as a percent this would be 33 1/3 % increase

After 3.94 hours, the price of stock A and stock B will become same.

What do you mean by price?

Price can be defined as the amount of money that get paid for something.

Lets assume that after x hours the price of stock A is equal to price of stock B.

Since the price of stock A is increasing at rate of 0.11 per hour, so after x hours it will become:

$12.15 + 0.11x

Since the price of stock B is decreasing at rate of 0.08 per hour, so after x hours it will become:

$12.90 - 0.08x

Equating both price to get the value of x:

12.15 + 0.11x = 12.90 - 0.08x

(0.11+0.08)x = 12.90 - 12.15

x = 0.75/0.19

x = 3.94

Hence, after 3.94 hours the price will be same.

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Yes, Polly is right. 28 bags can be filled.

Polly has a full 5 kg sack of rice.

Each full bag contains 350 g of rice.

Solution:

5 Kg is 5000g.

Therefore,

5000/350 = 14.29

That is 14 bags in total.

Polly assumes that the rice from 2 sacks will fill twice as many bags as the rice from 1 sack.

Therefore,

2 * 5000/350 = 28.57 bags which is twice 14 bags.

Therefore, her assumption is right.

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Answer:

120 denim jeans were left

Step-by-step explanation:

320 - 50% = 160 left at the end of december

160 - 25% = 120 left at the end of January

Answer:1: 4^n+52: 3^8+n3: 2^n4: 2^nStep-by-step explanation:For number 1, since we have multiplication, we just add the powers, so we get 4^n+5For number 2, it's the same thing, so 3^8+nFor number 3, since it's division, we subtract, therefore it will be 2^2n-n, which you can simplify to 2^nFor number 4, it's also the same thing, we get 2^3n-2n, which we can also simplify to 2^nHope this helped :D

Step-by-step explanation:

is used in answer

Answer:

A. 2^n

B. 5^(5n+7)

Step-by-step explanation:

Answer:

Solution Below.

Step-by-step explanation:

This question tests on the concept of angle properties.

From the question above, we can form up an equation:

x + 2x + (x + 30) = 180 (Sum of angles in a triangle)

Now, we can solve for x to find the angles of each side.

[tex]x + 2 x + x + 30 = 180 \\ 4x + 30 \\ 4x = 150 \\ x = 37.5[/tex]

Now we can find the angles for each side:

x = 37.5

2x = 2 × 37.5 = 75

x + 30 = 37.5 + 30 = 67.5

Answer:

37.5, 75, and 67.5

Step-by-step explanation:

The angles of a triangle add up to 180 so everything inside is equal to 180.

180=x+2x+x+30, simplify

180=4x+30, subtract 30 on both sides

150=4x, divide 4 on each  side

37.5=x

solve now knowing x

x= 37.5

x+30= 67.5

2x= 75

Answer: yes it is interesting because u also know more about finance and you would have a much easier life after this

Step-by-step explanation:

a claim that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block.

For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

Why are theorems and postulates crucial in geometry?

The foundation of any mathematical system, including geometry, algebra, and trigonometry, are postulates and theorems. Mathematicians have created entire systems of mathematics by utilizing postulates to argue theorems that can then be proved by other theorems.

A statement that has been proven true or that can be proven is known as a theorem in mathematics. A logical argument that uses the deductive system's inference rules to establish a theorem is called a proof.

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95 % is the percentage of person that have diabetes that also tested positive for the disease.

To do this we would have to loot at the top of the table and the information that is at the left hand side of the table.

At the top we have the column that is tagged, test powitive and the test negative columns.

On the side we have the have diabetes and do not have diabetes row. We are interested in the people that have diabetes and also have tested positive to the disease.

On the table, this is tagged as 36.1%

Then the total = 38%

hence we would have

36.1%/38% x 100

= 0.361 / 0.38 x 100

= 0.95 x 100

= 95%

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Answer: 33

Step-by-step explanation:

We can make the unknown number x and set the question as:

x-10=23

By adding 10 on both sides the equation would look like so

x=33

And so your answer would be 33.

The monomial if the expression is the square of that monomial is; ⁵/₄a⁶b³

A monomial is defined as a polynomial, which has only one term or defined as an algebraic expression with a single term.

We are given the expression;

1⁹/₁₆ a¹²b⁶

Now, we can convert the mixed fraction to improper fraction to get;

²⁵/₁₆a¹²b⁶

The question is asking for the monomial, and the given is squared. What we will do is to extract that square from expression, and ensure that it's done applying a squared root, because that's the opposite operation of a squared power:

√(²⁵/₁₆a¹²b⁶) = ⁵/₄a⁶b³

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The constant of proportionality based on the information regarding Micah is 1/2

The constant of proportionality simply implies that the ratio which relates to the values has a constant value. This is represented as k.

In this case, for every $5 that Micha saves, by parent give him $10.

Let the amount that he saves be y

Let the amount that was given to him be x.

The constant is k.

This will be:

y = kx

5 = 10k

Divide

k = 5/10

k = 1/2

The constant of proportionality is 1/2.

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Using a system of equations, it is found that she bought:

To find how many bags of each candy she bought, we have to solve a system of equations, in which the variables are given as follows:

She bought three more bags of Reese's than lollipops, hence the first equation is:

y = x + 3.

She bought two fewer bags of Starbursts than lollipops, hence the second equation is:

z = x - 2.

Bags of lollipops cost $3.75 each, bags of Reese's cost $5.50 each and bags of Starbursts cost $4.25 each. She spent a total of $48.50, hence the third equation is:

3.75x + 5.5y + 4.25z = 48.50.

We have the variables y and z as a function of x, hence we can replace them into the third equation and solve for x as follows:

3.75x + 5.5(x + 3) + 4.25(x - 2) = 48.50

13.50x + 8.50 = 48.5.

13.50x = 40.50.

x = 40.50/13.50.

x = 3. (number of lollipops bags).

Hence the number of Reese's bags is:

y = x + 3 = 3 + 3 = 6.

The number of Starbursts bags is:

z = x - 2 = 3 - 2 = 1.

The problems asks for the number of bags of each candy that was purchased.

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The expressions that are equal (equivalent) to 2.65 + 3.78 include the following:

B. 3.78 + 2.65

D. 9.51- 3.08

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to determine the expressions that are equivalent to the given expression. Therefore, we would evaluate each of the expressions as follows:

Expression = 2.65 + 3.78

Expression = 6.43.

From the group of answer choices, we have:

Expression A = 2.56 + 3.86

Expression A = 6.42 (not equivalent).

Expression B = 3.78 + 2.65

Expression B = 6.43 (equivalent).

Expression C = 10 - 3.67

Expression C = 6.33 (not equivalent).

Expression D = 9.51- 3.08

Expression D = 6.43 (equivalent).

Expression E = 9.51- 3.08

Expression E = 5.43 (not equivalent).

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Complete Question:

What are all the expressions that are equal to 2.65+3.78?

A. 2.56 + 3.86

B. 3.78 + 2.65

C. 10 - 3.67

D. 9.51- 3.08

E. 8.21 - 2.78.

The equivalent expression of the expression 1.1 × 10 - 32.2 × 10⁴ will be

⇒ - 3,31,989

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is;

⇒ 1.1 × 10 - 32.2 × 10⁴

Now,

Solve the expression as;

The expression is;

⇒ 1.1 × 10 - 32.2 × 10⁴

⇒ 11 - 3,22,000

⇒ - 3,31,989

So, 1.1 × 10 - 32.2 × 10⁴ =  - 3,31,989

Thus, The equivalent expression of the expression 1.1 × 10 - 32.2 × 10⁴ will be

⇒ - 3,31,989

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Answer:

y = (5/2)x + 1 or

y =  2.5x + 1

Step-by-step explanation:

The slope-intercept form of the equation of a line is

y = mx + b

where m = slope, b = y-intercept

Slope = rise / run

where rise is the difference in y-values of two points on the line and run = difference in x values for the same two points'

Here the points are (2, 6) and (-2, -4)

rise = 6 - (-4) = 6 + 4 = 10

run = 2 - (-2) = 2 + 2 = 4

Slope = 10/4 = 5/2

Equation is

y = (5/2))x + b

To calculate b, plug in x, y values for (2, 6) to get
6 = (5/2) x 2 + b

6 = 5 + b

b = 6 - 5 = 1

Equation of line is

y = (5/2)x + 1

Maggie made a mistake while combining similar terms of x using vertical angles; the result is -3x rather than 3x, hence the right answer is x = 9.

When two lines intersect, vertical angles are two angles that are opposed by the same vertex and are congruent, meaning they have the same measure.

The vertical angles for this issue are as follows:

4x + 2.

7x - 25.

Since they agree, the following equation may be used to determine the variable x:

4x + 2 = 7x - 25.

The following results from shifting all terms with x to the left side of the equality and all terms that are constant to the right side, with the opposite signal:

4x - 7x = -25 - 2

Combining similar phrases yields the following results:

-3x = -27.

Maggie made a mistake here since 4x - 7x = -3x, thus the proper answer is as follows:

3x = 27

x = 27/3

x = 9.

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The domain of the set of ordered pairs is {-6, 4, 5, -5, 8,} and the range is {7, -9, 2, 9, -8)} which are represented as a function.

The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.

Given the set of ordered pairs as :

{(-6,7),(4,-9),(5,2),(-5,9),(8,-8)}

Since the domain is the set containing the x-coordinates of all ordered pairs.

So the domain = {-6, 4, 5, -5, 8,}

And the range is the set containing the y-coordinates of all ordered pairs.

So the range = {7, -9, 2, 9, -8)}

Thus, the domain of the set of ordered pairs is {-6, 4, 5, -5, 8,} and the range is {7, -9, 2, 9, -8)}. which are represented as a function.

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Answer:

| -0.125 | >  | 0.0125 |

Step-by-step explanation:

Due to the absolute value signs, the negative sign is null and void. Therefore, 0.125 > 0.0125.

Answer:

0.1375

Step-by-step explanation: