In how many ways can Harold, Steve, John, Roslyn, Marian and Connie line up so that no two of Harold, Steve and John are next to each other ?
There are four general arrangents of boy/girl to consider:
BGBGBG, GBGBGB, BGGBGB, and BGBGGB.
For any one of these four basic arrangements, the boys can be
rearranged (permuted) among themselves in 3 × 2 × 1 = 6 different
ways. Similarly, the three girls can be rearranged among
themselves in 6 ways. Since the boys and girls can be rearranged
independently, the number of ways to create any one of the four
basic arrangements is 6 × 6 = 36.
So the total number of ways that 3 boys and 3 girls can line up so
that no two of the three boys are next to each other is
4 × 36 = 144 .

Answer:

send the picture clearly i will help uou surely

The correct option is (a) 48.

In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.

In the equation:

b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.

To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.

In this case, we can do this by multiplying both sides of the equation by 4.

This cancels out the denominator of the fraction on the left side, and we get,

b = 12*4= 48.

This means that when b is equal to 48, the equation b/4 = 12 is true.

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Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.

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The inequality which shows that Shelby should work for h hours is given by 15.5 h - 300 ≥ 280.

Given that,

Rent = 300 dollars

Shelby wants to have at least $280 left over after paying rent.

The total earnings of Shelby calculated in a week are given as, 15.5 h

where,

h is the number of hours

To that we have to substract the rent amount, and we'll get how much does she have left after paying rent,

15.5 h - 300

And she wants this amount to be at least 280 dollars. The inequality can therefore be expressed as follows,

15.5 h - 300 ≥ 280

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The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.

Suppose you choose a red/black card:

The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].

Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].

Suppose you choose a red/red card:

The probability of choosing red and red card is 2/6.

Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .

Considering we see a single side of the card we have the following probability:

[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]

The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].

The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].

So, the conditional probability of both red sides is given as:

[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]

Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].

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The length of ST is 16 units.

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

We have to given that;

Point P is the midpoint of ST.

SP = x + 4, and ST = 4x

Since, P is the midpoint of ST.

Hence, We get;

⇒ SP = PT

And, ST = 2 SP

Substitute all values we get;

⇒ 4x = 2 (x + 4)

⇒ 4x = 2x + 8

⇒ 4x - 2x = 8

⇒ 2x = 8

⇒ x = 4

Thus, The value of ST = 4x

                                  = 4×4

                                  = 16

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Answer: The scale factor is a ratio that compares the dimensions of an object to a copy of that object. To find the scale factor from the original picture to the copy, you can divide the length of the copy by the length of the original.

In this case, the length of the original picture is 8 feet and the length of the copy is 1/2 a foot.

So the scale factor is:

1/2 a foot / 8 feet = 1/16

This means that the copy is 1/16 the size of the original. This means that, for each inch or foot on the original, the same length on the copy is 1/16 of that length.

It's also common to express scale factor as a ratio or a fraction of the original, which in this case is 1/16

It's worth mentioning that you could use this same method to find the scale factor for any other dimension of the picture, such as width, height and so on.

Step-by-step explanation:

Answer:

a. 1.05

b. 0.95

Step-by-step explanation:

a. 5 percent increase

5% = 0.05

Because it is increasing, so we add 1

1 + 0.05 = 1.05

b. 12 percent decrease

12% = 0.12

Because it is decreasing, so subtract 1

1 - 0.05 = 0.95

So, the answer is

a. 1.05

b. 0.95

To list the sides of a triangle in order from shortest to longest, you can follow these steps - Measure the length of each side of the triangle using a ruler or measuring tape. Then, write down the lengths of each side in a list. Sort the list in ascending order. The shortest side will be at the top of the list, and the longest side will be at the bottom.

A triangle is a polygon with three sides. By the property of a triangle which is the sum of any two sides of a triangle is greater than the third side. This property is known as the "Triangle Inequality Theorem".

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I believe this is correct.

A is: -4, -6, 2

B is: -4, 6

Answer:

m<BCD=60

Step-by-step explanation:

4x+6=7x-12

3x=18

x=6

4(6)+6

24+6

30

30+30=60

======================================================

Reason:

Use the HL (hypotenuse leg) theorem to prove that triangle BCF is congruent to triangle DCF.

It then leads to the fact that angle BCF is congruent to angle DCF.

Set those angle expressions equal to one another. Solve for x.

angle BCF = angle DCF

4x+6 = 7x-12

4x-7x = -12-6

-3x = -18

x = -18/(-3)

x = 6

Then,

Both angles are the same measure to confirm the correct x value.

Lastly, add up those angles to get angle BCD.

30+30 = 60 degrees is the final answer.

Answer:g

Step-by-step explanation:

g

Answer:

Step-by-step explanation:

2/9 + x = 11/18

x = 11/18 - 2/9

x = 63/162

x = 7/18

2/9 + 7/18 = 11/18

11/18 = 11/18

The problem can be solved using algebra. Let's say the discount rate is x, then the price after discount is:

60000 (1 - x/100)

The price after VAT is:

60000 (1 - x/100) (1 + y/100) = 58986

Where y is the rate of VAT.

Rearranging the equation we get:

(1 - x/100) (1 + y/100) = 58986/60000

Multiply both sides by 100 to get rid of the fractions:

100 (1 - x/100) (1 + y/100) = 981

Expanding and grouping like terms, we get:

100 - x + 100y - xy = 981

We can see that x is in two terms, so we can move one side of the equation and get:

100 - x + 100y = 981 + x

x = (981 + x - 100 + 100y)/100 = (981 + xy - 100y)/100

Now we have x in only one term and we know the value of x is 10%, so we can substitute it:

10 + 10y = 9.81

Solving for y we can find that y = 0.81 or 81%

So the VAT rate is 81%

An expression which is equivalent to given [tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex] is 5 / (z + 5)

The correct answer is an option (B)

Consider given quotient.

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5z+15} }[/tex]

Consider expression 5z + 15

We can write this expression as 5(z + 3) by  taking out the common factor 5.

So given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{z+3}{5(z+3)} }[/tex]

As we know a fraction is put in lowest terms by cancelling out the common factors of the numerator and the denominator.

For fraction [tex]\frac{z+3}{5(z+3)}[/tex] , the common term is z + 3.

So, [tex]\frac{z+3}{5(z+3)} = \frac{1}{5}[/tex]

We know that for fractions a/b and c/d where b ≠ 0, d ≠ 0, if we take quotient of these fraction then that would be,

(a/b) / (c/d) = (a/b) × (d/c)

So, given quotient would be,

[tex]\frac{\frac{1}{z+5} }{\frac{1}{5} }\\\\\\=\frac{1}{z+5} \times \frac{5}{1} \\\\\\=\frac{1\times 5}{(z + 5)\times 1}[/tex]

= 5 / (z + 5)

Therefore, an equivalent expression is: 5 / (z + 5)

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On solving the provided question, we can say that the sum of the two expressions will be -4n + 6

It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: (Mathematical Operator, Number/Variable, Expression) A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)It is possible to compare expressions and phrases.

Expression, Number/Variable, and Mathematical Operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

let the two expression be

-4nand 6 and the sum will be -4n + 6

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The area of the garden whose length and width as given in the task content is; 30 (x + 2) square units.

It follows from the task content that the expression which represents the area of the garden plot whose dimensions are as given.

Recall that Area, A = length × width.

Therefore, since length = 6 (√(x + 2)) units

The width = (5 √(x + 2) ) units

Hence, the area of the garden plot as required in the task content is; 6 (√(x + 2)) × ( 5 √(x + 2) )

= 30 (x + 2) square units

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Answer:

y(2-10)2(12+3x)...

Step-by-step explanation:

first make groups of the numbers

y2 with 10 y they both have y in common

so you can write it as y(2-10)

after 24 with 6x they both have 2in common (2×12=24)

so you can write it as 2(12+3x)

and you can do the rest with the same technique

Step-by-step explanation:  12 - 14 is 2 years

                                               14 - 15 is 1 year

                                               15 - 17 is 3 years

I would say the rang is 1 -3 years apart

Hope this helps any

Answer:

4 sweets per friend

Step-by-step explanation:

so first you want to minus 10 sweets since she ate 10 leaving her with 40 sweets. then she gives 8 sweets to her brother leaving her with 32 sweets left. If you divide the remaining sweets ( 32 ) by 8 you get 4 sweets per friend

Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2

3.5 x 4 + 11 x 2.2 = 14 + 24.2

3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.

Using BODMAS,

B-Bracket

O-Of

D-Division

M-Multiplication

A-Addition

S-Subtraction

Multiplication comes first before addition, so

3.5×4=17

+

11×2.2=24.2

17+24.2=41.2

The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangles are congruent triangles. Then the ratio of the corresponding sides will be equal to one. Then the equation is given as,

4x + 17 = 7

Simplify the equation, then we have

4x + 17 = 7

4x = 7 - 17

4x = - 10

x = - 10/4

x = - 2.5

The equation is 4x + 17 = 7. Then the value of the variable 'x' will be negative 2.5.

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The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.

A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.

Given that,

When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.

According to the question,

P(x) = 6bˣ

Put p(x) = 51 and x = 6

51 = 6b⁶

17/2 = b⁶

b = [17/2]¹/⁶

b = 1.43

The b value that must be simplified is given as 1.43. A is the proper answer.

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In given right triangle ACB, the ratios for sin A and cos A :

sin(A) = 48/50

cos(A) = 14/50

Consider the following diagram.

In a right triangle ACB, the angle ACB = 90 degrees.

We know that in right triangle for an angle θ, the trigonmetric ratios are:

sin(θ) = opposite side of θ/ hypotenuse

cos(θ) = adjacent side of θ / hypotenuse

Here, side AC = 14 units, side CB = 48 units and the hypotenuse AB = 50 units

We need to find the ratios for sin A and cos A

In right triangle ACB for angle A,

sin(A) = opposite side of angle A/ hypotenuse

sin(A) = CB/AB

sin(A) = 48/50

And cos(A) = adjacent side of A / hypotenuse

cos(A) = AC/AB

cos(A) = 14/50

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Answer:

y ≤ [tex]\frac{1}{3}[/tex] x - 4

Step-by-step explanation:

the first step is to obtain the equation of the line.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (3, - 3) ← 2 points on the line

m = [tex]\frac{-3-(-4)}{3-0}[/tex] = [tex]\frac{-3+4}{3}[/tex] = [tex]\frac{1}{3}[/tex]

the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4

y = [tex]\frac{1}{3}[/tex] x - 4 ← equation of the line

----------------------------------------------

the shaded region below the line indicates the values that are less than y

the solid line indicates that y can equal the values on the line (≤ )

the solution is then

y ≤ [tex]\frac{1}{3}[/tex] x - 4

You can differentiate best time, worst time and average time of an algorithm like this:

Best time = fastest completion time with optimal inputs.

Worst time = slowest completion time, with pessimistic inputs.

Average time = arithmetic mean

The average-case complexity of an algorithm is the amount of a computational resource (typically time) used by the algorithm, averaged over all potential inputs, according to computational complexity theory. The worst-case complexity, which takes into account the algorithm's maximum complexity given all potential inputs, is frequently contrasted with it.

There are three main reasons to investigate average-case complexity. First off, while some problems may be insurmountable in the worst case, the inputs that cause this behaviour may only occasionally occur in practise, so the average-case complexity may be a better indicator of an algorithm's performance.

Second, tools and techniques to create challenging problems are provided by average-case complexity analysis. These tools and techniques can be used in fields like derandomization and cryptography.

Third, average-case complexity enables the most effective algorithm in practise to be distinguished from algorithms with equivalent best case complexity.

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Answer:

infinity/undefined (both are acceptable)

Undefined is actually the best answer in college but your answer key might put it as infinity.

Step-by-step explanation:

Observe that the x coordinates of the two points are exactly the same at 12.

This reduces the possibility of the line being a horizontal or a vertical line.

Imagine, if x coordinates is always the same, it means that you are only varying y and that happens when you move up and down the graph.

Hence, the line is a straight vertical line. (Line equation: x = 12)

Gradient/Slope of a vertical line = infinity/undefined.

The slope of the given line is Undefined

The slope of the line when two points in the line is given is given by

m=(y₂-y₁)/(x₂-x₁)

The points are (12,0) and (12,9)

m=(9-0)/(12-12)

  = 9/0

  =Undefined

The slope of the line is Undefined

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Answer: Its B

Step-by-step explanation:

[tex]24x+15=25x+45[/tex]

Subtract 25x from both sides:

[tex]24x+15-25x=25x+45-25x[/tex]

[tex]-x+15=45[/tex]

Subtract 15 from both sides:

[tex]-x+15-15=45-15[/tex]

[tex]-x=30[/tex]

Divide both sides by -1(to remove negative from variable):

[tex]\dfrac{-x}{-1} =\dfrac{30}{-1}[/tex]

[tex]\fbox{x = -30}[/tex]

Answer:

[tex] \sf \: x = - 30[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ 24x + 15 = 25x + 45

Then the value of x will be,

→ 24x + 15 = 25x + 45

→ 24x - 25x = 45 - 15

→ -x = 30

→ [ x = -30 ]

Hence, the value of x is -30.