how many ways are there for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other?

A total of 112 combinations are possible out of all possible combinations  when a coin is tossed  10 times and having total of 4 tails and have different start and end faces.

For the given question we have 2 conditions:

condition 1:

when the start turn have head face then the end turn must have tails face as it is given that start and end have different faces.

so in this case 1st and last position is fixed so we have exactly 8 positions.

and given that out of 10 times there must be total of 4 tails and we discussed that last face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.

so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is = 8 combination 5  = [tex]8_C__5[/tex] =56 ways

conditon 2:

 when the start turn have tail face then the end turn must have head face as it is given that start and end have different faces.

so in this case 1st and last position is fixed so we have exactly 8 positions

and given that out of 10 times there must be total of 4 tails and we discussed that first face already have tail face so now out of 8 available positons we have exactly 3 tails in it and rest 5 must be heads.

so we have 8 available positions and we can select any 5 out of them and the number of ways of selection of this is =8 combination 5 =  [tex]8_C__5[/tex] =56 ways

so total number of ways is = no. of ways condition 1+ no. of ways condition 2 = 56 +56 = 112 ways

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Answer: C -  square root of 74

Step-by-step explanation: took the test and got it right. hope this helps.

have a good day :)

Answer:

[tex]\sqrt{74}[/tex]

Step-by-step explanation:

There can be 8 possible outcomes present in the sample space

The probability that one switch is not working is 3% or 0.03

We need to find the number of possible outcomes in the sample space that can be possible

The first switch can be working or not

The second switch might be working or not

so does the third switch, it might be working or not working

And each switch is independent to one another

The number of outcomes can be

2 x 2 x 2 = 8

Therefore, the number of outcomes are there in the sample space is 8

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The choice that correctly names angles 2 and 3 is called the: D. vertical angles.

Two angles are named vertical angles if both angles form a pair of angles that share the same vertex both not the same side, and they are on the opposite sides of two straight lines that intersect each other.

Given the image above, it shows that angle 2 and angle 3 form a pair that shares the same vertex when two straight lines intersect, and both angles are non-adjacent angles, that is they do not share any common side with each other.

Therefore, according to the definition given above, the angles 2 and 3 can be correctly named as: D. vertical angles.

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To solve this problem, we can set up a system of equations to represent the given information. Let x represent the cost of one steak burger. Then we can set up the following system of equations:

3x + 2(f) = 18

2x + 3(f) = 15.75

Where f represents the cost of one order of fries.

Subtracting the second equation from the first equation gives us:

x = 18 - 2(f) - 15.75 + 3(f)

= 18 - 15.75

= 2.25

Therefore, the cost of one steak burger is $2.25, which is answer choice C.

The piece of wood that is needed to build each brace 5√2 feet.

Let  the piece of wood that be  needed to build each brace x feet.

A bookcase is 5 feet high and 5 feet wide, so

By condition we can write (5^2)+(5^2)=x^2

⇒25+25=x^2
⇒ 50=x^2

x=√50
prime factors:

50=2 × 5 × 5  

 50 = 2 × 5^2

√50 = √(25 × 2) = 5√2

The piece of wood that is needed to build each brace 5√2 feet .

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Answer:

y = 18 + 12x

Step-by-step explanation:

To find the total cost Mr. Montenegro pays in dollars when x shirts are ordered, we can use the equation y = 18 + 12x, where y is the total cost in dollars and x is the number of shirts ordered. This equation takes into account the delivery fee of $18 and the cost of each shirt, which is $12. Therefore, we can use the equation y = 18 + 12x to find the total cost Mr. Montenegro pays when he orders x shirts.

Answer: 0.5 Liters

Step-by-step explanation:

1 Liter = 1000 milliliters

500 milliliters = 0.5 Liters

I just need to take 500 divided by 1000 = 0.5 Liters

Answer:

40

Step-by-step explanation:

Answer:

  45

Step-by-step explanation:

You want to know the number of line segments that can be drawn between pairs of points in a group of 10 distinct points.

From the first point, 9 segments can be drawn.

From the second point 8 more segments can be drawn. (The segment to the first point has already been counted.)

From the third point, 7 more segments can be drawn. The total number of segments will be the sum of integers from 1 through 9:

  9(10)/2 = 45

45 line segments can be drawn.

__

Additional comment

This is identical to the "handshake" problem: the number of handshakes in a group of 10 people if each shakes hands with all the others.

Answer:

2. ......................

Answer:

2

Step-by-step explanation:

1 + 1 = 2

I hope my answer helps you :)

Answer:

2 or Window

Step-by-step explanation:

1 + 1 = 2

OR

1 + 1 = WINDOW!

The special segment that matches the picture is the Median.

What is the median segment?

A median is a line segment that connects any triangle vertex to the middle of the opposite side. It is also the path that connects an angle's opposite internal side to its midpoint. At the centroid, they coexist.

From the figure, the given triangle in which segment is concurrent at the centroid. It bisects each side of the triangle into two equal parts.

Hence, the special segment that matches the picture is the Median.

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Answer:

1.

2(2x-5)-7(2x-1)=3

Multiply both sides of the equation by 14, the least common multiple of 7,2.

2(2x−5)−7(2x−1)=42

Use the distributive property to multiply 2 by 2x−5.

4x−10−7(2x−1)=42

Use the distributive property to multiply −7 by 2x−1.

4x−10−14x+7=42

Combine 4x and −14x to get −10x.

−10x−10+7=42

Add −10 and 7 to get −3.

−10x−3=42

Add 3 to both sides.

−10x=42+3

Add 42 and 3 to get 45.

−10x=45

Divide both sides by −10.

x= −10/45

​Reduce the fraction  to lowest terms by extracting and canceling out 5.

x=− 2/9

​

2. I don't know this one. Sorry.

3. is in the file

By using normal distribution of probability, it can be calculated that-

a) When x = 142, z = 1.4

b) When x = 130, z = 0.6

c) When x = 103, z = -1.2

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by

f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{z^2}{2}}[/tex]

Where z = [tex]\frac{x - \mu}{\sigma}[/tex] , [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation

Here Systolic blood pressure is normally distributed

Mean = 121

Standard deviation = 15

a) x = 142

z = [tex]\frac{142 - 121}{15}[/tex] = 1.4

b) x = 130

z = [tex]\frac{130 - 121}{15}\\[/tex] = 0.6

c) x = 103

z = [tex]\frac{103 - 121}{15}[/tex] = -1.2

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The triangles JKL and XYZ are congruent by Side-Angle-Side Theorem as KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V.

Herein we find a case of two triangles that we must prove that they are congruent, this is a congruency problem. Two triangles are congruent if the two triangles share the same sides in the same order. In accordance to the figure, we find the given assumptions:

KL ≅ XV, JK ≅ VZ, ∠ K ≅ ∠V

This assumptions satisfies the Side-Angle-Side Theorem and according to it we conclude that the triangles JKL and XYZ.

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Answer:

[tex]2^3 * 3 * 7[/tex]

Step-by-step explanation:

Linked below.

Find two factors and break down individually. Circle prime numbers. If there are more than one of the same prime number, write as an exponent:

i.e. 6 x 6 = [tex]6^{2}[/tex]

The function that models the number of bottles, B, collected during week n is; B(n) = 256(¹/₂)ⁿ⁻¹

The formula for the nth term of a geometric sequence is;

aₙ = arⁿ⁻¹

where;

a is first term

r is common ratio

n is position of term

We are given that;

a = 256 bottles

r = ¹/₂

Thus;

B(n) = 256(¹/₂)ⁿ⁻¹

Thus, we conclude that B(n) represents the required function.

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Answer:

y > -2/3x + 2, y [tex]\geq[/tex] x

[tex]\left \{ {{y > -2/3x + 2} \atop {y \geq x}} \right.[/tex]

Step-by-step explanation:

Knowledge Needed

A system of linear inequalities is graphing 2 lines.

If the line's y side is less than it's x-side (y </ [tex]\leq[/tex] x), shade below.

If the line's y side is greater than it's x-side (y </ [tex]\leq[/tex] x), shade above.

If the line is dotted, it is < or >.

If the line is filled in, it is [tex]\leq[/tex] or [tex]\geq[/tex].

Where both regions are shaded is the solution.

Question

Examine the dotted line.

1) We know it is < or > because it is dotted.

2) We know it is y > .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 2.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is -2/3.

y > -2/3x + 2

Examine the solid line.

1) We know it is [tex]\geq[/tex] or [tex]\leq[/tex] because it is solid.

2) We know it is y [tex]\geq[/tex] .... because if it was less than, it would be shaded below, which is impossible because the shaded region is above.

3) We know the y-intercept, when x=0, is 0.

4) We know the slope, how much the y-value of a line changed when the x-value changes by 1, is 1.

y [tex]\geq[/tex] 1x + 0

y [tex]\geq[/tex] x

The solution to the linear inequality is when both lines are shaded in (true), which means both lines are the solution together.

y > -2/3x + 2, y [tex]\geq[/tex] x

Answer:

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

Find the lines first, then determine inequalities based on the shaded region and types of lines.

One line has positive slope and passes through the origin. Its x and y-coordinates are same, hence it is:

The shaded region is above this line and the line is solid, therefore the inequality is:

The second line has a negative slope and it has y-intercept at (0, 2), x- intercept at (3, 0).

Its slope is m = (0 - 2)/(3 - 0) = - 2/3.

So the line is:

Again, the shaded region is above the line, and the line is dashed, hence the inequality is:

Answer: root 70

Step-by-step explanation:

starting info:

KL = 2NM

KM = 20

NO = 7

Using the fact the ratio of similar sides must be equal:

KL/NO = KM/NM

Therefore sub in values…

KL/7 = 20/NM

As KL = 2NM

2NM/7 = 20/NM

Rearrange:

2(NM)^2 = 140

(NM)^2 = 70

NM = root(70)

(Obviously take positive as can’t have negative length)

Answer:

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

Add up all the numbers to get the end of month figure.

Convert mixed fractions to sum of whole and fractions, then combine whole numbers and fractions, bringing all to common denominator of 16.

Answer:

h = 20 mean h can only be 20

h < 20 means h can only be a number that is smaller than 20, can't be exactly 20

Step-by-step explanation:

h = 20

This means the variable h can only be 20; it can't be lower or higher than 20.

h < 20

This means the variable h can only be smaller than 20; this means the number can only be below 20 and can't be exactly 20.

Answer:

x = $2351

Step-by-step explanation:

Answer: x=23

Step-by-step explanation:

1. First we need to find how much needs to be multiplied by 25, so 525/25=21.

2. Now that we know that x-2=21, we do 21+2.

3. 21+2=23, so x=23

Please give brainliest.

Joan saved a total of $78 from her $390 weekly income each week.

What is percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. Percentage means 1 part from hundreds and represented by the symbol '%'. Percentages have no dimensions. Therefore, it is called a dimensionless number.

Percentage = (value/total value)× 100

We have, Joan's income = $390/week

Saving = 20% from her weekly salary.

We have to calculate how much does she save each week. Joan save 20% of her weekly income (i.e $390). let Joan saved $x each week from her sallary. The saved income in dollars each week by Joan i.e ($x) is equals to 20% of 390

x =( 20/100)× 390

=> x = 390/5

=> x = 78

Hence, Joan saves $78 each week.

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Answer:

16%

Step-by-step explanation:

Let's assume the original price of the item was Rs. 100.

After the price increased by 45%, the new price became:

New price = Original price + (45% of Original price)

New price = 100 + (0.45 x 100)

New price = Rs. 145

Now, the price dropped by 20% from the increased price of Rs. 145:

Final price = New price - (20% of New price)

Final price = 145 - (0.2 x 145)

Final price = Rs. 116

We can calculate the overall change in price by finding the difference between the final price and the original price:

Overall change in price = Final price - Original price

Overall change in price = 116 - 100

Overall change in price = 16

So, the price increased by Rs. 16. To find the percentage increase, we can use the formula:

Percentage increase = (Overall change in price / Original price) x 100%

Plugging in the values, we get:

Percentage increase = (16 / 100) x 100%

Percentage increase = 16%

Therefore, the price of the item increased by 16%.

BRAINLIEST PLEASE

The percentage by which the price increased is; 16%

Percentage Increase

Let the price of an item be denoted as x

Now, we are told that the price of the item increased by 45%. Thus means that the price will be; 1.45x

Now, the price after inflation decreased by 20% or 0.2. Thus;

Final price is now; 1.45x(1 - 0.2)

⇒ 0.8(1.45x)

⇒ 1.16 x

Since the original price is x, then;

Difference in price = 1.16x - x

Difference in price = 0.16x

In percentage, this difference in price represents a 16% increase.

The complete question is;

Due to inflation, the price of an item increased by 45% and then dropped by 20%. By what percent did the price increase?

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P (two red counters) = 1/15

P (two green counters) = 2/15

P (two yellow counters) = 1/145

P (white and then red) = 1/30

P (white or yellow, in either order but not both) = 3/10

P (white or red, in either order but not both) = 2/5

The probability of drawing a white or yellow counter first and then any

color second = 7/30

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red counters = 3

Number of green counters = 4

Number of yellow counters = 2

Number of white counters = 1

Total number of counters = 3 + 4 + 2 + 1 = 10

The probability of drawing 2 red counters.

= [tex]^3C_2[/tex] / [tex]^{10}C_2[/tex]

= 3 / 5 x 9

= 1/ 15

The probability of drawing 2 green counters.

= [tex]^4C_2[/tex] / [tex]^{10}C_2[/tex]

= 2 x 3 / 5 x 9

= 2/15

The probability of drawing 2 yellow counters.

= [tex]^2C_2[/tex] / [tex]^{10}C_2[/tex]

= 1 / 45

The probability of drawing one white and then one red counter.

= 1/10 x [tex]^3C_1[/tex]/[tex]^{9}C_1[/tex]

= 1/10 x 3/9

= 1/10 x 1/3

= 1/30

The probability of drawing one white or one yellow counter.

= 1/10 + 2/10

= 3/10

The probability of drawing one white or one red counter.

= 1/10 + 3/10

= 4/10

= 2/5

The probability of drawing one white or one yellow counter and one any counter.

= 3/10 x 7/9

= 7/30

Thus,

The required probabilities are given above.

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Answer: 20 days

Step-by-step explanation:

First, we find the food provisioned for 1 man will last for how many days

Take 80 times 30 = 2400 days

Now we know that 40 more joined

80 + 40 = 120 serve

So, we take 2400 divided by 120 = 20 days