Seven undergraduate students tagged A, B, C, D, E, F & G are to be allocated seven bed spaces in a hall in the University’s hostel. Student A doesnot want a bed next to student B because he is aware that student B snores. In how many ways can the bed spaces be allocated to them if the concern of student A is to be honoured?​

Answer:

[tex]6\sqrt{2}+3\sqrt{10}[/tex]

Step-by-step explanation:

Use the Distributive Property. Remember that you can multiply the numbers under a square root whether or not they're the same. But you can ONLY add square roots when the square root part is the same.

[tex]\sqrt{3}(2\sqrt{6}+\sqrt{30})\\= \sqrt{3}(2\sqrt{6})+\sqrt{3}(\sqrt{30})\\=2\sqrt{18}+\sqrt{90}[/tex]

Simplify each square root part:

[tex]2\sqrt{18}+\sqrt{90}\\=2(3\sqrt{2})+3\sqrt{10}\\=6\sqrt{2}+3\sqrt{10}[/tex]

Since the square root parts are different, you cannot simplify any further.

Over a given period of time, Seth sold more water bottles than Hayden.

To compare the number of water bottles sold by Seth and Hayden, we need to find out the equation for Seth's sales rate. Looking at the graph, we can see that Seth sold 10 bottles on day 1, 20 bottles on day 2, 30 bottles on day 3, and 40 bottles on day 4.

We can find the average daily sales rate for Seth by dividing the total bottles sold by the number of days:

Average daily sales rate for Seth = (10+20+30+40)/4 = 25

The equation given for Hayden's sales rate is y = 11x, where y represents the number of bottles sold and x represents the number of days. This equation shows that Hayden sells 11 bottles per day.

Comparing the two sales rates, we can see that Seth sold more water bottles. On average, Seth sold 25 bottles per day, while Hayden sold only 11 bottles per day. Therefore, over a given period of time, Seth sold more water bottles than Hayden.

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The most appropriate measure of variability to use in this case is the IQR (Interquartile Range) of 13.

The reason for this is that the data appears to be skewed towards the higher values, with more donations in the higher range (from 40 to 59 dollars) and fewer in the lower range (from 10 to 39 dollars).

Using the range (which is the difference between the highest and lowest values) would not accurately represent the variability of the data, as it would be heavily influenced by the outliers. On the other hand, the IQR, which is the range of the middle 50% of the data, is a more robust measure of variability that is not influenced by outliers. Therefore, the IQR of 13 is the most appropriate measure of variability to use in this case.

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Answer:

Casey's monthly payment is $150.
Anita's monthly payment is $230.

Step-by-step explanation:

Part A:

The system of equations that describes this situation is:

a + c = Total monthly bill

a = c + 80

where a represents Anita's monthly payment, c represents Casey's monthly payment, and Total monthly bill represents the combined bills of Anita and Casey.

Part B:

To solve the system, we can substitute the second equation into the first equation and get:

(c + 80) + c = Total monthly bill

Simplifying this equation, we get:

2c + 80 = Total monthly bill

We also know that over the course of 4 months, their combined bills are $1,520. So we can write:

4(Total monthly bill) = 1520

Substituting the equation for Total monthly bill from the previous step, we get:

4(2c + 80) = 1520

Simplifying this equation, we get:

8c + 320 = 1520

Subtracting 320 from both sides, we get:

8c = 1200

Dividing both sides by 8, we get:

c = 150

So Casey's monthly payment is $150. To find Anita's monthly payment, we can use the second equation from Part A:

a = c + 80

a = 150 + 80

a = 230

Therefore, Anita's monthly payment is $230.

Answer:  6

Step-by-step explanation:

you just get those numbers and times them 3 times 2 is 6

Answer:

exponential graph

Step-by-step explanation:

it is a exponential graph the is negative ,if you substitute x values and find the points to plot you'll see how it is plotted

Answer:

See graph

Step-by-step explanation:

The graph of any function can be identified by making an x-y table.

Choose some values for x (often -2, -1, 0, 1, 2)

f(-2) = - 2^(-2) = - 1/4

f(-1) =  - 2^(-1) = - 1/2

f(-0) =  - 2^(-0) = - 1

f(1) =  - 2^(1) = - 2

f(2) =  - 2^(2) = - 4

Answer:

Step-by-step explanation:

The margin of error is ±0.3. This means that the actual average number of vehicles per household in the population is expected to be between 1.5 (1.8 - 0.3) and 2.1 (1.8 + 0.3).

To calculate the range of the margin of error in terms of the number of vehicles, we can multiply the margin of error by the square root of the sample size (100) to get:

0.3 * sqrt(100) = 3

So the margin of error in terms of the number of vehicles is ±3.

Therefore, the number of vehicles included in the margin of error is between 1.5 * 50,000 = 75,000 and 2.1 * 50,000 = 105,000.

So the range of the margin of error in terms of the number of vehicles is 30,000, and the number of vehicles included in the margin of error is 30,000.

the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,

In the given question,

Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.

From the problem, we know that:

The first mechanic worked for 20 hours, so he charged 20x dollars.

The second mechanic worked for 15 hours, so he charged 15y dollars.

Together, they charged a total of $2600, so we have:

20x + 15y = 2600

The sum of the two rates was $155 per hour, so we have:

x + y = 155

We can use these two equations to solve for x and y. First, we can rewrite the second equation as:

y = 155 - x

Then, we can substitute this expression for y into the first equation:

20x + 15(155 - x) = 2600

Simplifying and solving for x, we get:

20x + 2325 - 15x = 2600

5x = 275

x = 55

Now that we know x, we can use the second equation to find y:

y = 155 - x = 155 - 55 = 100

Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.

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Olivia could have used a combination of a rotation and a translation to move ABCDE onto A"B"C"D"E".

Angelica's transformed figure will not match A"B"C"D"E" because reflecting ABCDE over the y-axis will change the order of the letters in the figure.

No, Michael is not correct.

Translating ABCDE diagonally by 8 units up and 10 units right will move each point in ABCDE the same distance horizontally and vertically, which will change the shape of the figure.

In order to match A"B"C"D"E", the transformation must preserve the order of the letters and the angles between the segments.

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Answer:

The two numbers are 494 and 504

Step-by-step explanation:

Let x = one of the numbers

Let y = the other number

x + y = 998

x - y = 10   or x = y + 10

Substitute y + 10 for x in the first equation and solve for y

x + y = 998

y + 10 + y = 998  Subtract 10 from both sides

y + y = 988  Combine like terms

2y = 988  Divide both sides by 2

y = 494

One of the numbers is 494.

x = y + 10  Substitute 494 for y

x = 494 + 10

x = 504

The other number is 504.

Check:

x + y = 998

504 + 494 = 998

998 = 998 checks

x - y = 10

504 - 494 = 10

10 = 10 checks

Helping in the name of Jesus.

Answer:

No solution.

Step-by-step explanation:

To solve this problem, all you have to do is graph the lines and see where they intersect.

This is what you would do to solve a normal problem. However, these lines are parallel this means that the solution to these lines is no soultion

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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Step-by-step explanation:

Compounding formula

FV = PV ( 1 + i )^n      FV = Future value (4000)       PV = present value

                      i = decimal interest per PERIOD = .09/365

                      n = periods = 2 1/4 yrs * 365 days/yr = 821.25 periods

4000 = PV ( 1 + .09/365)^821.25

Solve for PV = $ 3266.83

Answer:-₍1,3₎

Step-by-step explanation:

To solve this system of equations, we can use the method of elimination to eliminate one of the variables. We can multiply the first equation by 5 and the second equation by -3, then add the two equations to eliminate $y$:

$(5)(2x + 3y = 4) \Rightarrow 10x + 15y = 20$

$(-3)(3x + 5y = 7) \Rightarrow -9x - 15y = -21$

Adding the equations, we get:

$10x + 15y - 9x - 15y = 20 - 21$

Simplifying, we get:

$x = -1$

Now we can substitute $x=-1$ into one of the original equations to solve for $y$. Using the first equation, we have:

$2(-1) + 3y = 4$

Solving for $y$, we get:

$y = 2$

Therefore, the solution to the system of equations is $x=-1$ and $y=2$. We can check this solution by substituting $x=-1$ and $y=2$ into the other two equations:

$3(-1) + 5(2) = 7$

$10(-1) + 15(2) = 20$

Both equations are true, so our solution is correct.

The cost per highlighter is approximately $1.

To find the cost per highlighter, we can use a system of equations. Let's call the cost per highlighter "h" and the cost per pen "p". Then, we can set up two equations based on the information given;

80h + 20p = 120 (day 1)

120h + 40p = 200 (day 2)

We can simplify these equations by dividing both sides by 20;

4h + p = 6 (day 1)

6h + 2p = 10 (day 2)

Now we can use the first equation to solve for p in terms of h;

p = 6 - 4h

Substitute this expression for p into second equation;

6h + 2(6 - 4h) = 10

Simplify and solve for h;

6h + 12 - 8h = 10

-2h = -2

h = 1

Therefore, the cost per highlighter is $1.

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Answer:

option c) x=-6

Step-by-step explanation:

-15x = 90

= x = 90/-15

= x = (-6)

The probability that the team wins the debate is 0.6475

P(win) = P(win | S)P(S) + P(win | J)P(J) + P(win | R)P(R)

= (0.25)(0.2) + (0.6)(0.35) + (0.85)(0.45)

= 0.6475

Therefore, the probability that the team wins the debate is 0.6475.

In order to simulate the probability that a Sophomore is never selected to give the closing argument in the next 5 debates, we can use the following steps:

Create a table of random digits with enough rows and columns to simulate the 5 debates. Each row represents a debate and each column represents a team member.

Assign the digits 0, 1, and 2 to represent the events that a sophomore, junior, and senior gives the closing argument, respectively.

Starting from the first row and first column, read the digits from the table and determine which team member gives the closing argument for the first debate.

If a sophomore is selected, record a 0 for that debate. Otherwise, record a 1.

Repeat steps 3 and 4 for the remaining debates, filling in the table as you go.

Calculate the proportion of simulations where a Sophomore is never selected to give the closing argument in the next 5 debates.

Repeat steps 1-6 many times (e.g., 10,000 times) to get a more accurate estimate of the probability.

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Answer:

i think its b sorry if  it's wrong

Step-by-step explanation:

Answer:

A. No, it is not possible. An equilateral triangle is also an equiangular triangle, meaning all of its angles measure 60°.

B. Yes, it is possible. By the Triangle Inequality Theorem:

15 + 15 > 20, and 20 + 15 > 15

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

In mathematics, an expression is a combination of numbers, variables, and operators that can be evaluated to produce a value. Expressions can be simple or complex and are used to represent mathematical relationships and operations.

To find -4 - 2 1/2 expression on the number line by drawing an arrow, we need to start at -4 and then move left by 2 1/2 units.

To do this, we can draw an arrow starting at -4 and then mark off 2 1/2 units to the left. One way to represent 2 1/2 units is to divide the space between -4 and -5 into two equal parts, and then mark off one of those parts.

The resulting arrow should end at -6 1/2. This is because -4 - 2 1/2 is equal to -6 1/2.

Here's an example of what the arrow would look like:

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Step-by-step explanation:

we just need to find out how many percentage of the daily goal each day, so let's assume that $50 is 100% of the daily goal.

Answer:

Area = ½* height(a+b)

Where;

a=4units

b=8units

h=6units

Therefore Area= ½*6(4+8)

= ½*6*12

=36sq.un

Answer:

24sq²

Step-by-step explanation:

Area = ( b1 + b2) x h

          ---------------------

                     2

Area =   (8 + 4) x 6

          ---------------------

                     2

Area =     (12) x 6

          ---------------------

                     2

A = 72/2

A = 36

A = 1/2 * b * h

A = (1/2) * 4 * 6

A = (1/2) * 24

A = 12

36 - 12 = 24sq²

I hope this helps!

If local city government wants to display the ages of the city citizen, It would be better to organize the data using a histogram.

A histogram is a graph that shows the distribution of a set of continuous data. The ages of city citizens can be considered as continuous data, as there are many possible values for age within a certain range.

A dot plot, on the other hand, is a graph that shows the distribution of a set of discrete data. Discrete data are values that can only take on specific, isolated values, like shoe sizes or the number of siblings a person has.

A histogram would be more effective for displaying the distribution of the ages of city citizens because it can show the range of ages in a more continuous manner, and provide a more precise representation of the frequency of the different age groups.

A dot plot, on the other hand, would be less effective, as it could be difficult to represent every age value as a single dot, and the resulting graph may not provide a clear indication of the distribution of ages.

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The percentage increase in the number of water bottles from February to April is 19%.

A company manufactures water bottles. The list describes the amount of water bottles manufactured in three months.

Therefore,

Therefore,

Number of water bottles in march = 4100 + 7% of 4100

Number of water bottles in march =4100 + 7 / 100 × 4100

Number of water bottles in march = 4100 + 287

Number of water bottles in march =  4387

Hence,

Number of water bottles manufactured in April = 4387 + 500 = 4887

Therefore,

percentage increase from February to April = 4887 - 4100 / 4100 × 100

percentage increase from February to April = 787 / 4100 × 100

percentage increase from February to April = 78700 / 4100

percentage increase from February to April = 19.1951219512

percentage increase from February to April = 19%

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The side length x of the given right angle triangle is: 14.97

When two sides of a right-angled triangle are given and one side is to be found, we can do so using the Pythagoras theorem. In the given triangle the base is x, the perpendicular is 10 and the hypotenuse is 18.

According to the Pythagoras Theorem, the following equation can be written as:

x² = 18² - 10²

x = √224

x = 14.97

Thus, that is the missing length of the given right triangle

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Answer:

(10, -10)

Step-by-step explanation:

This are the farest the graph can go unless you want (100,-100)

Change the values from negative to positive and positive to negative to get the most farest results

Answer: D

Step-by-step explanation:

I graphed so you can see.  Count how far each are away.

(5,8) is 12 away

(-7,-5) is 13 away

So you answer is D

Or

You can also think of it as, for, (5, 8)  only the x changed so you only moved in the x direction.  subtract the numbers 5-(-7)=12

For (-7,-5) you only moved in the y direction, so subtract those 8-(-5)=13

The zeros of the quadratic profit function are explained as:

x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made

The quadratic function is given as:

f(x) = −x² + 50x − 264

The general form of expression of a quadratic function is:

f(x) = ax² + bx + c

The quadratic formula to find the zeros is:

x = [-b ± √(b² - 4ac)]/2a

Thus, we have the zeros as:

x = [-50 ± √((-50)² - 4(-1 * -264))]/2(-1)

x = 6 and x = 44

This represents number of monthly memberships where no profit is made.

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