An art teacher has 4 1 8 4 8 1 ​ gallons of paint to pour into containers. If each container holds 3 8 8 3 ​ gallon, how many containers can they fill?

Answer:

  6

Step-by-step explanation:

You want the x-coordinate of the midpoint of segment AB with endpoint coordinates A(21, 5) and B(-9, -13).

The midpoint of a line segment has coordinates that are the average of the endpoint coordinates:

  M = (A +B)/2

  M = ((21, 5) +(-9, -13))/2 = (12, -8)/2

  M = (6, -4)

The midpoint of AB is (6, -4).

The x-coordinate of the midpoint is 6.

Answer:

Number of students in each row = 12

Total number of rows = 9

Step-by-step explanation:

We have to assume that each row can seat the same number of students

Find the GCF(greatest common factor) of 60 and 48 to find the number of students in each row

60 = 12 x 5

48 = 12 x 4

The GCF = 12

So there are 12 students per row

If there are 60 third-grade students they will occupy 60/12 = 5 rows
48 fourth grade students will occupy 48/12 = 4 rows

Therefore the total number of rows = 5 + 4 = 9 rows

Answer:

a)  600 foxes

b)  720 foxes

Step-by-step explanation:

See attached spreadsheet.

The rate of population increase is 20% each year.  To find a new year's population, multiply the previous year's population by 0.20 (20%) and add that to the previous year.  Year 1 would be (500)*(0.20) = 100 new foxes which are added to the year 0 population of 500, which means there are (500+100) or 600 foxes in year 1.

Year 2:  (0.20)*(600) = 120 new foxes

Add 120 to the existing 600 to find 720 foxes in year 2,

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

A formula that can be used to predict the fox population for any year, n, would be:

     P(n) = 500*(1+0.20)^n

 where P(n) is the popluation at year n.  The 500 is the population at year 0 (the starting population).  (1+0.20) is the growth for each year (120%, which means the original population plus 20%).  That is raised to the year of interest, n.  [When n=0, (1+0.20)^0 = 1]

The organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.

To answer this question, we can use a bipartite graph as a model. A bipartite graph is a graph that has two sets of vertices, X and Y, with edges only between vertices from different sets. In this case, we can have one set of vertices representing the teams in one pool and the other set of vertices representing the teams in the other pool.

We can start by drawing a bipartite graph with 14 vertices, 7 in each set. Each vertex represents a team, and we can label them as T1, T2, ..., T14. Now, we need to add edges to represent the games that each team will play.

For each team in one pool, we can add 5 edges to connect it to 5 different teams in the same pool, and 2 edges to connect it to 2 different teams in the other pool.

After adding all the edges, we can see that each team has 7 edges connected to it, representing the 7 games that it will play. However, we also need to make sure that each team plays against distinct opponents. To do this, we can check if there are any duplicate edges in the graph.

If there are no duplicate edges, then the schedule can be used as it is. But if there are duplicate edges, then the schedule cannot be used and the organizers need to come up with a different plan.

In this case, we can see that there are no duplicate edges in the graph, which means that the schedule can be used as it is. Therefore, the organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.

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Answer:

Below

Step-by-step explanation:

See image attached

Answer:

x² + 4xy + 4y²

Step-by-step explanation:

(x + 2y )²

= (x + 2y) (x + 2y)

= x² + 2xy + 2xy + 4y²

= x² + 4xy + 4y²

So, the answer is  x² + 4xy + 4y²

Step-by-step explanation:

We can solve for x-y by isolating the term on one side of the equation and simplifying:

5(x-y) + 4 = 7

5(x-y) = 7 - 4

5(x-y) = 3

Next, we can divide both sides by 5:

x - y = 3/5

Therefore, the value of x-y is 3/5.

The first group has a higher proportion of "A" students 0.2

To determine which is better, we need to compare the proportions of "A" students in each group.

For the first group, the proportion of "A" students is:

8/40 = 0.2

For the second group, the proportion of "A" students is:

9/50 = 0.18

Therefore, the first group has a higher proportion of "A" students, and we can say that it is "better" in terms of producing "A" students. However, it is important to note that this is just one aspect of performance and there may be other factors to consider as well.

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The probability of obtaining exactly four tails {( T,T,T,T)}, when flipping four coins is equals to the 1/16 = 0.0625.

Independent Events : If the result of one event does not influence the result of another event, then the events are referred to as independent. In other words, it can be said that both events can happen simultaneously without interference. Probability is defined as a chance of occurrence of an event. Let E be the event that exactly four tails when flipping four coins. As we know that, when One coin is flip, total outcomes = 2 = { H,T}

So, 4 coins flipped, total possible outcomes = 16

Probability of getting tail on flipping one coin = 1/2

That is exactly four tails when flipping four coins are independent events. Therefore, the probability of obtaining four tails in a row in 4 flips of a coin is the product of probability in 4 flips. Since each flipping of a coin is independent, so

the probability of obtaining exactly four tails when flipping four coins = P(X = 4)

=( 1/2)(1/2)(1/2)(1/2) = (1/2)⁴

= 0.0625

Hence, required probability is 0.0625.

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The value of x as per the similarity of triangles is = 7.1.

If two triangles' sides have the same ratio or proportion and their angles are the same (corresponding angles), then the triangles will resemble one another (corresponding sides).

Similar triangles may have varied side lengths when compared individually, but they must all have the same ratio of their side lengths and equal angles.

Now in the figure, the triangles are similar.

So, sides of the triangles will be proportional to each other.

Now, 9/15 = 4.3/x

⇒ x = (4.3 × 15)/ 9

⇒ x = 7.1

Therefore, the value of x as per the similarity of triangles is = 7.1.

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The distribution of X is a hypergeometric distribution, he probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is 0.317 and the mean value of hypergeometric distribution is 1.187.

a. The distribution of X is a hypergeometric distribution with the following parameters:

N = 18 (total number of individuals)
K = 8 (number of individuals taking the test for the first time)
n = 6 (number of individuals randomly assigned to a particular examiner)

b. The probability mass function of a hypergeometric distribution is given by:

P(X = x) = (K choose x) * ((N-K) choose (n-x)) / (N choose n)
So, for example, the probability that exactly 2 of the 6 individuals assigned to the examiner are taking the test for the first time is:
P(X = 2) = (8 choose 2) * (10 choose 4) / (18 choose 6) = 28 * 210 / 18564 = 0.317

c. The mean value of a hypergeometric distribution is given by:

E(X) = n * (K/N) = 6 * (8/18) = 2.667
The standard deviation of a hypergeometric distribution is given by:
SD(X) = sqrt(n * (K/N) * ((N-K)/N) * ((N-n)/(N-1))) = sqrt(6 * (8/18) * (10/18) * (12/17)) = 1.187

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Therefore , the solution of the given problem of slope comes out to be  y = 15x + 10.

A line's steepness is determined by its slope. In gradient based equations, a situation known as gradient overflow can happen. One can determine the slope by dividing the sum of a run (width differential) and rise (climbing distinction) between two places. The equation with the hill variation, y = mx + b, is used to model the fixed path issue. where grade is mm, a = bc, and the line's y-intercept is situated; (0, b).

Here,

A racer:

Due to the fact that the race begins at the beginning, the y-intercept

is 0.

We can select any two locations from the table and use the following formula to determine the slope:

=> Slope Equals (Distance Change) / (change in time)

As an illustration, if we select the coordinates (1, 10) and (3, 40), we obtain:

=>  slope = (40 - 10) / (3 - 1) = 30 / 2 = 15

As a result, Racer A's calculation is:

=>  y = 15x

Runner B:

As an illustration, if we select the coordinates (1, 25) and (3, 55), we obtain:

=> slope = (55 - 25) / (3 - 1) = 30 / 2 = 15

As a result, Racer B's calculation is:

=>  y = 15x + 20

Runner B

The race begins at a distance of 10 feet, so the y-intercept is 10.

We can select any two locations from the table and use the following formula to determine the slope:

Slope Equals (Distance Change) / (change in time)

As an illustration, if we select the coordinates (1, 35) and (3, 65), we obtain:

=>  slope = (65 - 35) / (3 - 1) = 30 / 2 = 15

As a result, Racer C's equation is:

=> y = 15x + 10

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Answer:

B

Step-by-step explanation:

Part II: Value of x=0

Part III: the lengths of the sides of EFG as EF = G = 11 and EG = -11.

Part IV: the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.

Value can be used to find the solution to an equation or to compare two or more values.

Part II: To find the value of x, we need to use measures for AC and EG. We can use the equation AC = 2x + 4 to solve for x.

We can rearrange the equation to 2x = AC - 4, and then substitute in the value of AC, which is 2x + 4.

This gives us 2x = 2x + 4 - 4, or 0 = 0

x = 0.

Part III: To find the lengths of the sides of EFG, we can use the equation EF = G + 7x - 11.

Substituting in the value of x, which is 0, we get

EF = G + 7 * 0 - 11,

or EF = G - 11.

Since EG = 7x - 11, substituting in the value of x gives us

EG = 7 * 0 - 11,

or EG = -11.

So EF = G and EG = -11

Part IV: To find the lengths of the sides of ABC, we can use the equation AB = 5x - 9, substituting in the value of x as 0.

This gives us AB = 5 * 0 - 9,

or AB = -9.

Since GF = 3x - 1 and AC = 2x + 4, substituting in the value of x gives us GF = 3 * 0 - 1,

or GF = -1,

and AC = 2 * 0 + 4

or AC = 4.

So AB = -9, GF = -1, and AC = 4, giving us the lengths of the sides of ABC as AB = -9, GF = -1, and AC = 4.

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The probability that the mean weight of 36 different women is between 140LB and 211LB is approximately 0.9874.

There can only be one value for a random variable. A random variable's value could be zero with a probability of zero. A probability distribution's total probabilities are always equal to one.

a. We must convert the weight to a typical normal distribution using the following formula in order to determine the likelihood that a randomly chosen woman weighs between 140LB and 211LB.

z = (x - μ) / σ

If the weight x, the mean weight, and the standard deviation are all given. The probability can then be determined using a calculator or a typical normal table.

When x=140LB, we get:

z = (140 - 165) / 45.6 = -0.5461

x = 211LB results in:

z = (211 - 165) / 45.6 = 1.0096

The area under the standard normal curve between z = -0.5461 and z = 1.0096 is found to be roughly 0.6267 using a typical normal table or calculator.

Hence, the likelihood that a lady chosen at random weighs between 140LB and 211LB is roughly 0.6267.

b. We must normalise the sample mean to a standard normal distribution using the following method in order to determine the likelihood that the mean weight of 36 individual women is between 140LB and 211LB.

z is equal to (x - ) / (n / sqrt(n)).

When n is the sample size, x is the sample mean weight, is the mean weight, and is the standard deviation. The probability can then be determined using a calculator or a typical normal table.

To solve this issue, we have:

μ = 165LB

σ = 45.6LB

n = 36

If x = 140 LB, we get:

z = (140 - 165) / (45.6 / sqrt(36)) = -2.4994

With x = 211LB, we get:

z = (211 - 165) / (45.6 / sqrt(36)) = 2.4994

The area under the standard normal curve between z = -2.4994 and z = 2.4994 is found to be around 0.9874 using a standard normal table or calculator.

Hence, there is a roughly 0.9874 percent chance that the average weight of 36 individual women falls between 140LB and 211LB.

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For rectangle type books,  the difference in the heights of their stacks of books is 15 3/4 inches.

What exactly is a rectangle?

A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.

In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.

The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The  area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.

Now,

To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:

Rick's stack = 3 x Trevor's stack

Rick's stack = 3 x 7 7/8 inches

Rick's stack = 23 5/8 inches

Now that we know the height of both stacks, we can find the difference between them:

Difference = Rick's stack - Trevor's stack

Difference = 23 5/8 inches - 7 7/8 inches

Difference = 15 6/8 inches

Difference = 15 3/4 inches

Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.

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The surface area of the cone is 305.30 inches squared.

The height of the cone is 7 inches and the diameter of the cone is 8 inches. Therefore, let's find the surface area of the cone as follows:

surface area of the cone = πr(r + l)

where

Hence,

r = 8 / 2 = 4 inches

l² = 7² + 4²

l = √49 + 16

l = √65

l = 8.0622577483

l = 8.06 inches

Therefore,

surface area of the cone = 3.14 × 8.06(4 + 8.06)

surface area of the cone = 25.3154893297(12.06)

surface area of the cone = 305.304801316

surface area of the cone = 305.30 inches squared

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Trey's rectangular prism will require more material to be constructed.

To determine which rectangular prism will require more material to construct, we need to calculate the surface area of each prism.

The surface area of a rectangular prism is given by the formula,

SA = 2×l×w + 2×l×h + 2×w×h

where l, w, and h are the length, width, and height of the prism, respectively.

For Trey's prism, the length is 12, the width is 7, and the height is 4. Therefore, the surface area of Trey's prism is:

SA of Trey = 2(12 x 7) + 2(12 x 4) + 2(7 x 4) = 336

For Matt's prism, the length is 10, the width is 6, and the height is 3. Therefore, the surface area of Matt's prism is,

SA of Matt = 2(10 x 6) + 2(10 x 3) + 2(6 x 3) = 192

Comparing the surface areas, we see that Trey's prism requires more material to construct since its surface area is larger than Matt's prism. Therefore, Trey's rectangular prism requires more material to construct than Matt's rectangular prism.

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The values of a and b  are -10 and 29, respectively of the curve.

What do you mean by turning point of a quadratic curve ?

The turning point of a quadratic curve is the point at which the curve changes direction from going up to going down, or vice versa. It is also known as the vertex of the parabola. The x-coordinate of the turning point is given by -b/2a, and the y-coordinate is the value of the function at that point.

Finding the values of a and b :

Given that the turning point of the curve is (5,4), we can write the following equations:

[tex]4 = 5^2 + 5a + b[/tex] (since the turning point lies on the curve)

[tex]0 = 2(5) + a[/tex] (since the derivative of the curve at the turning point is 0)

Simplifying the second equation gives us:

[tex]a = -10[/tex]

Substituting this value of a in the first equation, we get:

[tex]4 = 5^2 - 50 + b[/tex]

[tex]b = 29[/tex]

Therefore, the values of a and b are -10 and 29, respectively.

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Expected loss for the retailer is $2288.4

There are three suppliers named S1, S2, and S3 who provide raw materials to a retailer. The probability of supplying the raw materials on time for S1, S2, and S3 are 0.85, 0.82, and 0.91 respectively. Let’s suppose that the retailer orders 500 units of raw material from S1, 120 units from S2, and 156 units from S3. The loss for the retailer is $20, $30, and $10 respectively for S1, S2, and S3. To find out the expected loss for the retailer, we can use the formula given below:Expected loss = (probability of loss) × (value of loss) + (probability of no loss) × (value of no loss)Let’s calculate the expected loss for each supplier separately.Supplier S1: The probability of not receiving raw material on time from S1 is 1 - 0.85 = 0.15. The expected loss due to S1 can be calculated as follows:Expected loss for S1 = (0.15) × (500 units) × ($20 per unit) = $1500Supplier S2: The probability of not receiving raw material on time from S2 is 1 - 0.82 = 0.18. The expected loss due to S2 can be calculated as follows:Expected loss for S2 = (0.18) × (120 units) × ($30 per unit) = $648Supplier S3: The probability of not receiving raw material on time from S3 is 1 - 0.91 = 0.09. The expected loss due to S3 can be calculated as follows:Expected loss for S3 = (0.09) × (156 units) × ($10 per unit) = $140.4Therefore, the total expected loss for the retailer can be calculated by adding the losses from all three suppliers.Total expected loss = $1500 + $648 + $140.4 = $2288.4Thus, the expected loss for the retailer is $2288.4.

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Step-by-step explanation:

ALGEBRA 2 HELP

(Please show work!)

A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)

a. Describe and correct the error in the notation.

b. Evaluate the corrected summation of the arithmetic series above.

�

8

=

S

8

=

c. Write the explicit and recursive formulas for the arithmetic series above,

Explicit:

�

�

=

a

n

=

Recursive:

If

�

1

=

a

1

=

Then for n > 1

�

�

=

a

n

=

the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.

To find the scale factor of the dilation, we can compare the corresponding side lengths of the two squares. The distance between the points (-5,5) and (5,5) is 10 units, which is also the length of the side of the original square. The distance between the points (-10,10) and (10,10) is 20 units, which is the length of the side of the dilated square. Therefore, the scale factor is:

Scale factor = Length of dilated square side / Length of original square side = 20 / 10 = 2

This means that the dilated square is twice as large as the original square.

To find the perimeter of the original square, we can add up the length of each side. Each side of the square has a length of 10 units, so the perimeter is:

Perimeter of original square = 4 × length of one side = 4 × 10 = 40 units

To find the perimeter of the dilated square, we can use the same method. Each side of the dilated square has a length of 20 units, so the perimeter is:

Perimeter of dilated square = 4 × length of one side = 4 × 20 = 80 units

Therefore, the perimeter of the original square is 40 units, and the perimeter of the dilated square is 80 units.

Dilation is a transformation that changes the size of an object but leaves its shape unchanged. In this case, the dilation of the square resulted in a larger square that was similar to the original square, meaning that the corresponding angles in the two squares were equal. The scale factor of the dilation determined the ratio of the side lengths of the two squares, and the perimeter of each square was proportional to its side length. Dilations are used in geometry to create similar figures and to scale up or down an object in size.

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Answer:

Plan A

The formula is

A=p (1+r)^t

A=2,000×(1+0.06)^(4)

A=2,524.95 ( future value )

Interest earned=A-p

Interest earned=2524.95-2000

Interest earned=524.95

Plan B

Use the simple interest formula

I=prt

I interest earned?

P principle 2000

R interest rate 0.13

T time 4years

I=2,000×0.13×4

I=1,040

The Answer is

Plan B; $1,040

Step-by-step explanation:

The graph of  f(x) = -x is attached.

The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.

For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.

f(x) = -x ----------(1)

Equation (1) can be written as  f(x) = -x+0

This is in the form of f(x)=mx+b,

where , m= -1, b=0

this  represents a line

Find the x and y-intercepts: ( consider f(x)=y)

Find x-intercept when y=0

=> 0=-x

=> x=0

Thus, x-intercept is (0,0)

Find y-intercept when x=0

=> y=-0 = 0

Thus, y-intercept is (0,0)

We need another point, because both intercepts are same

When x= 1, y= -1

The point is (1,-1)

Plot these points and join them with a line.

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Complete Question:



Which of the following is the graph of f(x) = x2?

Click on the graph until the correct graph appears.

To decrease a number by 16%, you should multiply it by 0.84.(1 - 0.16 = 0.84).

When you reduce a number by a percentage, you are subtracting that percentage from it. For example, if you were to decrease 100 by 16%, you would subtract 16 from 100 to get 84.

This is also known as a percentage decrease, which is the opposite of a percentage increase.

Using the formula for percentage decrease, we get:

Percentage decrease = (Decrease in value / Original value) × 100

We're told that to decrease a number by 37%, you multiply it by 0.63.

Therefore, we can write:

0.63 = (Decrease in value / Original value) × 1000.63 × Original value = Decrease in value

We want to find what you multiply a number by to decrease it by 16%, so let's call that value x.

So: x = (Decrease in value / Original value) × 100%

So, we can substitute in the values we know to solve for x:

x = (0.16 × Original value / Original value) × 100%x = 0.16 × 100%x = 16%

Therefore, to decrease a number by 16%, you should multiply it by 0.84.

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Answer:

7y=-91

Step-by-step explanation:

-2x + 2y = 8 (multiply the second equation by 2)

12x + 2y = 22

Adding the two equations, we get:

10x = 30

Therefore, x = 3.

Substituting x = 3 into the second equation, we get:

6(3) + y = 11

Simplifying, we get:

y = -13

Finally, we can find the value of 7y:

7y = 7(-13) = -91

So their cat weighs 4.38 kilograms now.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.

Algebraic expressions can take many different forms, but some common examples include:

3x + 7

2a^2 + 5ab - 3b^2

(x + 2)(x - 5)

4x^2 - 9.

Let's start by figuring out how much the cat weighs now. We know that the cat weighs 7.3 times what it did when it was a kitten, and it weighed 0.6 kilograms when it was a kitten.

To find out how much the cat weighs now, we can multiply its original weight by 7.3:

0.6 kilograms x 7.3 = 4.38 kilograms

Therefore, So their cat weighs 4.38 kilograms now.

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