What is the best approximation of the solution to the system to the nearest integer values?

(7, 1)


(7, 0)


(1, 7)


(0, 6)

As a result, the window has a 6 square feet square space.

What makes something rectangular?

It features four right angles and two sets of parallel sides. An equiangular quadrilateral is another name for a rectangle. The reason for this is that a rectangle is indeed a quadrilateral form (4-sided shape) with parallel sides that are equal to each other and four corners with 90-degree angles.

Since area is usually measured in square feet, we must convert the provided dimensions from inches to feet in order to determine the window's area in square feet. 12 centimeters make up one foot, so

Length in feet = 36 inches / 12 inches/foot = 3 feet

Width in feet = 24 inches / 12 inches/foot = 2 feet

The window's square-footage is as follows:

Area = Length x Width = 3 feet x 2 feet = 6 square feet

Therefore, the area of the window in square feet is 6 square feet.

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answer

7.24

explanation

40% of 6000 = 2400

6000-2400=3600

labour's cost = 2400

material cost = 3600

15% of 2400 = 360

2400 + 360 = 2760

20% of 3600 = 720

3600 - 720 = 2880

2760 + 2880 = 5560

6000 : 5560 = 92.76

gap = 100.00 - 92.76

= 7.24

Answer:

126 mi²

Step-by-step explanation:

Surface Area of a Rectangular Prism :

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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a. This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).

b. This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).

c. This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).

a. The mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand can be represented as:

sj = sj-1 + xj - dj

This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).

b. If the production capacity for period j is given by Cj, the constraint that should be added is:

xj ≤ Cj

This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).

c. If inventory requirements for period j mandate an ending inventory of at least Ij, the constraint that should be added is:

sj ≥ Ij

This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).

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Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

The point-slope form of an equation of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line

m is the slope of the line.

We can use the given point (−5,−2) as (x1,y1)

Choose any value for the slope m to write the equation of the line in point-slope form.

For example:

Option 1:

Let's choose the slope m to be 2.

Then the equation of the line becomes:

y - (-2) = 2(x - (-5))

Simplifying the equation:

y + 2 = 2(x + 5)

Option 2:

Let's choose the slope m to be -3.

Then the equation of the line becomes:

y - (-2) = -3(x - (-5))

Simplifying the equation:

y + 2 = -3(x + 5)

Either option is valid and correctly written in point-slope form using the point (−5,−2) as (x1,y1).

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Answer:

I would have helped you but I just started learning about this

Answer:

6.

18+18 = 36

hence

x = 16

7.

x = 7 × 2

x = 14

Answer:

\((x-12)^2\) & \( 144\)

Step-by-step explanation:

The Equation given to us is ,

\(\implies x^2 -24x + \cdots \)

Here we need to find the value of the blank such that it is a perfect square.

This can be in the form of ,

\(\implies (a-b)^2 = a^2+b^2-2ab \)

On looking at equation ,

\(\implies x^2 -2(12)x + \cdots \)

For the whole equation to be whole square , the number that should replace the blank is 12² .

\(\implies x^2 -2(12)x + 12^2\\\\\implies (x-12)^2\)

Therefore 144 should be added .

Note that the use of the term "implicitly" in the question suggests that there is some other equation or context that defines y, but without that information, we can only assume that y is an arbitrary function. To differentiate 4/9 with respect to an implicitly defined function, we first need to clarify what that function is.

Let's call it y, so we have: 4/9 = f(y)
Now, we can differentiate both sides with respect to y using the chain rule: d/dy (4/9) = d/dy (f(y))
0 = f'(y)
So, the derivative of 4/9 with respect to an implicitly defined function y is 0. We can write this as:
d/dy (4/9) = 0
Note that the use of the term "implicitly" in the question suggests that there is some other equation or context that defines y, but without that information, we can only assume that y is an arbitrary function.

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The inequalities that represent the problem is 5h + 2.50t ≤ 60

Each hamburger costs $5 and each taco costs $2.50.

He has a total of $60 to spend on hamburgers and tacos.

The inequalities that would be used to  represent the possible values for the number of hamburgers purchased, h, and the number of tacos purchased, t is as follows:

Therefore,

h = number of hamburgers purchased

t = the number of tacos purchased

Hence,

5h + 2.50t ≤ 60

Therefore, the inequalities that represent the problem is 5h + 2.50t ≤ 60

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Answer:

g(x) = -2^x

Step-by-step explanation:

This is an exponential function from the looks of the value for x as it decreases toward the negative value (increase in the absolute value calculation) y is constricted from its vigorous values down to the fractional components of an equation of the standard appearance of y = C^x. For this, try some values. x = 1 y = 2, x = 2 y = 4. There is a trend that is established through these points, and g(x) = -2^x seems to follow this trend as it is reflect across the x-axis. Enter points, it is confirmed and a graphing calculator further substantiates. Try for yourself!

Answer:

160 musics

Step-by-step explanation:

let the total amount/charges be y

let the number of musics be x

For members total

y=48+0.99x-------1

For non-members total

y=1.29x-------------2

we are expected to solve for the number of music where members and non members get to pay the same amount

equating 1 and 2 we have

48+0.99x=1.29x

48=1.29x-0.99x

48= 0.3x

x=48/0.3

x=160 musics

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

Step-by-step explanation:

6÷2 = 3  and   18÷6 = 3  so:  q = 3

\(a_n=a_1\cdot q^{n-1}\\\\a_1=2\\q=3\\n=15\\\\a_{15}=2\cdot3^{15-1}\\\\a_{15}=2\cdot3^{14}\\\\a_{15}=9\,565\,938\)

Answer:

9 565 938

Step-by-step explanation:

The company's ending inventory on March 20, using the averaging method, would be $75.

Based on the information given, the company purchased a total of 20 footballs - 10 for $5 each and 10 for $7 each. The total cost of these purchases would be (10 * $5) + (10 * $7) = $50 + $70 = $120.

Since the company sold 9 footballs on March 20, the cost of the sold footballs would be 9 * $5 (as per the averaging method). Therefore, the cost of the sold footballs is $45.

To calculate the ending inventory, we subtract the cost of the sold footballs from the total cost of the purchases. Thus, the ending inventory would be $120 - $45 = $75.

In conclusion, the company's ending inventory on March 20, using the averaging method, would be $75.

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Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

Answer:

\(3\frac{1}{3}\) or \(\frac{10}{3}\)

Step-by-step explanation:

We could use the combined rate equation to find the combined rate of work.

Combined rate of work formula: \(\frac{1}{t_{b}} = \frac{1}{t_{1} } + \frac{1}{t_{2} }\), where \(t_{1}\) is the individual time for object A, \(t_{2}\) the individual time for object B and \(t_{b}\) is the time for A and B together.

The time it takes Irina to paint the room alone, \(t_{1}\) = 5 hours

The time it takes Paulo to paint the room, \(t_{2}\) = 10 hours

1) Substitute object A (Irina) and B (Paulo) into the formula given above, and change \(t_{b}\) into an \(x\).

\(\frac{1}{{x}} = \frac{1}{5 } + \frac{1}{10 }\)

2) Add the fractions.

\(\frac{1}{x} = \frac{3}{10}\)

3) Solve for the \(x\).

\(x(3) = 1(10)\\3x = 10\\x = \frac{10}{3} \\\)

4) Change them into a mixed fraction.

\(3\frac{1}{3}\)

Note: \(\frac{10}{3}\) or \(3\frac{1}{3}\) are both correct. Write the answer according to the question. In this case, there is no specific rule, so I choose \(3\frac{1}{3}\).

Answer:

See below

Step-by-step explanation:

Note

\(a, b, c \in \mathbb{R}\)

A quadratic equation is in the format

\(ax^2+bx+c \text{ where } a\neq 0\)

The constant \(a\) can't be zero because it would turn into a linear equation.

On the other hand, a quadratic trinomial is

\(ax^2+bx+c \text{ where } a,b,c\neq 0\)

\(a, b, c\) are non-zero constants.

Basically, a quadratic trinomial is an equation where the highest power is two and it has three terms.

Answer:

c is correct

Step-by-step explanation:

8w +(w+4) +5w

9w+4+5w

The lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is attached

From the question, we have the following parameters that can be used in our computation:

–3x – 2 = 2x + 8

The above equation can be splitted by introducing the variable y

using the above as a guide, we have the following:

y = –3x – 2

y = 2x + 8

This means that the lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is added as an attachment

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Answer:

Graph the line using the slope and y-intercept, or two points.

Slope:

2

y-intercept:

(0,−4)

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Answer:  

Miguel babysits for 3 hours and earns $15. Which represents the unit rate?

Option  D

(D) $5 per hour

Step-by-step explanation:

$5.00 Per Hour Represents unit rate,  15 / 3 = 5

The value of the series is frac{11}{18}. This series converges. To see why, we can use the comparison test with the series sum_{n=1}^infty frac{1}{n^2}, which is a known convergent series.

Specifically, we have frac{1}{n(n+3)} < frac{1}{n^2} for all n >= 1, and so by comparison, the given series converges as well.
To find the value of the series, we can use partial fractions to write:
frac{1}{n(n+3)} = frac{1}{3n} - frac{1}{3(n+3)}
Then, we can split up the series into two telescoping sums:
sum_{n=1}^infty frac{1}{n(n+3)} = sum_{n=1}^infty (frac{1}{3n} - frac{1}{3(n+3)})
= (frac{1}{3(1)} - frac{1}{3(4)}) + (frac{1}{3(2)} - frac{1}{3(5)}) + (frac{1}{3(3)} - frac{1}{3(6)}) + ...
Notice that most of the terms cancel out, leaving us with just:
sum_{n=1}^infty frac{1}{n(n+3)} = frac{1}{3} (1 + frac{1}{2} + frac{1}{3})
= frac{11}{18}
Therefore, the value of the series is frac{11}{18}.

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The above prompt has to do with linear functions. The answers to same are given below.

12-14) the graph of the functions are attached accordingly.

15) a) The cost of buying s songs can be calculated using the following function:

C(s) = 0.9s

b) To find the cost of buying 5 songs, we can substitute s = 5 into the function:

C(5) = 0.9(5) = 4.5

So the cost of buying 5 songs is $4.50.

16) he linear function that relates y to x. y = (1/3)x + 3

We can see that the x-coordinates increase by 3 as we move from one point to the next, and the y-coordinates increase by 1 as we move from one point to the next. This suggests that the slope of the line connecting these points is:

slope = (change in y) / (change in x) = 1/3

We can then use the point-slope form of the equation of a line, using one of the points, say (-6,1), as the reference point:

y - y1 = m(x - x1)

where y1 = 1, x1 = -6, and m = 1/3. Substituting in these values, we get:

y - 1 = (1/3)(x + 6)

Expanding and simplifying, we get:

y = (1/3)x + 3

This is the linear function that relates y to x.

17) Since all values of y are constant (-7) regardless of the value of x, we cannot write a linear function that relates y to x. Instead, we can say that y is a constant function with a value of -7. In other words, y = -7 for all values of x.

18) a. To write the linear function that relates y to x, we need to find the slope and y-intercept of the line that passes through the given points. Using the formula for slope, we have:

slope = (change in y) / (change in x)

= (y2 - y1) / (x2 - x1)

= (15 - 12) / (8 - 6)

= 1.5

Using the slope-intercept form of a linear function (y = mx + b), where m is the slope and b is the y-intercept, we can write:

y = 1.5x + b

To find the value of b, we can use any of the given points. Let's use (6, 12):

12 = 1.5(6) + b

b = 3

Therefore, the linear function that relates y to x is:

y = 1.5x + 3

b. The slope of the linear function is 1.5. This means that for every increase of one week in the puppy's age, its weight increases by 1.5 pounds on average. The y-intercept of the function is 3, which means that when the puppy is born (at 0 weeks), its weight is estimated to be 3 pounds.

c. To find out after how many weeks the puppy will weigh 33 pounds, we can use the linear function we found in part (a):

y = 1.5x + 3

Substitute y = 33 and solve for x:

33 = 1.5x + 3

30 = 1.5x

x = 20

Therefore, the puppy will weigh 33 pounds after 20 weeks.

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In the home run derby competition the percent of hits that were home run is: 25.8%

Information about the problem:

To solve this exercise we have to apply the percentage formula:

hits were home (%) = (home runs/ hits) * 100

hits were home (%) = (32/ 124) * 100

hits were home (%) = 0.2580 * 100

hits were home (%) = 25.8%

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

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Answer:

Step-by-step explanation:

-31

Answer:

-31

Step-by-step explanation:

just enter -5 into x and solve

By using the formula and substituting the z-score, Rylee did approximately 58.6 sit-ups.

The mean, also known as the average, is a measure of central tendency that represents the sum of a set of numbers divided by the number of items in the set. It is calculated by adding all the numbers in the set and dividing the sum by the total number of numbers.

A z-score, also known as a standard score, is a measure of how many standard deviations a data point is from the mean of a data set. It is calculated by subtracting the mean of the data set from the value of the data point and dividing the result by the standard deviation of the data set.

To find the number of sit-ups that Rylee did, we can use the formula for converting a z-score to a raw score:

X = μ + z * σ

where X is the raw score (the number of sit-ups in this case), μ is the mean, z is the z-score, and σ is the standard deviation.

Plugging in the given values, we get:

X = 46 + 1.8 * 7 = 46 + 12.6 = 58.6

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