solve 3y^{2} - (y + 2) (y - 2)

Answer:

Exact Form:

7/8

Decimal Form:

0.875

The recursive formula f(n+1) = f(n) + 5, you can find any term in the sequence by starting with the initial term and adding 5 repeatedly.

To represent the given arithmetic sequence where 5 is added to each term to determine each successive term, the recursive formula can be expressed as: f(n+1) = f(n) + 5

In this formula, f(n+1) represents the next term in the sequence, while f(n) represents the current term. By adding 5 to each term, we can generate the next term in the sequence.

For example, let's assume the first term of the sequence is f(1) = a. Then, the second term would be f(2) = a + 5. The third term would be f(3) = (a + 5) + 5 = a + 10, and so on.

By using the recursive formula f(n+1) = f(n) + 5, you can find any term in the sequence by starting with the initial term and adding 5 repeatedly.

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Answer:

The expression becomes:

Explanation:

We want to solve the expression:

First of all, notice there is a mixed fraction in the expression. This can be converted into an improper fraction. Doing that, the expressioin becomes:

Next, we remove the bracket by multiplying each element in the bracket by 4.

Which becomes:

Now, we make this expression a single fraction as:

Answer:

In picture

Step-by-step explanation:

Hope I answered it correctly.

Please give me brainliest if it help you, thanks!

The firm will shut down in the short run due to the inability to cover total costs with the marginal cost (MC) below both the average total cost (ATC) and the marginal revenue (MR). Thus, the correct option is :

(c) shut down in the short run.

To analyze the firm's situation, we need to consider the relationship between costs, revenues, and profits.

Option a. "maximize its profit by producing in the short run" is not correct because the firm is experiencing losses. When MC is below ATC, it indicates that the firm is making losses on each unit produced.

Option b. "minimize its losses by producing in the short run" is also not correct. While producing in the short run can help reduce losses compared to not producing at all, the firm is still unable to cover its total costs.

Option d. "realize a loss of $5 per unit of output" is not accurate based on the given information. The exact loss per unit of output cannot be determined solely from the given data.

Now, let's discuss why option c. "shut down in the short run" is the correct choice.

In the short run, a firm should shut down when it cannot cover its variable costs. In this scenario, MC is equal to AVC at $8, indicating that the firm is just able to cover its variable costs. However, MC is below both ATC ($12) and MR ($7), indicating that the firm is unable to generate enough revenue to cover its total costs.

By shutting down in the short run, the firm avoids incurring further losses associated with fixed costs. Although it will still incur losses equal to its fixed costs, it prevents additional losses from adding up.

Therefore, the correct option is c. "shut down in the short run" as the firm cannot cover its total costs and is experiencing losses.

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Answer:

the Anwers D

Step-by-step explanation:

Answer:

I would say D

Step-by-step explanation:

If it isn't D try A

Answer:

x=2,y=−5

Step-by-step explanation:

The expression "100 1/2" has the greatest value among the given options.

To determine which expression has the greatest value among the given options, we need to evaluate each expression and compare the results.

Let's calculate the value of each expression:

8 3/2 = 8 + 3/2 = 16/2 + 3/2 = 19/2

4 5/2 = 4 + 5/2 = 8/2 + 5/2 = 13/2

100 1/2 = 100 + 1/2 = 200/2 + 1/2 = 201/2

9 3/2 = 9 + 3/2 = 18/2 + 3/2 = 21/2

8 2/3 = 8 + 2/3 = 24/3 + 2/3 = 26/3

Now, let's compare the values:

19/2 ≈ 9.5

13/2 ≈ 6.5

201/2 ≈ 100.5

21/2 ≈ 10.5

26/3 ≈ 8.67

From the calculations, we can see that the expression with the greatest value is "100 1/2," which is approximately 100.5.

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The area of the field in square meters is approximately 679.2431 m².Given: Width (W) of rectangular field in a park = 66.5ftLength (L) of rectangular field in a park = 110ftArea

(A) of rectangular field in a park in square meters.We can solve this question using the following steps;Convert the measurements from feet to meters.Use the formula of the area of a rectangle to find out the answer.1. Converting from feet to meters1ft = 0.3048m

Now we can convert W and L to meters

W = 66.5ft × 0.3048 m/ft ≈ 20.27 m

L = 110ft × 0.3048 m/ft ≈ 33.53 m2. Find the area of the rectangle

The formula for the area of the rectangle is given as;A = L × W

Substituting the known values, we have;

A = 33.53 m × 20.27 mA = 679.2431 m²

Therefore, the area of the field in square meters is approximately 679.2431 m².

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Answer:

A. Population A will require a larger sample size.

Step-by-step explanation:

A highly skewed distribution shows that too much data is concentrated where it is highly skewed.

If the sample size in increased the data may not concentrate at the same point and the skewness is normal that is it is mesokurtic.

The normal curve called the mesokurtic is neither very peaked nor very flat topped.

Populations A and B cannot have the same sample size as there is difference in their skewness.

Therefore option C and D are incorrect.

Option B is also incorrect because if  B will require a larger sample size then the skewness may almost finish and the data may have the same concentration at all points.It will become flat topped i.e platy kurtic.

So only option A is correct.

In creasing the sample size will make the curve normal and mesokurtic.

The equation is true for any value of "c". We can't solve for "c" as it will cancel out during the simplification process.

To find the volume of "c" in the equation -3/2(x+4)=9-4x, we first need to isolate the variable "c" on one side of the equation.

Starting with the given equation:

-3/2(x+4)=9-4x

First, distribute the -3/2 to the term in the parentheses:

-3/2 × x - 3/2 × 4 = 9 - 4x

Simplify by multiplying:

-3/2x - 6 = 9 - 4x

Next, add 4x to both sides to get all the x terms on one side of the equation:

-3/2x + 4x - 6 = 9

Simplify by combining like terms:

5/2x - 6 = 9

Add 6 to both sides:

5/2x = 15

Finally, divide both sides by 5/2 to isolate the variable "x":

x = 6

Now we have found the value of "x". To find the value of "c", we can substitute this value of "x" back into the original equation and solve for "c":

-3/2(x+4)=9-4x

-3/2(6+4)=9-4(6)

-3/2(10)=9-24

-15 = -15

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The problem demonstrates inverse variation, where the cost per person (c) is inversely proportional to the number of people (p). As evidenced by the given information, when 44 people go, the cost is $30 per person, and when 20 people go, the cost increases to $66 per person.

If the cost per person, c, varies inversely with the number of people, p, on the trip, we can set up the following equation:

c = k/p

where k is the constant of variation.

We are given that when 44 people go on the trip, the cost per person is $30. We can use this information to solve for the constant of variation, k:

30 = k/44

To find k, we multiply both sides of the equation by 44:

k = 30 * 44

k = 1320

Now we can use the value of k to determine the cost per person when 20 people go on the trip:

c = k/p

c = 1320/20

c = 66

Therefore, if 20 people go on the trip, it will cost $66 per person.

The correct term for the relationship described in the problem is "indirect variation," also known as "inverse variation." In an inverse variation, as one quantity increases, the other quantity decreases, and vice versa. The equation representing this relationship is of the form y = k/x, where y and x are the two variables, and k is the constant of variation. In this case, the cost per person (c) and the number of people (p) exhibit an inverse variation relationship.

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Solutions for he inequalities are as follows;

9. n ≤ -6                10. a ≥ 15           11. p ≥ -17          12.   v < 4

13. The slope is 1           14. The slope is 0.83

15. The slope is 0.22   16. the slope is 0.32

The solution to the following inequalities is as follows;

9. -26 ≥ 5n + 4                                   10. -116 ≥ 4 - 8a  

5n + 4 ≤ -26                                         4 - 8a ≤ -116

5n ≤ -26 - 4                                         - 8a ≤ -116 - 4 ⇒ - 8a ≤ -120

5n ≤ -30                                             multiply both side by -1

Divide both sides by 5                       8a ≥ 120 ⇒ a ≥ 15

n ≤ -6

11. 61 ≥ -3p + 10                                        12. -18 < -7v + 10

-3p + 10 ≤ 61                                             -7v + 10 > -18

-3p ≤ 61 - 10                                              -7v > -18 -10

-3p ≤ 51                                                     -7v > -28

Divide both sides by -3                             v < 4

p ≥ -17

13 To find the slope between two points (x1, y1) and (x2, y2), we use the formula: Slope = (y2 - y1) / (x2 - x1)

some of the coordinates for graph 13 are (-1, 0) (0, 1) (-2, -1) (1, 2)

When we input the values into the coordinates, its becomes

Slope between (-1, 0) and (0, 1):

Slope = (1 - 0) / (0 - (-1)) = 1 / 1 = 1

Slope between (0, 1) and (-2, -1):

Slope = (-1 - 1) / (-2 - 0) = -2 / -2 = 1

the slope for all pairs of coordinates is 1.

14.  (-2, 0)  (-3, -1), (3, 4)

Slope between (0, 1.5) and (-3, -1):

Slope = (-1 - 1.5) / (-3 - 0) = -2.5 / -3 ≈ 0.83

Slope between (-3, -1) and (3, 4):

Slope = (4 - (-1)) / (3 - (-3)) = 5 / 6 ≈ 0.83

15. Find the slope of the line through each pair of points

(12, -9) (-15, -15)

Using the formula Slope = (y2 - y1) / (x2 - x1), we input the values to be

Slope = (-15 - (-9)) / (-15 - 12)

= 0.22

16. (-11, -15) (11, -8)

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

For the given coordinates:

Slope between (-11, -15) and (11, -8):

Slope = (-8 - (-15)) / (11 - (-11)) = 0.32

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Explanation

Step 1

2 lines are parallel if they have the same slope, so

a) let's check the slope of the given line

it is in the form

so, the slope of the line we are looking for is 8

Step 2

Now, to find the equation of the line, we can use this expression

then, Let

replace,

therefore, the answer is

I hope this helps you

Answer:u 2

Step-by-step explanation:

The given box plot answers are,

a) 6

b) 5

c)3

d) 5

What is box plot?

   A suitable graphical representation of the concentration of the data is provided by box plots, often known as box-and-whisker plots or box-whisker plots. They also demonstrate how remote the extreme numbers are from the bulk of the data. Five numbers are used to create a box plot: the minimum value, first quartiles, median, third quartile, and maximum value.

Here in the given box plot middle line value is called median .Then ,

Median = 6

Now the maximum quartile = 8

The minimum quartile = 3

Now IQR is difference between the minimum and maximum quartile.

Then ,

=> IQR = 8-3 =5

Therefore the answers are

a) 6

b) 5

c)3

d) 5

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In a rhombus, the diagonals intersect at an angle of 90º.

Let O be the intersection of both diagonals.

Since the diagonals on a parallelogram intersect at the middle point, and all the sides of a rhombus have the same meaure, then all the triangles that are formed (ROS, TOS, TOQ, ROQ) are congruent.

Then, we know that:

Since the angles 3 and 2 are complementary angles, then:

Since the angles 4 and 3 are congruent, then:

Therefore:

Answer:

Rent: $80

Revenue: $1280

Step-by-step explanation:

We can solve this by representing the problem as an expression and finding the maximum of that

We know that revenue = number of sales * average price. If x represents the amount of 5 dollar increases, then we subtract x from 20 to get the total number of sales. For example, if there was 1 5 dollar increase, the number of sales would be 20-1 = 19. Similarly, the average price is equal to 60 + 5x, as we add $5 for each x. For example, if there were 3 $5 increases, it would cost 60 + 3 * 5 = 75 per room.

Therefore,

revenue = (20-x) * (60 + 5x)

= 1200 + 100x - 60x - 5x²

= -5x²+40x+1200

This is a quadratic expression -- we know it is one because it is of form ax²+bx+c, where a=-5, b=40, and c = 1200. Because the a is negative, the quadratic expression (which forms a parabola) opens downward, meaning that there is a peak of the expression at its vertex.

The x value of the vertex of a parabola given this form for the quadratic expression is (-b/2a) , which is (-40/(2*(-5))) = -40/-10 = 4 here, and plugging that into our equation,

y= -5x²+40x+1200

= -5 (4)²+40(4) + 1200

= -5 * 16 + 160 + 1200

= 1280 as our maximum revenue

Therefore, the amount of 5 dollar increases is 4, making the average price equal to 60 + 5 * 4 = 80 dollars

Answer: I’m not smart sorry

Step-by-step explanation:

Answer:

The circumference is 50.24 in

Step-by-step explanation:

The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.

False, each objective function line is unique and not necessarily parallel to every other objective function line in a problem.

In a multi-objective optimization problem, each objective function represents a different optimization criterion or goal. These objectives can have different slopes and directions, resulting in objective function lines that are not necessarily parallel to each other. The objectives may have conflicting or complementary relationships, leading to different trade-offs and possibilities in the optimization process. Therefore, it is incorrect to assume that all objective function lines are parallel in a problem.

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We need to check if lines ℓ and k are parallel. For two lines to be parallel, they must have the same slope and different y-intercepts.Let's compare the given lines:Line ℓ: y = 34x + 6Slope of line ℓ = 34Line k: y = 34x - 7Slope of line k = 34We see that the slope of lines ℓ and k is the same (34), which means that they could be parallel.

However, we still need to check if they have different y-intercepts. Line ℓ: y = 34x + 6 has a y-intercept of 6.Line k: y = 34x - 7 has a y-intercept of -7.So, lines ℓ and k have different y-intercepts, which means they are not parallel. Therefore, the correct answer is b) No.In slope-intercept form, the equation of a line is y = mx + b, where m is the slope of the line and b is its y-intercept. In this case, both lines have the same slope of 34 (the coefficient of x). The y-intercepts are different (+6 for line l and -7 for line k). Thus, the lines are not parallel.

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The answer is option a) Yes. Lines ℓ and k are parallel to each other.

The two distinct lines defined by the following two equations in slope-intercept form are:

Line ℓ: y = 34x + 6

Line k: y = 34x - 7

To determine if the lines are parallel, we need to compare their slopes since two non-vertical lines are parallel if and only if their slopes are equal.

Both lines are in slope-intercept form, so we can immediately read off their slopes:

Line ℓ has a slope of 34, and line k has a slope of 34.

Both the lines ℓ and k have the same slope of 34.

Hence, the answer is option a) Yes. Lines ℓ and k are parallel to each other.

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Answer:

132/11 = 12

204/12 = 17

17 hours

Answer: 50 oranges

Step-by-step explanation:

1 kg = 1000 g - 4 kg = 4000 g 4000g/80g= 50 (This gives the number of oranges in the box since each orange weighs 80 grams.)

There is no difference between the mean IQ levels of people who were reared by their natural parents and those who were not.

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Answer:  The equations are  A= 600 + 125w    and A = 1100 + 50w.  Look into the steps for more information.

Step-by-step explanation:

Zypel's situation can be represented by the equation,  A= 600 + 125w   where  A is the amount of money she will have after w weeks.

The same way we can represent Joshua's situation by the equation  

A = 1100 + 50w        where a is also the amount of money he will save after w weeks.

It says that there are 4 weeks in one month which means there will be 16 weeks in 4 months.

Now input 16 into the equations for w and solve for A.

A = 600 + 125(16)

A= 600 + 2000

A = 2600      

So Zypel will save $2600 in a 4 months

A = 1100 + 50(16)

A= 1100 +800

A= 1900  

So Zypel will save more than Joshua in four months.

The probability that the first ball is yellow if the second ball is black is 1/14. The correct option is D.

The given question is a classic example of dependent events in probability. As the balls are drawn without replacement, the second event's outcome will depend on the outcome of the first event.

Probability = Number of favorable events/ Total number of events

The probability of the first ball being yellow is \((5/15)\), while the probability of the second ball being black is \((3/14)\).

Mathematically represented as P(Yellow ball on the first draw) = P(Yellow ball) = \(5/15\)

P(Blackball on second draw given Yellow ball on the first draw) = P(Blackball | Yellow ball) = \(3/14\)

As both the events are dependent, we need to find the joint probability of both the events, which can be calculated as P(Yellow ball on the first draw and Blackball on the second draw) = P(Yellow ball) × P(Blackball | Yellow ball)

P (Yellow ball on the first draw and blackball on second draw) = \((5/15) × (3/14) = 3/42 = 1/14.\)

Therefore, the correct option is D.

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Answer: A) 3\8

Explanation..

A-0.375

B-0.6666...

C-0.6666...

D-0.777777...

A terminating decimal is a decimal with an end-digit

Also a repeating decimal is a decimal (that repeats)

Ex. 3.8767676767..

The required length of the missing side is 9.28 units for the given triangle.

As shown triangle:

∠A = 104°

∠B = 47°

∠C = 29°

Side c = 7 units

Let's denote the length of the missing side as x.

Using the Law of Sines:

sin(A)/a = sin(B)/b = sin(C)/c

We know the values of angles A, B, and C, as well as the length of side c. Plugging in these values, we get:

sin(104°)/x = sin(47°)/7

To find x, we can rearrange the equation and solve for x:

x = (7 × sin(104°)) / sin(47°)

Using a calculator, to get the value of x:

x ≈ 9.28

Therefore, the length of side a (in front of angle A) is approximately 9.28 units.

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