Otis is cutting a long piece of wood trim into smaller pieces for an art project. the line plot shows the length of the smaller pieces of wood.

1/3 has 5 x

1/2 has 4 x

2/3 has 2 x

how many pieces of wood will be at least 1/2 foot in length?

The measure of dispersion is a statistical term that refers to the degree of variability in a set of data. The extent to which the data in the set deviate from the mean or the central value is referred to as the measure of dispersion. There are several measures of dispersion, and some of them are more suitable for certain types of data than others. The following is not a measure of dispersion:

Mode. Mode is not a measure of dispersion, but rather a measure of central tendency. It represents the most frequent value in a data set. In statistics, the mode is the most common value in a data set, which is usually the highest peak of a frequency distribution graph. In summary, mode is not a measure of dispersion, but rather a measure of central tendency. Standard deviation, range, and interquartile range are all measures of dispersion. Standard deviation is a measure of how spread out the data is from the mean, while range and interquartile range are measures of how much the data is spread out from the minimum and maximum values or the median, respectively.

Therefore, if you want to find the amount of variability in a data set, you should use one of these three measures of dispersion. To summarize, the mode is not a measure of dispersion, while standard deviation, range, and interquartile range are measures of dispersion.

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Answer:

a = 15

Step-by-step explanation:

Substitute b = 12 , a = 9 into the equation

12 = \(\sqrt{a^2-9^2}\)

12 = \(\sqrt{a^2-81}\) ← square both sides

144 = a² - 81 ( add 81 to both sides )

225 = a² ( take square root of both sides )

± \(\sqrt{225}\) = a , then

a = ± 15

a > 0 , so a = 15

Answer: I believe C. 18a5 is the correct answer

The top right graph could show the arrow's height above the ground over time.

The initial and the final height are both at eye level, which is the reference height, that is, a height of zero.

This means that the beginning and at the end of the graph, it is touching the x-axis, hence either the top right or bottom left graphs are correct.

The trajectory of the arrow is in the format of a concave down parabola, hitting it's maximum height and then coming back down to eye leve.

Hence the top right graph could show the arrow's height above the ground over time.

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Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1

a) The probability of matching exactly 5 out of 5 winning numbers is given by the number of ways to choose 5 winning numbers out of 40, divided by the total number of possible outcomes:

Probability of matching 5 out of 5 = (Number of ways to choose 5 winning numbers out of 40) / (Total number of possible outcomes)

The number of ways to choose 5 winning numbers out of 40 is given by the combination formula:

C(40,5) = 40! / (5! * (40-5)!) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008

The total number of possible outcomes is the number of ways to choose any 5 numbers out of 40, which is also given by the combination formula:

C(40,5) = 40! / (5! * (40-5)!) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008

Therefore, the probability of matching exactly 5 out of 5 winning numbers is:

Probability of matching 5 out of 5 = 658008 / 658008 = 1

b) The probability of matching exactly 4 out of 5 winning numbers is given by the number of ways to choose 4 winning numbers out of 5 and one non-winning number out of 35, divided by the total number of possible outcomes:

Probability of matching 4 out of 5 = (Number of ways to choose 4 winning numbers out of 5) * (Number of ways to choose 1 non-winning number out of 35) / (Total number of possible outcomes)

The number of ways to choose 4 winning numbers out of 5 is 5, since there are 5 different ways to choose which of the 5 winning numbers will not be matched.

The number of ways to choose 1 non-winning number out of 35 is given by the combination formula:

C(35,1) = 35

The total number of possible outcomes is the same as before:

C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008

Therefore, the probability of matching exactly 4 out of 5 winning numbers is:

Probability of matching 4 out of 5 = 5 * 35 / 658008 = 0.000189

c) The probability of matching exactly 3 out of 5 winning numbers is given by the number of ways to choose 3 winning numbers out of 5 and two non-winning numbers out of 35, divided by the total number of possible outcomes:

Probability of matching 3 out of 5 = (Number of ways to choose 3 winning numbers out of 5) * (Number of ways to choose 2 non-winning numbers out of 35) / (Total number of possible outcomes)

The number of ways to choose 3 winning numbers out of 5 is given by the combination formula:

C(5,3) = 5! / (3! * (5-3)!) = 10

The number of ways to choose 2 non-winning numbers out of 35 is given by the combination formula:

C(35,2) = 35! / (2! * (35-2)!) = 35 * 34 / (2 * 1) = 595

The total number of possible outcomes is the same as before:

C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008

Therefore, the probability of matching exactly 3 out of 5 winning numbers is:

Probability of matching 3 out of 5 = 10 * 595 / 658008 = 0.00905

d) The probability of matching exactly 2 out of 5 winning numbers is given by the number of ways to choose 2 winning numbers out of 5 and three non-winning numbers out of 35, divided by the total number of possible outcomes:

Probability of matching 2 out of 5 = (Number of ways to choose 2 winning numbers out of 5) * (Number of ways to choose 3 non-winning numbers out of 35) / (Total number of possible outcomes)

The number of ways to choose 2 winning numbers out of 5 is given by the combination formula:

C(5,2) = 5! / (2! * (5-2)!) = 10

The number of ways to choose 3 non-winning numbers out of 35 is given by the combination formula:

C(35,3) = 35! / (3! * (35-3)!) = 35 * 34 * 33 / (3 * 2 * 1) = 6545

The total number of possible outcomes is the same as before:

C(40,5) = 40 * 39 * 38 * 37 * 36 / (5 * 4 * 3 * 2 * 1) = 658008

Therefore, the probability of matching exactly 2 out of 5 winning numbers is:

Probability of matching 2 out of 5 = 10 * 6545 / 658008 = 0.0998

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a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

19.5 cm

Step-by-step explanation:

the remaining height = 1200 /(12×8)

= 1200/96 = 12.5 cm

so, the height of the tank = 7+ 12.5 = 19.5 cm

\(\displaystyle\bf \boxed{V=abh \ ; \ 1dm^3=1litre=1000cm^3} \\\\a=12cm \ ; \ b=8 cm ;\: h_1=7 \; ; \ h_0=h_1+h_2=?\\\\abh_2=1,2litre=1,2dm^3\ = 1200cm^3\\\\ 8\cdot 12 h_2=1200\\\\h_2=12.5 cm\: then \\\\h_0= 7+12,5=19,5 \\\\Answer : the \ height \ of \ the \ tank \ is \ 19,5 cm\)

Answer:

Rectangle.

Step-by-step explanation:

The 2 dimensional section would be a rectangle.

Answer:

rectangle

Step-by-step explanation:

The future value of the loan is approximately $10,070.29.

To find the interest on the loan, we can use the formula:Interest = Principal × Rate × Time

Given:

Principal (P) = $6000

Rate (R) = 8% per year (0.08 as a decimal)

Time (T) = 6 months (0.5 years)

Plugging in the values into the formula:

Interest = $6000 × 0.08 × 0.5 = $240

Therefore, the interest on the loan is $240.

To find the future value of the loan, we can use the formula for simple interest:

Future Value = Principal + Interest

Given:

Principal (P) = $6000

Interest = $240

Plugging in the values into the formula:

Future Value = $6000 + $240 = $6240

Therefore, the future value of the loan is $6240.

For the second scenario:

Given:

Principal (P) = $9275

Rate (R) = 7.57% per year (0.0757 as a decimal)

Time (T) = 13 months (13/12 years)

To find the interest, we can use the same formula:

Interest = Principal × Rate × Time

Plugging in the values into the formula:

Interest = $9275 × 0.0757 × (13/12) = $795.29

Therefore, the interest on the loan is approximately $795.29.

To find the future value of the loan, we can use the same formula as before:

Future Value = Principal + Interest

Plugging in the values into the formula:

Future Value = $9275 + $795.29 = $10,070.29

Therefore, the future value of the loan is approximately $10,070.29.

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The fox population predicted to be in the year 2022 is 53,110 foxes.

The change in population for a specific location over time is known as population growth. The formula to calculate population growth is given as \(P = P_0(1+r)^t\) where P is the population at time t, r is the growth rate, and P₀ is the initial population.

The time period is calculated from the initial and final years,  

t = 2022 - 2012 = 10 years.

Given the initial population is 24,600 and the rate is 8% = 0.08.

Then, the predicted population in the year 2022 is calculated as,

\(\begin{aligned}P&=24,600(1+0.08)^{10}\\&=53,109.55\\&\approx53,110\end{aligned}\)

The answer is 53,110 foxes.

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The perimeter of the rectangle is 145cm

Area of a Square can be given as = length × Breadth. Therefore, the area of square = L x B square units. and the perimeter of a square = 4 × side units.

Given that all sides of a square are the same, Its area = 25 x 25

= 625cm²

We were told the area of the square is the same as the rectangle.

We can use the area of the square to find the value of the length of the rectangle.

625 = L x 10

L = 625/10

L = 62.5cm

With these information, we can find the perimeter of both the square and the rectangle.

Perimeter is the sum of all sides.

Square = 25 + 25 + 25 + 25

= 100cm

Rectangle = 62.5 + 62.5 + 10 + 10

= 145cm

From this solution, it is quite obvious the rectangle has a bigger perimeter.

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Answer:

NO WRONG (6T)(5S)+7 IS WRONG YOU ARE SOPOSED TO ADD THAT 6+5=11      11+7=18    18 DIVIDED BY 7=2.5

Step-by-step explanation:

SORRY FO CAPLOCK THAT HOW I TYPE SIR

The probability that the point lies in the shaded region is the ratio of the area of the shaded region to the total area of the figure.

To find the area of the shaded region, we need to subtract the area of the unshaded region from the total area of the figure. Let's assume that the total area of the figure is A and the area of the unshaded region is B. Then the area of the shaded region would be A - B.

To find the probability, we divide the area of the shaded region by the total area of the figure. So, the probability would be (A - B)/A or 1 - (B/A).

Without knowing the specific figure and the area of the shaded and unshaded regions, it's difficult to provide a numerical answer to this question. However, the general approach to finding the probability of a point lying in a shaded region is to use the formula mentioned in the main answer.

For example, let's say we have a circle with a radius of 5 units and a shaded sector that covers 90 degrees of the circle. To find the area of the shaded region, we would first find the area of the whole circle using the formula A = πr², where r is the radius of the circle. So, the total area of the circle would be A = π(5)² = 25π.

Next, we would find the area of the shaded sector by using the formula for the area of a sector, which is A = (θ/360)πr², where θ is the central angle of the sector. In this case, the central angle is 90 degrees, so θ = 90. Substituting the values, we get A = (90/360)π(5)²= 6.25π.

To find the area of the unshaded region, we would subtract the area of the shaded sector from the area of the circle. So, B = 25π - 6.25π = 18.75π.

Finally, we can use the formula mentioned in the answer to find the probability of a point lying in the shaded region. The probability would be (A - B)/A or 1 - (B/A). Substituting the values, we get the probability as (25π - 18.75π)/25π or 1 - (18.75π/25π) = 0.25 or 25%.

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Answer:

6

Step-by-step explanation:

To breakeven means that you made exactly as much money as you spent, so if you spent $50 to make lemonade, you would need to make $50 in profits from selling to break even

first subtract the cost of making each horse from the price of selling each horse (you do this to find out how much profits he makes from one horse):

125 - 75 = 50

now divide 300 by 50 to find out how many horses need to be made to break even:

300 ÷ 50 = 6

Answer:

12.5

Step-by-step explanation:

3.75 divided by 0.3 is equal to 12.5

so 4.5 divided by 0.3 is equal to 15

Answer:

12.5

Step-by-step explanation:

The equation 12 - 11 = 2.13 + 11 has no solutions in the complex plane, The equation |10 + √3| < 8.13 is satisfied when 10 + √3 is negative.

The equation |2 - 3| = 1.213 is satisfied when the magnitude of -1 is equal to 1.

We have,

(i) To solve the equation 12 - 11 = 2.13 + 11 in the complex plane:

12 - 11 = 2.13 + 11

1 = 26 + 11

1 = 37

The equation is not satisfied for any complex numbers since there is no complex number that makes the equation true.

(ii) To solve the inequality |10 + ∛3| < 2.13 + 2(3):

|10 + ∛3| = |10 + √3|

To determine the values of 10 + √3 that satisfy the inequality, we compare it with the right-hand side:

|10 + √3| < 2.13 + 2(3)

|10 + √3| < 2.13 + 6

|10 + √3| < 8.13

This inequality implies that the absolute value of 10 + √3 must be less than 8.13.

To solve this inequality, we consider two cases:

Case 1: 10 + √3 > 0

In this case, |10 + √3| = 10 + √3. So we have:

10 + √3 < 8.13

√3 < -1.87

This is not true since the square root of a positive number is always non-negative.

Case 2: 10 + √3 < 0

In this case, |10 + √3| = -(10 + √3). So we have:

-(10 + √3) < 8.13

-10 - √3 < 8.13

-√3 < 18.13

This is true since the negative square root of a positive number is always negative.

Therefore, the inequality is satisfied when 10 + √3 is negative.

(iii) To solve the equation |2 - 3| = 1.213:

|2 - 3| = |-1|

The absolute value of -1 is 1.

Therefore, the equation is satisfied when the magnitude of -1 is equal to 1.

So, the two points that satisfy the equation are -1 and 1 in the complex plane.

Thus,

The equation 12 - 11 = 2.13 + 11 has no solutions in the complex plane, The equation |10 + √3| < 8.13 is satisfied when 10 + √3 is negative.

The equation |2 - 3| = 1.213 is satisfied when the magnitude of -1 is equal to 1.

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Answer:

-4

Step-by-step explanation:

the highest f(x) value on the table is at -4 on the x column

Expression for the nth term of the sequence: (n + 1) / (n + 3).The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

To find the expression for the nth term of the sequence, we observe that each term can be expressed as (n + 1) divided by (n + 3), where n represents the position of the term in the sequence.

Let's verify this formula with the given terms:

For n = 1: (1 + 1) / (1 + 3) = 2 / 4 = 1/2 (first term of the sequence)

For n = 2: (2 + 1) / (2 + 3) = 3 / 5 (second term of the sequence)

For n = 3: (3 + 1) / (3 + 3) = 4 / 6 (third term of the sequence)

For n = 4: (4 + 1) / (4 + 3) = 5 / 7 (fourth term of the sequence)

For n = 5: (5 + 1) / (5 + 3) = 6 / 8 = 3 / 4 (fifth term of the sequence)

Therefore, the first five terms of the given sequence are: 1/2, 3/5, 4/6, 5/7, 3/4.

The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

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The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer: Y = 5X

Step-by-step explanation:

Answer:

$0.22/rod and 40 cm^2

Step-by-step explanation:

The price per pretzel rod is the unit price, $4.40/(20 rods) = $0.22/rod

The area of this parallelogram is A = (base)(height) = (10 cm)(4 cm) =40 cm^2

The trinomial expression that represents C is

C = -3x² - 18x + 19

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

C = G - 3F ______(1)

F = 2x² + 6x - 5

G = 3x² + 4

Substituting F and G in (1)

C = 3x² + 4 - 3(2x² + 6x - 5)

C = 3x² + 4 - 6x² - 18x + 15

C = -3x² - 18x + 19

Thus,

The trinomial expression is

C = -3x² - 18x + 19

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there are 33 pleasing ordered triples.

We are given a set {1, 2, 3, 4, 5, 6}. We need to count the number of pleasing ordered triples (a, b, c), where a < b < c, and a, b, c are elements of the set.

Condition (b) requires that both b and c be greater than a. Since a can take any value from 1 to 4, the number of possibilities for (a, b, c) is:

For a = 1, there are 4 choices for b (2, 3, 4, 5) and 5 choices for c (3, 4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 4 × 4 - 1 = 15 pleasing triples with a = 1.

For a = 2, there are 3 choices for b (3, 4, 5) and 4 choices for c (4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 3 × 4 - 1 = 11 pleasing triples with a = 2.

For a = 3, there are 2 choices for b (4, 5) and 3 choices for c (5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 2 × 3 - 1 = 5 pleasing triples with a = 3.

For a = 4, there is only 1 choice for b (5) and 2 choices for c (6, 5). Therefore, there is only 1 × 2 = 2 pleasing triples with a = 4.

The total number of pleasing ordered triples is:

15 + 11 + 5 + 2 = 33

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\(\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}\)

It would be written as a =± 11

The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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The slope of the line that contains these points is 0.75.

The slope of a line is the change in y-values divided by the change in x-values. In other words, it is the rise over the run. We can use the points given to calculate the slope.

Let's take the first two points (9, -24) and (13, -21) and use the formula for slope:

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

slope = (-21 - (-24)) / (13 - 9)

slope = (3) / (4)

slope = 0.75

We can do the same with the other two points (17, -18) and (21, -15):

slope = (-15 - (-18)) / (21 - 17)

slope = (3) / (4)

slope = 0.75

Since the slope is the same for both sets of points, we can conclude that the slope of the line that contains these points is 0.75.

The slope of the line that contains these points is 0.75.

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The expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards. The correct option is B.

The area of the gray region is the area of the rectangular backyard minus the area of the circular pond.

The area of the rectangular backyard is given as 6x+14x-12 square yards, which simplifies to 20x-12 square yards.

The area of the circular pond is given as 3x²-4x+5 square yards.

So, the area of the gray region is:

(20x-12) - (3x²-4x+5)

= 20x-12 - 3x²+4x-5

= 3x²+10x-17

Therefore, the expression that represents the area of the gray region, the area of the land remaining in the backyard is 3x²+10x-17 square yards.

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The instantaneous voltage of the sine wave for the given phase angles are:

a. θ = 15 degrees

V = 100 mV * sin(15°) = 25.98 mV

b. θ = 50 degrees

V = 100 mV * sin(50°) = 76.60 mV

c. θ = 90 degrees

V = 100 mV * sin(90°) = 100 mV

d. θ = 150 degrees

V = 100 mV * sin(150°) = -64.28 mV

e. θ = 180 degrees

V = 100 mV * sin(180°) = 0 mV

f. θ = 240 degrees

V = 100 mV * sin(240°) = 64.28 mV

g. θ = 330 degrees

V = 100 mV * sin(330°) = -76.60 mV

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