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The equation of the line is 9x+8y + 19 = 0 and 5x - 4y+ 19 = 0 According to the given graphs, these are the equations of the graph.

Consider two points on the blue line.

The points are (5, -8) and ( -3,1 ).

Equation of the blue line is:

y - 1 = [tex]\frac{-8-1}{5+3} (x+3)[/tex]

8 (y - 1) = -9 ( x + 3)

8y - 8 = -9x -27

9x + 8y + 19 = 0

Therefore, the Equation of the blue line is 9x + 8y + 19 = 0.

Consider two points on the red line.

The points are (-3, 1) and ( 1,6 ).

Equation of the red line is:

y - 1 = [tex]\frac{6-1}{1+3} (x+3)[/tex]

4 (y - 1) = 5 (x + 3)

4y - 4 = 5x + 15

5x - 4y+ 19 = 0

Therefore, the Equation of the red line is 5x - 4y+ 19 = 0.

Hence, the equations for the given blue and red lines are completed.

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The cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

Thus, οptiοn D is cοrrect.

Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetry using the principles οf algebra.

The rectangle IJKL is fοrmed by cοnnecting the pοints I, J, K, and L in a clοckwise οr cοunterclοckwise manner. Since I and J have the same x-cοοrdinate and are οn οppοsite sides οf the x-axis, and L and K have the same y-cοοrdinate and are οn οppοsite sides οf the y-axis, it fοllοws that the diagοnals οf the rectangle IJKL intersect at the οrigin (0,0).

Therefοre, the cοοrdinates οf the fοurth vertex K must be the reflectiοn οf the pοint L(-4,3) acrοss the οrigin, which is (4,-3).

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The probability of obtaining a sample result of a mean of $470 or more if the true population mean is 460 is very low, almost zero.

To calculate the probability of obtaining a sample result of a mean of $470 or more, we need to use the sampling distribution of the mean.

Assuming that the sample size is large enough and that the sample means are normally distributed, we can use the central limit theorem to approximate the sampling distribution of the mean to a normal distribution. We can standardize the sample mean using the formula

z = (x - μ) / σ,

where x is the sample mean, μ is the population mean, and σ is the standard error of the mean.

In our case, we want to find the probability of obtaining a sample mean of $470 or more. We can convert this to a z-score by standardizing it using the formula

z = (470 - 460) / (σ / √n),

where n is the sample size.

If the sample size is 100 and the population standard deviation is 10, then the standard error of the mean is 1. We can then calculate the z-score as

=> z = (470 - 460) / (1 / √100) = 10.

We can look up the probability of obtaining a z-score of 10 or greater in a standard normal distribution table, which is almost zero.

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In the following question, Yes, the confidence interval suggests that the difference observed in this sample will also generalize to the larger population.

What is a confidence interval? A confidence interval is a probability statement that provides an interval of plausible values that are likely to contain the value of a population parameter. It is a way to infer the population parameter value from sample data.

A confidence interval is calculated as a range of values that are predicted to include the unknown population parameter, based on the sample statistic. The confidence interval suggests that the difference, if any, observed in this sample will also generalize to the larger population.

A confidence interval with a high level of confidence (e.g. 95%) would have a wider range of values and a higher probability of including the population parameter. The interpretation of the confidence interval is that we are 95% confident that the actual population parameter falls within the calculated interval. Therefore, it implies that the sample data is likely to be representative of the population data.

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The perimeter of the rectangle is approximately 208.9 meters.

To find the perimeter of the rectangle, we need to know the length of the other side.

Let's use the formula for the area of a rectangle:

area = length x width

We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:

length = area / width

length = 717.8 / 7.4

length ≈ 97.05 m

Now we have both the length and width of the rectangle, so we can find the perimeter:

perimeter = 2 x (length + width)

perimeter = 2 x (97.05 + 7.4)

perimeter = 2 x 104.45

perimeter = 208.9 m

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Answer:

(a) Pour montrer que la suite (Un) est géométrique, il suffit de vérifier que le quotient de deux termes consécutifs est constant. Soit n un entier naturel non nul. Alors :

Un+1 / Un = (Un-4) / (Un) = 1 - 5/Un

Donc, pour tout n E N*, on a :

Un+1 / Un = 1 - 5/Un = (Un / Un) - (5/Un) = (Un - 5) / Un

On a bien trouvé une raison q = -5/1, et un premier terme U1 = U1 - 5.

(b) La raison de la suite (Un) est q = -5/1. En utilisant la formule générale de la suite géométrique, on obtient :

Un = U1 * q^(n-1) = (U1 - 5) * (-5)^(n-1)

En particulier, on a :

U_n = U_1 * q^{n-1} = (U_1 - 5) * (-5)^{n-1} = U_12 = (U_1 - 5) * (-5)^{12-1}

(c) On n'a pas suffisamment d'informations pour déterminer la valeur de U1, donc on ne peut pas calculer directement la valeur de U12.

Answer:

The area that represents elements contained in the complement of the intersection of swimmers and weightlifters is the region outside the circles labeled as D. Therefore, the answer is D.

Step-by-step explanation:

chatgpt

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Using the scale factor of 4:1, the side lengths of the real objects are:

B. Side a is 5 inches long and side b is 4.5 inches long.

A scale factor is a number that represents the ratio of the size or dimensions of an object in relation to another object. It is a proportional relationship between two similar objects, where the scale factor is the ratio of any corresponding lengths or dimensions.

Thus, given that the scale factor is 4:1, it means 4 inches of the scale drawing represents 1 inch of the real object.

Therefore, the sides would be:

Side a = 20/4 = 5 in.

Side b = 18/4 = 4.5 in

The answer is B.

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The coordinate of the point U that divides the line ST in the ratio 2:5 is: (12:6)

The formula for the division of line segments in the ratio m:n is

P = {[(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]}

We are given the coordinates of line Segment ST as: S(10, 2) and T(17, 16)

Thus, if the ratio is 2:5, we have:

U(x, y) = {[(2*17 + 5*10)/(2 + 5)], [(2*16 + 5*2)/(2 + 5)]}

U(x, y) = (84/7), (42/7)

U(x, y) = (12, 6)

Thus, that is the coordinate of the point U that divides the line ST in the ratio 2:5.

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The height of the trapezium is 5mm, given that the two parallel sides have lengths of 6mm and 8mm, and the area of the trapezium is 35mm².

To find the height of a trapezium given its area and the lengths of its parallel sides, we use the formula:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides, h is the height, and Area is the area of the trapezium.

In this case, we are given that the area of the trapezium is 35mm², and we know that the two parallel sides have lengths 6mm and 8mm. So, we can substitute these values into the formula and solve for h:

35 = (6+8) x h/2

Simplifying the right-hand side of the equation, we can combine the two lengths of the parallel sides and multiply by h, and then divide by 2 to get:

35 = 14h / 2

Multiplying both sides by 2, we get:

70 = 14h

Dividing both sides by 14, we get:

h = 5

Therefore, the height of the trapezium is 5mm.

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Answer:

g(x) = (x + 3)2 - 2

Step-by-step explanation:

I think that's the one I just did this class so

Answer:c 4.2 cups

Step-by-step explanation:

just do 63 divided 15

The probability of observing exactly 4 errors in the carpet is 0.0165 or 1.65%.

The number of weaving errors in a twenty-foot by ten-foot roll of carpet follows a Poisson distribution with a mean of 0.5. We can use the Poisson probability distribution formula to find the probability of observing exactly 4 errors in the carpet:

[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4![/tex]

where X is the random variable representing the number of weaving errors. Plugging in the values, we get:

[tex]P(X = 4) = (e^{-0.5} * 0.5^4) / 4! = 0.0165[/tex] (rounded to four decimal places)

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Total volume of the composite figure using volume of cuboid formula is = 120ft³.

A cuboid's volume is a measurement of how much room it occupies. A three-dimensional shape with dimensions of length, breadth, and height is the cuboid. We can keep stacking them, starting with a rectangular sheet, until we achieve a shape with a particular length, breadth, and height.

The shape of this stack of sheets is a cuboid, which has 6 faces, 12 edges, and 8 vertices. The (unit)³ is used to represent a cuboid's volume.

In the given figure,

Length of cuboid = 6ft.

Breadth of cuboid = 3ft.

Height of cuboid = 5ft.

Length of second cuboid = 4ft.

Height of second cuboid = 5ft.

Breadth of second cuboid = 3ft.

Volume of first cuboid = length × breadth × height.

= 6 × 3 × 5

= 90ft³

Volume of second cuboid = 4 × 3 × 5

= 60ft³

Now the second cuboid is half.

So, volume becomes = 60/2

= 30ft³.

So, total volume of the figure = 90 + 30 = 120ft³.

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The error made by the student is in simplifying the expression inside the square root.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The student made an error in simplifying the expression inside the square root.

The expression should be simplified as follows:

25 + 4(2)(-12) = 25 - 96 = -71

So the correct expression inside the square root is -71, not 121.

Therefore, the correct solution using the Quadratic Formula is:

x = (-(-5) ± √((-5)² - 4(2)(-12)))/(2(2))

x = (5 ± √(25 + 96))/4

x = (5 ± √121)/4

x = (5 ± 11)/4

Hence, the solutions are x = -3 and x = 4/2, which simplifies to x = 2.

Therefore, the error made by the student is in simplifying the expression inside the square root.

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During bracket off, when 6x⁴ * 6x⁴= 36x⁸ instead of 36x¹⁶ using Perfect square method.

When 4y² * 4y² = 16y^4 instead of 25y⁴⁴ gotten in the question. To correct the error, using the perfect square method, it can be corrected.

The answer will be (6x⁸ - 5y²)(6x⁸ + 5y²)The last error found is sign rule-4y^2  x -4y^2 = +16y⁴ instead of -4y² * +4y² = -16y⁴

Perfect square is  is a number that is generated by multiplying two equal integers by each other.

Given 36x¹⁶ - 25y⁴

The rule = A difference of two perfect squares, A² - B²²  can be factored into (A+B) x (A-B)36x¹⁶ is a perfect square = 6₂ * x⁸2)= (6x⁸)^225y⁴ is also a perfect square= 5² * x²(2)= (5x²)²

Using the rule for Perfect square,

When A² - B² = (A + B) x (A - B)

So,(6x⁸)₂ - (5x²)²

=(6x⁸ + 5x²) * (6x⁸ - 5x²)

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Answer:

Step-by-step explanation:

every second we are increasing the sides by 4.4 in all 3 dimensions. This must mean that we need to do 4.4x4.4x4.4 to get

85.184in^3 per second

Population will be 43,160 in 76 years if a town doubles its size every 38 years if the current population is 6,790.

Since the town doubles in size every 38 years, we can use the formula:

P = P0 * 2^(t/T)

where P0 is the initial population, P is the population after time t, and T is the doubling time (38 years in this case).

We know that the current population is P0 = 6,790, and we want to find the population in 76 years, which is t = 76. Plugging these values into the formula, we get:

P = 6,790 * 2^(76/38)

P = 6,790 * 2^2

P = 6,790 * 4

P = 27,160

Therefore, the population of the town will be 27,160 in 76 years.

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Answer:

2/9yd²

Step-by-step explanation:

We know that area is calculated by length × width, so we will do the same here. To get the area, we must multiply 1/3 by 2/3.

1/3 × 2/3 is 2/9. So, the area of the rectangle is 2/9yd². :D

The new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.

To find out how much paint the new box would need and how much sugar it would hold, follow these steps:
1. The original box holds 15 cups of sugar, and it takes 2 ounces of paint to cover it completely. When you double the dimensions of the box, areas are scaled by [tex]k^2[/tex] (k is the scale factor), and volumes are scaled by[tex]k^3.[/tex]
2. Since you double the dimensions, the scale factor k is 2.
3. The surface area of the box will be scaled by [tex]k^2, which is 2^2 = 4.[/tex]So, the new box will need 4 times the amount of paint that the original box needed. Since the original box needed 2 ounces of paint, the new box will need 2 × 4 = 8 ounces of paint.
4. The volume of the box will be scaled by [tex]k^3, which is 2^3 = 8[/tex]. So, the new box will hold 8 times the amount of sugar that the original box held. Since the original box held 15 cups of sugar, the new box will hold 15 × 8 = 120 cups of sugar.
In conclusion, the new box would need approximately 8 ounces of paint and would hold 120 cups of sugar.

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The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.

The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.

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The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165

Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.

Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:

E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365

The variance of X is

Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312

The standard deviation of X is

SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67

To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375

P(X <= 375) = F(375)

where F(x) = P(X <= x) is the CDF of X.

Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67

Z = (X - E(X)) / SD(X)

Z follows a standard normal distribution with mean 0 and standard deviation 1.

P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))

= P(Z <= (375 - 365) / 17.67)

= P(Z <= 0.566)

Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.

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The given question is incomplete, the complete question is :

A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?

1: The measure of arc JML is: arc JML = 176°

3: m∠WXY = 59°

5: The measure of the arc is: arc FE = 54°

7: The measure of the angles are: m∠A  = 79° and m∠B  = 112°

9: The value of x is: x = 9

No. 1

The measure of inscribed angle is half the measure of its intercepted arc. That is:

∠ JKL = 1/2 * arc JML

88 = 1/2 * arc JML

arc JML = 2 * 88

arc JML = 176°

No. 3

arc WY =  360 - 86 - 156 = 118° (sum of angles in a circle)

m∠WXY = 1/2 * arc WY

m∠WXY = 1/2 * 118

m∠WXY = 59°

No. 5

An angle inscribed in a semicircle is a right angle. Thus, m∠DFE = 90°

m∠EDF = 180 - 90 - 63 = 27° (sum of angles in a triangle)

m∠EDF  = 1/2 * arc FE

27°  = 1/2 * arc FE

arc FE = 2 * 27

arc FE = 54°

No. 7

The opposite angle in a cyclic quadrilateral add up to 180°. That is:

m∠A + m∠C  = 180°

m∠A + 101 = 180

m∠A  = 180 - 101

m∠A  = 79°

m∠B + m∠D  = 180°

m∠B + 68 = 180

m∠B  = 180 - 68

m∠B  = 112°

No. 9

67 = 1/2 * (16x - 10)

67 * 2 = (16x - 10)

16x - 10 = 134

16x  = 134 + 10

16x = 144

x = 144/16

x = 9

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The solution to the system of equations is: x = 1/2 and y = 4. The steps and justification are given below.

Given the equations, -4x + y = 2 and 4x + y = 6, the following shows the justification for each step taken to solve the system.

Step                                   Justification                                            

1. 2y = 8                            1. Add the equations

2. y = 4                             2. Divide each side by 2

3. 4x + y = 6                     3. Write equation 2

4. 4x + (4) = 6                   4. Substitute 4 for y

5. 4x = 2                           5. Subtract 4 from each side

6. x = 1/2                           6. Divide each side by 4

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The correct interpretations of the given quantity are C and E.

C. Your daily viewing time is greater than 90% of all Netflix users.

E. 90% of all Netflix users viewing times per day are less than your daily viewing time.

To understand the correct interpretation, we need to first understand what the 90th percentile means. It refers to the value below which 90% of the data falls.

If your daily viewing time is in the 90th percentile of all Netflix users, it means that your viewing time is greater than 90% of all users. In other words, only 10% of users watch more Netflix than you, and your viewing time is greater than the viewing time of 90% of users.

Therefore, options C and E are the correct interpretations.

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Complete Question:

Suppose the amount of time (in minutes) per day that you spend watching Netflix is in the 90th percentile of all account users. Which interpretation(s) of this quantity are correct? Select ALL that apply.

A. You spend approximately 90 minutes per day watching Netflix.

B. 90% of all viewers spend more time on Netflix per day than you.

C. Your daily viewing time is greater than 90% of all Netflix users.

D. There is a 90% probability that a randomly selected viewer spends less time than you watching Netflix per day.

E. 90% of all Netflix user viewing times per day are less than your daily viewing time.

F. 90% of all Netflix user viewing times per day are less than or equal to your daily viewing time.

Answer:

Step-by-step explanation:

To find when people stop watching the video, we need to find the maximum point of the quadratic function y = -0.75x² + 9.75x.

The x-coordinate of the maximum point of a quadratic function can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic function.

Using the formula with a = -0.75 and b = 9.75, we get:

x = -9.75 / 2(-0.75)

x = -9.75 / -1.5

x = 6.5

Therefore, the maximum number of views per day will occur on the 6.5th day after the video was posted.

To determine when people stop watching the video, we need to check the values of y after this point.

When x > 6.5, the quadratic function becomes negative, which means that the number of views per day will start to decrease. Therefore, people stop watching the video after 6.5 days (or sometime around the 7th day).

2 and 2/3 divided by 6 equals 4/9.

So, 2 and 2/3 divided by 6,

we can simplify it step by step as follows:

First, we need to convert the mixed numbers 2 and 2/3 to an improper fraction:

2 and 2/3 = (2 × 3 + 2) / 3 = 8/3

Therefore, the expression becomes:

8/3 ÷ 6

To divide fractions, we need to invert the second fraction and multiply:

8/3 ÷ 6 = 8/3 × 1/6

Simplifying the multiplication of fractions:

8/3 × 1/6 = (8 × 1) / (3 × 6) = 8/18

Now, we can simplify the fraction 8/18 by dividing both the numerator and denominator by their greatest common factor, which is 2:

8/18 = (8 ÷ 2) / (18 ÷ 2) = 4/9

Therefore, 2 and 2/3 divided by 6 equals 4/9.

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Translation: The blue figure can be moved to the red figure by a translation of three units to the right and one unit down.

Reflection: The blue figure can be moved to the red figure by a reflection over the x-axis.

Rotation: The blue figure can also be moved to the red figure by a rotation of 90 degrees counterclockwise.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

To demonstrate this transformation, imagine the blue figure being shifted three units to the right and one unit down, such that it is now completely overlapping the red figure.

This transformation can be visualized by imagining the figure being flipped along the x-axis, so that the right side of the figure is now on the left side and vice versa.

To demonstrate this transformation, imagine the blue figure being spun 90 degrees counterclockwise, so that the top of the figure is now on the left side and the bottom is on the right side. This rotation will align the figure with the red figure.

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Answer:

x > 3

Step-by-step explanation:

This is an open circle, meaning there will be no equal sign.

The line is going to the right of 3, meaning x > 3

So, our inequality is x > 3

There are 4896 ways of arranging 7 pets in a row of 7 chairs such that at least 2 cats are next to each other.

Arrangement of entities can be done using permutation and combination in mathematics.

Consider the distributions where 2 cats are not next to each other as

C D C D C D C.

There are 4! ways to seat the cats, and 3! ways to seat the dogs that gets us N=4! 3! = 144

There are a total of 7!=5040 possible ways to seat both cats and dogs.

At least 2 cats seat together= All possible arrangements- None of the cat seat together.

Thus the number of seatings where at least 2 cats are adjacent is

5040-144 = 4896

So, there are 4896 arrangements can be made so that at least 2 of the cats seat together.

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