Two cars are driving away from an intersection in perpendicular directions. The first cars velocity isms 7 meters per second and the second cars velocity is 3 meters per second. At a certain instant, the first car is 5 meters from the intersection and the second car is 12 meters from the intersection. What is the rate of change of the distance between the cars at that instant?

All monuments cast a shadow when the sun is shining, as they block the sunlight and create a shadow on the ground or nearby surfaces. T

The size and shape of the shadow will depend on the position of the sun in the sky, the orientation of the monument, and its size and shape.

Some famous monuments that cast impressive shadows include the Pyramids of Giza, the Eiffel Tower, the Washington Monument, and the Stonehenge.

We can use proportions to solve the problem.

Let x be the length of Kyle's shadow.

We know that the length of the monument's shadow is 16 feet, and its height is  [tex]64 f[/tex] Feet. So the ratio of the length of the monument's shadow to its height is:

[tex]16/64 = 1/4[/tex]

This ratio is equal to the ratio of Kyle's shadow length to his height:

[tex]x/6.25 = 1/4[/tex]

To solve for x, we can cross-multiply:

[tex]x = 6.25/4 = 1.5625[/tex]

Therefore, the length of Kyle's shadow is approximately [tex]1.56[/tex] feet (or  [tex]18.72 inches)[/tex] .

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The absolute value of inequality representing the range of John's weight is | x - 156 | ≤ 8.

An absolute value inequality is an inequality that contains an absolute value expression. The absolute value of a number represents the distance between that number and zero on a number line.

An absolute value expression is a mathematical expression that contains an absolute value function, denoted by vertical bars around a number or expression. The absolute value of a number is its distance from zero on a number line, so an absolute value expression represents a positive number, regardless of whether the original number was positive or negative.

As per the given question,

If John weighed 156 pounds give or take 8 pounds ten years ago, then his weight could have been anywhere from 156 - 8 = 148 pounds to 156 + 8 = 164 pounds.

To write this as an absolute value inequality, we can let x represent John's weight, and use the absolute value to represent the distance from the mean weight of 156 pounds. The inequality would be:

| x - 156 | ≤ 8

This inequality says that the distance between John's weight (x) and the mean weight of 156 pounds must be less than or equal to 8 pounds. In other words, John's weight must be within 8 pounds of 156, which represents the range of possible weights he could have had ten years ago.

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In the following question, among the conditions given, For the page reference string provided, the number of page faults for the following page replacement algorithms are as follows: A. FIFO: 8-page faults, B. Optimal: 6-page faults, C. LRU: 7-page faults.

To learn about them in brief-
A. FIFO: 8-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 0, 1, 2
Step 7: 0, 1, 2
Step 8: 0, 1, 3
Step 9: 2, 7, 1
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
B. Optimal: 6-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 2, 3
Step 6: 1, 2, 3
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 1, 0, 3
Step 10: 2, 0, 3
Step 11: 2, 1, 0
Step 12: 2, 1, 3
Step 13: 2, 0, 3
Step 14: 1, 0, 3
Step 15: 1, 2, 0
C. LRU: 7-page faults
At each given time, the pages in memory are:
Step 1: 0
Step 2: 0, 1
Step 3: 0, 1, 7
Step 4: 0, 1, 2
Step 5: 0, 1, 2
Step 6: 1, 0, 2
Step 7: 1, 0, 3
Step 8: 1, 2, 0
Step 9: 2, 0, 3
Step 10: 2, 1, 0
Step 11: 2, 1, 3
Step 12: 0, 1, 3
Step 13: 0, 2, 3
Step 14: 1, 2, 3
Step 15: 1, 0, 3

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The cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 expression Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

The equation "Cost (s) of 1 Game: 12.70 - n +9" gives the cost of playing Decimal Decisions, but we don't know the number of n, thus we can't determine the overall cost for a group of n persons.

Similarly, the cost of playing Ratio Rage is provided by the equation "Cost(s) of 1 Game: 5.5-3 RATIO RAGE!", but we don't know the value of the game's ratio.

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Answer:

The appropriate set of hypotheses for Fay's significance test is:

Null Hypothesis: p = 0.26 (the proportion of people in Fay's city who can speak more than one language is the same as the national average)

Alternative Hypothesis: p > 0.26 (the proportion of people in Fay's city who can speak more than one language is higher than the national average)

In other words, Fay is testing if the proportion of people in her city who speak more than one language is significantly different from the national average of 26%. The null hypothesis assumes that the proportion is the same as the national average, while the alternative hypothesis assumes that it is higher.

To conduct her significance test, Fay would need to collect a random sample of people from her city and determine how many of them speak more than one language. Based on this sample proportion, she can calculate a test statistic and determine if it is significantly different from what would be expected under the null hypothesis. If the test statistic is sufficiently large, she can reject the null hypothesis and conclude that the proportion of people in her city who speak more than one language is higher than the national average.

Step-by-step explanation:

Answer:4

Step-by-step explanation:

4

If Lainey bought a set of 20 markers for $6, then the cost of one marker is $0.30.

To determine the cost of 1 marker, we need to divide the total cost of the set of markers by the number of markers in the set.

Lainey bought a set of 20 markers for $6, so the cost of the set is $6. To find the cost of 1 marker, we divide the cost of the set by the number of markers in the set:

Cost of 1 marker = Total cost of set / Number of markers in set

Cost of 1 marker = $6 / 20

Cost of 1 marker = $0.30

Therefore, the cost of 1 marker is $0.30.

In summary, to determine the cost of 1 item in a set, we divide the total cost of the set by the number of items in the set. In this case, Lainey bought a set of 20 markers for $6, so the cost of 1 marker is $0.30.

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Complete question is:

Lainey bought a set of 20 markers for $6. What is the cost of 1 marker?  

Answer: To solve the equation 16=3x-7/2, you can follow these steps:

Multiply both sides of the equation by 2 to get rid of the fraction:

16 * 2 = (3x - 7/2) * 2

32 = 6x - 7

Add 7 to both sides of the equation to isolate the term with x:

32 + 7 = 6x

39 = 6x

Divide both sides of the equation by 6 to solve for x:

39 / 6 = x

6.5 = x

Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.

Step-by-step explanation:

Answer:

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ㅤㅤ [tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}[/tex]

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Step-by-step explanation:

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[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}[/tex]

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[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]

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━━━━━━━━━━━

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[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]

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• Substituting the value of (x) in the given equation,

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[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]

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[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]

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As LHS = RHS,

Hence Verified

The survey ratings provide valuable feedback for drivers who are looking for quality tires for their vehicles. These ratings can give insight on steering responsiveness, how quickly a tire wears, and overall customer satisfaction. Drivers can also see how their tire of choice stacks up against other tires, making it easier to make an informed decision when shopping for tires.

The Tire Rack is America’s leading online distributor of tires and wheels. They conduct extensive testing to ensure that customers are provided with the most suitable tires for their vehicles, driving styles, and driving conditions. They also use an independent consumer survey to help drivers gain insight on long-term tire experiences.

The following data show survey ratings on a 1-10 scale, with 10 being the highest rating, of 18 maximum performance summer tires, as of February 3, 2009 (Tire Rack website). The variables are Steering (steering responsiveness), Tread Wear (quickness of wear), and Buy Again (overall tire satisfaction and desire to purchase the same tire again). The Yokohama Aegis LS4 has a Steering rating of 7.9, Tread Wear rating of 7, and Buy Again rating of 7.1. The Dunlop SP20 FE has a Steering rating of 5.7, Tread Wear rating of 5, and Buy Again rating of 3.3.

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Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!

We have shown that KLMN has four congruent sides and opposite sides are parallel and perpendicular, which makes KLMN a square.

What is a graph?

A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)^2 + (-5 - 0)^2) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)^2 + (-9 - (-5))^2) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)^2 + (-4 - (-9))^2) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)^2 + (0 - (-4))^2) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can see that the slopes of KL and MN are negative reciprocals, as are the slopes of LM and NK. This means that opposite sides are parallel and perpendicular, respectively, which is another necessary condition for a square.

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We have demonstrated that KLMN is a square since it has four congruent sides and opposite sides that are parallel and perpendicular.

What is graph?

A visual representation of the variation of one variable with relation to one or more other variables, such as a collection of dots, lines, line segments, curves, or regions.

To determine if KLMN is a square, we need to check if all four sides are congruent and if opposite angles are congruent.

We can find the length of each side using the distance formula:

KL = sqrt((10 - 6)² + (-5 - 0)²) = sqrt(16 + 25) = sqrt(41)

LM = sqrt((5 - 10)² + (-9 - (-5))²) = sqrt(25 + 16) = sqrt(41)

MN = sqrt((1 - 5)² + (-4 - (-9))²) = sqrt(16 + 25) = sqrt(41)

NK = sqrt((6 - 1)² + (0 - (-4))²) = sqrt(25 + 16) = sqrt(41)

So all four sides have the same length of sqrt(41), which is a necessary condition for a square.

To check if opposite angles are congruent, we can find the slope of each pair of opposite sides:

slope KL = (-5 - 0)/(10 - 6) = -5/4

slope MN = (-4 - (-9))/(1 - 5) = 5/4

slope LM = (-9 - (-5))/(5 - 10) = -4/5

slope NK = (0 - (-4))/(6 - 1) = 4/5

We can observe that the slopes of KL, MN, LM, and NK are all negative reciprocals. Another prerequisite for a square is that the opposing sides must be parallel and perpendicular, respectively.

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Nicolas drinks 3/2 liters of water in total - 1/3 liters of water in the morning, 1/2 liter of water at lunch, and 2/3 liter of water during basketball practice.

Nicolas drinks to third liter of water in the morning, which is 1/3 liters of water. At lunchtime, he drinks 1/2 litre of water. During basketball practice, he drinks another 2/3 liter of water.

To find the total amount of water that Nicolas drinks, we need to add these quantities together:

Total amount of water = 1/3 + 1/2 + 2/3

To add these fractions, we need to find a common denominator, which is 6 in this case. We can convert each fraction to have a denominator of 6 as follows:

1/3 = 2/6

1/2 = 3/6

2/3 = 4/6

Now we can add the fractions with the same denominator:

Total amount of water = 2/6 + 3/6 + 4/6

Total amount of water = 9/6

We can simplify this fraction by dividing both the numerator and denominator by 3:

Total amount of water = 3/2

Therefore, Nicolas drinks 3/2 litres of water in total.

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Answer: 8

Step-by-step explanation:

The sum of the interior angles in a triangle in 180.

So we can add up all the values and set it equal to 180 to find x.

4x + (5x + 5) + 103 = 180

9x + 108 = 180

9x = 72

x = 8

Answer:

x=8

Step-by-step explanation:

4x+5x+5+103=180

9x+108=180

9x=180-108

9x=72

x=72÷9

x=8

Answer: 50 uk pounds

Step-by-step explanation:

Step-by-step explanation:

See image below

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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Answer:

Step-by-step explanation:

(a) The formula to calculate the amount of money in the account after t years with an initial deposit of P and an annual interest rate r compounded annually is:

A = P(1 + r)^t

In this case, P = $500, r = 0.015 (1.5% expressed as decimal), and the interest is compounded annually, so the equation is:

A = 500(1 + 0.015)^t

Simplifying this gives:

A = 500(1.015)^t

Therefore, the equation that represents the amount of money in the savings account as a function of time in years is A = 500(1.015)^t.

(b) To find the amount of time it takes for the account balance to reach $800, we can set the equation A = 500(1.015)^t equal to 800 and solve for t:

500(1.015)^t = 800

Dividing both sides by 500:

(1.015)^t = 1.6

Taking the natural logarithm of both sides:

ln(1.015)^t = ln(1.6)

Using the power rule of logarithms:

t ln(1.015) = ln(1.6)

Dividing both sides by ln(1.015):

t = ln(1.6) / ln(1.015)

Using a calculator:

t ≈ 24.7

Therefore, it takes approximately 24.7 years for the account balance to reach $800.

The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.

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Answer:

10 is the answer of q u estion

The probability of selecting a diamond or 9 is 1/13.

Step by step explanation: There are 4 suits (diamonds, clubs, hearts, and spades) and 13 ranks (2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace). The probability of selecting a card from a standard deck of 52 cards is 1/52.

To calculate the probability of selecting a diamond or a 9, you must first calculate the total number of diamonds and nines in the deck, which is 8 (4 diamonds and 4 nines). The probability of selecting a diamond or 9 is 8/52, which reduces to 1/13.

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Answer: 3

Step-by-step explanation:

3rd, lands on a vowel.

Answer: The spinner lands on a vowel.

Step-by-step explanation:

Probability to land on purple section: 1/10

Probability to land on letter D: 1/10

Probability to land on vowel: 3/10 (A, E, I)

Probability to land on red section: 2/10

3/10 > 2/10 > 1/10

The percentage of students passing the partial exam is:

Option c. 70%

To answer this question, we use the Z-table. We have:

Given, mean (μ) = 120 and standard deviation (σ) = 17
Passing Score = 111

To find out what percentage of students passed the midterm, we need to find the probability that a score picked at random from the distribution is greater than or equal to 111. We can convert this score into a standard score (Z-score) using the Z-table. We have:

Z-score = (111 - μ) / σ
       = (111 - 120) / 17
       = -0.53

Using the Z-table, we can find the area (probability) to the left of this Z-score as follows:

Area to the left of Z-score = 0.2981 (from Z-table)

The area to the right of this Z-score (i.e. the probability that a score picked at random from the distribution is greater than or equal to 111) is:

Area to the right of Z-score = 1 - 0.2981
                           = 0.7019
                           = 70.19%

Therefore, the percentage of students who passed the midterm is approximately 70% (Option C).

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Answer:

C. 70%

Step-by-step explanation:

A graph of Triangle ABC after a dilation with a scale factor of 1/2 and center of dilation at D (-5, 5) is shown in the image attached below.

In Geometry, dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/2 centered at the point D (-5, 5) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, we have;

Coordinate A = (1, -1)  →  (1/2(1 - (-5)) + (-5), 1/2(-1 - 5) +5)

Coordinate A = (1, -1)  →  (1/2(6) - 5, 1/2(-6) + 5)

Coordinate A' = (-2, 2).

For coordinate B, we have;

Coordinate B = (1, -3)  →  (1/2(1 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate B = (1, -3)  →  (1/2(6) - 5, 1/2(-8) + 5)

Coordinate B' = (-2, 1).

For coordinate C, we have;

Coordinate C = (3, -3)  →  (1/2(3 - (-5)) + (-5), 1/3(-3 - 5) +5)

Coordinate C = (3, -3)  →  (1/2(8) - 5, 1/2(-8) + 5)

Coordinate C' = (-1, 1).

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Answer: m= 2    n =7

Step-by-step explanation:

i think to find the answer you can make the sides equal each other so 7m+4 = 9m  2m=4m m =2

and for the other angle

2n-1 = n+6  n - 1 = 6 n = 7

Step-by-step explanation:

1)561

2)5

3)40

4)90

5)3

6)500

7)200

8)100

9)5

10)50

Therefore , the solution of the given problem of area comes out to be the area of the resulting picture is therefore 28 units.

By calculating how much space would be needed to fully cover its exterior, its overall size can be calculated. The neighboring area is considered when selecting a comparable item for a rectangular design. The surface area of something determines its overall dimensions. The number of sides between a cuboid four trapezoidal curves determines how much water it can hold.

Here,

The following algorithm determines the area of a parallelogram:

=> Base area * height

We can write: given that the trapezoid RKMT has an area of 343 units2,

=>  Base(RKMT) x Height(RKMT) = Area(RKMT) = 343

All of the parallelogram's linear measurements (lengths and widths) are multiplied by 2/7 when it is dilated by a scale factor of 2/7. As a result, the expanded parallelogram's base and height will be as follows:

=>  base(dilated) equals base x (2/7)(RKMT)

=>  Height(dilated) = Height * (2/7)(RKMT)

The dilated parallelogram's size will be as follows:

=> Area(dilated) = base(dilated) x height(dilated)

=>  (2/7) x base(RKMT) x (2/7) x height(RKMT)

=>  (4/49) x Area(RKMT)

=> (4/49) x 343

=> 28

The area of the resulting picture is therefore 28 units2.

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The total number of pairwise comparisons for k is (k*(k-1))/2.

There are (k*(k-1))/2 pairwise comparisons in a completely randomized design with k treatments. For example, if there are 4 treatments, there will be 6 pairwise comparisons (4C2 = 6). Here's the explanation:In a completely randomized design, the treatments are randomly assigned to the experimental units. The main objective of such a design is to determine whether the treatment means are different from each other or not.To compare the treatment means, we use the mean square between treatments (MST) and mean square error (MSE). The test statistic used to compare the means is F = MST/MSE.The ANOVA table for a completely randomized design has the following format:Source of variationSum of SquaresDegrees of freedomMean SquareF-testtreatmentSS(k-1)k-1MST=MSTrMSEResidualSSTn-kMSEReference: https://www.stat.yale.edu/Courses/1997-98/101/anovar.htmNow, we need to compare each pair of treatments using a multiple comparisons procedure. A pairwise comparison involves comparing the means of two treatments only.The total number of pairwise comparisons is given by the combination formula:$$ \frac{k!}{2!(k-2)!} = \frac{k(k-1)}{2} $$Therefore, the total number of pairwise comparisons for k is (k*(k-1))/2.

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Answer:

Step-by-step explanation:

-11 +23-46+ (-12) =

12 - 46 + (-12) =

-34 - 12 =

-46

Answer:

  (1, 3) ∪ (5, ∞)

Step-by-step explanation:

You want the solution to the inequality ((x -1)(x -5))/(x -3) > 0.

The sign of the function changes at values of x that make the factors zero, at x = 1, 3, 5. The function is positive for x > 5, so will also be positive for 1 < x < 3

The solution is ...

  1 < x < 3  or  5 < x

__

Additional comment

If any linear factor has an even degree (even multiplicity), there will not be a sign change. The numerator factors correspond to function zeros. The denominator factors correspond to function vertical asymptotes.

The attached graph shows zeros at x=1 and x=5, and a vertical asymptote with a sign change at x=3.

Answer:

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(e): Approximately normal with mean 5.5 days and standard deviation 0.26 days.

What is standard deviation?

Standard deviation is a measure of the spread or dispersion of a set of data from its mean or average. It measures how far the values in a dataset are from the mean of the dataset.

The sample size needed for this approximation to hold depends on the shape of the population distribution, but a commonly used rule of thumb is that a sample size of at least 30 is sufficient for most cases.

In this case, the sample size is 100, which is larger than 30, so we can use the central limit theorem to approximate the sampling distribution of the sample mean.

The mean of the population distribution is 5.5 days, and the standard deviation is 2.6 days. The standard deviation of the sampling distribution of the sample mean can be approximated using the formula:

standard deviation of the sample mean = standard deviation of the population / square root of sample size

= 2.6 / sqrt(100)

= 0.26

Therefore, the best description of the sampling distribution of x is option (e): approximately normal with mean 5.5 days and standard deviation 0.26 days.

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the perimeter of the 3-on-3 court is 86 meters.

Why it is?

The lengths of the 3-on-3 court (perimeter only) are:

Length: 28 meters

Width: 15 meters

To calculate the length and width of the 3-on-3 court, we can use the dimensions provided by FIBA, the international basketball federation. According to FIBA, the official size of a 3-on-3 court is 15 meters in width and 28 meters in length.

The perimeter of the 3-on-3 court is the sum of all four sides, which can be calculated as follows:

Perimeter = 2 × Length + 2 × Width

Substituting the values of length and width from FIBA's dimensions, we get:

Perimeter = 2 × 28 meters + 2 × 15 meters = 56 meters + 30 meters = 86 meters

Therefore, the perimeter of the 3-on-3 court is 86 meters. It's important to note that the dimensions of the court may vary depending on the location and the level of play, so it's always a good idea to check the official regulations before setting up a court.

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