let x1 and x2 be two independent random variables both with mean 10 and variance 5. let y 2x1 x2 3 2. find the mean and the variance of y.

Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Answer: 4 is the average rate of change

Step-by-step explanation:

The equation to find the average rate of change is:

So f(2)= 11 and f(5)=23 then you plug these numbers in:

[tex]\frac{23-11}{5-2}[/tex] = [tex]\frac{12}{3}[/tex] = 4

The given information is inconsistent.

Answer: Let x and y be the amount invested in stocks A and B from the information given in the question, we have:x + y = total amount invested....(1)And also, the income from stock A and stock B are 5500 and (280-5500) = -5220 respectively.Now, if the income from a stock is negative, it means the investor loses money, i.e. invested more than the income received.So, we have:0.10x - 0.09y = 5500... (2)Multiplying equation (1) by 0.09 and subtracting from equation (2) multiplied by 10, we get:1.01x = 109900=> x = 108910Therefore, the amount invested in stock A is $108910, and the amount invested in stock B is:280 - 108910 = $(-108630)But since a negative value of investment doesn't make sense, it means there is no solution to this problem. So, the given information is inconsistent.

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Therefore, Person A is approximately 95.17 miles away from the building.

To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.

Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.

Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.

First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:

height = 8tan(77) ≈ 61.23 miles.

Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:

x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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Answer:

2/9 + 5/36 = 17/36

So the probability of getting 2 marbles of the same color is 17/36 or 0.472.

Answer:

17/36

Step-by-step explanation:

209 went to the first game.

192+17=209

Happy to help.

Therefore, we need 6 pounds of pecans and 10 pounds of cashews to form 16 pounds of a nut mixture worth $6.50 per pound.

by the question.

Let x be the number of pounds of pecans and y be the number of pounds of cashews in the mixture.

We know that the total weight of the mixture is 16 pounds. Therefore, we have:

[tex]x + y = 16[/tex]

We also know that the mixture is worth $6.50 per pound. This means that the total cost of the mixture is:

[tex]16($6.50) = $104[/tex]

The cost of the pecans is $4 per pound, and the cost of the cashews is $8 per pound. Therefore, the total cost of the pecans in the mixture is 4x, and the total cost of the cashews is 8y. So we have:

4x + 8y = $104

Now we have two equations with two variables. We can solve for x and y using substitution or elimination.

Let's use substitution. We can rearrange the first equation to solve for x:

[tex]x = 16 - y[/tex]

Substitute this expression for x into the second equation:

[tex]4x + 8y = $104[/tex]

[tex]4(16 - y) + 8y = $104[/tex]

[tex]64 - 4y + 8y = $104[/tex]

[tex]4y = $40[/tex]

[tex]y = 10[/tex]

Now we know that there are 10 pounds of cashews in the mixture. We can use the first equation to find the number of pounds of pecans:

[tex]x + y = 16[/tex]

[tex]x + 10 = 16[/tex]

[tex]x = 6[/tex]

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Answer: -1x + 2y = 5

Step-by-step explanation:

let me know if i got this right for you broski

Answer:

y= x+7

Step-by-step explanation:

y= mx+c

substitute to find c

5= -1(2) + c

c = 7

therefore slope = -1, (2, 5) in standard form is y=x+7

Using the vertex form the quadratic model for Jordan's monthly revenue is y = 20 / 9(x - 13.5)² + 844.44.

We can use the vertex form of a quadratic equation to create a model for Jordan's monthly revenue:

y = a(x - h)² + k

where y is the monthly revenue, x is the price that Jordan sets for all pieces, and (h, k) is the vertex of the parabola. We can find the vertex by using the formula:

h = -b / 2a

where b and a are coefficients in the standard form of the quadratic equation (y = ax² + bx + c).

To get started, we can substitute two points from the given data to form a system of equations:

864 = a(12 - h)² + k

884 = a(13 - h)² + k

When we deduct the first equation from the second, we obtain:

20 = a(13 - h)² - a(12 - h)²

Simplifying, we get:

20 = a(25 - 24h + h²) - a(16 - 24h + h²)

20 = 9a(h² - 1)

Solving for a, we get:

a = 20 / 9(h² - 1)

Next, we can use the third point to solve for h:

896 = a(14 - h)² + k

Substituting the expression we found for a, we get:

896 = 20 / 9(h² - 1)(14 - h)² + k

Simplifying, we get:

h = 13.5

Now we can solve for k by substituting in the values we found for h and a:

864 = a(12 - h)² + k

k = 844.44

Finally, we can write the quadratic model for Jordan's monthly revenue using the values we found for h, k, and a:

y = 20 / 9(x - 13.5)² + 844.44

Therefore, the quadratic model for Jordan's monthly revenue is:

y = 20 / 9(x - 13.5)² + 844.44

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The question is -

Jordan sells jewelry online. Monthly revenue varies as a function of the single price that Jordan sets for all pieces. Use vertex form to create a quadratic model for Jordon’s monthly revenue.

Price(s)           12       13      14      15     16

Revenue(s)   864    884   896  900  896

If an Estate dealer sells houses and makes a commission of GHc3750 for the first house sold and receives GHc500 increase in commission for each additional house sold, for reaching a total commission of GHc6500, she must have sold 6.5 houses.

The number of houses the estate dealer sold to reach a total commission of GHc6500 can be determined using the mathematical operations of subtraction, division, and addition.

The total commission received = GHc6,500

The commission for the first house = GHc3,750

The commission for the remaining houses sold = GHc2,750 (GHc6,500 - GHc3,750)

The commission for additional sale of each house = GHc500

The number of additional houses sold = 5.5 (GHc2,750/GHc500)

The total number of houses sold = 6.5 (5.5 + 1 or the first house)

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The country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

A medal is a small, flat, and usually round piece of metal that is awarded to individuals or groups as a symbol of recognition or honor for achievement, bravery, or other notable deeds. Medals can be made of various materials, such as gold, silver, bronze, or other alloys, and they often feature intricate designs or engravings that reflect the significance of the award.

According to the circle graph, gold medals make up 20% of the total medals, which means the country won 20% of 150 medals as gold, or 0.2 x 150 = 30 gold medals.

Similarly, silver medals make up 30% of the total medals, which means the country won 30% of 150 medals as silver, or 0.3 x 150 = 45 silver medals.

Finally, bronze medals make up 50% of the total medals, which means the country won 50% of 150 medals as bronze, or 0.5 x 150 = 75 bronze medals.

Therefore, the country won 45 silver medals and 75 bronze medals, for a total of 45 + 75 = 120 non-gold medals.

So the answer is 120.

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Sampling distribution of sample means with size 10, drawn randomly from a population with unknown mean and standard deviation, is approximately normal. It has a mean of 32 and a standard deviation of 6.32 (standard error of the mean). Option D is correct.

The sampling distribution of the mean of a large enough sample size follows a normal distribution, even if the underlying population is skewed.

The formula for the standard deviation of the sampling distribution of the mean is( σ / [tex](\sqrt(n))[/tex] ) ,

where sigma is the standard deviation of the population and n is the sample size.

Substituting the values, we get:

standard deviation of sampling distribution =[tex]20/(\sqrt(10))[/tex]= 6.32

Therefore, the sampling distribution of all possible samples of size 10 is approximately normal with a mean of 32 and a standard deviation of 6.32.

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In response to the stated question, we may state that To conclude, the function problem's relation is a function for all x values except x between 3 and 4.

In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.

If and only if each input has precisely one output, a relation is a function. To determine whether the connection stated in the issue is a function, we must examine whether any x values have more than one output.

We may achieve this by putting the specified points on a graph and looking for vertical lines that cross the graph more than once. If so, the relationship is not a function.

We may create the following graph with the supplied points:

    |                    

8  |                    

    |                    

7  |              ●      

    |                    

6  |           ●        

    |                    

5  |                    

    |                    

4  |          ●          

    |                    

3  |              ●      

    |                    

2  |    ●                

    |                    

 1  |                    

    |                    

0  |                    

    |                    

-1 |                    

    |                    

-2 |                    

    |                    

-3 |                    

    |                    

-4 |                    

    |                    

    |_____________________

       -4  -3  -2  -1  0  1  2  3  4

Apart for the line travelling through the points (3, 2) and (4, 2), there is no vertical line that intersects the graph in more than one spot (4, -3). As a result, if x is between 3 and 4, the relation specified in the issue is not a function.

To conclude, the problem's relation is a function for all x values except x between 3 and 4.

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Therefore , the solution of the given problem of percentage comes out to be were tuned in to a specific program or show at a given moment.

A number or figure stated as a fraction of 100 is referred to as "a%" in statistics. The versions that begin with "pct," "pct," and "pc" are also uncommon. The common way to indicate it is with the numeral "%," though. Furthermore, there are no indicators and a flat ratio of every single thing to the total number. Percentages are basically integers because they frequently add up to 100.

Here,

The TV ratings, also known as the TV audience share, are a measurement of the proportion of all television-owning households that are watching the same program at the same moment.

Networks and marketers use it as a gauge of a TV show's popularity to decide how successful a program will be and how much to charge for advertising during it.

Companies like Nielsen, which use a sample of homes with televisions to estimate the audience size for a given program or show, are usually in charge of gathering the TV ratings.

TV ratings are expressed as a proportion of all households with televisions that were tuned in to a specific program or show at a given moment.

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From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

a. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:

x ≥ 0 (non-negative amount of loam soil)

y ≥ 0 (non-negative amount of peat soil)

x + y ≤ 120 (total amount of soil sold is at most 120 tons)

x ≤ 60 (maximum amount of loam soil available is 60 tons)

y ≤ 90 (maximum amount of peat soil available is 90 tons)

To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;

The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:

P(x, y) = 50x + 75y

To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.

The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:

P(0, 0) = 0

P(60, 0) = 3000

P(60, 60) = 9000

P(30, 90) = 6750

P(0, 90) = 6750

Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.

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Answer: 7.8%

Step-by-step explanation:

Because it is.

Answer:

a. The sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time for several reasons. Firstly, in 1936, only a small fraction of the US population had magazine subscriptions or owned cars, telephones or club memberships. Hence, the sample was biased towards the more affluent and educated sections of society, and did not include a representative cross-section of the population. Secondly, the sample was limited to people who could read and write, which excluded many poor and illiterate people who may have had different political views.

b. The low response rate of 2,300,000 out of the 10,000,000 postcards sent out indicates a response rate of only 23%. This means that the sample was not a random sample, and that the respondents were not representative of the larger population. Low response rates tend to increase sampling error and decrease the reliability of the sample.

c. These problems are examples of nonsampling error, which occur due to factors other than the sample selection process. The bias in the sample resulted from the sampling frame, which was not representative of the population, and the low response rate.

d. Quota sampling is an example of non-probability sampling, where researchers select a specific number of participants from different subgroups of the population based on predetermined quotas. In this method, the goal is to obtain a sample that is representative of the population in terms of certain characteristics, such as age, gender, or ethnicity. Quota sampling was used by George Gallup in 1936, and is still used today in various forms, such as stratified sampling.

(please could you kindly mark my answer as brainliest)

x +|x|

= 7 + |7|

= 7 + 7

= 14

because determine of | 7 | is 7

Based on the information in the graph, it can be inferred that the false sentence is: The ball landed 11 feet from the person (option C).

To identify the false option we must read all the options and check them with the information in the graph:

According to the above, the correct answer to this question would be option C because the sentence is false with respect to the information in the graph.

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She must purchase and sell at least 61 jars to make a profit of $214.

First, calculate the cost per jar of honey that Alissa purchased:

$65/6 jars = $10.83/jar

Then, calculate the selling price per jar of honey:

$72/5 jars = $14.40/Jar

The profit per jar of honey is the selling price minus the cost price:

$14.40 - $10.83 = $3.57/jar

To find the number of jars that Alissa needs to sell to make a profit of $214, divide the total profit by the profit per jar:

$214 ÷ $3.57/jar ≈ 60.03 jars

Since Alissa cannot sell 0.03 of a jar of honey, she must purchase and sell at least 61 jars to make a profit of $214.

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The data we get from the question is a random experiment can result in one of the outcomes {a,b,c,d} with probabilities from that information, P(A U B U C) = 0.8.
         

The given probabilities of events and outcomes are:

       P({a}) = 0.4,P({b}) = 0.1,P({c}) = 0.3,P({d}) 0.2

 So the given events are:

        A = {a,b},B = {b,c,d},C = {d}

   We have to find P(A U B U C) Using the formula of the probability of the union of two events,

    we get:

          P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)

Now we will find the values of all probabilities:

                  P(A) = P({a}) + P({b})

                         = 0.4 + 0.1

                         = 0.5

                   P(B) = P({b}) + P({c}) + P({d})

                          = 0.1 + 0.3 + 0.2

                           = 0.6

                   P(C) = P({d})

                            = 0.2

                      P(A ∩ B) = P({b})

                                     = 0.1

                      P(A ∩ C) = P({d})

                                     = 0.2

                      P(B ∩ C) = P({d})

                                     = 0.2

               P(A ∩ B ∩ C) = 0

 (No common event) Put all the above values in the formula:

           P(A U B U C) = P(A) + P(B) + P(C) - P(A ∩ B) - P(A ∩ C) - P(B ∩ C) +

                                     P(A ∩ B ∩ C)

                                 = 0.5 + 0.6 + 0.2 - 0.1 - 0.2 - 0.2 + 0

                                 = 0.8

         Therefore, P(A U B U C) = 0.8 is the required probability.

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Step-by-step explanation:

4x + y^2 + 2y =  - 5

4x = - y^2 -2y - 5          

4x = - (y^2 + 2y)   - 5      'complete the square' for y

4x = - ( y +1)^2   + 1    - 5

 x = - 1/4 ( y+1)^2  - 1             vertex is at -1, -1

-14x+2y^2-8y -20 = 0

14x = 2y^2 -8y-20

14x = 2 ( y^2 - 4y) - 20     complete the square for y

14x = 2(y-2)^2  -8 - 20

x = 1/7 ( y-2)^2 - 2                Vertex is at   -2 , 2

The solution to the system of equations y=-7x-29 and y=-3x-9 using elimination method is x = 5 and y = -64.

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. In this case, we can eliminate y by subtracting the second equation from the first. This gives us:

y - y = -7x - 29 - (-3x - 9)

0 = -4x - 20

Simplifying this equation, we get:

x = 5

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:

y = -7x - 29

y = -7(5) - 29

y = -64

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Complete question is:

Solve the given System of equations by elimination method

y=-7x-29,  y=-3x-9

On the first day of ticket sales for the school’s spring musical, 46 senior citizen tickets and 44 child tickets were sold, bringing the total number of tickets sold to 362.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

The second day saw a slightly lower number of tickets sold, with two senior citizen tickets and 25 child tickets purchased, for a total of 85. The price of a senior citizen ticket and a child ticket was likely the same on both days, and likely the same price as it is for the rest of the ticket sales.

The school likely has a set price for tickets, which would not change as the number goes up or down. It is common for schools to give discounts for senior citizens, so the price of their tickets is usually lower than the price of a child ticket. The school set the prices of the tickets in a way that would bring in the most money, while still being affordable for the community to attend.

The school likely had a plan in place for how many tickets they wanted to sell and what prices they wanted to set. They also likely had a goal of how much money they wanted to bring in from the ticket sales. After the two days of ticket sales, the school was able to see how many tickets were sold and how much money was collected. This can help the school to adjust their plan, if necessary, to reach their goal.

The money brought in from the ticket sales will likely help the school to cover the costs of putting on the musical. It may also help to pay for any other expenses associated with the production of the show. The school may also use the money to purchase new materials or supplies for the performing arts department.

Overall, the school was able to bring in a total of 447 from the two days of ticket sales. This money will help to ensure that the school’s spring musical is a success. The school was also able to offer discounted tickets to senior citizens, which allowed more people to attend the show.

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The price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

Jack's school is selling tickets to a spring Musical. On the first day of ticket sales, the school sold a total of 362 tickets, 46 of which were senior citizen tickets and 44 of which were child tickets. On the second day of ticket sales, the school sold two senior citizen tickets and 25 child tickets, for a total of 85 tickets.

To calculate the price of each ticket, we can divide the total amount taken in by the number of tickets sold. For senior citizen tickets, the total amount taken in was 85, and two were sold, so the price of a senior citizen ticket is 85/2 = 42.50. For child tickets, the total amount taken in was 85, and 25 were sold, so the price of a child ticket is 85/25 = 3.40.

In conclusion, the price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

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The value of' b' is 27 when' a' is three.

The presented equation is a x 9 = b, wherein' a' is a variable and' b' is the product of' a' and nine. we are asked to find the value of' b' when' a' is 3.

Substituting the value of' a' into the equation, we get

3 x 9 = b

27 = b

Thus, the value of' b' is 27 when' a' is three.

On this equation,' a' is a variable, this means that that its cost can trade. still, the value of' b' is dependent on the price of' a'. whilst' a' is 3, the price of' b' is 27. this is an illustration of a easy linear equation, in which the value of one variable is dependent on the figure of any other variable, and can be used to model real-global situations.

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The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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Check the picture below.

The conclusion which is correct about given situation is D) The p-value (0.001) is less than the significance level (0.01), which means we reject the null hypothesis that the proportion of boxes with broken glass is equal to or less than 8%.

We have convincing evidence to suggest that the actual proportion of boxes with broken glass is greater than 8%. Therefore, we can conclude that the glass manufacturer's belief is supported by the sample data.

This conclusion is based on the fact that the p-value is less than the significance level, indicating that the observed data is unlikely to have occurred by chance alone assuming the null hypothesis is true.

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Statement d is also correct because it means the same thing as statement b, just using different phrasing.

It consists of two sides, left-hand side (LHS) and right-hand side (RHS), separated by an equal sign (=). The equation represents a relationship between the expressions on both sides, indicating that they have the same value.

The two correct statements that describe the equation y = 4 × 18 are:

b. The value of y is 4 times as many as 18.

d. The value of y is 4 times as much as 18.

Statement b is correct because the equation y = 4 × 18 means that y is equal to 4 times the value of 18, or y = 4 × 18 = 72.

Statement d is also correct because it means the same thing as statement b, just using different phrasing. "As much as" and "many as" are interchangeable in this context, and both mean "multiplied by."

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Using trigonometry, the distance between the two vessels when the second boat enters the lighthouse's radius is 13.46 miles.

The relationships between angles and length ratios are investigated in the branch of mathematics known as trigonometry. The use of geometry in astronomical study led to the establishment of the field during the Hellenistic era in the third century BC.

The distance between the two boats when the second boat enters the radius of the lighthouse light is 13.46 miles using trigonometry.

A triangle is a polygon with three edges and three vertices. It belongs to the basic geometric shapes. A triangle with the vertices A, B, and C is represented by the Δ ABC.

Any three points that are not collinear create a singular triangle and a singular plane in Euclidean geometry. (i.e. a two-dimensional Euclidean space). In other words, every triangle is a part of a plane, and that triangle is a part of only one plane. In the Euclidean plane, all triangles are contained within a single plane, but in higher-dimensional Euclidean spaces, this is no longer the case. This page covers triangles in Euclidean geometry, especially the Euclidean plane, unless otherwise specified.

In this question,

The side of the isosceles triangle is given by,

l=2a sin(θ/2)

where a= 18 miles

θ= 44°

l= 2*18*sin 22°

= 36*0.374

= 13.46 miles

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