An airliner carries 400 passengers and has doors with a height of 78 in. heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 in. if a male passenger is randomly selected, find the probability that he can fit through the doorway without bending

Therefore, we can see that the UK has a higher population density than Spain.

In mathematics, "square" usually refers to the operation of multiplying a number by itself. When we square a number, we write it as that number raised to the power of 2, or we can use the symbol "^2" to indicate that we are squaring the number.

For example, the square of 3 is. \(3^2\), which is equal to 9. Similarly, the square of -5 is. \((-5) ^2\), which is equal to 25. In general, we can square any real number (positive, negative, or zero) to get a non-negative result.

We can also use the term "square" to refer to a geometric shape that has four equal sides and four right angles, such as a square on a checkerboard or a piece of paper.

by the question.

For the UK:

\(Population density = Population /Area\)

\(= 66,000,000 /95,000\)

\(= 694.74 people per square mile\)

For Spain:

\(Population density = Population / Area\)

\(= 47,000,000 / 195,000\)

\(= 241.03 people per square mile\)

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The x-axis and y-axis are two parallel number lines that meet at (0, 0) to form the shape of the letter t.

Geometric objects and mathematical equations are represented on the coordinate plane, a two-dimensional graph. It is made up of the x-axis and y-axis, two parallel number lines that meet at the starting point (0, 0). The horizontal coordinate is represented by the x-axis, while the vertical coordinate is represented by the y-axis. They combine to create the Cartesian coordinate system.

Positive numbers are labelled to the right of the origin and negative values are labelled to the left of the origin on the x-axis. Positive numbers are written above the origin of the y-axis, and negative numbers are written below it. An ordered pair (x, y), where x denotes the horizontal coordinate and y denotes the vertical coordinate, is used to represent each point on the coordinate plane.

For graphing linear equations, quadratic equations, and other functions, the coordinate plane is a helpful tool. Additionally, it is employed to depict geometric forms like polygons, circles, and lines. The distance between two points, the slope of a line, and other significant features of mathematical objects can be calculated by graphing points on the coordinate plane. With applications in physics, engineering, economics, and computer science, the coordinate plane is a fundamental idea in mathematics.

The graph is shown below when y=1.

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Graph attached below,

The coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given equation is y = \(\frac{1}{2}x-4\).

Now put x= 1 then y = \(\frac{1}{2}\times1-4 =\frac{1-8}{2}=\frac{-7}{2}=-3.5\)

Now put x=2 then \(y=\frac{1}{2}\times2-4=1-4=-3\)

Now put x=4 then \(y=\frac{1}{2}\times4-4=2-4=-2\)

Now put x=6 then \(y=\frac{1}{2}\times6-4=3-4=-1\)

Then coordinates of the plane is

x       y

1       -3.5

2      -3

4      -2

6      -1.

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Answer:

m

=

0.8

¯

3

Step-by-step explanation:

We would use two means from independent samples. The design is independent samples because the runners and bikers are two different groups and their participation in one sport does not affect the other.

To answer your question, you would use "two means from independent samples." Here's why:

1. You are comparing the resting heart rates of two separate groups (runners and bikers), which makes them independent samples. Participants were only allowed to participate in one sport, further confirming their independence.

2. You are comparing the average resting heart rates of these two groups, which requires using means rather than proportions. Proportions would be used if you were comparing percentages or ratios.

We would compare the mean resting heart rate of the runners to the mean resting heart rate of the bikers who cover more than 5 miles.
So, the appropriate statistical test for this scenario is a comparison of two means from independent samples.

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a) For chi-squared distribution with v=3 degrees of freedom, the statistic that can be constructed using Xi's is:

X2 = Σ i=1 3 (Xi − i)2 / 3.

X2 has chi-squared distribution with 3 degrees of freedom.

b) For t-distribution with v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

T = (X1 − 1) / [(X2/2)0.5].

T has t-distribution with 2 degrees of freedom.

c) For F-distribution with v1=1 and v=2 degrees of freedom, the statistic that can be constructed using Xi's is:

F = [(X1 − 1)/1] / [(Σi=2 to 3 Xi2) / 2].

F has F-distribution with 1 and 2 degrees of freedom.

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Yes, it is true that if A and B are square and invertible matrices, then AB is also invertible, and its inverse is given by\((AB)^{(-1) }= B^{(-1)}A^{(-1).\)

To see why this is true, consider the product\((AB)(B^{(-1)}A^{(-1)}).\)

Using the associative property of matrix multiplication, we can rearrange this expression as

\((A(BB^{(-1)})A^{(-1)}) = (AIA^{(-1)}) = AA^{(-1)} = I,\)

where I is the identity matrix.

Similarly, we can show that \((B^{(-1)}A^{(-1)})(AB) = I,\) which means that

\((AB)^{(-1) }= B^{(-1)}A^{(-1).\)

Therefore, we conclude that if A and B are square and invertible matrices, then AB is invertible, and its inverse is given by \((AB)^{(-1)} = B^{(-1)}A^{(-1).\)

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The width of the frame should be 9 inches. We can start by finding the dimensions of the watercolor if its ratio is 5:6. Let's assume that the width of the watercolor is 5x, then the height would be 6x.

According to the problem, the actual dimensions of the watercolor are 10.5 in by 14 in. We can set up a proportion to find the value of x:

10.5 / 5 = 14 / 6

Simplifying this proportion, we get:

2.1 = 2.333...

This means that the width of the watercolor is 2.1 times larger than what it should be to maintain the 5:6 ratio.

To find the desired width of the watercolor, we can divide the actual width by 2.1:

10.5 / 2.1 = 5

Therefore, the desired width of the watercolor is 5 inches.

Now we can find the width of the frame by subtracting the desired width from the actual width of the watercolor:

14 - 5 = 9

So the width of the frame should be 9 inches.

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We get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).

We are given a multiplication expression:

( + 7 ) ( - 4)

We need to write this expression as a repeated addition

Repeated addition means when we add the same digits many times that is repeatedly.

For example: 3 + 3 + 3 + 3 or 8 + 8 + 8 + 8 or 5 + 5 + 5 +5 etc.

Here, we can see that -4 is multiplied by 7

It means that - 4 will be added 7 times repeatedly to form the expression

So, we get that:

= ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 )

Therefore, we get the repeated addition as ( - 4 ) + ( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ) +( - 4 ).

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The nights required by Quinn in order to knit a total of 70 centimeters of the scarf is equal to 35.

The number of nights required by Quinn in order to knit a total of 70cm of the scarf can be calculated using multiplication. Multiplication can be described as one of the four basic arithmetic operations in which we perform the repeated addition of the same number or value. This problem can be solved using cross-multiplication as follows;

2 nights = 4 cm of scarf

x nights = 70 cm of scarf

70 × 2 = 4(x)

140 = 4(x)

x = 140 / 4

x = 35

Therefore, Quinn will have to spend 35 nights knitting in order to knit a total of 70 centimeters of the scarf.

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The approximate ordered pair for the outlier for trend of the data is at the coordinate (6, 80).

Another name for a scatter plot is an XY graph, scatter chart, or scattergram. The scatter diagram displays the relationship between pairs of numerical data by graphing them with one variable on each axis. The following scenarios either call for the usage of scatter plots.

In the case of paired numerical data, when more than one value of the dependent variable is associated with a particular value of the independent variable. While evaluating the relationships between variables, it might be helpful to look for potential problem-solving reasons, see whether two products that seem connected both have the same root cause, and so on.

From the given graph we see that the point (6, 80) lies outside the trend of the data.

Hence, the approximate ordered pair for the outlier for trend of the data is at the coordinate (6, 80).

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To determine the variance of a geometric random variable X with parameter p, we can use the conditional variance formula.

The formula for the variance of a geometric random variable is given by:

Var(X) = (1 - p) / (p^2)

Where p is the parameter of the geometric distribution, representing the probability of success on each trial.

This formula assumes that the random variable X represents the number of trials required until the first success in a sequence of independent Bernoulli trials, where each trial has a probability of success p.

By plugging in the value of p into the formula, you can calculate the variance of the geometric random variable X.

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The lower quartile of the given set of numbers 4, 6, 7, 8, 10, 12, 20 is 6. So, correct option is B.

To find the lower quartile of a set of numbers, we first need to arrange them in ascending order. The given numbers are: 4, 6, 7, 8, 10, 12, 20.

Next, we divide the data set into four equal parts. The lower quartile is the median of the lower half of the data set. In this case, the lower half is 4, 6, and 7.

To determine the median of the lower half, we need to find the middle value. Since we have an odd number of data points in the lower half, the middle value is the single value between the two extremes. In this case, the median is 6.

This corresponds to option (b) in the given choices: 6.

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Answer:

Step-by-step explanation:

Use Pythagorean to find the missing side x of the triangle.

It is a hypotenuse with other sides 18 in and half of 15 in:

The perimeter is:

System of equations used to represent the amount of money spend by Juan on buying roses and camations is given by :

3x + 1.50y = 18 , y = 3x.

Number of roses bought by 2.4 and camations is 7.2.

No ,it is not viable.

As given in the question,

Total amount of money spend by $18

Cost of each rose = $3

Cost of each camations = $1.50

Number of camations = 3 times the number of roses

Let 'x' represents the number of roses

And 'y' represents the number of camations

System of equation is given by :

3x + 1.50y = 18

y = 3x

Simplify the system of equation using substitution we get,

3x +(1.50)(3x) = 18

⇒ 3x + 4.5x = 18

⇒ 7.5x = 18

⇒ x= 18/7.5

⇒x = 2.4

⇒y = 7.2

Number of roses and camations are in decimal .

Solution is not viable.

Therefore, the system of equation for the given condition is given by

3x + 1.50y = 18 , y = 3x and solution is not viable.

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Answer:

8.333333333333333

Step-by-step explanation:

Answer:

25/3 - Or in a simpler form 8 1/3

Step-by-step explanation:

I multiplied 15 by 5/9. I hope this helps :)

Answer:

The answer is c. 81.76%

The truth value of the given proposition is "false".

The truth value of the given proposition can be evaluated using the following steps:

Convert the binary representation of the numbers to decimal:

0 = 0

~1 = -1 (invert the bits of 1 to get -2 in two's complement representation and add 1)

10 = 2

Apply the comparison operator "=" between the left and right sides of the equation:

(0 = -1) = 2

Evaluate the left side of the equation, which is false, because 0 is not equal to -1.

Evaluate the right side of the equation, which is true, because 2 is a nonzero value.

Apply the comparison operator "=" between the results of step 3 and step 4, which yields:

false = true

Therefore, the truth value of the given proposition is "false".

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Answer: 7:5

Step-by-step explanation: 14/2 = 7 and 10/2 = 5

I am truly sorry if it was wrong or i did not understand ty.

- ♥ Roxy ♥

Answer:

97, that's the answer.

Answer: 97.1

Step-by-step explanation: the tenth is the first number after the decimal place so in your question that number is the 0 and the number next to it is 8 so, our 0 needs to change because 8 is bigger than 5 on the number line which makes our 0 increase to 1. You don't need to change the whole number at all.

Each child will receive the 1.1 cup of milk.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that a container of milk contains 8 cups of milk. if paul sets aside \(1\dfrac{2}{5}\) cups of milk for use in a recipe , then we get the leftover;

8  -  \(1\frac{2}{5}\) = 8 -  7/5

= 40- 7/5

= 33/5

= 6.6

The the rest cups of milk = 6.6

Then the rest evenly among his three children 6.6/3 = 1.1

Hence, Each child will receive the 1.1 cup of milk.

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Answer:

$0.60

Step-by-step explanation:

Given that:

The ratio of number of cookies to the cost of cookies as:

Number of cookies : Cost of cookies = 15 : 9

It means, we get 15\(x\) number of cookies when we pay $9\(x\).

To find:

An equivalent ratio to represent the cost of 1 cookie.

Solution:

Here, we have to find nothing but the unit price or the price of 1 cookie.

This can simply be done by dividing the total cost of cookies with the total number of cookies.

Total cost of 15\(x\) cookies is given as $9\(x\)

Using unitary method:

Let us divide both the sides with 15\(x\), we get:

Total cost of \(\frac{15x}{15x}\) cookies is given as \(\frac{\$9x}{15x}\)

Total cost of 1 cookie is given as $0.60

Answer:

In the first rectangle,

one side =15*1=15

other side = 15* 3=45

in the second rectangle,

one side = 25*1=25

other side= 25*3=75

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

12=7y+12

-12    -12

0=7y

/7   /7

undefined

you can't solve this as you can't divide 0 by a number

Answer:

Step-by-step explanation:

  12 = 7y + 12

 -12        -12

0    =  7y

/7        /7

0 = y

The amount of the money after 7 years with a rate of 13% with an initial amount of $400 will be $ 941.04.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

Tanvi opened a savings account and deposited $400.00 as principal.

The account earns 13% interest, compounded annually.

Then the balance after 7 years will be

We know the compound interest formula.

A = P (1 + r)ⁿ

We have

P = $ 400

r = 13%

n = 7 years

Then we have

A = 400 x (1 + 0.13)⁷

A = 400 x 1.13⁷

A = 400 x 2.3526

A = $ 941.04

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Option D is the right option. The maximum height of the ball was 2.5 seconds after it was thrown.

Let b and h be the zeros of the function f(x). If this statement is true, then f(x)= k(x-a)(x-b) would be our equation. Let k be our coefficient.

From the given table,

At t = 0

h(0)= 0

At t = 5

h(5) = 0

So, 0 and 5 are the zeros of the function h(t).

h(t)=k(t-0)(t-5)

h(t)=k(t)(t-5)

Now substitute any point from the table i.e, (2, 96) in [1] to find k.

96=k(2)(2-5)

96=k(2)(-3)

Now, we simplify!

96=-6k

k=-16

Now, we have the equation for h(t)

h(t)=-16(t-5)

h(1)=-16t^2+80t

Initial height of the ball: h(0) = 0   To find the maximum height of the ball, we will use the quadratic equation  y=ax^2+bx+c.....[2], the the axis of symmetry is given by: x=-b/2a

Now that we know b= -16 and h= 80 we can perform this equation to find out for t:

t=-80/2(-16)=80/32=2.5 seconds

We can now come to the conclusion that the statement "The maximum height of the ball was reached 2.5 seconds after it was thrown." is the one true statement.

I hope this helps!!  o(〃＾▽＾〃)o

The probability that Andy chooses red and his boss approves is 6.4%

The correct option is option c.

Let A be the probability that Andy chooses red

Let B be the probability that his boss approves

probability of A = 0.32

probability of B = 0.20

\(P (A and B) = P(A) \times P(B)\\P (A and B) = 0.32 X 0.20 P\\P (A and B) = 0.064\)

Convert the 0.064 to percentage, multiply it by 100.

=0.064 x 100

=6.4%

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Answer:

a) y= ⅔x -4

b) -4

Step-by-step explanation:

Please see the attached pictures for the full solution.

Answer:

  (c)  f(-1) = 0

Step-by-step explanation:

For a given value of x, the table tells you the value of f(x). If you want to know the value of f(-1), you have to look for the line of the table that has x = -1.

That is the 2nd line of the table. It tells you f(-1) = 0.