A concrete beam may fail either by shear (S) or flexure (F). Suppose that three failed beams are randomly selected and the type of failure is determined for each one. Let X = the number of beams among the three selected that failed by shear. List each outcome in the sample space for the original random experiment of selecting three failed beams and denoting the type of failure along with each outcome's associated value of x.

Answer:

Step-by-step explanation:

Expanding (x + y)^2, we get:

(x + y)^2 = x^2 + 2xy + y^2

We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:

(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42

Therefore, (x + y)^2 = 42.

The percent tip Ruby left was 27%.

What is percent?

A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

Calculate the tip amount:

The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:

Tip = Total cost - Cost of meal

Tip = $34.29 - $27

Tip = $7.29

Calculate the percent tip:

The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:

Percent tip = (Tip / Cost of meal) x 100%

Percent tip = ($7.29 / $27) x 100%

Percent tip = 27%

Therefore, the percent tip Ruby left was 27%.

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Answer: 16.2 km

Step-by-step explanation:

The height of the triangle can be found using the area formula for triangles:

Area = (1/2) × base × height

Rearranging the formula to solve for the height gives:

height = (2 × Area) / base

In this case, the area of the triangle is 64.8 km² and the base is given as 8 km. So, the height of the triangle can be calculated as:

height = (2 × 64.8 km²) / 8 km

height = 16.2 km

Answer:

7.2 km

Step-by-step explanation:

the formula for the area of a triangle is 1/2*b*h where b is its base and h is its height. now let's solve for the height

64.8=1/2*18h

64.8=9h

64.8/9=h

7.2 km=h

The interquartile range is 16.00

To construct a box and whisker plot in Excel using the Quartile.INC function for the given data, follow these steps:

1) Enter the data into a column in Excel.

2) Select the data column and click on the "Insert" tab in the top menu.

3) Click on "Insert Statistic Chart" and select "Box and Whisker" from the dropdown menu.

4) In the "Chart Elements" menu on the right, click on the arrow next to "Axis Titles" and select "Primary Vertical Axis Title" to add a title for the y-axis.

5) Label the y-axis "Number of Rooms Sold".

6) Right-click on the y-axis and select "Format Axis" from the dropdown menu.

7) In the "Number" menu, select "Number" as the category and set the number of decimal places to 0.

8) In the "Chart Elements" menu, click on the arrow next to "Chart Title" and select "None" to remove the chart title.

9) The resulting box and whisker plot should show the quartiles, the median, and any outliers.

To find the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3). The Quartile.INC function in Excel returns the exclusive quartiles (i.e., does not include the median in either quartile), so the interquartile range is calculated as:

IQR = Q3 - Q1

Using the Quartile.INC function with the given data, we get:

Q1 = 78.5

Q3 = 94.5

Therefore, the interquartile range is

IQR = Q3 - Q1 = 94.5 - 78.5 = 16

Rounding to two decimal places, the interquartile range is 16.00.

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An equation in Ax + By=C form for this line include the following: -3x + y = 19.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-6, 1), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (1) = 3(x - (-6))

y - 1 = 3x + 18

y = 3x + 18 + 1

y = 3x + 19

In standard form, we have:

-3x + y = 19.

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Answer:

B

Step-by-step explanation:

Based on the information provided, it is not possible to determine the hypothesis of the tire company. Therefore, options C and D can be eliminated.

Option A suggests that no hypothesis was provided, which may be possible. However, it is implied that the hypothesis was related to the proposed improved performance in wet conditions of the new tire. Therefore, option A may not be the best answer.

Option B suggests that the hypothesis was neither verified nor refuted. This is a common outcome in many experiments, and it is possible that the tire company may draw this conclusion based on the data. Therefore, option B is the most likely answer.

So, the tire company MOST LIKELY would infer that the hypothesis was neither verified nor refuted based on this data.

The graph shown is the graph of the cotangent function.

The graph of the cotangent function, cot(x), is a periodic function that has a period of 2π. The cotangent function is the reciprocal of the tangent function, so its graph is related to the graph of the tangent function.

Like the tangent function, the cotangent function has singularities at x = (n + 1/2)π where n is an integer. At these points, the function has a vertical asymptote, meaning it approaches positive and negative infinity as x approaches (n + 1/2)π from either side.

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The average rate of change of the population per year is -5666.66

From the question, we have the following parameters that can be used in our computation:

Year  Population

1972  1,090,000

1982  1,060,000

1992  940,000

2002 860,000

2012 800,000

2022 770,000

Given that the year is from 1972, we have

year 20 = 1992  940,000

year 50 = 2022 770,000

So, we have

Average rate = Difference in values/Difference in years

This gives

Average rate = (770,000 - 940,000)/30

Evaluate

Average rate = -5666.66

Hence, the rate is -5666.66

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The volume of the right cone is (c) 400π cm cube

From the question, we have the following parameters that can be used in our computation:

Radius = 10 cm

Height = 12 cm

The volume of the cone is calculated as

Volume = 1/3πr²h

Substitute the known values in the above equation, so, we have the following representation

Volume = 1/3π * 10² * 12

Evaluate

Volume = 400π

Hence, the volume is 400π cm cube

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Given the planes [tex]4x-5y+z=4[/tex] and [tex]5x-4y+3z=-2[/tex], find the angle between them.

Using the formula,

[tex]\theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

Where vector, [tex]A= < 4,-5,1 >[/tex] and vector [tex]B= < 5,-4,3 >[/tex].

Plug these values into the formula above...

[tex]\Longrightarrow \theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{(4)(5)+(-5)(-4)+(1)(3) }{\sqrt{(4)^2+(-5)^2+(1)^2}\sqrt{(5)^2+(-4)^2+(3)^2} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{\sqrt{42}\sqrt{50} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{10\sqrt{21} } )[/tex]

[tex]\Longrightarrow \theta \approx 20.2\textdegree[/tex]

Answer:

83 There is an elixir

total quantity of elixir = 500 mL

quantity of elixir use in one dose = 6 mL

number of dose in 500 mL = 500/6

83.333

The rate of the current is 5/11 of the speed of the barge in still water.

Let's call the speed of the barge in still water "s" (in miles per hour) and the speed of the current "c" (also in miles per hour).

When the barge travels upstream (against the current), its effective speed is reduced by the speed of the current, so the speed of the barge relative to the riverbank is (s - c). On the return trip, the current is going in the same direction as the barge, so the effective speed of the barge relative to the riverbank is (s + c).

distance upstream = (s - c) x 8 miles

distance downstream = (s + c) x 3 miles

(s - c) x 8 = (s + c) x 3

8s - 8c = 3s + 3c

5s = 11c

c = 5s/11

Therefore, the rate of the current is 5/11 of the speed of the barge in still water.

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Answer:

C

Step-by-step explanation:

180-2x-2=180*7/9

x=19

The exact value of the expression tan(0/2) for the given value of 0 is 0.

In mathematics, it is important to understand how to simplify expressions and solve for their exact values. One such expression is tan(0/2), where 0 is a given value. In this explanation, we will break down the steps to simplify this expression and find its exact value without using a calculator.

The expression we are given is tan(0/2), which can be simplified using the formula for the tangent of half an angle. This formula states that tan(x/2) = sin(x) / (1 + cos(x)).

In our given expression, we have x = 0, so we can substitute it into the formula and get:

tan(0/2) = sin(0) / (1 + cos(0))

Now, we know that sin(0) = 0 and cos(0) = 1, so we can simplify further:

tan(0/2) = 0 / (1 + 1) = 0/2 = 0

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The graph is plotted and attached

The oxygen level will be increasing as time goes on

In 0.5 weeks the oxygen level will return to 75% of its normal level

This is the end behavior of the graph, of the function f(t) = t^2 − t + 1, the graph shows that as t tends to infinity. the oxygen level will continue to increase.

The graph is plotted and attached

From the problem. the normal level of oxygen is at f(0) = 1

75% of 1 = 0.75

From the graph, the oxygen level will return to normal level in 1 week(1, 1) and at 0.5 the oxygen level is 0.75, (0.5,0.75). This is the vertex of the graph.

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Answer:

$66,600

Step-by-step explanation:

First you add everything up.

50,000 + 1,400 = 51,400

51,400 + 2,500 = 53,900

53,900 + 1,600 = 55,500

Now you need to get 20% of 55,500

20% of 55,500 is 11,100

Now you add them

55,500 + 11,100 = 66,600

The value of the equation is 4.19p = -6.1

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

2.3p - 10.1 = 6.5p - 4 - 0.01p

On simplifying , we get

Adding 4 on both sides , we get

2.3p - 6.1p = 6.49p

Subtracting 2.3p on both sides , we get

4.19p = -6.1

Now , the value of the equation similar to 4.19p = -6.1 is 2.3p - 6.1p = 6.49p

Hence , the equation is 4.19p = -6.1

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The inequality in standard form that represents the restaurant owner's

desired revenue is x² + 2x - 80 ≤ -65.

Inequalities are defined as the expressions consisting of both variables and constants connected by inequality signs like ≠, >, <, ≤ and ≥.

Part A :

Cost : 10 + x

Customers : 16 - 2x

Part B :

Given that,

Hourly revenue = Price paid by each customer × average number of customers per hour.

Price paid by each customer = 10 + x

Average customers per hour = 16 - 2x

Given that the restaurant owner wants a minimum revenue of $130 per hour.

(10 + x) (16 - 2x) ≥ 130

(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130

160 + 16x - 20x - 2x² ≥ 130

-2x² - 4x + 160 ≥ 130

Dividing the equation throughout by -2,

x² + 2x - 80 ≤ -65

The inequality sign changes as we multiply or divide with a negative number.

Hence the required inequality is x² + 2x - 80 ≤ -65.

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The complete question is given below.

Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Part A

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.

Part B

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.

The answer is C) 6 units of consumption goods.

What is Cost of producing?

The overall cost incurred by a business to manufacture a product or provide services is referred to as the cost of production. Supplies and raw materials consumed during production, as well as labor costs, are often included in production costs.

The opportunity cost of producing 3 units of capital is 6 units of consumption goods, as we can see from the data in the production possibilities curve.

Moving from producing 4 units of capital to producing 3 units of capital involves giving up 3 units of consumption goods (from 7 to 4), and moving from producing 3 units of capital to producing 2 units of capital involves giving up another 3 units of consumption goods (from 4 to 1).

Therefore, the opportunity cost of producing 3 units of capital is 6 units of consumption goods.

So, the answer is C) 6 units of consumption goods.

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Lab2.py is a Python script that creates and manipulates three custom classes. The classes are as follows:

1. Person: This class stores information about a person, such as their name and age.

2. Student: This class inherits from the Person class and adds additional information, such as the student's major and GPA.

3. Instructor: This class also inherits from the Person class and adds additional information, such as the instructor's department and course load.

A file lab2.py and define three classes, polygon, rectangle, triangle is:

class Polygon:

 def __init__(self, number_of_sides):

   self.number_of_sides = number_of_sides

class Rectangle(Polygon):

 def __init__(self, length, width):

   Polygon.__init__(self, 4)

   self.length = length

   self.width = width

 def area(self):

   return self.length * self.width

class Triangle(Polygon):

 def __init__(self, base, height):

   Polygon.__init__(self, 3)

   self.base = base

   self.height = height

 def area(self):

   return 0.5 * self.base * self.height

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Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

The graph of the function f(x) = 4sin(2x) is illustrated in the image.

A periodic function has a range that is determined for a fixed interval and a domain that includes all real number values.

Any function that has a positive real integer p such that f (x + p) = f (x), with all x being real values, is said to be periodic.

We know sin(x) is a periodic function with amplitude 1 and a period of 2π.

Therefore, A periodic function with amplitude 4 and period π would be,

f(x) = 4sin(2x).

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The like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

Terms whose variables (such as x or y) with any exponents (such as the 2 in x²) are the same are called like terms,

Examples: 7x and 2x are like terms because they are both "x".

Given are some pairs of expressions, we are asked to identify which are like terms,

We know that, according to the definition of the like terms,

Like terms are those terms which contain the same variable which is raised to the same power,

Therefore, the expressions showing the like terms are,

3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

Because, they have same variable with same powers.

Hence, the like terms in the given options are 3x⁴ and 2x⁴, 2x² and 3x², 2x and 3x

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The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

If the given solution set is {-10, 9}.

Then the quadratic equation can be written in factored form as:

(x + 10) (x - 9) = 0

Expanding the product,

x² + x - 90 = 0

Therefore,

The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.

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The given statement indicates that (a) Your average pay is $40 (b) The standard deviation is 45.12 (c) If you retain both positions, your anticipated income is $400.

Because it aids in comprehending observations when the data is dispersed, standard deviation is significant. The standard error of the data will be higher the more evenly spread the data is.

a) On average, you make $220 - $180 = $40 more from Job A.

b) The standard deviation of the difference in the amount you make from Job A and Job B is given by:

σ(A - B) = √[σ(A)² + σ(B)²]

= √[(30)² + (35)²]

≈ 45.12

c) To determine whether to take the deal, we need to compare the expected earnings from the two scenarios. If you quit Job B and accept your mom's offer, your total earnings would be:

Earnings = (1/2) × $220 + $100 = $210

On the other hand, if you keep both jobs, your expected earnings would be:

Earnings = $220 + $180 = $400

Since $400 is greater than $210, you would not take the deal if making the most money is the most important thing to you.

It is important to remember that this choice may also be influenced by aspects like the amount of time and effort needed for each work, the chance for professional advancement, job security, and other non-financial considerations.

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Answer:

its only -11x^2

Step-by-step explanation:

2x^2 and -11x^2 have the same variable.

The value of the third quartile is approximately 7.00, rounding it up to two decimal places.

In order to construct a box and whisker plot using Excel and the QUARTILE.INC function we will follow the steps -

Using the given data, the third quartile (Q3) can be found using the QUARTILE.INC function in Excel as follows -

Using this method, rounding the result to two decimal places we get,

Q3 = QUARTILE.INC({7, 6, 7, 6, 7, 8, 3, 2, 6}, 3)

Q3 ≈ 7.00 (rounded to two decimal places)

Therefore, the value of the third quartile is approximately 7.00.

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Answer:

the value of x will be 9 they all are similar so we will just take ratios and do cross multiplication