A survey conducted on a reasonably random sample of 203 undergraduates asked, among many other questions, about the number of exclusive relationships these students have been in. The histogram below shows the distribution of the data from this sample. The sample average is 3.2 with a standard deviation of 1.97. Estimate the average number of exclusive relationships Duke students have been in using a 90% confidence interval and interpret this interval in context. Check any conditions required for in- ference, and note any assumptions you must make as you proceed with your calculations and conclusions.

The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter

The symbol π and the word "pi" are both used to refer to the mathematical constant that represents the ratio of a circle's circumference to its diameter. The symbol π is a Greek letter that has been used to represent this constant for centuries, while the word "pi" is the commonly accepted English-language term for this constant.

They are two different representations of the same mathematical concept. The symbol π is used extensively in mathematical formulas, while the word "pi" is used more colloquially to refer to this constant in everyday conversation.

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  LN/RT = NM/TS is the correct option in congruent triangle .

What in mathematics is congruent?

If two shapes are similar in size and shape, they are said to be congruent. The mirror image of one shape is the same as the other if two shapes are congruent.

                          Congruent refers to objects that are precisely the same size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

  In ΔLMN ≅ ΔRST

 In triangle are congruent .

    LN/RT = NM/TS

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Answer:

Step-by-step explanation:

When a circle is inscribed in a semicircle, the diameter of the circle is equal to the radius of the semicircle. So, the diameter of the circle in this case is equal to 4.

Let O be the center of the circle and A, B, C be three points of intersection between the circle and the semicircle.   Area of the shaded region = (Area of the semicircle) - (Area of the circle) - (Area of ΔABC)Area of the semicircle with radius 2 = (1/2)π(2)² = 2πArea of the circle with diameter 4 = π(2²) = 4π Side of triangle ΔABC = 2, Radius of the circle = 2. The height of the triangle is equal to the radius of the circle, i.e., 2. Therefore, ΔABC is an equilateral triangle with a side of length 2. Area of an equilateral triangle with side s = (s²√3)/4. Area of the equilateral triangle ΔABC = (2²√3)/4 = √3The area of the shaded region = 2π - 4π - √3 = 2π - 4π/3 = 2π/3. Fraction of the semicircle's area that is shaded = Shaded area / Total area of the semicircle= (2π/3)/ (2π)= 1/3Therefore, the fraction of the semicircle's area that is shaded is 1/3. Answer: (D) 2/3.

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According to the given information, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The values of  x=-2  and  x=2  satisfy the equation  4x²=16, so  4x²-16=0  is true for both  x=-2  and  x=2.

The equation  x²=-4  has no real solutions, so it is not true for either  x=-2  or  x=2.

The equation  3x²+12=0  is not true for either  x=-2  or  x=2 , because  3x²+12  is always positive for any real value of  x .

The equation  2(x-2)²=0  is only true for  x=2 , because plugging in  x=-2  gives  2(-4)² =32 ≠0.

Therefore, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0 .

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The statement "Hazardous chemicals are only found in industrial settings, so school employees do have responsibilities regarding them" is False.

What are hazardous chemicals?

Hazardous chemicals are substances that can cause harm to living beings when exposed to them. They are also known as hazardous substances, and they are found in various forms such as solids, liquids, gases, and dust. Hazardous chemicals pose a significant danger to human health and the environment, and they are found in both industrial and non-industrial settings.

What is the role of school employees regarding hazardous chemicals?

School employees have a responsibility to ensure that students and staff are safe from hazardous chemicals.

School laboratories and art rooms are examples of locations where hazardous chemicals may be found.

School employees must ensure that hazardous chemicals are properly labeled and stored, and they must provide safety training and equipment to students and staff who work with hazardous chemicals.

Therefore, it is not true that school employees do not have any responsibilities regarding hazardous chemicals, even though they are not found exclusively in industrial settings.

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Answer:

[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of p.}[/tex]

[tex]\textsf{Note that we are given \underline{Vertical Angles}, and a \underline{perpendicular} set of lines.}[/tex]

[tex]\large\underline{\textsf{What are Vertical Angles?}}[/tex]

[tex]\textsf{Vertical Angles are 2 angles that are opposite from each other, and share a}[/tex]

[tex]\textsf{common vertex point. (center point) Vertical Angles are congruent as they are}[/tex]

[tex]\textsf{formed by the same 2 intersecting lines.}[/tex]

[tex]\large\underline{\textsf{What are Perpendicular Lines?}}[/tex]

[tex]\textsf{Perpendicular Lines are 2 sets of lines that intersect each other with opposite}[/tex]

[tex]\textsf{reciprocal slopes. Perpendicular Lines form 4 right angles that are 90}^{\circ}.[/tex]

[tex]\large\underline{\textsf{Identifying Vertical Angles;}}[/tex]

[tex]\textsf{Remember that vertical angles are opposite from each other, and are congruent.}[/tex]

[tex]\textsf{We are given 1 measure of an angle, and this angle has a measure of 35.3}^{\circ}.[/tex]

[tex]\textsf{The angle opposite to it, (below angle p) is opposite from our angle.}[/tex]

[tex]\textsf{We have identified our vertical angle, now let's identify p.}[/tex]

[tex]\large\underline{\textsf{Identifying m} \tt \angle p;}[/tex]

[tex]\textsf{We should know that we are Perpendicular lines, and angle p is overlapped in one.}[/tex]

[tex]\textsf{This means that these angles are \underline{Complements}, angles that add up to 90}^{\circ}.[/tex]

[tex]\textsf{Because we know that the other angle inside the right angle is 35.3}^{\circ}, \ \textsf{we are}[/tex]

[tex]\textsf{able to set up an equation to find p.}[/tex]

[tex]\tt p = 90^{\circ} - 35.3^{\circ}[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\large\boxed{\tt m \angle p = 54.7^{\circ}}[/tex]

Answer:

x^2 - 4x + 6 = 0

Step-by-step explanation:

x^2 + 2 - 4x = -4

x^2 - 4x + 2 + 4 = 0

x^2 - 4x + 6 = 0

Answer:

Omg I HATE IXL sm!!

Step-by-step explanation:

$637.51

Hence, the value of  variable in the given expression x is 8

An angle is formed when two straight lines  meet at a common endpoint.

∠1 = 7x - 4

∠2 = 3x + 28

A secant line that crosses two parallel lines produces these angles. After that, these angles were congruent, which means that their measures are equal.

Then, equaling  both given expressions and solving for x,  we get:

Step1: subtract 3x both sides

7x - 4 = 3x + 28

Step2: add 4 both sides

7x - 3x - 4 = 28

Step2: simplify like terms

7x - 3x = 28 + 4  

Step3: divide by 4 both sides

4x = 32  

x = 32/4

x = 8

Hence, the value of x is 8.

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So, the explicit formula for this problem would be: V(t) = $3200 × (1 + 0.09)[tex]^{t}[/tex].

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, x, ÷, etc.) that represents a mathematical quantity or relationship. Expressions can be as simple as a single number or variable, or they can be complex and involve multiple terms and operations. Examples of expressions include 2x + 5, 3y - 7, and (a + b)(c - d).

Here,

Explicit Formula:

The explicit formula for calculating the value of the necklace after t years, with an annual growth rate of r, can be given as:

V(t) = V(0) × (1 + r)ⁿ

Here, V(0) is the initial value of the necklace, which is $3200 in this case, and t is the number of years. The growth rate is 9%, which can be expressed as 0.09.

So, the explicit formula for this problem would be:

V(t) = $3200 × (1 + 0.09)ⁿ

Recursive Formula:

The recursive formula for calculating the value of the necklace after t years, with an annual growth rate of r, can be given as:

V(t) = V(t-1) × (1 + r)

Here, V(t-1) is the value of the necklace in the previous year, and t is the number of years. The initial value V(0) is $3200, so we can use this value to calculate the value of the necklace in the subsequent years.

So, the recursive formula for this problem would be:

V(0) = $3200

V(t) = V(t-1) × (1 + 0.09)

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As a result, the vertices' values when mirrored along the x-axis are W' (-5,-0), X' (0,-2), and Y'. (-1,3).

In this case, coordinates refer to the edges of a grid structure. Latitude and longitude are often combined to form GPS measurements. Lines of latitude measure how far north and south are from the center of the earth, which is located at 0 degrees north and south.

When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.

For point W (-5,0), reflecting across the x-axis results in the point W' (-5,-0).

For point X (0,2), reflecting across the x-axis results in the point X' (0,-2).

For point Y (-1,-3), reflecting across the x-axis results in the point Y' (-1,3).

Therefore, the coordinates of the vertices when reflected across the x-axis are:

W' (-5,-0), X' (0,-2), Y' (-1,3).

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The theoretical probability of stopping on the color blue when spinning a spinner with the colors red, yellow, blue, and green is 25% or 1/4.

A spinner is a tool that spins around an arrow or a pointer that points towards the numbers, colors, or pictures around its edge. The probability of a certain event is the likelihood of that event occurring. In this case, we need to find the theoretical probability of stopping on the color blue.

We have four colors on the spinner, so the probability of stopping on blue can be found using the formula of theoretical probability.

The formula for theoretical probability is:

number of favorable outcomes / total number of outcomes.

Since we have four colors on the spinner, the total number of outcomes is 4. The favorable outcomes are the number of times the spinner will land on blue, which is 1.

So the probability of stopping on the color blue can be calculated as follows:

1 (favorable outcome) / 4 (total number of outcomes) = 1/4

So, the theoretical probability of stopping on the color blue is 1/4. This is because there is an equal chance of landing on any of the four colors, and since there are four colors, each has a 25% chance of being selected.

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Aki's Bicycle Designs should build 1.75 hundred, or 175, bicycles to minimize the average cost per bicycle.

To find the number of bicycles Aki's Bicycle Designs should build to minimize the average cost per bicycle, we need to find the minimum point of the given quadratic function C(x).

First, we can find the derivative of C(x) concerning x:

C'(x) = 0.4x - 0.7

Then, we can set C'(x) equal to zero and solve for x:

0.4x - 0.7 = 0

0.4x = 0.7

x = 1.75

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Answer: 4.2 percent

Step-by-step explanation: Your welcome

Option D : Matching a 3D shape to its net requires visual spatial reasoning and knowledge of geometry.

A net is a two-dimensional pattern that can be folded to form a three-dimensional shape. It shows how the faces of a 3D shape are connected and arranged in a flat layout. The process of making a net involves taking apart a 3D object and flattening it out without stretching or bending any of the faces.

A net must accurately represent the dimensions and features of the 3D shape it represents, such as the shape and size of each face, the number of edges and vertices, and the angles between the faces.

Some common 3D shapes that can be represented by nets include cubes, pyramids, prisms, cylinders, and cones. Nets can be created using various methods, such as drawing them by hand, using computer software, or printing them from online sources. When constructing a 3D object from a net, it is important to fold and join the edges carefully to ensure that the final shape is accurate and stable.

Therefore, the correct net that matches the 3D shape is option D.

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a. The probability that all four units are good is 0.2067 (approx),

b. The probability that exactly two units are good is 0.0226 (approx).

Given a shipment of 13 microwave ovens contains four defective units and a vending company purchases four units at random, we need to calculate the probability of the following events:

(a) all four units are good.

(b) exactly two units are good.

(a) What is the probability that all four units are good?

To solve this, we need to use the formula for the probability of an intersection of independent events.

Since the probability of getting a good unit is 9/13, then the probability of getting 4 good units in a row is calculated as follows:

P(All 4 units are good) = P(Good unit) × P(Good unit) × P(Good unit) × P(Good unit) = 9/13 × 9/13 × 9/13 × 9/13 = 47829609/232044048 = 0.2067 (approx)

(b) What is the probability that exactly two units are good?

Here, we need to use the binomial probability formula since the number of good units follows a binomial distribution. We need to find the probability of getting exactly 2 good units, given that we are purchasing 4 units.

P(exactly 2 units are good) = C(4,2) × P(Good unit)² × P(Defective unit)²

= 6 × (9/13)² × (4/13)²

= 52488/2320440

= 0.0226 (approx)

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Answer:

y=1/4x

Step-by-step explanation:a direct variation equation is y=kx. if y=1/4x, then when x=8, y=2.

the rule for g that represents a vertical stretch by a factor of 6, followed by a translation 5 units down of the graph of f(x) = log₀(x) is g(x) = 6log₀(x) - 5.

The given function is f(x) = log₀(x)

To stretch the graph of f(x) vertically by a factor of 6, we multiply f(x) by 6, which gives:

g(x) = 6log₀(x)

To translate the graph of g(x) down 5 units, we subtract 5 from g(x), which gives:

g(x) = 6log₀(x) - 5

the concept of factors can also be applied to functions. Given a function f(x), a factor of f(x) is another function g(x) such that f(x) can be written as the product of g(x) and another function h(x).a factor is a number or algebraic expression that divides another number or algebraic expression evenly, leaving no remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because each of these numbers can divide 12 without leaving a remainder.

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Therefore , the solution of the given problem of equation comes out to be it can also be expressed as c = 1/4b, indicating that 1/4 cup of flour is used to make each order of brownies.

Variable words are commonly used in complex algorithms to show uniformity between two incompatible claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of an unique formula that splits 12 into two parts and can be used to analyze data received from y + 7, normalization in this case yields b + 7.

Here,

B. The connection between the independent factor (cups of flour) and the one that is dependent is modeled by the equation

=> b = 4c. (batches of brownies).

According to this calculation, 4 cups of flour are required to make one batch of brownies.

The equation can also be expressed as

=>  c = 1/4b, indicating that 1/4 cup of flour is used to make each order of brownies.

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Answer:

432

Step-by-step explanation:

go 16x27 and that is your answer

Answer:

The area of the figureo will be 432

BECAUSE :-

You have to multiply 16 × 27 = 432

Hope Its Help You !!

Therefore, the area of the figure is 48 square units.

Perimeter is the total distance around the boundary of a two-dimensional shape. It is calculated by adding up the lengths of all the sides of the shape. The perimeter is usually measured in units such as inches, centimeters, or meters, depending on the size of the shape.

To find the perimeter of the figure, we add up the lengths of all the sides:

Given by the question.

Perimeter = 6 + 8 + 10 + 5 = 29

Therefore, the perimeter of the figure is 29 units.

To find the area of the figure, we need to use the formula for the area of a trapezoid, which is:

Area = (1/2) x (sum of parallel sides) x (distance between them)

The distance between the parallel sides is the height of the trapezoid. To find the height, we need to use the Pythagorean theorem, since the trapezoid is a right trapezoid.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex]= [tex]c^{2}[/tex]

where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.

In this case, a = 6, b = 8, and c = 10. So, we have:

[tex]6^{2}[/tex] + [tex]8^{2}[/tex] = [tex]10^{2}[/tex]

36 + 64 = 100

100 = [tex]10^{2}[/tex]

Therefore, the height of the trapezoid is:

h = [tex]\sqrt{c^{2}-b^{2} }[/tex] = [tex]\sqrt{10^{2}-8^{2} }[/tex]= √36 = 6

Now we can plug in the values for the sum of the parallel sides and the height to get the area:

Area = (1/2) x (6 + 10) x 6 = 48

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a) The probability that a battery does not reach the milestone in its first 8 hours of usage is 0.014 or 1.4%. b)  The probability of this goal being met is 0.002 or 0.2%. c) The smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.

(a) To calculate the probability that a battery does not reach the milestone in its first 8 hours of usage, we need to calculate the area under the normal curve to the right of 8 hours. We can use the standard normal distribution to do this by first standardizing the value of 8 hours using the formula:

z = (x - mu) / sigma

where x is the value of 8 hours, mu is the mean of the distribution (7.36 hours), and sigma is the standard deviation (0.29 hours). Substituting these values, we get:

z = (8 - 7.36) / 0.29 = 2.21

Using a standard normal table or a calculator, we can find that the area to the right of z = 2.21 is approximately 0.014.

(b) We want to find the probability that at least 10 batteries out of a pack of 12 last until 7.5 hours of usage. This is a binomial distribution with n = 12 and p = the probability that a single battery lasts until 7.5 hours.

To find p, we can use the standard normal distribution again by standardizing the value of 7.5 hours:

z = (7.5 - 7.36) / 0.29 = 0.48

Using a standard normal table or a calculator, we can find that the area to the right of z = 0.48 is approximately 0.316. Therefore, the probability that a single battery lasts until 7.5 hours is 0.316.

Now we can use the binomial distribution formula to calculate the probability that at least 10 batteries out of 12 last until 7.5 hours:

P(X >= 10) = 1 - P(X < 10)

where X is the number of batteries that last until 7.5 hours, and P(X < 10) is the cumulative probability of 9 or fewer batteries lasting until 7.5 hours. Using a binomial calculator or a standard normal table, we can find that:

P(X < 10) = 0.998

Therefore, P(X >= 10) = 1 - 0.998 = 0.002 or 0.2%.

(c) We want to find the smallest value of n such that the probability of at least 10 batteries out of n lasting until 7.5 hours is greater than 1%. This is equivalent to finding the smallest n such that:

P(X >= 10) > 0.01

Using a binomial calculator or a standard normal table, we can find that:

P(X < 10) = 0.989 when n = 10

P(X < 10) = 0.970 when n = 11

P(X < 10) = 0.942 when n = 12

Therefore, the smallest value of n that satisfies P(X >= 10) > 0.01 is n = 13.

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Your question is incomplete, but probably the complete question is :

Suppose that a brand of AA batteries reaches a significant milestone to their death on average after 7.36 hours, with standard deviation of 0.29 hours. Assume that when this milestone occurs follows a normal distribution.

(a) Calculate the probability that a battery does not reach this milestone in its first 8 hours of usage.

(b) Suppose that the company wants to sell a pack of n batteries of which (at least) 10 will last until 7.5 hours of usage. If n 12, what is the probability of this goal being met?

(c) How many batteries n should be in the package in order for the probability to exceed 1%? Give the smallest number n which works.

that's the final answer

The weighted average of the numbers −4 and 5, with weight three-fifths on the first number and two-fifths on the second number is option (b) -0.4

The weighted average of two numbers is calculated by multiplying each number by its corresponding weight, adding the results, and then dividing by the total weight.

In this case, the first number is -4 and its weight is 3/5, while the second number is 5 and its weight is 2/5. Therefore, the weighted average can be calculated as follows:

weighted average = (-4)(3/5) + (5)(2/5)

= -12/5 + 10/5

Add the numbers

= -2/5

= -0.4

Therefore, the correct option is (b) - 0.4

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Answer

bring down 6

why?

bring down 6 to show there are 2 tens and 6 ones that still need to be divided

If you take a wheel's radius of 4.16 cm and divide it by 2 to get its diameter, you should write 8.32 cm instead of 8 cm.

The breadth of a circle is two times the sweep. Therefore, if the wheel has a radius of 4.16 cm, its diameter will be

2 x 4.16 = 8.32 cm.

If the measurement is going to be used for precise engineering or calculations, it is essential to write the result as 8.32 cm because this is a measurement that is more accurate than rounding it off to 8 cm. Working with the most accurate measurement is always preferable because rounding off can result in errors.

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Cold weather can affect battery performance, Make sure the battery is in good condition and fully charged.

The issue with your 1997 f150 4.6 starting great when left inside overnight but needing to crank and crank if left outside overnight could be due to a few factors.

To troubleshoot this problem, follow these steps:

. Check the battery: Cold weather can affect battery performance. Make sure the battery is in good condition and fully charged.


. Test the starter motor: The starter motor might struggle to turn the engine over when it's cold outside. Check the starter motor's connections and operation, and replace it if necessary.

. Assess the engine coolant temperature sensor (ECT sensor): If the ECT sensor is not functioning properly. Test the ECT sensor and replace it if it's faulty.

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