A tangent segment is a line segment that has a point on the tangent line and on the center of the circle.

Answer:

Step-by-step explanation:

Hanne Keiling is a senior digital communications expert with over eight years of experience ideating, executing and launching user-first experiences to achieve business goals. She is a former Indeed editorial team member who helped job seekers be successful on Indeed throughout their job search and into their careers.

Introducing yourself well sets the stage for a professional conversation whether at a networking event, with a colleague or at the beginning of an interview. One tool that many people use to make introductions simple and effective is the elevator pitch.

Below, you will find several elevator pitch examples along with tips to help ideate, craft and deliver your personal message.

Video: How To Create the Perfect Elevator Pitch - Plus Examples

Jenn, a certified career coach, helps you tell a compelling story about who you are and where you are going in under two minutes.

Bus 18 is the more consistent bus, due to the lower IQR.

What is the median?

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.

Here, we have

For groups of 15 students, we have that:

The first half is composed of the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed of the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 18 are given as follows:

Q1 = 12.

Q3 = 18.

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 2 = 16.

Hence, Bus 18 is the more consistent bus, due to the lower IQR.

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The values of g(-4) = 0

                        g(-2) = 2

                        g(0) = 2

                        g(3) = -1

                        g(4) = -2

What is a function?

In mathematics, a function is a rule which assigns a unique output value to each input value in a given set. It shows a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Functions are typically represented by an equation or a graph, and they play an important role in various fields of mathematics, science, engineering, and technology.

Using the given piecewise defined function:

g(x) = x + 4, −5 ≤ x ≤ −1

         2 − x, −1 < x ≤ 5

We can evaluate g at different values in its domain as follows:

g(−4) = (-4) + 4 = 0

g(−2) = (-2) + 4 = 2

g(0) = 2 - 0 = 2

g(3) = 2 - 3 = -1

g(4) = 2 - 4 = -2

Therefore:

g(-4) = 0

g(-2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

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Yes, it is an observational study because the groups are not randomly assigned by the researchers. Instead, the students self-select which group to join based on their own TV watching habits.

An observational study is a type of study where the researchers observe the people in the study and take measurements or survey them. The researchers do not modify or control any variable in this type of study. In other words, an observational study observes, records and concludes based on the observation of data collected. It does not make use of control groups or experimental treatments in order to arrive at a conclusion.

From the given question, this is an observational study because the groups were not randomly assigned by the researchers; rather, the students self-selected which group they wanted to join based on their television-watching habits. Additionally, the researchers did not manipulate any variables or conditions, and the study only measured the characteristics and behaviors of the two pre-existing groups. Therefore, the researchers could only observe the differences between the groups, but they could not determine causality or control any extraneous variables that may have influenced the results.

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The volume of a pyramid is 2.4 cm^3.

Let's begin by finding the area of the square base. Since the perimeter of the base is 4.7 cm, the length of one side of the square is 4.7 cm / 4 = 1.175 cm. The area of the square base is then

Area = (side length)^2 = (1.175 cm)^2 = 1.38 cm^2

Now, we can use the formula for the volume of a pyramid

Volume = (1/3) x Base Area x Height

Substituting the values we found, we get

Volume = (1/3) x 1.38 cm^2 x 4.7 cm

Volume = 2.3974 cm^3

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 2.4 cm^3.

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The given question is incomplete, the complete question is:

Find the volume of a pyramid with a square base, where the perimeter of the base is

4.7 cm and the height of the pyramid is 4.7 cm. Round your answer to the nearest tenth of a cubic centimeter

Answer:

my answer is 60

Step-by-step explanation:

when the people who respond 70-30 =40

40-10=30 the ans is 30

Answer:

10

Step-by-step explanation:

according to the formula of y = P(1-r)^x, P is the initial value, and in this case it looks like it is 10 :)

Answer:

56 feet

Step-by-step explanation:

This is a trigonometry problem. It makes use of tangent. You can take the tangent of an angle and it will equal the side opposite divided by the side adjacent that isn't the hypotenuse.

In this case the angle is 35 degrees.

Tangent of the angle = opposite/ adjacent side

Tan(35) = (x)/(80)

Tan(35) = 0.7 so

(0.7)= (X)/(80)

Using algebra each side can be multiplied by 80.

(80)(.7)=X

56=x

X is in feet, so X is equal to 56 feet.

Hope this helps!

For given functions, the correct statement is D i.e. The graph of h is the graph of g vertically shifted up 1 unit.

What is the definition of a function?

A function is a rule or correspondence in mathematics that assigns each element in a set (called the domain) to a unique element in another set (called the range). In other terms, a function is a connection between two sets of numbers or quantities that creates exactly one output value for each input value (or argument).

Now,

The function h(x) = g(x) + 1 is obtained by taking the function g(x) = x² and adding 1 to its output for every input value of x. This means that the graph of h will be the same as the graph of g, but shifted up by 1 unit for all points on the graph.

Therefore, the correct statement that describes how the graph of h is different from the graph of g is:

D. The graph of h is the graph of g vertically shifted up 1 unit.

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=============================================

Explanation:

x = number of cups

y = total height

We have these ordered pairs

(x1,y1) = (2,16)

(x2,y2) = (4,20)

Let's find the slope of the line through those points.

[tex](x_1,y_1) = (2,16) \text{ and } (x_2,y_2) = (4,20)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{20 - 16}{4 - 2}\\\\m = \frac{4}{2}\\\\m = 2\\\\[/tex]

A slope of 2, aka 2/1, means each time x goes up by 1, the y value goes up by 2.

It means each time we add a cup, the total height goes up by 2 cm.

This isn't the final answer, but it helps get us there.

------------

We'll then use point-slope form to determine the equation.

[tex]y-y_1 = m(x - x_1)\\\\y-16 = 2(x - 2)\\\\y = 2(x - 2)+16\\\\y = 2x - 4+16\\\\y = 2x + 12\\\\[/tex]

The last step is to plug x = 1 into that equation to determine the height of 1 cup.

So,

[tex]y = 2x + 12\\\\y = 2*1 + 12\\\\y = 2 + 12\\\\y = 14\\\\[/tex]

We have x = 1 cup lead to a total height of y = 14 cm.

The final answer is 14 cm.

-----------------

Notice that adding on 2 cm (the slope) gets us to 14+2 = 16 cm which is the height of two cups stacked together. A lot of the 2nd cup's height is part of the 1st cup's height. Only the 2 cm at the top is going to be added.

We could see that if we used x = 2.

[tex]y = 2x + 12\\\\y = 2*2 + 12\\\\y = 4 + 12\\\\y = 16\\\\[/tex]

That confirms the left-most part of the diagram.

Now try x = 4.

[tex]y = 2x + 12\\\\y = 2*4 + 12\\\\y = 8 + 12\\\\y = 20\\\\[/tex]

That works as well. It helps confirm we have the correct equation, and also confirms the final answer is correct. Another way to confirm is to either graph or use a table.

If you wanted to find the height of 8 cups, then,

[tex]y = 2x + 12\\\\y = 2*8 + 12\\\\y = 16 + 12\\\\y = 28\\\\[/tex]

The statements and reasons that completes the table that proves the triangles are congruent are;

1. 1. Given, 2. Alternate interior angles theorem, 3. SAS Postulate

2. 1. Given, 2. All right angles are congruent, 3. Definition of midpoint, 4. ASA Postulate

3. 1. [tex]\overline{TM}[/tex] ≅ [tex]\overline{PR}[/tex], 2. [tex]\overline{TM}[/tex] ≅ [tex]\overline{RP}[/tex], 3. ∠M ≅ ∠R, and ∠T ≅ ∠P, 4. ΔTEM ≅ ΔTER

Congruent triangles are triangles that have exactly the same shape and size.

The completed the tables that prove the congruence of the triangles are presented as follows;

1. Statements                                           Reasons

1. [tex]\overline{AB}[/tex] ≅ [tex]\overline{DC}[/tex]            [tex]{}[/tex]                             1. Given

2. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]            [tex]{}[/tex]                            2. Reflexive property

3. [tex]\overline{AB}[/tex] || [tex]\overline{DC}[/tex]            [tex]{}[/tex]                             3. Given

4. ∠BAC ≅ ∠DCA [tex]{}[/tex]                              4. Alternate interior angles theorem

5. ΔABC ≅ ΔCDA [tex]{}[/tex]                              5. SAS Postulate

2. Statement  [tex]{}[/tex]                                        Reasons

1. [tex]\overline{RS}[/tex] ⊥ [tex]\overline{ST}[/tex]; [tex]\overline{TU}[/tex]⊥ [tex]\overline{ST}[/tex]                       1. Given

2. m∠S = 90°; m∠T = 90° [tex]{}[/tex]              2. Definition of right angles

3. ∠S ≅ ∠T [tex]{}[/tex]                                     3. All right angles are congruent angles

4. V is the midpoint of [tex]\overline{ST}[/tex]              4. Given

5. [tex]\overline{SV}[/tex] ≅ [tex]\overline{TV}[/tex]                                     5. Definition of midpoint

6. ∠RVS ≅ ∠UVT [tex]{}[/tex]                           6. Vertical angles are congruent

7. ΔRSV ≅ ΔUTV [tex]{}[/tex]                           7. ASA Postulate

3. The completed statements in the table are provided as follows;

Statement           [tex]{}[/tex]                         Reason

1. [tex]\overline{TM}[/tex] ≅ [tex]\overline{PR}[/tex]                             [tex]{}[/tex]    1. Given

2. [tex]\overline{TM}[/tex] ║ [tex]\overline{PR}[/tex]                               2. Given

3. ∠M ≅ ∠R  [tex]{}[/tex]                              3. If two parallel lines are cut by a    

   ∠T ≅ ∠P                                     transversal then alternate interior

                                           [tex]{}[/tex]            angles are congruent

4. ΔTEM ≅ ΔPER [tex]{}[/tex]                       4. ASA

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1) In the set of triangles given, x = 48ft. The triangle are similar because the ratio of each side to the others are the same that is - 5:3
2) In this case, x = 16ft.
The Ratio is 1:1, thus they are similar.

1)

a )To solve for x, we must state that:

50/30 = 80/x

To solve for x in the equation:

50/30 = 80/x

You can begin by cross-multiplying the fractions. That means multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives:

50x = 30 * 80

Simplifying the right-hand side of the equation:

50x = 2400

Now, to solve for x, you can divide both sides of the equation by 50:

x = 2400/50

Simplifying this expression:

x = 48

Therefore, x is equal to 48.

b) The ratio is the comparison of two quantities. In this case, the ratio can be found by simplifying the fractions on both sides of the equation:

50/30 = 5/3

80/48 = 5/3 (by dividing both numerator and denominator by 16)

Therefore, the ratio is 5:3, which means that the two quantities being compared are in the ratio of 5 to 3.

2)

a) To solve for x, we must state that:

if 6/4.5 = x/12

To solve for x in the equation:

6 / 4.5 = x / 12
6 * 12 = 4.5 * x
x = (6 * 12) / 4.5
x = 72 / 4.5

x = 16

b)

To justify that both triangles are similar, we must look at the ratio of their sides.


The ratio between the first fraction 6/4.5 and the second fraction 16/12 can be found by simplifying both fractions to their lowest terms and then comparing the resulting values.

To simplify 6/4.5, we can divide both the numerator and denominator by their greatest common factor, which is 1.

6/4.5 = (6 ÷ 1)/(4.5 ÷ 1) = 6/4.5

To simplify 16/12, we can divide both the numerator and denominator by their greatest common factor, which is 4.

So the simplified ratio between the two fractions is:

6/4.5 : 16/12

= 6/4.5 : 4/3

To compare these ratios, we can cross-multiply to get:

(6 * 3) : (4.5 * 4) = 18 : 18 = 1 : 1

Therefore, the ratio between 6/4.5 and 16/12 is 1:1 or simply 1.

This means the two triangles are similar.

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Answer:

a

Step-by-step explanation:

-3(a-b) < 0

-3a + 3b < 0

-3a < -3b / : (-3)

a > b

1) The answer is C) MuItipIy/divide bοth sides by the same nοn-zerο cοnstant.

2)The sοIutiοn tο bοth equatiοns is the same.

EquivaIent equatiοns are aIgebraic equatiοns that are having identicaI rοοts οr sοIutiοns.

1) Tο get Equatiοn B BB frοm Equatiοn A AA, we need tο muItipIy/divide bοth sides οf Equatiοn A AA by the same nοn-zerο cοnstant. In this case, we can muItipIy bοth sides by 5/3 tο get:

5/3 * 5x = 5/3 * 3x

SimpIifying, we get:

25/3 x = 15/3 x

Which is Equatiοn B BB.

Therefοre, the answer is C) MuItipIy/divide bοth sides by the same nοn-zerο cοnstant.

2) Yes, the equatiοns are equivaIent. When we muItipIy bοth sides οf Equatiοn A AA by 5/3, we are essentiaIIy muItipIying the entire equatiοn by 1, since 5/3 divided by 5/3 is equaI tο 1. Therefοre, the sοIutiοn tο bοth equatiοns is the same.

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The value of the computer after 5 years is $189.84 and [tex]v = 800 * (3/4)^t[/tex] , where v is the value of the computer t years after it is purchased.

1. The computer costs $800 initially and loses 1/4 or 25% of its value every year. We can represent this decrease in value using the following formula:

[tex]v = 800 * (1 - 1/4)^t[/tex]

where v is the value of the computer t years after it is purchased. Simplifying this equation, we get:

[tex]v = 800 * (3/4)^t[/tex]

2. To find the value of the computer when t is 5, we can substitute t = 5 into the equation we derived in step 1:

[tex]v = 800 * (3/4)^5[/tex]

[tex]v = 800 * 0.2373[/tex]

[tex]v = 189.84[/tex]

This means that the value of the computer after 5 years is $189.84. This value is less than the initial cost of the computer, which was $800. It indicates that the computer has significantly depreciated in value over time, losing approximately 76% of its initial value.

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The complete question is :

A computer costs $800. It loses 1/4 of its value every year after it is purchased.

1. Write an equation representing the value, v, of the computer, t years after it is purchased.

2. Use your equation to find v when t is 5. What does this value of v mean?

The value of x when triangles CDE and CBA are similar is 9.

In geometry, a triangle is a polygon with three sides and three angles. It is one of the most basic and fundamental shapes in mathematics, and it appears frequently in geometry, trigonometry, and other branches of mathematics. A triangle can be classified based on the length of its sides and the measure of its angles. Triangles have many important properties and relationships that make them useful in mathematics and other fields. For example, the sum of the interior angles of a triangle is always 180 degrees, and the Pythagorean theorem relates the sides of a right triangle to the length of its hypotenuse. Triangles also appear frequently in trigonometry, where they are used to model and solve problems involving angles and distances.

Here,

Since the triangles CDE and CBA are similar, we know that the corresponding sides are proportional. Therefore, we can set up the following proportion:

CD / CB = DE / BA

Substituting the given values, we get:

30 / (11x + 11) = 21 / 77

Cross-multiplying and simplifying, we get:

30 * 77 = 21 * (11x + 11)

2310 = 231x + 231

Subtracting 231 from both sides, we get:

2079 = 231x

Dividing both sides by 231, we get:

x = 9

Therefore, the value of x is 9.

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The triangles is necessary congruent.

In geometry, two triangles are said to be congruent if they have the same size and shape. This means that all corresponding sides and angles of the triangles are equal. When two triangles are congruent, it is denoted by the symbol ≅ between the two triangles.

The SAS (Side-Angle-Side) rule, also known as the SSA (Side-Side-Angle) rule, is a theorem in geometry that states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

In the given triangle ΔROP and ΔDCE

∠R=∠C(Given)

OR=CE(Given)

OP=DE(Given)

Hence, ΔROP is congruent to ΔDCE by SAS rule.

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Step-by-step explanation:

You can prove congruency by  four methods

SSS    You do not have this in your diagram
SAS    nor this
ASA        nor this
AAS          nor this
AAA            nor this

You DO have S S A  .....but you cannot use this to prove congruency

So you have to conclude the triangles are NON CONGRUENT

   ( though they MIGHT be....you just cannot prove it using SSA)

The correct answer is: √(6² + 2²), and tan⁻¹(2/6) represents the magnitude and direction angle of the vector.

What is Pythagoras' Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The magnitude of a vector is the length of the vector. For a vector that passes from the origin to the point (6,2),

the magnitude can be calculated using the Pythagorean theorem, which states that for a right triangle with legs of length a and b and hypotenuse of length c,

c² = a² + b².

In this case, the vector is the hypotenuse of a right triangle with legs of length 6 and 2, so the magnitude is:

magnitude = √(6² + 2²) = √(40) = 2*√(10)

The direction angle of a vector is the angle that the vector makes with the positive x-axis, measured counterclockwise. The direction angle can be calculated using the inverse tangent function, which is the inverse of the tangent function. In this case, the direction angle is:

direction angle = tan⁻¹(2/6) = tan⁻¹(1/3)

Therefore, the correct answer is: √(6² + 2²), and tan⁻¹(2/6) represents the magnitude and direction angle of the vector.

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Rounding to the nearest tenth of a meter, we get the width of the rectangle to be approximately 7.5 meters.

Area is a measure of the size of a two-dimensional surface, such as the surface of a plane or a geometric shape. It is usually measured in square units, such as square meters (m²) or square feet (ft²).

Here,

Let's assume that the width of the rectangle is x meters. Then, according to the problem statement, the length of the rectangle is 3x meters. The area of a rectangle is given by the formula:

A = length x width

Substituting the values from the problem statement, we get:

170 = (3x) x (x)

Simplifying and solving for x, we get:

3x² = 170

x² = 56.67

x ≈ 7.5

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Oliver's result of 85.4° for angle A is wrong. This is because the sum of angles of a triangle should add up to 180°.

Triangles are classified according to the lengths of their sides and the measure of their angles.

In this triangle, we have two angles, angle A and angle B. If angle A is 85.4°, then angle B must be 94.6°. But, the angles of a triangle should add up to 180°, which is not the case here.

We can solve for angle A using the Law of Cosines:

Cos A = (b² + c² - a²)/2(bc)

A = [tex]cos^{-1}[(15^2 + 10^2 - 12^2)/2(15)(10)]}[/tex]

A = [tex]cos^{-1}(0.6)}[/tex]

A = 36.86°

Therefore, the correct size of angle A is 36.86°. Oliver's result of 85.4° is incorrect.

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Answer: Let's assume that Denise buys "x" pounds of pecans and "y" pounds of almonds. Since she wants to buy a mixture of nuts that weighs 5 pounds, we can write:

x + y = 5

We also know that Denise plans to spend $35.74 on nuts. The cost of the pecans and almonds combined is:

8.15x + 6.48y

So, we can write another equation:

8.15x + 6.48y = 35.74

We now have two equations with two variables, which we can solve simultaneously. Let's solve for "y" in the first equation:

y = 5 - x

We can substitute this expression for "y" into the second equation:

8.15x + 6.48(5 - x) = 35.74

Simplifying this equation, we get:

8.15x + 32.4 - 6.48x = 35.74

1.67x = 3.34

x = 2

So, Denise will buy 2 pounds of pecans. We can substitute this value of "x" back into the first equation to find the amount of almonds she will buy:

2 + y = 5

y = 3

Therefore, Denise will buy 2 pounds of pecans and 3 pounds of almonds.

Step-by-step explanation:

Answer

4.879

Step-by-step explanation:

The chart has been completed and the information has been given below:

Annually $9200 6% 15 9200(1+0.06)15 $22084.34

Semi-Annually $9200 6/2 = 3% 15*2 = 30 9200(1+0.03)30 $22330.81

Quaterly $9200 6/4 = 1.5% 15*4 = 60 9200(1+0.015)​​​​​60 $22477.62

Monthly $9200 6/(12*15) = 1/30 %

15*12*15 = 2700

9200(1+1/(30*100))2700

$22624.96

Weekly $9200 6/(15*52) = 1/130 15*52*15 = 11700

9200(1+1/(130*100))11700

$22627.57

Daily $9200 6/(15*365) = 2/1825

15*365*15 = 82125

9200(1+2/(1825*100))82125

$22628.24

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Answer:

D. 29

Step-by-step explanation:

To find the distance between two points (x1, y1) and (x2, y2), we use the distance formula:

[tex] \rm \: Distance = \sqrt{((x2-x1)² + (y2-y1)²)} [/tex]

Here, the two points are (-1, -1) and (19, 20).

[tex] \rm \: x1 = -1, y1 = -1[/tex]

[tex] \rm \: x2 = 19, y2 = 20[/tex]

Using the distance formula, we get:

[tex] \rm \: Distance = \sqrt{((19-(-1))² + (20-(-1))²)} [/tex]

[tex] = \sqrt{((20)² + (21)²)} [/tex]

[tex] \rm \: = \sqrt{(400 + 441)} [/tex]

[tex] \rm \: = \sqrt{841} [/tex]

[tex] \rm \: = 29[/tex]

Answer:

Step-by-step explanation:

4+8

9+9

=36

Answer:

This is a function because a function is anything that will give you an output  when you give it an input, in this case you could give it an input of 0 and it will give you 2. if you give it 1 it will give you 3.

Step-by-step explanation:

:)

After answering the presented question, we can conclude that  it will function take 36 months for the total cost to reach $2005.

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

inverse function

[tex]c(x) = 55x + 25\\c(x) - 25 = 55x\\x = (c(x) - 25) / 55\\c^(-1)(x) = (x - 25) / 55\\c(x) = 55x + 25 = 2005\\55x = 1980\\x = 36\\[/tex]

it will take 36 months for the total cost to reach $2005.

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A random sample of 30 employees of a local company has been taken to measure the systolic blood pressure (mm hg). using only the sample information, a 99% confidence interval estimate for the mean systolic blood pressure (mm hg) for all employees of the company is 113.206 to 126.794. The value of the sample standard deviation (mm Hg) is approximately 2.639.

To find the sample standard deviation (mm Hg), we need to use the given information. Here is the solution:

Given information:

Sample size, n = 30

Confidence interval = 99%

Confidence interval limits = 113.206 to 126.794

Formula to find standard deviation:

σ = (CI width) / (2 × Zα/2)

Whereσ = Sample standard deviation

CI = Confidence interval width

Zα/2 = Z-score for a given confidence interval

Let's calculate the confidence interval width:

CI width = Upper Limit - Lower Limit

CI width = 126.794 - 113.206

CI width = 13.588

To find the z-score for a 99% confidence interval, we can use a z-table or calculator.

The z-score for a 99% confidence interval is 2.576. So,

substituting the values in the formula, we get:

σ = 13.588 / (2 × 2.576)σ = 13.588 / 5.152σ ≈ 2.639 mm Hg

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There are 8 cutting machines and each machine can cut 4 cases every 15 seconds, or 16 cases per minute (4 cases/15 seconds x 60 seconds/minute = 16 cases/minute). Therefore, all 8 machines can cut a total of 8 x 16 = 128 cases per minute.

If 25% of the machines are removed for maintenance, then 2 machines (25% of 8) will be taken out of service. This leaves 6 machines to continue cutting phone cases.

The 6 remaining machines can cut 6 x 16 = 96 cases per minute (since each machine still cuts 16 cases per minute). Therefore, the 6 remaining machines cut 128 - 96 = 32 fewer cases per minute than all 8 machines together.

So the answer is that the remaining machines cut 32 fewer cases per minute when compared to the number of cases per minute all 8 machines cut.

Therefore, the rate/slope between the two given points is 60.

In mathematics, slope refers to the steepness or incline of a line. It measures how much a line rises or falls over a certain horizontal distance, which is called the "run." Slope is usually denoted by the letter m and is defined as the ratio of the change in y (the vertical distance) to the change in x (the horizontal distance) between any two points on the line.

Here,

1. To find the rate/slope between the coordinates (1,60) and (2,120), we can use the slope formula:

slope = (change in y) / (change in x)

So, we have:

slope = (120 - 60) / (2 - 1)

= 60 / 1

= 60

2. The equation given is y = 65x, where x is the time in hours and y is the number of miles. To find the rate/slope, we can see that the equation is in the form of y = mx, where m is the slope. So, the slope of this equation is 65. Therefore, the rate/slope for the given equation is 65.

3.The slope of the graph is the change in y over the change in x for any two points on the line, whereas the slope of the equation is the coefficient of x. In this case, the slope of the graph is not given, so we cannot compare it directly to the slope of the equation.

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