In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 61 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Let α = 0.05. State the null and alternative hypotheses.
Select one:
a. H_o : µ = 45 H_a, :μ > 45
b. H_o : µ= 40 H_a : µ> 40
C. H_o : µ = 40 H_a : µ
d. H_o : µ ≤ 45 . H_a : µ> 45

b. Based on the result from previous problem the p-value found from t-table ranges from _______ to ________
c. should we reject the null hypothesis ?

Answer:

40 degrees

Step-by-step explanation:

all angles add to 180* in a triangle

65+75=140

subtract from 180, you get 40 which is your answer

We calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).= 0.25%. ( fictional )

To calculate the average change in the inflation rate, we require the inflation rates for each of the five years, including 2021. Let's assume the inflation rates for the five years are: 2.5%, 3.2%, 2.8%, 4.1%, and 3.9%.

To find the change in inflation rate for each consecutive year, we subtract the inflation rate of the previous year from the inflation rate of the current year. For example, the change in inflation rate from 2020 to 2021 would be 3.2% - 2.5% = 0.7%.

Next, we calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).

Finally, we divide the sum by the number of years (five in this case) to find the average change in the inflation rate over the five-year period. After rounding the result to two decimal places, we will have the desired average change in the inflation rate.

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1. The graph that has a slope of -2/3 and a y-intercept of 2 is given as follows:

Graph of a line passing through the points (0,2) and (3,0).

2. The graph that represents the equation y = 0.5x - 1 is given as follows:

Graph of a line passing through the points (-2,-2) and (0,-1).

3. The graph that represents the relation is given as follows:

Graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point (0,58) and (1, 56).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the graph that has a slope of -2/3 and a y-intercept of 2, we have that:

The y-intercept and the slope of the equation y = 0.5x - 1 is given as follows:

-1, meaning that the function passes through the point (0,-1).

When x = -2, the value of the function is given as follows:

y = 0.5(-2) - 1

y = -1 - 1

y = -2.

Hence the other point is (-2,-2).

For the relation in item 3, we have that when x increases by 3, y decays by 6, hence the slope m is given as follows:

m = -6/3

m = -2.

Hence:

y = -2x + b.

When x = 2, y = 54, hence the intercept b is given as follows:

54 = -2(2) + b

b = 58.

Hence the function is:

y = -2x + 58.

The points are:

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Answer:

678

2

679

Step-by-step explanation:

Number of people: 5426

Capacity of table: 8

How many tables are full?

How many people are sitting at a table that is not full?

or

How many tables are needed for all 5,426 people?​

To find the derivative of p(x) = x^3, we can use the power rule of differentiation.  The power rule states that if we have a function of the form f(x) = x^n,

where n is a constant, then the derivative is given by f'(x) = nx^(n-1). Applying this rule to p(x) = x^3, we get p'(x) = 3x^(3-1) = 3*x^2.

b) To find the derivative of p(x) = 3xlnx + x, we need to use the product rule and the chain rule. The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by (uv)' = u'v + uv'. Applying the product rule and the chain rule to p(x), we find that p'(x) = 3lnx + 3 + 1 = 3*lnx + 4.

c) To find the derivative of p(x) = x(nx + x^3), we can use the product rule. Applying the product rule, we get p'(x) = nx^2 + 3x^2 + x*(2nx + 3x^2) = nx^2 + 3x^2 + 2nx^2 + 3x^3 = (n + 2n + 3)x^2 + (3 + 3n)x^3 = (3n + 2n + 3)x^2 + (3 + 3n)x^3 = (5n + 3)x^2 + (3 + 3n)x^3.

d) To find the derivative of p(x) = x^2lnx + x^2, we need to use the product rule and the chain rule. Applying the product rule and the chain rule, we find that p'(x) = 2xlnx + x + x^2*(1/x) = 2xlnx + x + x = 2xlnx + 2x.

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The derivative of p(x) = x³ * ln(x) can be found using the product rule and the chain rule of differentiation. The correct answer is D. p(x) = x² * ln(x) + x².

To find the derivative of p(x) = x³ * ln(x), we need to use the product rule and the chain rule of differentiation. The product rule states that if we have a function of the form f(x) = g(x) * h(x), then the derivative is given by f'(x) = g'(x) * h(x) + g(x) * h'(x).

Applying the product rule to p(x) = x³ * ln(x), we have:

p'(x) = (3x² * ln(x)) + (x³ * 1/x)

= 3x² * ln(x) + x².

Therefore, the correct answer is D. p(x) = x² * ln(x) + x².

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The following are the zeros for the function h (x) = x2 + 3x - 8: - x= -4 and x=2.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where xX and yY with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y.

The function's zero is a value of x that makes it equal to zero. In other words, the equation f(x) = 0 leads to a zero.

By putting h(x) equal to zero and figuring out x, we may determine the zeroes for the function h(x) = x2 + 3x - 8.

h(x) = x² + 3x - 8 = 0

We may factor the left side of the equation to find x:

x² + 3x - 8 = (x-2)(x+4) = 0

We set each factor to zero and solve for x to discover the zeroes:

x-2 = 0 or x+4 = 0

x = 2 or x = -4

Consequently, the function's zeros are x = 2 and x = -4.

So, A is the right response. x = -4 and x = 2

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The complete question is

What are the zeros of the function h (x) = x² + 3x - 8?

A. x = -4 and x = -2

B. x= -8 and x = 2

C. x = -2 and x = 8

D. x = 2 and x = 8

To verify the inverse we can use Horizontal Line Test.

Suppose F is a function.

F does not have an inverse if any horizontal line crosses the graph of f more than once. If no horizontal line crosses the graph of F more than once, then F does have an inverse. In mathematics, having an inverse is a very significant quality, and it has a name.

If and only if a function f has an inverse, then it is one-to-one. The following definition, which is also the one that is most frequently used, is equivalent. If f(a) = f(b) implies a = b for all a and b in its domain, then a function f is one-to-one.

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1. Expanding the expression ln(r/5s) using the laws of logarithms:

ln(r/5s) = ln(r) - ln(5s)

2. Combining the expression log2(\(x^2\) - 49) - log2(x - 7) using the laws of logarithms:

\(log2(x^2 - 49) - log2(x - 7) = log2((x^2 - 49)/(x - 7))\)

what is expression?

In mathematics, an expression refers to a combination of numbers, variables, and mathematical operations, without an equal sign, that represents a value or a mathematical relationship. Expressions can be as simple as a single number or variable, or they can involve complex combinations of terms and operations.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:

6 cm^2

Step-by-step explanation:

If a circle has a diameter of 30 centimeters and a sector has a central angle of 240 degrees, the area of the sector is approximately 471.24 square centimeters.

To find the area of a sector, we need to use the formula A = (θ/360)πr², where θ is the central angle, r is the radius, and π is a constant equal to 3.14. Since the diameter of the circle is 30 centimeters, the radius is half of that, or 15 centimeters. The central angle of the sector is 240 degrees, so we can plug in these values to get A = (240/360)π(15)². Simplifying, we get A = (2/3)π(225), which is approximately 471.24 square centimeters. Therefore, the area of the sector is approximately 471.24 square centimeters.

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Answer:

y = - 9x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )

m = \(\frac{-31-50}{5-(-4)}\) = \(\frac{-81}{5+4}\) = \(\frac{-81}{9}\) = - 9 , then

y = - 9x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, - 31 )

- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )

14 = c

y = - 9x + 14 ← equation of line

Answer: True

Step-by-step explanation: Dilations do not change the angle measure. All line segments are changed by the same factor, therefore the angle remains the same.  

Therefore , the solution of the given problem of surface area comes out to be 212 square feet of the wall are therefore covered by the design.

The total size of the object can be determined by calculating how much room would be required to completely cover its exterior. When choosing a similar product with a cylindrical form, the environment is taken into account. Anything's total dimensions are determined by its surface area. The amount of water that a cuboid can hold depends on the number of sides that link its four trapezoidal shapes.

Here,

We must first determine the area of each individual form before adding them together to determine the portion of the wall that the design covers.

Taking a look at the rectangle first, we can observe that it has the following area:

=> 120 square feet=  10 feet x 12 feet.

=> 40 square feet =  (1/2)(10 ft)(8 ft).

Consequently, the two triangles' combined area is:

=> 80 square feet =  2 x 40 square feet.

=> (12 square feet) = (1/2)(6 ft)(4 ft).

The total area of all the shapes is as follows:

=> 212 square feet=  120 square feet, 80 square feet, and 12 square feet.

=> 212 square feet of the wall are therefore covered by the design.

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Answer: the answer is 261 ^2 ft!

Step-by-step explanation:

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

Answer:

4v3

Step-by-step explanation:

Thus, the positive value of δ, the absolute value δ = 0.448 using the chain rule of differentiation, not one of the options given.

To solve for δ, we need to use the chain rule of differentiation. Starting with equation (i), we can take the derivative of both sides with respect to δ:
d/dδ(a/10) = d/dδ(7.52)

Using the chain rule, we can simplify the left side of the equation:
d/dδ(a/10) = (d/d(a/10))(a/10)' = (1/10)(a/10)'

Now we can substitute in the given value for d/dδ(a/10) and solve for (a/10)':
-33.865 = (1/10)(a/10)'
(a/10)' = -338.65

Now we can use equation (i) and substitute in the value for (a/10) and (a/10)':
7.52 = a/10
-338.65 = (a/10)'

Multiplying these equations together, we get:
-2540.468 = a'

Finally, we can use the derivative of the given equation to solve for δ:

a = 75.2δ
a' = 75.2
-2540.468 = 75.2
δ = -33.77/75.2
δ = -0.448

However, the problem asks for a positive value of δ, so we take the absolute value:
δ = 0.448

Therefore, the answer is not one of the options given in the question.

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We have this expression:

We need to do the following steps to solve the equation for t:

Then, t is the same as:

Then, the answer is (A - p)/pr.

The solution of the radical expression is as follows:

a. 3√7 + 4√28 - √20 = 11√7 - 2√5

b. √27 - √12 + √75 = 6√3

Radical expressions are algebraic expressions involving radicals.  The expression consist of roots of an algebraic expression.

Therefore, let's reduce the radical expression as much as possible.

Therefore,

a.

3√7 + 4√28 - √20

3√7 + 4√4 × 7 - √4 × 5

3√7 + 8√7 - 2√5

11√7 - 2√5

b.

√27 - √12 + √75

√9 × 3 - √4 × 3 + √25 × 3

3√3 - 2√3 + 5√3

√3 + 5√3

6√3

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Answer:

-1

Step-by-step explanation:

Because the nembers before 0 are negitave and the ones after it are positive the equation to find the answer is (-3)(+2) and if you don't know how you add the two like: -3 +2

- negative

+ positive (which also goes for adding 2)

The inequality is shown in that number line 3 ≥ x > 2

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

In order to express inequalities on a number line, we mark a straight line and indicate the endpoints with either an open circle or a closed circle.

An open circle indicates that it does not include the value.

A closed circle indicates that the value is included.

These numbers solution set consists of all real numbers between -3 and 2.

Since 2 has an open circle, it excludes '2,' but it does include everything higher, up to and including -3, which has a closed circle.

Thus, we can represent this using the inequality 3 ≥ x > 2.

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The estimated minimum and maximum numbers of people in the town who spend more than 2 hours a day on their smartphones is given as follows:

The amounts are obtained applying the proportions in the context of the problem.

The percentages are the estimate plus/minus the margin of error, hence:

Hence, out of 17247 people, the amounts are given as follows:

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The one of many solutions of the system is x = 0 and y = 0.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

A system of equations,

x + 6y = 0

30y = -5x

Simplifying,

x + 6y = 0

Both are the same equation,

so there are infinitely many solution possibles.

Therefore, solution is x = 0 and y = 0.

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The correct option of the given question is option (c)  fissure.

When coding the phrase "supravesical fissure of urinary bladder," the main term to reference in the index is c. fissure.

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The main term to reference in the index when coding the phrase "supravesical fissure of urinary bladder" is c. fissure.

In medical coding, the index is typically organized alphabetically based on the main terms or significant words within medical terminology. In this case, "fissure" is the main term that represents the specific condition or anatomical feature being coded.

The other terms, such as "urinary," "bladder," and "supravesical," provide additional context but are not the primary focus when searching for the appropriate code in the index.

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Answer: Factoring:  27-u3  

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0-b3 =

           a3-b3

Check :  27  is the cube of  3  

Check :  u3 is the cube of   u1

Factorization is :

            (3 - u)  •  (9 + 3u + u2)

Step-by-step explanation:

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer: 0.5-2.4x=12.5

Step-by-step explanation:

-2.4(-5)=12

0.5+12=12.5

Answer:

f > -1

Step-by-step explanation:

I hope this helps!

The double points of the following conic section x' + 4xy + 3y - 2xz - 4yz + 2 = 0 is  x = 1, y = 0, z = 1

The equation that represents double points of the conic section x" + 2xy + y - 8xz - 8yz + 16 = 0 is x + y - 4z = 0

The equation of the tangent line at point P(2,0) is x - 2y - 2z = 0

The first question asks to calculate the double points of a given conic section. The conic section is represented by the equation:

x' + 4xy + 3y - 2xz - 4yz + 2 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x = 1, y = 0, z = 1

These values represent the double points of the conic section.

In the second question, we are again asked to calculate the double points of a conic section. The equation is:

x" + 2xy + y - 8xz - 8yz + 16 = 0

To find the double points, we need to solve the equation for the variables x, y, and z. The solution is:

x + y - 4z = 0

This equation represents the double points of the conic section.

Finally, in the third question, we are asked to calculate the tangent line at the point P(2,0) of a conic section. The equation of the conic section is:

x - 4xy - y' + 2x - 4y - 8 = 0

To find the tangent line at point P(2,0), we need to differentiate the equation with respect to x. The derivative is:

1 - 4y + 2 - 4 = -2 - 4y

At point P(2,0), the value of y is 0. Plugging in this value, we get:

-2 - 4(0) = -2

Therefore, the equation of the tangent line at point P(2,0) is:

x - 2y - 2z = 0

This equation represents the tangent line at point P(2,0) of the conic section.


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