Calculate E(X) and then E(5−X). E(X)
E(5−X)
​
=
=
​
(b) Would the repair facility be better off charging a flat fee of $90 or else the amount $[ (5−X)
150
​
]?[ Note: It is not generally true that E( Y
C
​
)= E(Y)
c
​
. ] The repair facility be better off charging a flat fee of $90 because E[ (5−X)
150
​
]=

The general solution of the differential equation y''(x) + y(x) = sec(x) tan(x) is y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x); here c₁ and c₂ are constants.

To solve the differential equation y''(x) + y(x) = sec(x) tan(x) using variation of parameters, we first need to find the solutions to the homogeneous equation y''(x) + y(x) = 0.

The auxiliary equation for the homogeneous equation is r² + 1 = 0, which has complex roots r = ±i.

The corresponding solutions to the homogeneous equation are y₁(x) = cos(x) and y₂(x) = sin(x).

Next, we need to find the particular solution using the method of variation of parameters. Let's assume the particular solution has the form y_p(x) = u(x)cos(x) + v(x)sin(x).

Now, we need to find u(x) and v(x) by substituting this form into the original differential equation and solving for u'(x) and v'(x).

Differentiating y_p(x), we get y_p'(x) = u'(x)cos(x) - u(x)sin(x) + v'(x)sin(x) + v(x)cos(x).

Taking the second derivative, y_p''(x) = -u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x).

Substituting these derivatives into the original differential equation, we have:

(-u(x)cos(x) - u'(x)sin(x) + v(x)sin(x) + v'(x)cos(x)) + (u(x)cos(x) + v(x)sin(x)) = sec(x)tan(x).

Simplifying, we get:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x).

To find u'(x) and v'(x), we solve the following system of equations:

u'(x)sin(x) + v'(x)cos(x) = sec(x)tan(x),

u(x)cos(x) + v(x)sin(x) = 0.

We can solve this system using various methods such as substitution or elimination.

Solving the system, we find:

u'(x) = sin(x)sec(x),

v'(x) = -cos(x)sec(x).

Integrating these expressions, we obtain:

u(x) = -ln|sec(x) + tan(x)| + C₁,

v(x) = -ln|sec(x) + tan(x)| + C₂.

Finally, the particular solution is given by:

y_p(x) = (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

The general solution to the differential equation is the sum of the homogeneous and particular solutions:

y(x) = c₁cos(x) + c₂sin(x) + (-ln|sec(x) + tan(x)| + C₁)cos(x) + (-ln|sec(x) + tan(x)| + C₂)sin(x).

Here, c₁ and c₂ are constants.

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Answer:

17C5+11C5

Step-by-step explanation:

Well there are 17 and chooses 5 that's 17C5

there are 11 men abd chooses 5 that's 11C5

so add them up

17C5+11C5

The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.

\(^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}\)

where,

n is the number of choices available,

r is the choices to be made.

Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.

Now, the number of ways for selection can be written as,

Number of ways in which men can be selected = ¹¹C₅ = 462

Number of ways in which women can be selected = ¹⁷C₅ = 6188

Further, the number of ways for selection can be written as,

Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected

Number of ways = 462 × 6188

Number of ways = 2,858,856

Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.

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Answer:

13/20

Step-by-step explanation:

Answer: It end in the hundredth place, so you have to write 65/100

65/100 simplifies to 13/20.

Step-by-step explanation: hope this helps

Answer:

Explanation:

Given the expression:

This can be written as a difference of two squares. But before that, we can rewrite the expression as:

So, as a different of two squares, we write:

Answer:

Step-by-step explanation:

s

Answer:

the distance from Minneapolis to Duluth is 137 miles

Step-by-step explanation:

The computation of the distance from Minneapolis to Duluth is shown below:

Given that

The cost per mile is $0.40

And, the total trip cost is $54.80

So based on the above information

The distance from Minneapolis to Duluth is

= $54.80 ÷ $0.40

= 137 miles

Hence, the distance from Minneapolis to Duluth is 137 miles

The same would be considered

The correct option is the fourth one, the slope and y-intercept are different.

Here we have the linear equation:

3x - 5y = 4

We know that it is dilated by a scale factor of 5/3, so let's find the dilation.

We can rewrite the linear equation as:

-5y = 4 - 3x

y =  (3/5)x - 4/5

Now let's apply the dilation:

y = (5/3)*[ (3/5)x - 4/5]

y = x - 4/3

Then we can see that the slope and the y-intercept are different, the correct option is 4.

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Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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Answer:

3

Step-by-step explanation:

(0,3)

Answer:

45+3m=C

Step-by-step explanation:

45+5x=60

5x=15

x=3

Answer:

8.777

It is a repeating decimal because it is only one number over and over

Step-by-step explanation:

7 divided by 9= .7777

Considering the curve x³y + y³ = sin y - x, the final i is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

Implicit differentiation is a technique used to differentiate equations that are not explicitly expressed in terms of one variable. It is particularly useful when you have an equation that defines a relationship between two or more variables, and you want to find the derivatives of those variables with respect to each other.

To find dy/dx for the curve x³y + y³ = sin y - x², the implicit differentiation will be used which involves differentiating both sides of the equation with respect to x.

It is expressed as follows;

\(\frac{d}{dx} x^3y + \frac{d}{dx} y^3 = \frac{d}{dx} sin(y) - \frac{d}{dx} x^2\)

Then we'll differentiate each term:

For the first term, x^3y, we'll use the product rule

\(\frac{d}{dx} x^3y = 3x^2y + x^3 \frac{dy}{dx}\)

For the second term, y^3, we'll also use the chain rule

\(\frac{d}{dx} y^3 = 3y^2 \frac{dy}{dx}\)

For the third term, sin(y), we'll again use the chain rule

\(\frac{d}{dx} sin(y) = cos(y) \frac{dy}{dx}\)

For the fourth term, x², we'll use the power rule

\(\frac{d}{dx} x^2 = 2x\)

Substituting these expressions back into the original equation, we get:

3x²y + x³(dy/dx) + 3y²(dy/dx) = cos(y)(dy/dx) - 2x

Simplifying the equation:3x²y + x³(dy/dx) + 3y²(dy/dx) - cos(y)(dy/dx) = -2x

Dividing both sides by 3y² - cos(y), we get:(x³ - cos(y))(dy/dx) = -2x / (3y² - cos(y))

Hence, the final answer is;\(\frac{dy}{dx} = \frac{-2x}{3y^2 - cos(y)} \div (x^3 - cos(y))\)

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Step-by-step explanation:

\( \frac{2}{3} y \: + \: 6 \: = \: 15\)

\( \frac{2}{3} y \: = \: 15 - 6\)

\( \frac{2}{3} y \: = \: 9\)

\( y \: = 9 \: \times \: \frac{3}{2} \)

y = 27/2

y = 13.5

Answer:

160 miles

Step-by-step explanation:

Company A form ​$130 a day plus $0.30 per mile

Company A = 130 + 0.30x

Company B charges ​$50 a day plus $0.80 per mile

Company B = 50 + 0.80x

Where,

x = number of miles

Equate the cost of company A and company B

130 + 0.30x = 50 + 0.80x

Collect like terms

130 - 50 = 0.80x - 0.30x

80 = 0.50x

Divide both sides by 0.50x

x = 80 / 0.50

= 160

x = 160 miles

The number of miles in a day at which the rental costs for Company A and Company B are the same is 160 miles

9514 1404 393

Answer:

  7 mpg

Step-by-step explanation:

The equation shown on the graph tells you the unit rate is 7. (The unit rate is the coefficient of x.)

The truck travels 7 miles per gallon of gas.

Answer:

1 and Q

Step-by-step explanation:

The first and second one, as The angle can be whatever number or letter correlates with that one. R is a different point, and QRS isn't an actual angle.

Hope this helps :)

Answer:

D. 6.28

Step-by-step explanation:

C= 2(3.14) R

R= D/2

2/2-1

R=1

C=2(3.14)1 (DON'T REALLY NEED THE !)

6.28

A strategy canvas is a visual framework used to analyze and compare the strategic positioning of different companies or products within an industry.

It is a tool developed by W. Chan Kim and Renée Mauborgne, the creators of the Blue Ocean Strategy, to help organizations identify and create new market spaces by differentiating their offerings.

The strategy canvas consists of two axes: the horizontal axis represents the key factors that the industry competes on, and the vertical axis represents the offering level or degree of offering provided for each factor. By plotting the current state of competing products or companies on the canvas, organizations can gain insights into the competitive landscape and identify areas of opportunity for innovation and differentiation.

The strategy canvas helps visualize the competitive factors that are driving the industry and highlights areas of convergence or similarity among existing offerings. It allows organizations to identify untapped market spaces where they can create unique value propositions and redefine the competitive boundaries.

To use a strategy canvas effectively, organizations need to analyze the key factors that customers value in the industry and assess the relative performance of their offerings compared to competitors. By identifying the factors where they are underperforming and overperforming, organizations can focus on enhancing their value proposition by reallocating resources, investing in areas of differentiation, and eliminating or reducing elements that do not create significant customer value.

A strategy canvas is a powerful tool for strategic analysis and innovation. It helps organizations visualize the competitive landscape, identify areas for differentiation, and create new market spaces by providing a clear understanding of customer preferences and the competitive factors that drive industry success.

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Answer:

30.1 ft²

Step-by-step explanation:

The area of a triangle with an included angle and two sides cam be found using the formula, A = ½*ab*sin(C)

a = 7 ft

b = 9 ft

C = 73°

Plug in the values

Area = ½*7*9*sin(73)

Area = 30.1235998 ≈ 30.1 ft² (nearest tenth)

(-19,7) (4, 15) hshw wjwhw

Step-by-step explanation:

priorities of operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

[(18 + 3×2) + 8 + 5×3] + 6

18 + 3×2 = 18 + 6 = 24

24 + 8 + 5×3 = 24 + 8 + 15 = 47

47 + 6 = 53

[(18 + 3×2) + 8 + 5×3] + 6 =

= 18 + 6 + 8 + 15 + 6 = 53

Answer:

B. 2

Step-by-step explanation:

To solve this, we need to divide 30 by 7. 30/7=4 R2

The remainder is 2, so there are 2 books left over.

Hope his helps and have an amazing day *^____^*

Answer:

2

Step-by-step explanation:

If 1 box holds 7 books...

2 boxes hold 14 books.

3 boxes hold 21 books.

4 boxes hold 28 books.

5 boxes hold 35 books.

However, since there are only 30 books, the 5th box won't be completely filled up. This gives us the answer: If Lamont fills up each box he would have 30-28, or 2 books left over.

Hope this helps!

Answer:

D. x^2-x-9-12/x-2

Step-by-step explanation:

We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:

    2 |   1   -3   -7    6

       |______2___-2__-18

       | 1   -1   -9  -12

The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.

So, we have:

(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)

Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).

Answer:

14 mph

Step-by-step explanation:

Speed of boat in calm water = x

Speed of current = y

Speed of boat with the current = 72 mi / 4 hr = 18 mph

Speed of boat against current = 40 mi / 4 hr = 10 mph

x + y = 18

x - y = 10

2x = 28

x = 14

Answer: 14 mph

Answer:

14 m/hr

Step-by-step explanation:

72 m / 4 hr = 18 m/hr

40 m / 4 hr = 10 m/hr

still water speed =  (18+ 10 )/2 = 14 m/hr

 current speed   (14 -x) 4 = 40

                       x = current speed = 4 m/hr

Answer:

(a) The total amount paid for the boat by Jina is $16,753.8 (b) the total interest paid on loan is $953.8.

Note: Kindly find an attached copy of the complete question below

Sources: The complete question was researched from Quizlet

Step-by-step explanation:

Solution

Given that

The fishing boat price =15,800

Jina made a down payment of =$3600 (took out the loan for the rest)

Thus

The rest amount = Loan amount

= (15,800 - 3600)

=$12,200

Now

Jina monthly payments  = $219.23 for 5 years

Jina total payment = $219.23 * 12 * 5

=$13,153.8

Thus

Jina 's down time payment + Total payment of loan becomes:

=( $13,153.8 + $3600)

=$16,753.8

(a) Jina's total amount paid for the boat  is $16,753.8

(b) The total interest paid on loan is given below:

=($$16,753.8 - $15,800)

= $953.8

The interquartile range for the given data set 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22, 3.26 is 2.16.

The middle two-thirds of your data set—the interquartile range, or IQR—contain the second and third quartiles. The interquartile range, as opposed to range, provides the range of the middle half of a data set. Range provides the spread of the entire data set. The statistical dispersion, or spread of the data, is measured in descriptive statistics by the interquartile range. In addition to the IQR, other names for it include the mid spread, middle 50%, fourth spread, and H-spread. The distinction between the data's 75th and 25th percentiles is what is meant by this term.

Given the data set is,

2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22, 3.26

First we have to arrange data set in the ascending order:

1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02

Here,

Median=(2.45+2.77)/2

Median=2.61

First Quartile Q₁=2.22

Third Quartile Q₃=4.38

Interquartile Range= Q₃- Q₁

=4.38-2.22

=2.16

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Answer:

110 ft  

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is  

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

 l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

The exact values of csc θ, cot θ, and cos θ are √2, -1, and -√2/2, respectively.

To find the exact values of csc θ, cot θ, and cos θ:

Step 1: Identify the coordinates of the point where the terminal side of angle θ intersects the unit circle, which are (-√2/2, √2/2).

Step 2: csc θ is the reciprocal of sin θ, which is equal to the y-coordinate of the point. Therefore, csc θ = 1/sin θ = 1/(√2/2) = √2.

Step 3: cot θ is found by dividing sin θ by cos θ. Since sin θ is the y-coordinate and cos θ is the x-coordinate,

cot θ = sin θ / cos θ = (√2/2) / (-√2/2) = -1.

Step 4: cos θ is simply the x-coordinate of the point, which is -√2/2.

Therefore, The exact values of csc θ, cot θ, and cos θ are √2, -1, and -√2/2, respectively.

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