Your family wants to purchase a new laptop with
a 17 inch widescreen (diagonal). The height of
the laptop is 10 inches. If the laptop case is 10.5
inches tall and 13 inches wide, will the laptop fit
in the case? Explain.

Answer:

-3x+3y-15

Step-by-step explanation:

;)

Answer:

-3x+3y-15

Step-by-step explanation:

-3*x= -3x

-3*-y= 3y

-3*5= -15

The solution to the differential equation y'''+3y''-4y=e^(-2x) using the method of variation of parameters is y(x) = c1 + c2e^(-4x) + c3e^x + [(1/4)e^(2x) - (1/2)x^2 + C1x + C2]e^(-2x) where c1, c2, c3, C1, and C2 are constants.

To find the particular solution y_p(x) using the method of variation of parameters, we first need to find the complementary solution y_c(x) by solving the characteristic equation: r^3 + 3r^2 - 4r = 0. Factoring out an r gives us r(r+4)(r-1) = 0, so the roots are r=0, r=-4, and r=1. Therefore, the complementary solution is y_c(x) = c1 + c2e^(-4x) + c3e^x.

Next, we assume that the particular solution has the form y_p(x) = u1(x)e^(-2x). Taking the derivatives of this form, we get y_p'(x) = u1'(x)e^(-2x) - 2u1(x)e^(-2x) and y_p''(x) = u1''(x)e^(-2x) - 4u1'(x)e^(-2x) + 4u1(x)e^(-2x). Substituting these into the differential equation and simplifying, we get:

u1''(x) = e^(2x)

To solve this equation for u1(x), we integrate twice: u1(x) = (1/4)e^(2x) - (1/2)x^2 + C1x + C2, where C1 and C2 are constants of integration.

Therefore, the particular solution is y_p(x) = [(1/4)e^(2x) - (1/2)x^2 + C1x + C2]e^(-2x).

Combining the complementary and particular solutions gives the general solution: y(x) = y_c(x) + y_p(x) = c1 + c2e^(-4x) + c3e^x + [(1/4)e^(2x) - (1/2)x^2 + C1x + C2]e^(-2x).

Thus, the solution to the differential equation y'''+3y''-4y=e^(-2x) using the method of variation of parameters is y(x) = c1 + c2e^(-4x) + c3e^x + [(1/4)e^(2x) - (1/2)x^2 + C1x + C2]e^(-2x) where c1, c2, c3, C1, and C2 are constants.

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James has a total of 21.9 kilograms of sand in his sandbox after adding the sand from the beach. To find the total weight of sand in James' sandbox, we need to convert the given weights from grams to kilograms.

James initially has 14,500 g of sand. To convert this to kilograms, we divide by 1000:

14,500 g ÷ 1000 = 14.5 kg

Next, James brings home an additional 7,400 g of sand from the beach. To convert this to kilograms, we divide by 1000:

7,400 g ÷ 1000 = 7.4 kg

To find the total weight of sand in James' sandbox, we add the initial amount of sand to the amount he brought from the beach:

14.5 kg + 7.4 kg = 21.9 kg

Therefore, James now has 21.9 kilograms of sand in his sandbox.

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The proportion that can be used to find the length of the actual wall, in feet, is x/4 inches = 10 feet/1 inch.

Given that Sheena made a scale drawing of her classroom with a scale of 1 inch = 10 feet, and the length of the wall in the drawing is 4 inches, we can set up a proportion to find the length of the actual wall in feet.

Let x represent the length of the actual wall in feet.

Using the scale of the drawing, we can set up the following proportion:

x feet / 4 inches = 10 feet / 1 inch

To solve for x, we can cross-multiply and solve the resulting equation:

x feet * 1 inch = 4 inches * 10 feet

x = (4 inches * 10 feet) / 1 inch

x = 40 feet

Therefore, the proportion that can be used to find the length of the actual wall, in feet, is x/4 inches = 10 feet/1 inch.

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The area of the window frame will be 136 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular pane of glass measuring 12 inches by 18 inches is surrounded by a wooden frame that is 2 inches wide.

The area of the rectangular window will be calculated as below:-

Area of window = Area of outer layer - Area of the inner layer

Area of window = 22 x 16 - 18 x 12

Area of window = 352 - 216

Area of window = 136 square inches

Therefore, the area of the window frame will be 136 square inches.

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Function is a set of ordered pairs that do not have same domain or x-value. That means in a set of ordered pairs, the domain cannot have same value.

The only relation that isn't function here is the last choice because in a set of ordered pairs, there are two -5's which is repetitive. Other choices do not have same x-values in one set except for the last choice.

Answer

Hope this helps and let me know if you have any doubts!

Answer:

10 x 21 = 210 divided by 2 = 105 x 2 = 210

Answer:

10 x 21 = 210 divided by 2 = 105 x 2 = 210

Step-by-step explanation:

The probability that exactly 5 out of 8 randomly selected people will not go to the restaurant is approximately 0.0238, or 2.38%.

To calculate the probability that 5 people out of 8 will not go to the restaurant, we need to consider the probability of each individual not going and then calculate the probability of this outcome occurring for exactly 5 out of the 8 people.

Let's break down the calculation step by step:

The probability that a single person does not go to the restaurant is 1 - 0.75 = 0.25. This is because if there is a 75% probability of going, then there is a 100% - 75% = 25% probability of not going.

To determine the probability of exactly 5 out of the 8 people not going, we use the binomial probability formula. The formula is as follows:

P(k successes) = C(n, k) × \(p^{k}\) × \((1-p)^{(n-k)}\)

Where:

P(k successes) is the probability of having k successes,

C(n, k) is the binomial coefficient, representing the number of ways to choose k items from a set of n items,

p is the probability of success (in this case, the probability of not going, which is 0.25), and

n is the total number of trials (in this case, the total number of people, which is 8).

Substituting the values into the formula:

P(5 people not going) = C(8, 5) × 0.25⁵ × (1-0.25)⁸⁻⁵

= 56  ×0.25⁵ ×0.75³

= 56  ×0.0009765625 ×0.421875

= 0.02381134

Therefore, the probability that exactly 5 out of 8 randomly selected people will not go to the restaurant is approximately 0.0238, or 2.38%.

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A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.

B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;

Option 1; f(n) = n + 100

Option 2; f(n) = n + 100x

C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900

A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.

For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.

B) For option 1, the function is;

f(n) = n + 100

For option 2, the function is;

f(n) = n + 100x

C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.

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Answer:

She should first perform the operation in the parentheses, you can reference the order of the operations based on PEMDAS.

Step-by-step explanation:

1. parentheses operations

2. multiply 4 x 3

3. add the value you get from the parentheses with -7

4. with that value add it to the product of 4 and 3

Hope that helped! :)

Answer:

Subtraction

Explanation:-

\(( 1.25 -0.4) \div7+ 4 \times 3\)

Using BODMAS Rule:-

In bracket, the operation subtraction should be performed first .

Answer:

53.9

Step-by-step explanation:

154x35=5390

5390÷100=53.9

Answer:

11 1/5  hope this can help you

Step-by-step explanation:

Answer:

Step-by-step explanation:

if we have the proportion

7/5=a/8

a=(7*8)/5=56/5= 11 1/5

Answer:

-1,512,390

Step-by-step explanation:

Given

a1 = 15

\(a_i = a_{i-1} -7\)

Let us generate the first three terms of the sequence

\(a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8\)

For \(a_3\)

\(a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1\)

Hence the first three terms ae 15, 8, 1...

This sequence forms an arithmetic progression with;

first term a = 15

common difference d = 8 - 15 = - -8 = -7

n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)

Using the formula;

\(S_n = \frac{n}{2}[2a + (n-1)d]\\\)

Substitute the given values;

\(S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390\)

Hence the sum of the first 660 terms of the sequence is  -1,512,390

Claudia will need 48 feet of trim for the border around the top of the walls and 144 square feet of flooring for the room's floor.

a) To calculate the amount of trim Claudia will need for the border around the top of the walls, we need to find the perimeter of the top of the room.

The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).

In this case, the length and width of the room are both 12 ft. So the perimeter of the top of the room is:

Perimeter = 2(12 ft + 12 ft) = 2(24 ft) = 48 ft.

Therefore, Claudia will need 48 feet of trim for the border around the top of the walls.

b) To determine the amount of flooring Claudia will need to buy, we need to calculate the area of the room's floor.

The area of a rectangle is given by the formula: Area = length × width.

In this case, the length of the room is 12 ft and the width is also 12 ft. So the area of the floor is:

Area = 12 ft × 12 ft = 144 square feet.

Therefore, Claudia will need to buy 144 square feet of flooring to cover the room's floor.

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Answer:

Step-by-step explanation:

x + y + n = 576

When something is 25% larger than something else, the effect is the same as multiplying by 1.25. Let's try it with an example

20 + (25/100)* 20 = 20 + 500/100 = 20 + 5 = 25. Now if you multiply 20 * 1.25 you get 25 which is just what you should get.

n = 1.25(x + y)                    Divide by 1.25

n / 1.25 = x + y                   Substitute n / 1.25 for x + y in the above equation    

n/1.25 + n = 576                Multiply everything by 1.25  

n + 1.25n = 576*1.25         Combine the left to get 2.25

2.25 n = 576 * 1.25           Divide by 2.25

n = 576*1.25 / 2.25    

n = 320

Answer:

goodjob

Step-by-step explanation:

D  (-18)

___________________________________________________________

The image always helps me, please don't be afraid to point out any mistakes, I hope I helped have a great day!

In the late Roman Republic, individuals would typically ensure they had essential items such as a tunic or clothing appropriate for the occasion, footwear, and possibly a small writing implement like a stylus.

During the late Roman Republic period, individuals would prioritize wearing appropriate clothing, such as a tunic, which was a basic garment worn by both men and women. Footwear, such as sandals or shoes, would also be essential to protect the feet while traveling. Carrying money or valuables was crucial for transactions and personal needs, ensuring they had the means to purchase goods or services.

Additionally, individuals might carry a small writing implement, such as a stylus, for taking notes, marking important information, or engaging in correspondence. These items would have been considered essential for individuals in the late Roman Republic when leaving their homes.

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Answer:

60 math problems.

Step-by-step explanation:

30/2.5=12

12*5=60

Answer:

50.6

Step-by-step explanation:

50.6*5.9=298.54/2=149.27

Answer:

16,849,464 ft³

Step-by-step explanation:

subtract the two volumes of the pyramids.

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Answer: I think the answer is -x^2+x-6

Step-by-step explanation: I think it's like this as it is in the image below. I hope it's right and helps you!

Answer:

-10

Step-by-step explanation:

c) If r=1 or -1, there is a perfect straight-line relationship between the two variables.

Option a) is incorrect. The correlation coefficient r measures the strength and direction of a linear relationship between two variables, not any type of association.

Option b) is incorrect. The correlation coefficient r is a unitless measure and does not change when we change the units of measurement of x, y, or both.

Option c) is correct. When r=1 or -1, it indicates a perfect straight-line relationship between the two variables. A positive value of 1 indicates a perfect positive linear relationship, while a negative value of -1 indicates a perfect negative linear relationship.

Option d) is incorrect. Outliers can have a significant impact on the value of r. Outliers can pull the regression line away from the majority of data points, leading to a weaker correlation.

Option e) is incorrect. If r=0, it means there is no linear relationship between the two variables. However, there might still be a non-linear relationship or other types of association between them.

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The answer is 10√2

please see the attached picture for full solution

Hope it helps

Good luck on your assignment