The coordinates of the vertices of a rectangle are (−5, 2), (−5, −2 1/3 ), (2 1/2 , 2), and (2 1/2 , −2 1/3 ). Find the perimeter of the rectangle.

The solution to the initial value problem y'' - 36y = 72t - 36e^(-6t), y(0) = 0, y'(0) = 49, is y(t) = 6 - 6t - 198e^(-6t)

To solve the initial value problem using the method of Laplace transforms, we will follow these steps:

Step 1: Take the Laplace transform of both sides of the given differential equation. We will use the notation L{y(t)} = Y(s) to represent the Laplace transform of y(t).

Taking the Laplace transform of the differential equation y'' - 36y = 72t - 36e^(-6t), we get:

s^2Y(s) - sy(0) - y'(0) - 36Y(s) = 72/s^2 - 36/(s + 6)

Since y(0) = 0 and y'(0) = 49, we have:

s^2Y(s) - 49 - 36Y(s) = 72/s^2 - 36/(s + 6)

Step 2: Rearrange the equation to solve for Y(s).

(s^2 - 36)Y(s) = 72/s^2 - 36/(s + 6) + 49

(s^2 - 36)Y(s) = (72 - 36s^2 + 6s + 294s^2 + 294s + 1764)/(s^2)

(s^2 - 36)Y(s) = (258s^2 + 6s + 1764)/(s^2)

Y(s) = (258s^2 + 6s + 1764)/(s^2(s^2 - 36))

Step 3: Decompose the right side of the equation into partial fractions.

Y(s) = A/s + B/s^2 + C/(s - 6) + D/(s + 6)

Multiply through by the common denominator (s^2(s^2 - 36)), and equate coefficients:

258s^2 + 6s + 1764 = A(s^2 - 36) + Bs(s - 6) + Cs^2 + D(s + 6)

Expand and collect like terms:

258s^2 + 6s + 1764 = As^2 - 36A + Bs^2 - 6Bs + Cs^2 + Ds + 6D

Equating coefficients of like terms, we get the following system of equations:

A + B + C = 0      (coefficient of s^2 terms)

-6A - 6B + D = 6   (coefficient of s terms)

-36A + 1764 + 258 = 0   (constant terms)

Solving this system of equations gives A = 6, B = -6, C = 0, and D = -198.

Step 4: Take the inverse Laplace transform to find y(t).

Using the table of Laplace transforms, we find the inverse Laplace transform of Y(s) to be:

y(t) = 6 + (-6t - 198e^(-6t))

Therefore, the solution to the initial value problem y'' - 36y = 72t - 36e^(-6t), y(0) = 0, y'(0) = 49, is y(t) = 6 - 6t - 198e^(-6t)

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The item in the Colleen's house that is most likely to meet the definition of a fixture is a tile.

A fixture is an item in a house that is permanently attached to a house with the use of a glue, nails or bolt. It would not be easy to remove fixtures from a house. Examples of fixtures are tiles, doors and windows.

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The shortest length possible in the given question is 4.0×\(10^{-10}\) cm .

Distance is measured by length. The quantity of length has the dimension of distance in the International System of Quantities. Most measurement systems choose a base unit for length from which all other units are derived. The metre serves as the fundamental unit of length in the International System of Units.

Most people interpret length to mean an object's longest dimension. Nevertheless, depending on the object's position, this is not always the case.

There are several terms for the length of a fixed object, including height, which is also known as vertical length or vertical extent, and width, breadth, or depth. When a base exists from which vertical measurements can be taken, height is used.

Nanometer(nm)- In the International System of Units (SI), a nanometer (American spelling) is a unit of length that is equal to 1000 picometres and one billionth (short scale) of a meter (0.000000001 m).

now , for find the shortest length we can covert all the given units into centimeter,

1 pm = \((10)^{-10}\) cm

1 nm = \((10)^{-7}\) cm

1 m =  100 cm

we have , 400 pm = 4× \((10)^{-8}\) cm

                4.0 nm  =  4 × \((10)^{-7}\) cm

      4.0 x \((10)^{-4}\)m = 4 × \((10)^{-2}\) cm

and   4.0 x \((10)^{-10}\) cm

hence , clearly it is shown that shortest length is 4.0 x \((10)^{-10}\) cm .

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The surface area of the solid formed by the triangular prism and cube will be 598.33 square inches.

A prism is a closed solid that has two parallel bases connected by a rectangle surface.

The height of a right triangular prism is 11/6 inches.

Each side of the triangular base measures 10 inches, and the height of the base is 26/3 inches.

The triangular prism is placed at top of a cube whose side measures 10 inches so that one of the triangular prism’s bases lies completely on one side of the cube.

Then the surface area of the prism will be

\(\rm Surface \ area = 5 \times (10 \times 10) + 0.5 \times 10 \times \dfrac{26}{3} + 3 \times 10 \times \dfrac{11}{6}\\\\\\Surface \ area = 598.33\ in^2\)

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To find the solution we will first find the difference between each number and mean, and then substitute the value in the formula of standard deviation.

The standard deviation is 8.4477 and the variance is 71.40.

Given to us

difference between each number and mean,

\(x_1 -\mu= 76-81 = -5\\ x_2-\mu = 87-81 = 6\\ x_3-\mu = 65-81 = -16\\ x_4-\mu = 88 -81 = 7\\ x_5-\mu = 67-81 = -14\\ x_6 -\mu= 84-81 = 3\\ x_7 -\mu= 77-81 = -4\\ x_8 -\mu= 81-81 = 1\\ x_9 -\mu= 91-81 = 10\\ x_{10}-\mu=85-81 = 4\\ x_{11} -\mu= 90-81 = 9\)

\(\sum(x-\mu)^2 = x_1^2+x_2^2+x_3^2+x_4^2+x_5^2+x_6^2+x_7^2+x_8^2+x_9^2+x_{10}^2+x_{11}^2\)

                 =  25 + 36 + 256 + 49 + 196 + 9 + 16 + 1 + 100 +16 + 81

                 = 785

\(\rm{ Standard\ Deviation = \sqrt{\dfrac{\sum{(X-\mu)^2}} {n}\)

                             \(\sigma= \sqrt{\dfrac{785}{11}}\\\\ \sigma = 8.4477\)

Variance = \(\sigma ^2\)

              = 71.40

Hence, the standard deviation is 8.4477 and the variance is 71.40.

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Answer:

Adimas found the mean of her 11 math test scores for the first semester.

x = StartFraction (76 + 87 + 65 + 88 + 67 + 84 + 77 + 82 + 91 + 85 + 90) Over 11 EndFraction = StartFraction 892 Over 11 EndFraction ≈ 81

Using 81 as the mean, find the variance of her grades rounded to the nearest hundredth.

σ2 =

71.36

Find the standard deviation of her grades rounded to the nearest hundredth.

σ =

8.45

Step-by-step explanation:

Edge 2022

Answer:

The number pie

Step-by-step explanation:

Find the area of a circle with a diameter of 4. How do you find they area of a circle?

To find the area of a circle use the formula \(\large\tt A=\pi r^2\) or \( \large\tt A=\pi \times r \times r\)

Where π = 3.14 correct to 2 decimal places, r = radius, and d = diameter. The radius is half of the diameter.

Therefore, the area of a circle is 12.56 sq. units

Answer:

339.6 cm²

Step-by-step explanation:

½×10.4×12

= 62.4 cm²

½×12×15.4×3

= 277.2 cm²

total = 277.2+62.4

= 339.6 cm²

Answer:

Yes they both are equal

The value of x in the given triangle in radical form is \(\sqrt{14}\)

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The tiniest and most well-known triplets are (3,4,5).

Pythagoras theorem states that the square of the longest side of a right angled triangle (called the hypotenuse) is equal to the sum of the squares of the other two sides.

From Pythagorean theorem.

a2+b2 = x2.

6+8=x2

x=\(\sqrt{14\\\)

Hence the solution of the above equation is \(\sqrt{14}\)

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Answer:

D.

5/5 is basically 1 whole number :)

Step-by-step explanation:

just look at the graphic : what value do we have on the cost side, when we have 1 pounds on the amount side ?

all the answer options specify a price per pound. that is why we only need to focus on the price for one pound.

we see in the graphic, that for 1 pound the price is $4.

just to make sure, we can also work with the directly specified point (0.5, 2), which means that 0.5 pounds cost $2.

and the function is clearly a straight line.

so, every point on the function has the same y/x ratio (slope).

therefore,

2/0.5 = 4

now, what point with x=1 has the same ratio ?

y/1 = 4

y = $4

perfect, the results are identical. so, $4 per pound is the correct answer.

A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

Bean advertised footwear on 29 of its 192 catalog pages.

we randomly survey 20 pages

the random variable X is

X = The number of pages that advertise footwear

It is given that 20 pages have been surveyed

so, X = 1, 2, 3.....20

The average value for binomial distribution can be calculated as follows

μ = np

= 20 (29/192)

= 580/192

=3.02

On average 3.02 pages expect to advertise footwear on them

Therefore, A) The random variable X is  The number of pages that advertise footwear

B) X = 1, 2, 3.....20

C) On average 3.02 pages expect to advertise footwear on them

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Option D is the correct answer. all angles in a triangle are acute

A triangle in which all three internal angles of the triangle are acute is also called an acute-angled triangle.

Properties are Acute angles:

We have the formula to calculate the area of the acute angle triangle = (½) × b × h square units.

Where,

“b” is the base of the triangle.

“h” is to be the height of a triangle.

If the sides are given, then we have to apply Heron’s formula:

The area of the acute triangle:

A=√S(S-a)(S-b)(S-c)

square units

Where S defines the semi-perimeter of a triangle

The S can be solved by using the formula:

S = (a + b + c)/2

The perimeter of an acute triangle is equal to the sum of the length of the sides of a triangle,

The perimeter  is given as:

Perimeter = a + b + c

It is measured in units.

a, b, and c are the sides of the triangle.

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270º

Step-by-step explanation:

A full circle is 360 degrees. So, 3/4 of a circle is 270.

Answer:

i think the answer is 95004

Step-by-step explanation:

Answer:

I think it will be one eighth times the volume

Step-by-step explanation:

Marcus is using a plant food to fertilize his garden his garden is a rectangle Marcus uses 1 cup of plant food for every square yard of his garden.

To solve it, we need to first find the area of Marcus's garden in square yards, and then multiply it by 1 cup of plant food per square yard. Finally, we need to convert the total cups to ounces using the given conversion rate.

Let the length of Marcus's garden is l yards and the width is w yards. Then the area of his garden in square yards is

A = lw.

If Marcus uses 1 cup of plant food per square yard, then he will use A cups of plant food in total.

To convert cups to ounces, we can use the given conversion rate of 4 cups per 28 ounces.

1 cup = 28/4 ounces

Therefore, the total weight of plant food Marcus uses in ounces is

Total weight = A * (28/4) ounces

By substituting A = lw, we get

Total weight = lw * (28/4) ounces

Total weight = 7lw ounces

Hence, the total weight of plant food Marcus uses to fertilize his garden is 7 times the product of the length and width of his garden, measured in yards.

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Answer: The form of payment that Courtney can lose and not get back would be cash.

Step-by-step explanation:

The reason why cash couldn't be returned back because it doesn't have a piece of U.S money wouldn't have a specific certified owner that they can be returned to.

Other forms of payment like credit cards, debit cards, and checks have specific bank information with the card holder's name on it so if Courtney actually lost one of those, she would be most likely to receive it back without any complicated  verification process.

Therefore, Courtney would not be able to receive her cash back if she accidentally loses it. Hope this helps you with your Imagine Math homework or assignment!

-From Certified 5th Grade Honors Student

A critical value, z subscript alpha (zα), denotes the boundary or cutoff point for a statistical test where the level of significance, also known as alpha (α), is set.

A critical value, z subscript alpha (zα), denotes the value at which the probability of observing a test statistic in the tail(s) of the sampling distribution equals the pre-determined significance level (alpha).

The critical value can be defined as the value that is compared with the parameter value in the hypothesis test to determine whether the null hypothesis will be rejected. If the value of the parameter is less than the critical value, the null hypothesis is rejected.

However, if the measured value is higher than the critical value, reject the null hypothesis and accept the alternative hypothesis. In other words, cropping divides the image into acceptable and unacceptable areas. If the value of the index falls within the rejection range, the rejection of the fact is rejected, otherwise the negative hypothesis is rejected.

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Answer: 1,3,5

Step-by-step explanation:

Just took the quiz

Answer:

2,3,5

Step-by-step explanation: i got it right on my test

i hope this helps sorry if it didn't

Answer:

6p=30

Step-by-step explanation:

Answer:  The answer would be letter B. -3; -44

Use the slope-intercept form  

y =  m x  +  b  to find the slope  m  and y-intercept  b .

Slope:  

− 3

y-intercept:  

( 0 ,  − 44 )

Step-by-step explanation:  B. -3; -44

Find the slope and y-intercept of the line.

6 x  +  2 y  =  − 88

Rewrite in slope-intercept form.

Tap for more steps...

y = − 3 x  −  44

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Slope:  

− 3

y-intercept:  

( 0 ,  − 44 )

image of graph

Therefore, the value of k in the relative frequency table is 5% when rounded to the nearest percent.

To find the value of k in the relative frequency table, we can use the information provided in the table. The total for each column represents 100%.

Looking at the third column labeled V, the entries are 42%, k, 53%. Since the total for this column is 100%, we can deduce that:

42% + k + 53% = 100%

Combining like terms:

95% + k = 100%

To isolate k, we subtract 95% from both sides:

k = 100% - 95%

k = 5%

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(-4 , 2 ) so x1 = -4 and y1 = 2. The slope is still 1/2 so m = 1/2. y = 1/2 x +4 final answer

The allowed housing expense may vary based on factors such as income level, location, and applicable tax laws.

It is advisable to consult with a tax professional or refer to relevant government guidelines to determine the specific allowed housing expense for your circumstances.

The allowed housing expense for the year depends on various factors, including income level, location, and tax laws. While the provided information mentions the earnings and deductions, it does not specify the regulations or guidelines governing housing expenses. The allowed housing expense may vary based on factors such as the cost of living in your area, applicable tax laws, and any specific regulations related to housing deductions.

To accurately determine the allowed housing expense, it is advisable to consult with a tax professional or refer to the relevant government guidelines. These sources can provide specific information on the deductions and allowances available for housing expenses based on your income level and location. They can guide you in determining the maximum housing expense that qualifies for deductions or exemptions within the tax framework applicable to your situation.

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In the given situation the given values can be correctly modeled by a (B) linear function.

What is a linear function?
A linear function has a straight line as its graph. A linear function has the form shown below. a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable.

The independent and dependent variables are X and Y, respectively.

In mathematics, the terms "linear function" refers to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

Therefore, in the given situation the given values can be correctly modeled by a (B) linear function.

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Answer:

Given that m = -2 and n = ¾,

m^2 x (n - 1) = (-2)^2 x (3/4 - 1) = 4 x (-1/4) = -1

n^2 - 3/m​ = (3/4)^2 - 3/(-2) = 9/16 + 3/2 = 9/16 + 24/16 = 33/16

Hope this helps!

:)

When the tangent line to the graph of g is at x = 4, an approximation to a zero of g is; C: x = 6.5

We are given that;

g(4) = 5

g'(4) = -2

Now, the general equation of a tangent line can be found using the formula; y – y₁ = m (x – x₁).

where;

m is the slope.

(x₁, y₁) is the coordinate points of the line.

Now, from the given values, we know that the slope at g'(4) is -2, thus we have the equation as;

y - 5 = -2(x - 4)

y = 5 - 2x + 8

y = -2x + 13

An approximation to a zero of g is;

-2x + 13 = 0

2x = 13

x = 13/2

x = 6.5

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