find the value of (1³+2³+3³)^-3/2​

To find the perimeter of a shape, you need to add up the measurements of all the sides to find it. I hope this helps. Let me know if you need some help with some perimeter problems :)

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

A polynomial is an expression consisting of coefficients and variables forming an equation.

Given the polynomial:

x³ + 2x² -x - 2

Factorizing:

= (x + 2)(x² - 1)

= (x + 2)(x + 1)(x - 1)

The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)

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Answer:

2

Step-by-step explanation:

9 ÷ 3 - 2 × 2

3 - 2 × 2

1 × 2

2

Answer:

54+2.50x=4.75x

x=24 video games

Step-by-step explanation:

54+2.50x=4.75x

54=2.25x

x=24

Check answer:

54+2.5(24)=2.25(24)

114=114

Answer:

  9.  AB = (40/3)√3

  10.  BC = (20/3)√3

Step-by-step explanation:

The ratios of side lengths in the "special" 30-60-90° triangle are ...

  1 : √3 : 2

__

If D is the point where the altitude meets AB, then we have for the left triangle ...

  CD : AD : CA = 1 : √3 : 2 = 10 : 10√3 : 20

and, for the right triangle ...

  BD : CD : BC = 1 : √3 : 2 = (10/√3) : 10 : (20/√3)

and for the large triangle ...

  BC : CA : AB = 1 : √3 : 2 = (20/√3) : 20 : (40/√3)

__

The hypotenuse of ΔABC is AB, shown above to be ...

  AB = 40/√3 = (40/3)√3

__

The shorter leg of ΔABC is BC, shown above to be ...

  BC = 20/√3 = (20/3)√3

In the 1st question , we are given with a rectangle whose breadth is 4x and length is 2x+5y and we need to find it's perimeter in simplified form . Now , as we knows that for any rectangle with Length 'l' and breadth 'b' it's perimeter is given by 2(l+b) . Now , applying the same concept in our question , we have

\({:\implies \quad \sf Perimeter=2(2x+5y+4x)}\)

\({:\implies \quad \sf Perimeter=2(6x+5y)}\)

\({:\implies \quad \sf Perimeter=2\times 6x+2\times 5y}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{Perimeter=12x+10y}}}\)

Now , in 2nd question , we are given That Jeanelle bought 3 chocolate bars more than as of Eashan , and Rameen bought twice as many as Jeanelle . So , now here assume that Eashan bought x chocolate bars . So , Jeanelle have (x+3) bars and Rameen have 2(x+3) bars and all chocolate bars add up to 17 .Now , According to question

\({:\implies \quad \sf x+(x+3)+2(x+3)=17}\)

\({:\implies \quad \sf x+x+3+2x+6=17}\)

\({:\implies \quad \sf (2x+x+x)+(3+6)=17}\)

\({:\implies \quad \sf 4x+9=17}\)

Subtracting 9 from both sides

\({:\implies \quad \sf 4x+\cancel{9}-\cancel{9}=17-9}\)

\({:\implies \quad \sf 4x=8}\)

\({:\implies \quad \sf x=\dfrac{8}{4}}\)

\({:\implies \quad \bf \therefore \quad \underline{\underline{x=2}}}\)

Now ,

The solution of the given initial value problem, x'' + 33.64x = 4cos(6t), with x(0) = x'(0) = 0, can be expressed as a sum of the homogeneous solution and the particular solution.

To find the solution, we start by solving the homogeneous equation, x'' + 33.64x = 0. The characteristic equation associated with this homogeneous equation is \(r^2 + 33.64 = 0\), which yields the roots

r = ±i√33.64. Thus, the homogeneous solution can be expressed as

x_h(t) = A*cos(√33.64*t) + B*sin(√33.64*t),

where A and B are constants determined by the initial conditions.

Next, we need to find the particular solution for the forced oscillation. Since the right-hand side of the equation is of the form Acos(ωt), where ω = 6, we assume a particular solution of the form x_p(t) = C*cos(ω*t + φ), where C and φ are constants to be determined. Taking the derivatives, we have x_p''(t) = -ω^2*C*cos(ω*t + φ) and x_p'(t) = -ω*C*sin(ω*t + φ). Substituting these into the original equation, we obtain -ω^2*C*cos(ω*t + φ) + 33.64*C*cos(ω*t + φ) = 4*cos(ω*t).

To satisfy this equation, the coefficient of the cosine term must be 4, while the coefficient of the sine term must be zero. This gives us two equations: -ω^2*C + 33.64*C = 4 and -ω*C = 0. Solving these equations, we find C = 4/(33.64 - ω^2) and φ = 0. Therefore, the particular solution is x_p(t) = (4/(33.64 - ω^2))*cos(ω*t).

Finally, we combine the homogeneous solution and the particular solution to obtain the complete solution:

x(t) = x_h(t) + x_p(t) = A*cos(√33.64*t) + B*sin(√33.64*t) + (4/(33.64 - ω^2))*cos(ω*t).

By substituting the initial conditions x(0) = x'(0) = 0 into this equation, we can determine the values of A and B. With the obtained values, the final solution for the initial value problem can be expressed in terms of the given constants and the trigonometric functions involved.

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The area of the triangle is 4.5 square unit.

We have, y= 4x/ (1 + x³)

Now, differentiating the above equation wrt to x we get

y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²

y'= -8x³ + 4/ (1+x³)²

When x = 1 then y' = -4/4 = -1

so, y -2 = -1 (x-1)

y= -x+ 3

Here the x intercept is (3, 0) and y intercept is (0, 3).

so, Area of Triangle is

= 1/2 x 3 x 3

= 9/2

= 4.5 square unit

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If 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

Given:

Volume of cube=64cm³

Hence:

Volume of the cube = a³

Volume of the cube, a³= 64 cm³

Using this formula

Cube edge length =∛(side)³

Let plug in the formula

Cube edge length =∛(64cm³)

Cube edge length=4cm

Therefore if 64 is a perfect cube the length of each edge of the block can be found. The edge length of a cube is: 4cm.

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Answer:

The first is not a function.  The second is.

Step-by-step explanation:

See attachment.

The equation of the parabola in vertex form is y = (1/20)(x + 7)^2 + 1.

To write the equation of a parabola in vertex form, we use the equation:

y = a(x - h)^2 + k

where (h, k) represents the vertex of the parabola.

Given that the vertex is (-7, 1), we have h = -7 and k = 1. Substituting these values into the equation, we get:

y = a(x + 7)^2 + 1

Now, we need to find the value of 'a' to complete the equation. Since the parabola passes through the point (10, 309/20), we can substitute these coordinates into the equation:

309/20 = a(10 + 7)^2 + 1

309/20 = a(17)^2 + 1

309/20 = a(289) + 1

309/20 = 289a + 1

To simplify the fraction, we multiply both sides by 20:

309 = 20(289a + 1)

309 = 5780a + 20

Now, we solve for 'a':

5780a = 309 - 20

5780a = 289

a = 289/5780

a = 1/20

Substituting this value of 'a' back into the equation, we have:

y = (1/20)(x + 7)^2 + 1

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Answer:

x ≥ -4

Step-by-step explanation:

4x+5 ≤ 2x-3

Collect like terms

4x-2x ≤ -3-5

Simplify

2x ≤ -8

Divide both sides by 2

2x / 2 ≤ -8 / 2

x ≥ -4

Answer:

Mean

Step-by-step explanation:

I said mean because it would allow both Carl and Tamera to average their scores and compare one side by side rather than comparing 6 each which would just be time consuming and it seems like it wouldn't be any other choices.

The class width that should be used for constructing the frequency distribution is 5.

To determine the class width for constructing a frequency distribution with 5 classes, we need to calculate the range of the variable and divide it by the number of classes.

Range = Maximum value - Minimum value

= 35 - 10

= 25

Class width = Range / Number of classes

= 25 / 5

= 5

Therefore, the class width that should be used for constructing the frequency distribution is 5.

The correct answer is (a) 5.

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Answer:

Representative.

Step-by-step explanation:

In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.

A representative sample has characteristics similar to those of the entire population and, therefore, can be used to draw a conclusion about the (general) population. Thus, it is considered typically to be a subset of population and can be used to accurately make conclusions and reflect the characteristics of the larger sample (population).

Answer:

156 ft

Step-by-step explanation:

area formula is:

length x width

(A= l*w)

12 x 13 = 156

The proportional relationship is given by y = 8.5x

Two variables are said to be proportion if an increase/decrease in one variable causes an increase/decrease in the other variable.

Let x represent the movie tickets and y represent the cost.

Since x and y are proportional, hence:

y ∝ x

y = rx

Where r is the constant of proportionality.

From the table to find x, when y = 17, x = 2, hence:

17 = 2r

r = 8,5

y = 8.5x

The proportional relationship is given by y = 8.5x

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By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

C infinite

Step-by-step explanation:

They are the exact same line. (Multiply the entire bottom equation by -1 and it's the same as the top)

To calculate the percent of variance that age at first birth shares with highest grade completed, we can use the coefficient of determination (R-squared). R-squared measures the proportion of the total variance in one variable that can be explained by another variable.

First, we need to perform a regression analysis to obtain the R-squared value. This can be done using statistical software or tools like Excel or SPSS.

Once you have the R-squared value, you can interpret it as the percentage of variance that age at first birth shares with highest grade completed. For example, if the R-squared value is 0.5, it means that 50% of the variance in age at first birth can be explained by the highest grade completed.

In conclusion, the R-squared value obtained from the regression analysis will provide the percentage of variance that age at first birth shares with highest grade completed. The higher the R-squared value, the stronger the relationship between the two variables.

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Answer:

1 ⅚ miles.

Step-by-step explanation:

Makayla wants to walk 6 miles. Since she has walked 4 1/6 miles (2 5/6 miles + 1 1/3 miles), you subtract this from 6 and you will get your answer.

Answer:

distance = 5 units

Step-by-step explanation:

we can calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (3, 4 )

d = \(\sqrt{(3-0)^2+(4-0)^2}\)

  = \(\sqrt{3^2+4^2}\)

  = \(\sqrt{9+16}\)

   = \(\sqrt{25}\)

   = 5

Formula to find the distance between two points is given by -

\( \small \underline{ \boxed{ \sf{ \pmb{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}}}\\\)

As per question, points are -

On substituting the values :-

\(\: \: \: \: \: \longrightarrow \sf {Distance(XQ) = \sqrt{ (0-4)^2 + (0-3)^2 }}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance (XQ)= \sqrt{ (-4)^2 + (-3)^2 }}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance(XQ) = \sqrt{ 16+9}}\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance (XQ)= \sqrt{ 25} }\\\)

\(\: \: \: \: \:\longrightarrow \sf {Distance(XQ) = 5}\\\)

\( \: \: \: \: \:\longrightarrow \boxed{ \tt{ \pmb{ \red{Distance(XQ) = 5 }}}}\\\)

\( \\ \therefore \underline{ \cal{ \pmb{The \:distance \: of \: the\: two \:points \: is \: \frak{\purple{ 5.} }}}}\\\)

It would require an equal amount of 15% acid solution and 85% acid solution, specifically 20 liters of each to produce 40 liters of a 50% acid solution,

To determine the amount of each solution needed, we can set up a system of equations based on the acid content:

Let's assume x represents the amount of the 15% acid solution in liters, and y represents the amount of the 85% acid solution in liters.

We have two conditions to consider:

1. The total volume of the solution: x + y = 40 (since the total volume required is 40 liters).

2. The acid content: 0.15x + 0.85y = 0.50 * 40 (since we want a 50% acid solution, which is half of the total volume).

Now, we can solve this system of equations. Let's use the substitution method.

From the first equation, we can express y in terms of x as y = 40 - x.

Substituting this value of y into the second equation, we get:

0.15x + 0.85(40 - x) = 0.50 * 40

0.15x + 34 - 0.85x = 20

0.15x - 0.85x = 20 - 34

-0.70x = -14

x = -14 / -0.70

x = 20

Substituting the value of x back into the first equation, we find:

20 + y = 40

y = 40 - 20

y = 20

Therefore, you need 20 liters of the 15% acid solution and 20 liters of the 85% acid solution to produce 40 liters of a 50% acid solution.

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In summary, fy(a,b) is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

The given expression represents the partial derivative of f(x, y) with respect to y, evaluated at (a, b):

fy(a,b) = lim┬(y→b)⁡〖[f(a,y) - f(a,b)]/(y - b)〗

Geometrically, this partial derivative represents the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

To see why this is the case, consider the following argument:

Let L be the limit in the expression given above.

Let h = y - b be the change in the y-coordinate from b to y.

Then, we can rewrite the limit as:

fy(a,b) = lim┬(h→0)⁡〖[f(a,b + h) - f(a,b)]/h〗

This expression represents the average rate of change of f(x, y) with respect to y over the interval [b, b + h].

As h approaches 0, this average rate of change approaches the instantaneous rate of change, which is the slope of the tangent line to the surface defined by f(x, y) at the point (a, b) in the y-direction.

Therefore, fy(a,b) is the partial derivative of f(x, y) with respect to y, evaluated at (a, b).

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The cyclist and the car will intersect at 11:50 AM.

To determine the approximate time and place at which the car and the cyclist passed each other the following calculation must be performed:

-The advance of each of the parts must be calculated, and the point where said movement coincides.

Therefore, the cyclist and the car will intersect at 11:50 AM.

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Answer:

-5

Step-by-step explanation:

Use the definition of slope:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

And replace any two coordinates into the equation:

\(m=\frac{11-6}{13-14} \\m=\frac{5}{-1}\\m=-5\)

Answer:

m (slope) = -5

Step-by-step explanation:

All you need to do is use 2 of these points. For this example, we will use

(13,11) and (14,6).

To solve, use rise/run. The y value (rise) goes down by 5, so your rise is -5. The x value (run) goes up by 1, so your run is 1.

Insert these values into rise/run to get -5/1. Simplify this to get -5.

The oxidation of one species allows the reduction of another, so the species being oxidized is called the reducing agent while the species being reduced is the oxidizing agent.

An oxidizing agent is a compound or element that participates in a redox (oxidation-reduction) reaction and accepts electrons from a different species. An oxidant is a chemical compound that easily transfers oxygen or another substance atoms in order to gain an electron. Oxidizing agents add oxygen to another substance or remove hydrogen from it.

A reducing agent is one of the reactants of a redox (oxidation-reduction)  reaction which reduces the other reactant by giving out electrons to the reactant. Reducing agents remove oxygen from another substance or add hydrogen to it.

In simple way, the substance to which oxygen is added or hydrogen is removed is said to be oxidized, and the substance oxidized is the reducing agent and the substance which gets reduced is the oxidizing agent.

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