A backyard is 40. 5 feet long and 25 feet wide. in order to install a pool, the yard needs to be reduced by a scale of one-third. what is the area of the reduced yard? feet2.

The planes intersect at the point (-19/21, -11/14, 1).

To determine how, if at all, the planes intersect, we need to solve the system of equations given by the three planes:

[2T/3A] 2x + 2y + z - 10 = 0

5x + 4y - 4z = 13

3x – 2z + 5y - 6 = 0

We can use elimination to solve this system. First, we can eliminate z from the second and third equations by multiplying the second equation by 2 and adding it to the third equation:

5x + 4y - 4z = 13

6x - 4z + 10y - 12 = 0

11x + 14y - 12 = 0

Next, we can eliminate z from the first and second equations by multiplying the first equation by 2 and subtracting the second equation from it:

4x + 4y + 2z - 20 = 0

-5x - 4y + 4z = -13

9x - y - 6z - 20 = 0

Now we have two equations in three variables. To eliminate y, we can multiply the second equation by 14 and subtract it from the first equation:

11x + 14y - 12 = 0

-70x - 56y + 56z = -182

-59x - 42z - 12 = 0

Finally, we can substitute this expression for x into one of the previous equations to find z:

3(59/42)z - 12/42 - 2y - 10 = 0

177z - 60 - 84y - 420 = 0

177z - 84y - 480 = 0

Now we have two equations in two variables, z and y. We can solve for y in terms of z from the second equation:

y = (177/84)z - (480/84)

Substituting this expression for y into the third equation, we can solve for z:

177z - 84[(177/84)z - (480/84)] - 480 = 0

177z - 177z + 480 - 480 = 0

This equation simplifies to 0=0, which means that z can be any value. Substituting z=1 into the expression for y, we get:

y = (177/84)(1) - (480/84) = -11/14

Substituting z=1 and y=-11/14 into the expression for x, we get:

x = (59/42)(1) - (12/42) + 2(-11/14) + 10 = -19/21

Therefore, the planes intersect at the point (-19/21, -11/14, 1).

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Answer:

C = 52

Step-by-step explanation:

sin(c/4) = sin(104/8)

sin(c/4) = 0.22495

c/4 = 13

c = 52

(a) The elasticity at p = $50 and q = 4502 is 2.778.

(b) The elasticity is elastic.

(c) An increase in price would result in a decrease in revenue.

(a) To find the elasticity when p = $50 and q = 4502, we first need to find the partial derivatives of q with respect to p and then use the elasticity formula:

Demand: 2p²q = 10000 + 9000p²

Partial derivative of q with respect to p: 4pq = 18000p

When p = $50 and q = 4502:

4(50)(4502) = 900800

Elasticity:

e = (p/q) * (dq/dp) = (50/4502) * (900800/18000) = 2.778

(b) To determine what type of elasticity this is, we look at the value of the elasticity calculated in part (a). Since the elasticity is greater than 1, we know that this is an elastic demand.

(c) To determine how the revenue would be affected by an increase in price, we need to look at the relationship between elasticity and revenue. If demand is elastic,

Then an increase in price will result in a decrease in total revenue, and if demand is inelastic, then an increase in price will result in an increase in total revenue.

Since we know that the demand is elastic (from part (b)), we can conclude that an increase in price will lead to a decrease in revenue.

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The value of x is 6 and the perimeter is 52 unints

From the question, we have the following parameters that can be used in our computation:

The figure

If the lines that appear to be tangent are tangent, then we have the following equation

x + 2 = 8

Evaluate the like terms

x = 6

The perimeter is the sum of the side lengths

So, we have

Perimeter = x + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

This gives

Perimeter = 6 + 2 + 8 + 5 + 5 + 9 + 9 + 4 + 4

Evaluate

Perimeter = 52

Hence, the perimeter is 52 unints

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Answer:

a = 3

b = 1

c = 5

d = 2

Step-by-step explanation:

To find the prime factorization of 600, we can use trial division by dividing by the smallest prime numbers until we reach a prime factor:

600 ÷ 2 = 300

300 ÷ 2 = 150

150 ÷ 2 = 75

75 ÷ 3 = 25

25 ÷ 5 = 5

Therefore, the prime factorization of 600 is:

600 = 2^3 × 3^1 × 5^2

So, a = 3, b = 1, c = 5, and d = 2.

Lizzie's divisibility test states that a number n is divisible by a certain number m if and only if the alternating sum of its two-digit chunks is divisible by m.

Lizzie's divisibility test involves breaking a positive integer into two-digit chunks, finding the alternating sum of these chunks, and then determining if the result is divisible by a certain number m.

To apply the test:

To prove that this is a divisibility test for m, you need to show that n is divisible by m if and only if the result of the alternating sum is divisible by m.

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According to the question the  graph the line -3x + 5y = 15, we can start by solving for y:

-3x + 5y = 15

5y = 3x + 15

y = (3/5)x + 3

As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).

Briefing :

Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.

To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.

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If the first cube has a volume of 125 cm³ and the second cube has a volume of 343 cm³, the difference in the area of one face of the second cube and the area of one face of the first cube is 24cm². The answer is B. 24 cm².

To find the difference in the area of one face of each cube, we first need to find the side length of each cube. Since the volume of a cube is equal to the side length cubed (V = s³), we can find the side length by taking the cube root of the volume.

For the first cube:
Volume = 125 cm³
Side length = cube root of 125 = 5 cm

For the second cube:
Volume = 343 cm³
Side length = cube root of 343 = 7 cm

Next, we find the area of one face of each cube. The area of one face of a cube is equal to the side length squared (A = s²).

Area of one face of the first cube:
A1 = 5² = 25 cm²

Area of one face of the second cube:
A2 = 7² = 49 cm²

Finally, find the difference in the area of one face of each cube:
Difference = A2 - A1 = 49 cm² - 25 cm² = 24 cm²

The answer is B. 24 cm².

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The given set of questions are solved under the condition of  parametric equations x(t)=sin(3t) and y(t)=cos(3t) .

Hence, the length of the curve from t= 0 to t= π is 3π.

Now,

A. To evaluate the velocity, we need to perform the derivative of x(t) and y(t) concerning t.

x'(t) = 3cos(3t)

y'(t) = -3sin(3t)

Therefore,  the velocity vector is

v(t) = <3cos(3t), -3sin(3t)>

B. To define the acceleration, we need to evaluate  the derivative of v(t) concerning t.

a(t) = v'(t) = <-9sin(3t), -9cos(3t)>

C. To describe  the speed, we need to calculate  the magnitude of the velocity vector.

|v(t)| = √((3cos(3t))² + (-3sin(3t))²)

= 3

D. In order to find the number of times at which the particle stops, to find when the speed is equal to zero.

|v(t)| = 0 when cos(3t) = 0

sin(3t) = 0.

Therefore,

cos(3t) = 0 when t = (π/6) + (nπ/3),

here n = integer.

sin(3t) = 0 when t = (nπ/3),

here n = integer.

E. To calculate the length of the curve from t=0 to t=π by performing  calculus

L = ∫[a,b] √((dx/dt)² + (dy/dt)²) dt

Therefore, a=0 and b=π.

L = ∫[0,π] √((3cos(3t))² + (-3sin(3t))²) dt

 = ∫[0,π] 3 dt

 = 3π

The given set of questions are solved under the condition of  parametric equations x(t)=sin(3t) and y(t)=cos(3t) .

Hence, the length of the curve from t=0 to t=π is 3π.

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The complete question is

A particle moves along a path in the xy-plane. the path is given by

the parametric equations x(t)=sin(3t) and y(t)=cos(3t), help with

steps A-E

a. Find the velocity

b. Find the acceleration.

c. Find the speed and simplify your answer completely.

d. Find any times at which the particle stops. Thoroughly explain your answer.

e. Use calculus to  find the length of the curve from t=0 to t = π , show your work.

Answer:  In bold

Step-by-step explanation:

The formula they gave is a rate

Let's solve for the rate first.

This equation is done for 3 years 2018-2021  that's why ^3

3.55 =  2.90(1+x)³                 >divide both sides by 2.90

1.224 = (1+x)³                         > take cube root of both sides

1.0697 =  1+x

x= .0697

so let's make our generic formula

[tex]y = 2.90(1+.0697)^{t}[/tex]        let t be years and let y=  price  

Let's calculate 2018, so this would be year 0

[tex]y = 2.90(1+.0697)^{0}[/tex]

y=$2.90   this is for 2018

They already gave you 2021 price

y=$3.55   this is for 2021

Rate of increase is .0697 

In 2025

That's 7 years=t

[tex]y = 2.90(1+.0697)^{7}[/tex]

y=$4.65    for 2025

The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .

To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).

The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.

This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.

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Based on the information, the three numbers are 14, 34, and 70.

Based on the information, the second number = 3x - 8

The third number is five times the first number, which can be written as:

third number = 5x

The sum of the three numbers is 118, so we can write an equation:

x + (3x - 8) + 5x = 118

9x - 8 = 118

Adding 8 to both sides:

9x = 126

x = 236 / 914

Now we can use this value of x to find the other two numbers:

second number = 3x - 8 = 3(14) - 8 = 34

third number = 5x = 5(14) = 70

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Answer:

it is the product of the independent and dependent variables

Step-by-step explanation:

I took a quiz and got that answer right

The constant of variation for an inverse variation relationship is always a fixed value.

Inverse variation is a relationship between two variables where an increase in one variable results in a decrease in the other variable, while a decrease in one variable results in an increase in the other variable.

Mathematically, this relationship is expressed as y = k/x, where k is the constant of variation.

The constant of variation represents the ratio of the two variables in the inverse variation relationship. It is a fixed value because it remains the same regardless of the values of the variables.

For example, if y varies inversely with x, and y = 4 when x = 2, then the constant of variation is k = xy = 4(2) = 8. This means that y will always be equal to 8/x in this inverse variation relationship.

Therefore, the constant of variation for an inverse variation relationship is always a fixed value, and it represents the ratio between the two variables in the relationship.

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The point of intersection between the two given equations is (3, -2).

The problem is asking to find the point of intersection between the two given equations:

y = (1/3)x - 3 ............... (equation 1)

y = -x + 1 ............... (equation 2)

To solve for the intersection point, we can set the two equations equal to each other:

(1/3)x - 3 = -x + 1

Simplifying and solving for x:

(1/3)x + x = 1 + 3

(4/3)x = 4

x = 3

Now that we know x = 3, we can substitute it into either of the two original equations to find y:

Using equation 1: y = (1/3)x - 3 = (1/3)(3) - 3 = -2

Using equation 2: y = -x + 1 = -(3) + 1 = -2

Therefore, the intersection point is (3, -2).

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The FICA tax will be $3595.5 on an income of $47,000.

Given that the principal amount = $47,000

Given that the FICA is taxed at the percentage of 7.65%

To findout the FICA tax we have to findout the 7.65% of money from the principal money $47,000.

The formula for finding the Y% of money from Z amount is = [tex]\frac{y}{100}[/tex] * Z

From the above formula, we can find the FICA tax.

FICA tax = [tex]\frac{7.65}{100}[/tex] * 47000 = 0.0765 * 47000 = 3595.5.

From the above solution, we can conclude that the FICA tax on an income of $47,000 is $3595.5

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The law of sines is solved and the triangle is given by the following relation

Given data ,

From the law of sines , we get

a / sin A = b / sin B = c / sin C

a)

C = 135° C = 45₁ B = 10°

So , the measure of triangle is

A/ ( 180 - 35 - 10 ) = A / 35

And , a/ ( sin 135/35 ) = sin 35 / a

On simplifying , we get

a = 36.50

Hence , the law of sines is solved

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To find the polynomial closest to another polynomial in an inner product space, you can follow these steps:

Choose an inner product on the space of polynomials. One common inner product on this space is the L2 inner product, which is defined as:

<f,g> = ∫a^b f(x)g(x) dx,

where a and b are the endpoints of the interval on which the polynomials are defined.

Let P be the space of polynomials of degree at most n, where n is the degree of the polynomial you want to approximate. Let f be the polynomial you want to approximate, and let g be an arbitrary polynomial in P.

Define the error between f and g as e = f - g.

Compute the inner product of e with itself:

<e,e> = ∫[tex]a^b (f(x) - g(x))^2 dx.[/tex]

Minimize this inner product with respect to g. This can be done by setting the derivative of <e,e> with respect to g equal to zero and solving for g.

The polynomial that minimizes the error is the polynomial closest to f in the L2 sense.

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The equation provided, "e3r + 6e2x + 7e et - 64 pestle da," is not an integral expression and does not have a variable of integration.

Additionally, the requested answer, "] +0," does not make sense in the context of the question. Please provide a complete and accurate question for me to assist you with. Hi! Based on your terms provided ("Integrals", "substitution", and "find"), I understand that you are looking to solve an integral using substitution. However, the integral you provided appears to have some typographical errors. Please provide the correct integral, and I'll be happy to help you solve it.

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The percentage of evergreen trees from the total combination of trees is 79%

The percentage of evergreen trees will be calculated using the formula -

Percentage of evergreen trees = number of evergreen trees/total number of trees × 100

Total number of trees = number of evergreen + deciduous trees

Total trees = 3160 + 840

Total trees = 4000

Percentage of evergreen trees = 3160/4000 × 100

Cancelled common zeroes in numerator and denominator and performing division

Percentage = 79%

Hence, the percentage of evergreen trees is 79%.

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The critical value for a right-tailed test of a population mean at α=0.10 level of significance with 20 degrees of freedom is 1.325.

The critical value for a left-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=15 is -1.345.

The critical value(s) for a two-tailed test of a population mean at the α=0.01 level of significance based on a sample size of n=11 is -2.718 and 2.718.

To find the critical values, we need to use a t-distribution table or a statistical software that provides the critical t-values for a specific level of significance and degrees of freedom.

For part (a), since it's a right-tailed test, the critical value will be positive, and we need to look for the t-value that corresponds to an area of 0.10 to the right of the mean in the t-distribution table. With 20 degrees of freedom, the critical value is 1.325.

For part (b), since it's a left-tailed test, the critical value will be negative, and we need to look for the t-value that corresponds to an area of 0.10 to the left of the mean in the t-distribution table. With 15 degrees of freedom, the critical value is -1.345.

For part (c), since it's a two-tailed test, we need to split the significance level equally between the two tails. We need to find the t-values that correspond to an area of 0.005 to the left of the mean and 0.005 to the right of the mean in the t-distribution table. With 11 degrees of freedom, the critical values are -2.718 and 2.718.

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The benchmark fractions are the most common fraction.

Such as 1/2, 0, 3/8 etc.

Mixed fractions are a type of fraction in which there is a whole number part and a fractional part. for example 17/3 would be 5 2/3 as a mixed fraction

The equation for the plane through the points Po(-3,-2,4), Qo(-5,-1,2), and Ro(1,1,5) is:

3x - 3y + 2z - 11 = 0

Using a coefficient of 7 for x, the equation of the plane is:

21x - 3y + 2z - 11 = 0

To find the equation of the plane, we can use the cross product of the vectors formed by the points Qo-Po and Ro-Po.

Let's call the vector formed by Qo-Po "u" and the vector formed by Ro-Po "v". Then, we can find the normal vector to the plane by taking the cross product of "u" and "v":

u = Qo - Po = (-5+3, -1+2, 2-4) = (-2,1,-2)

v = Ro - Po = (1+3, 1+2, 5-4) = (4,3,1)

n = u x v = (1(2) - (-2)(3), (-2)(4) - 1(1), (-2)(3) - 1(4)) = (8,-7,-10)

Now that we have the normal vector to the plane, we can find the equation of the plane by using the point-normal form of the equation of a plane:

n · (P - Po) = 0

where "·" denotes the dot product, P is any point on the plane, and Po is one of the given points on the plane.

Let's use the point Po(-3,-2,4) to find the equation of the plane:

n · (P - Po) = 0

(8,-7,-10) · (x+3, y+2, z-4) = 0

8(x+3) - 7(y+2) - 10(z-4) = 0

8x - 7y - 10z + 11 = 0

So the equation of the plane through the points Po, Qo, and Ro is:

3x - 3y + 2z - 11 = 0

To use a coefficient of 7 for x, we can simply multiply both sides of the equation by 7:

21x - 21y + 14z - 77 = 0

Simplifying, we get:

21x - 3y + 2z - 11 = 0

Therefore, the equation of the plane with a coefficient of 7 for x is 21x - 3y + 2z - 11 = 0.

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The distance between the two scout patrols is approximately 11.66 kilometers.

We can see that the situation forms a right triangle with the hypotenuse representing the distance between the two scout patrols. Let's call this distance d.

Each patrol initially hikes 5 kilometers in opposite directions. This means that the distance between them at this point is 10 kilometers (5 km + 5 km).

Then, each patrol turns 90 degrees to their right and hikes 6 kilometers. This means that they travel along the legs of the right triangle, which have a length of 6 kilometers.

Using the Pythagorean theorem, we can solve for the hypotenuse:

d² = 10² + 6²

d² = 136

d ≈ 11.66 km

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Answer:

answer choice C

Step-by-step explanation:

The playground is a rectangle.

To find the area of a rectangle, we use the formula:

Area = Length x Width

The length is 25 yards.

The width is 68 yards.

Plugging these into the area formula:

Area = 25 x 68 = 1,700 square yards

Of the options, the closest choice is:

1,710 square yards

The area is 1,710 square yards.

The average rate of change is -0.1295, under the condition the given exponential decay function is f (t) = 2(0. 95).

In order to find the average rate of change from x=0 to x=4 for the given exponential decay function [tex]f(t) = 2(0.95)^{t}[/tex], we need to find the slope of the line that passes through the points (0,f(0)) and (4,f(4)).

f(0) = 2(0.95)⁰ = 2

f(4) = 2(0.95)⁴ ≈ 1.482

The slope of the line passing through these two points is:

(f(4) - f(0))/(4 - 0)

= (1.482 - 2)/4

≈ -0.1295

Therefore, the average rate of change from x=0 to x=4 is approximately -0.1295.

An exponential decay function is a form of a function that reduces at a constant rate over time. It is a type of  mathematical model used to present many real-world phenomena such as radioactive decay, population growth, and the depreciation of assets.

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Answer:

89

Step-by-step explanation:

construct the formula to obtain the total of marks in first 9 tests:

79 = x/9

79 * 9 = 711

x = 711

so to get 80% in the next test we construct this formula:

80 = 711 + y / 9 + 1

the value we get for y is 89

to confirm the answer, 711+89/10 gives us 80, which is the correct value we want

The coordinates for H’I’D’E’ after a reflection over the y-axis include the following:

H' (-1, 4).

I' (-2, -1).

D' (-4, -3).

D' (-5, 3).

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given quadrilateral HIDE, we have the following coordinates:

(x, y)                             →                 (-x, y).

Coordinate H = (1, 4)   →  Coordinate H' = (-(1), 4) = (-1, 4).

Coordinate I = (2, -1)   →  Coordinate I' = (-(2), -1) = (-2, -1).

Coordinate D = (4, -3)   →  Coordinate D' = (-(4), -3) = (-4, -3).

Coordinate E = (5, 3)   →  Coordinate D' = (-(5), 3) = (-5, 3).

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To find the vector a = AB, we subtract the coordinates of point A from the coordinates of point B:

a = B - A = (-2,4,3) - (4,-6,-3) = (-2-4, 4+6, 3+3) = (-6, 10, 6)
The vector a can be written as a column vector with angle brackets: a = < -6, 10, 6 >.
To find the vector AB (a), we need to subtract the coordinates of point A from the coordinates of point B. Here's the calculation:

a = B - A
a = (-2, 4, 3) - (4, -6, -3)
Now, subtract each corresponding coordinate:

a = (-2 - 4, 4 - (-6), 3 - (-3))
a = (-6, 10, 6)
So, the vector AB (a) is <-6, 10, 6>.

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The inequality that represents the cost of each cookie is C ≤ $2, where C is the cost of each cookie.

An inequality is a mathematical expression that shows a relationship between two values that may not be equal. To represent the cost of each cookie using an inequality, we can first determine the cost per cookie by dividing the total cost of a box by the number of cookies in each box. In this case, that would be $16 divided by 8 cookies.

Let C represent the cost of an individual cookie. Since the most a box can cost is $16, the highest cost per cookie would be $16 / 8 = $2. To express this situation as an inequality, we can write:

C ≤ $2

This inequality indicates that the cost of each cookie (C) must be less than or equal to $2, ensuring that the total cost for a box of cookies does not exceed the maximum price of $16. By using this inequality, we can evaluate different cookie flavors and their respective costs to confirm that they meet Cindy's Sweet Treats' pricing requirements.

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Inflation is an important factor to consider when planning future purchases.

The Inflation Calculator does not provide the inflation-adjusted price for a fancy leather couch 10 years from now because it relies on historical data and cannot predict future inflation rates accurately.

Inflation rates are influenced by various economic factors and can fluctuate over time.

Therefore, it's difficult to determine the exact future cost of items with certainty. However, you can use historical trends as a general guide to estimate potential increases in cost due to inflation.

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