18. Simplify the complex fraction.

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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The limit as a definite integral on the given interval. lim n→[infinity] n xi ln(1 xi2) δx, [2, 6] {62xlnc 1+X2} dx

As per the given question

Lim n - infinite n xi ln (1×i2) € x = (A,B) =(2,6)

We have to put the formula of Reimann sum

That is Rn = Sigma x ni = 1f (xi) ∆x

Comparing the evolved formula with the given expression we get

f (xi) = xi ln (1×2i)

Back substitute the variable x for xi

Thus the definite integral is

( 6 2 x ln (1+X2)) dx

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The area of the shaded region of the circle is 10.972 square inches.

The formula for area of a circle sector is;

A = (θ/360) * πr²

We are given;

Radius of circle = 92 inches

Central angle = 7π/15

Thus;

Area of given sector = (7π/15)/360 * π * 92²

Area of given sector = 7π/15 * 1/360 * π * 92²

Area of given sector = 10.972 square inches

Thus, we can conclude that the area of the shaded region of the circle is 10.972 square inches.

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The number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                               Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             325

Low grade               18                             9              540

Operating cost      16000                     12000

Time                        37                                34

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 16000x + 12000y

Subject to:

5x + 20y >= 325

18x + 9y >= 540

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (25, 10)

This means that

Mine 1 hour = 25 hours

Mine 2 hour = 10 hours

Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 25 hours and Mine 2 hour = 10 hours

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The expression that represents five less than the sum of mark's and hatch's ages is ( h + m ) - 5

Given,

Mark's age is represented by m

Hatch's age is represented by h

To find an expression that shows the required relation, that is, five less than the sum of mark's and hatch's ages, we need to establish a relation between the given variables.

Sum of mark's and hatch's ages can be represented as ( m + h )

Five less than the sum of mark's and hatch's ages can be represented as ( m + h ) - 5.

Therefore, by establishing a relation between the given variables, we get the expression that represents five less than the sum of mark's and hatch's ages as ( h + m ) - 5.

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Answer:

2 pints

Step-by-step explanation:

if you add all of it up you get 2 pints.

1/4*8 = 2 pints

Answer: V = 75.4

Step-by-step explanation: Assuming this is a cylinder we can use the formula πr^2*h. All we have to do is plug in the numbers for the equation. Since we know radius is half of the diameter we can set radius to 2. h represents height.

So since the formula is saying we need to square the radius. We multiply 2*2=4

We can then plug this in for r squared.

Making our equation=  π*4*6 = 75.4

The mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

We use the rotation of 90 degree to find the mapping of 270 degrees.

The rotation of 270 degree clockwise is same as the anticlockwise rotation of 90 degrees about the origin.

So the mapping of 270 degree clockwise rotation is exactly the mapping of 90 degree anti clockwise rotation.

Now the mapping of 90 degree anti clockwise rotation is  (x, y) -----> (-y, x).

So the mapping representing a rotation of 270 degree clockwise about the origin is (x, y) -----> (-y, x)

This implies that a point (x, y) on the co-ordinate plane becomes (-y, x) after a clockwise 270 degree rotation.

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A function assigns the value of each element of one set to the other specific element of another set. The person can see upto 9.996 meters.

A function assigns the value of each element of one set to the other specific element of another set.

Given that  a person's eye level is h meters above sea level and she can see d kilometers to the horizon, then d=3.57√(h).

Now, using the same given function we can find the distance up to which the person will be able to see to the horizon. Therefore, we can write,

d=3.57√(h)

d = 3.57 √(7.84)

d = 3.57 × 2.8

d = 9.996

Hence, the person can see upto 9.996 meters.

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Answer:

C is greater than or equal to -23

Step-by-step explanation:

- 28 + 5 = -23

Answer: 0.16666

Step-by-step explanation:

You need to move the decimal point over

[tex]\frac{5.9}{35.4} \\ \\ \frac{59}{354}=\frac{59.0}{354} =\frac{0.16666}{554}[/tex]

Answer:

191+192

Step-by-step explanation:

According to the given statement this is a type of stratified sampling.

Stratified random sampling is often when researchers want to know about different subgroups or based on the entire population being studied. For instance, if one is interested in differences between groups based on race, gender, or gender.

she measures her blood sugar level at 3 randomly selected times during each part of the day.

So,

This is a type of stratified sampling.

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I understand that the question you are looking for is :

To determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day.

What type of sampling is used?

Answer:

3

Step-by-step explanation:

[tex]\sqrt[3]{27}[/tex]

= [tex]\sqrt[3]{3^3}[/tex]

= 3

The parametric equations are line through (0,0,0) in the direction of the vector v=uxw=(1,2,1).

The line through (0,0,0) and perpendicular to both U=(-2,1,0) and

w=(-1,0,1)

Therefore the line through (0,0,0) and parallel to (-2,1,0)

[tex]*10919-1-2, î+1=3618 = (1) ņ - (-2)5+ (1)a • Î +21 + û[/tex]

=(1,2,1)

Therefore direction ratio of the line through (0,0,0) is (1,2,1) Therefore for equation of the line through (0,0,0) and perpendicular to both (-2,1,0) and [tex]w=(-1,0,17 is (0,, z) = (0,0,0) + x (1,2,1),[/tex] & is constant.

[tex].: X (1,4,2)= (0, 1, 0)+ [1,2,1][/tex]

Therefore parametric of the line through (0,0,0) in the direction of the vector v=uxw=(1,2,1)

Equivalent Equation of a Plane in Vector Form

The equation for a plane in the real number system R, where r is the position vector of any point on the plane and n is either a normal vector perpendicular to the plane or a parallel vector.

The normal vector must be perpendicular to both as the vectors are both parallel to the plane. Recall that a vector that is perpendicular to both vectors is created by taking the cross product of two vectors. This cross product's characteristic can be used to compute a normal vector to the plane, which results in the normal vector.

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Answer:

0.11 yards

Step-by-step explanation:

To convert centimeters to yards, find the needed unit conversions:

[tex]cm(\frac{in}{cm})(\frac{ft}{in})(\frac{yd}{ft})[/tex]

Convert centimeters to inches, inches to feet, then feet to yards!

Now replace the values with the correct quantities:

[tex]10cm(\frac{1in}{2.54cm})(\frac{1 ft}{12 in})(\frac{1 yd}{3 ft})[/tex]

Finally, simplify and cross-cancel the units:

[tex]0.10936... yd[/tex]

Round to the nearest hundredth:

[tex]0.11 yd[/tex]

Answer:

[tex]x = 61[/tex]

Step-by-step explanation:

See the attached image for explanation

Check the picture below.

The simplified form of the given expression is x raise to the power of one-thirty.

Given the indices expression (x^1/2/(x^1/3)^1/5

Using the indices law below:

a^m/a^n = a^m-n

(a^m)^n

Applying the law above to the given equation

(x^1/2/(x^1/3)^1/5 = (x^1/2-1/3)^1/5

(x^1/2/(x^1/3)^1/5 = (x^1/6)^1/5

(x^1/2/(x^1/3)^1/5 = x^1/30

Hence the simplified form of the given expression is x raise to the power of one-thirty.

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Answer:

123910-w137762 cotkw

naodiskd

Answer:  $41.50  41 dollars and 50 cents in profit

Step-by-step explanation:

First, 1.25x48=60

Second, 60-18.50=41.50

Answer:

$41.50

Step-by-step explanation:

So we know that Gavin bought 48 water bottles before the game for $18.50. We also know that he sold the water bottles for $1.25 each.

If we want to know how much profit he made, we first have to find the amount of money he received.

To find this, we need to multiply the number of water bottles by the price for each bottle;

48 × $1.25

This gives us a total of $60.

Now to find the profit, we have to subtract the amount he paid for the water bottles by the total he made;

$60 - $18.50

This means he made a profit of $41.50.

hope this makes sense! <3

cluster sampling is the type of sampling is used.

In cluster sampling, a population is divided into clusters, which are smaller groups. They then choose a sample at random from these clusters. Often employed to investigate huge populations, particularly those that are extensively geographically distributed, cluster sampling is a probability sampling technique. Typically, clusters used by researchers are already-existing groups like cities or schools. Clusters are frequently more homogeneous than the population as a whole since they are typically naturally occurring groups, such as schools, cities, or houses. When conducting your study, you should be aware of this as it might compromise the validity of your findings.

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The x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

X Intercept is defined as the point where the line crosses the X axis .

For Example : if the line x+y=2 crosses the x axis at 2 ,  then it's x intercept will be (2,0).

Y Intercept is defined as the point where the line crosses the Y axis.

For Example ; if the line x+y=2 crosses the y axis at 2 , then it's Y intercept will be (0,2) .

In the given question

7x-9y=35

To find the x intercept we substitute the value of y=0,

On substituting  y=0 we get

7x=35

x=5

The x intercept is (5,0).

To find the y intercept we substitute the value of x=0,

On substituting x=0 we get ,

-9y=35

y=-35/9

The y intercept is (0,-35/9) .

Therefore , the x intercept and y intercept of 7x-9y=35 is (5,0) and (0,-35/9) respectively .

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Answer:

450 eggs

Step-by-step explanation:

if an egg box can hold 10 eggs

then 45x10=450

The perimeter of the right triangle is 30 units.

The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.

Let's break the information into smaller chunk.

The shorter leg of a right triangle is 8 less than the hypotenuse.

The longer leg is one less than the hypotenuse.

The hypotenuse is the longest side of a right triangle.

Therefore,

let

the hypotenuse = x

short leg = x - 8

long leg = x - 1

Applying Pythagorean theorem in the given right triangle.

c² = a² + b²

where

(x - 1)² + (x - 8)² = x²

(x - 1)(x - 1) + (x - 8)(x - 8) = x²

x² - x - x + 1 + x² - 8x - 8x + 64 = x²

2x² - 18x + 65 = x²

x² - 18x + 65 = 0

(x - 13)(x - 5) = 0

Therefore,

x = 5 and x = 13

13² - 5² = a²

169 - 25 = a²

a = √144

a = 12

So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.

perimeter of the right triangle = 13 + 5 + 12 = 30

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Answer:

number of fish caught between 60 and 75 cm =40

Step-by-step explanation:

Answer:

f(x) = 2

Step-by-step explanation:

What is the value of the function f(x) = 8x when x = 0.25?

substitute in 0.25 for x to get:

f(x) = 8(0.25)

f(x) = 2

a-/ |-5-10| = 15 ; |-2√2-√12|=2√3+√12 ; |-π-4π|=5π

The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.

It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.

Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.

It follows that all sides of the room are equal and the length of each side can be determined as;

s = √Area; since Area = s².

s = √775

s = 27.839 ft.

Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.

However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;

= 27.839 - 3 -3 = 21.839 ft on all sides.

Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.

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Answer: a=-0.75

Step-by-step explanation:

14a - (2a +9)=2/3 (12a-18)​

14a - 2a -9=2/3 * 6(2a-3)​

12a-9=2*6/3 (2a-3)​

12a-9=2*2(2a-3)​

12a-9=4(2a-3)​

12a-9=8a-12

4a-9=-12

4a=-3

a=-3/4

a=-0.75