A pool measuring 18 meters by 20 meters is surrounded by a path of uniform width, as shown in the figure. If the area of the pool and the
path combined is 1520 square meters, what is the width of the path?
18
20
20+ 2x
18+2x

The function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

We are given that:

The parking garage charges $ 3 per hour if the car is parked there for less than 2 hours.

So, we get that:

Parking fees = 3 x for 0 ≤ x ≤ 2

Now, we get that, if the car is parked for more than 2 hours and less than 5 hours, then the parking fee is

6 + 4 ( x - 2) for 2 < x ≤ 5

Now, we are given that it charges a fixed fee of $ 20 if car is parked for more than 5 hours. So, the parking fee will be

20 for x > 5

So, the function becomes:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

Therefore, we get that, the function will become:

f ( x ) = 3 x ; 0 ≤ x ≤ 2

f ( x ) = 6 + 4 ( x - 2) for 2 < x ≤ 5

f ( x ) = 20 for x > 5

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The population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer as per the concept of statistics.

What are statistics?

A population is a total group from which a statistical sample is taken in statistics. Here, the manager only inquires about the fifth customer's pleasure after becoming interested in his drive-through staff. Therefore, those customers who do not use the drive-thru window at this restaurant are not part of the sample population about whom it is possible to inquire.

As a result, the population of this fast food business is made up of all customers who use the drive-thru window, whereas the sample, or representative group of the population, is made up of every fifth customer.

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Step-by-step explanation:

speed = mph or miles/hour

so, when we are dealing with a distance and compare the time spent on the distance, we have to divide distance by speed

miles / miles/hour = hour

so, we have

m/4 + m/3 = 2

as the sum of the time it took to walk the distance at 4mph and the time it took to walk the distance at 3 mph is 2 hours.

now we multiply by the denominators one after the other to eliminate the fractions.

m + 4m/3 = 8

3m + 4m = 24

7m = 24

m = 24/7 = 3.428571429... miles

The following figures are Line, Ray, Line Segment, Parallelogram and Cuboid in the sequential order.

a) Line - A line is a two-dimensional figure. It is a group of points joining together to form a single entity which extends in both directions infinitely. It has no end points.

b) Ray - A ray is a two-dimensional figure. It is a group of points joining together to form a single entity, but it extends infinitely in only one direction. It has one end point.

c) Line segment - A line segment is a two-dimensional figure. It is a group of points joining together to form a single entity, but it does not extend infinitely in any direction. It has two end points and a finite length.

d) Parallelogram - A parallelogram is a two-dimensional figure having 4 sides whose opposite sides are equal in length and also parallel to each other. The diagonals of the parallelogram intersect each other at equal distance.

e) Cuboid - A cuboid is a three-dimensional figure made up of rectangular faces of varying length, breadth and height. The opposite faces of a cuboid are similar in dimensions. It has 12 edges, 12 vertices and 6 faces.

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Answer:

Step-by-step explanation:

See attachment

The required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

To determine the simplified value of  x² +7x +12 divided by x + 2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
As per the given data,
Division of function,
=  x² +7x +12/ x + 2
= x² + 7x + 10 + 2 / x +2
= (x + 5)(x + 2) + 2 / x + 2
= (x + 5) (x + 2) / x + 2 + 2 / x + 2
= x + 5  + 2 / (x + 2)

Thus, the required simplified value of x² +7x +12 divided by x + 2 is x + 5 + [2 / (x + 2)].

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The common statistical method of expressing the precision of a series of repetitive measurements is the standard deviation.

It should be noted that the standard deviation is the measure of how dispersed the data is in relation to the mean.

It should be noted low standard deviation implies that data are clustered around the mean, and high standard deviation means data are more spread out.

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The problem two thirds(6j+9)=3j+7 has one solution.

The given problem is 2/3(6j + 9) = 3j + 7

In order to determine the number of solutions, take the following steps:

Expand the bracket on the left:

(2/3 x 6j) + (2/3 x 9)

4j + 6

4j + 6 = 3j + 7

Combine similar terms :

4j - 3j = 7 - 6

Add similar terms

j = 1

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The type of solution to the given simultaneous equations is no solution

When it comes to linear simultaneous equations as given in the question, there are different types such as; one solution, no solution or infinitely many solution.

We are given the simultaneous equations;

y = 5x + 4   ---(1)

y = 5x - 2   ----(2)

Using elimination method, subtract eq 1 from eq 2 to get;

0 = -2 - 4

0 = -6

0 cannot be equal to -6 and as such there is no value of x that makes the simultaneous equations true. Thus, the type of solution to the given simultaneous equations is no solution

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Answer:

Range is 12 and mean is -6

Step-by-step explanation:

To find the mean, add together all the numbers and divide by 7.

Let the height of the cup be h and the extra length be d.

So, when the one cup is placed over another the total height will be h+d.

So, when the one cup is placed over another the total height will be h + d.

When the four cup is placed over each another h + 3d = 11 cm.

So the generalised equation will h +(n-1)d where n is the total number of cups.

When the eight cup is placed over each another = h + 7d = 16.4 cm

h + 3d = 11 cm

h + 7d = 16.4 cm

On solving the above two equation we will get d = 1.35 cm and h = 6.95 cm

So when we put 10 cups on each other  = h +9d

6.95 + (9*1.35) = 19.1

Hence, the height of 10 cup will be 19.1cm.

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The system of inequalities are:

h + c ≤ 100

3h + 3.5c ≥ 80

Here are inequality signs and what they mean:

Here are the system of inequalities :

number of hamburgers sold + number of cheeseburger sold  ≤  total number of buns

(cost of one hamburger x number of hamburger sold) + (number of cheeseburger sold x number of cheeseburger sold) ≥ $80

h + c ≤ 100

3h + 3.5c ≥ 80

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129 is the value of expression .

What is PEMDAS?

We use , P/E/M/D/A/S (Parenthesis, Exponents, Multiply, Divide, Add, and Subtract)

8^2 + 9(12/3*2) - 7

= 64 + 9(8) -7

= 64 + 72 - 7

= 129

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If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.

Let d = the distance to the turn around point

Time = Distance/ Speed

Up time + Down time = 2hrs

d/2 +d/8 =2

Multiply by 8

8×d/2 +8×d/8 =8 (2)

4d + d = 16

5d = 16

Divide both side by 5d

d=16/5

d = 3.2 miles to turn around

Hence,

Round trip = (3.2 miles ×2)

Round trip= 6.4 miles

Therefore If a fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then started downstream to his start point. How far did the fisherman row if the entire trip took 2 hours is: 6.4 miles.

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72/8 = 9,

9x5 = 45 boys

Therefore answer is 45 boys

The composed function for the surface area of the cube for any given volume of an inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The function used to find the radius r of a sphere given volume V,

r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex]

The function used to find the length of the side s of the cube depending on the radius r of the sphere, s(r) = 2r

The function used to find the surface area A of the cube depending on the side of the cube s, A(s) = 6s²

We need to find the composed function for the surface area A of the cube for any given volume V of an inscribed sphere. i.e., A(V)

We have, A(s) = 6s²

Substituting function for s to A(s)

⇒ A(s(r)) = 6(2r)² = 24r²

Substituting function for r into A(s(r)),

⇒ A(s(r(V))) = 24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

So the function for the surface area of the cube depending on the volume of the inscribed sphere, A(V) =  24( [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex])²

The question is incomplete. Find the complete question below:

Consider a cube with an inscribed sphere. The function  r(V) = [tex]\sqrt[3]{\frac{3V}{4\pi} }[/tex] can be used to find the radius, r, of a sphere given the volume, V . The function  s(r) = 2r can be used to find the side length of the cube, s , depending on the radius of the sphere. The function A(s) = 6s² can be used to find the surface area,  A , of the cube. Which is the composed function for the surface area of the cube for any given volume of an inscribed sphere?

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Answer:

Answer is D

Step-by-step explanation:

The angle between a diagonal of a cube and an adjacent edge is 54.75°;

Assuming the length of a side of the cube as 1 unit, the three sides are given by the vectors;

a = (1, 0, 0)

b = (0, 1, 0)

c = (0, 0, 1)

The diagonal is given by the vector, v = (1, 1, 1)

The angle between the diagonal and one edge of the cube is given by

cos θ = v. a / |v|.|a|

v. a = (1, 1, 1).(1, 0, 0)

= 1(1) + 1(0) + 1(0

= 1 + 0 + 0

v. a = 1

Magnitude of vector V = √[(1)² + (1)² + (1)²]

|v| = √3

Similarly, |a| = √1;

So, |v|.|a| = √3.√1 = √3

Now, cos θ = 1/√3

So, θ = cos¹(1/√3)

θ = 54.75°

Therefore, the required angle is 54.75°.

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Answer:

-4[tex]\leq[/tex]a<7

Step-by-step explanation:

-20[tex]\leq[/tex]5a -10<25  add 10

+10       +10  +10

-20 [tex]\leq[/tex]5a<35  Divide all the way through by 5

-4[tex]\leq[/tex]a<7

The position of the bicyclist at t=8 minutes is 3.2 km

Speed is the rate of change of position of an object in any direction.

position the way in which something or someone is placed or arranged.

when time t = 6 position d = 5

when time t = 5 position d = 2

when time t = 8 position d = x

therefore we can say

8 / x = 5 / 2

x = 8 * 2 /5

  = 3.2 km.

Hence the position of the bicyclist at t=8 minutes is 3.2 km.

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complete question:

The position "d" of a bicyclist (measured in kilometers) is a linear function of time "t" (measured in minutes). At time t=6 minutes, the position is d=5 km. If the bicyclists travels at 2 km for every 5 minutes, find the position of the bicyclist at t=8 minutes.

The number of co-workers that like gumdrops and chocolate is 7 (option b).

The mathematical operations that would be used to determine the answer are addition and subtraction.

Addition is determining the total value or summing two or more numbers. The sign used to represent addition is +. Subtraction is the process of determining the difference between two or more numbers. The sign used to denote subtraction is -.

The first step is to add the total number of people who like a particular type of candy : 10 + 8 + 2 + 3 + 5 = 28

The second step is to subtract that number gotten in the previous step from the total number of co-workers.

Co-workers that like both chocolate and gum drops = 35 - 28 = 7

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5n² can be expressed as, 5n² =  3² x 5⁵ x x⁶

Given that n can be written as the product of the primes as

n = 3 x 5² x x³

This expression for n is called the prime factorization of n.

We need to express 5n² as such a product of primes.

For that taking square of n, add the power 2 with the existing powers of 3,5 and x,

So, n² = ( 3 x 5² x x³)² = 3² x 5⁴ x x⁶

So 5n² = 5(3² x 5⁴ x x⁶)

Multiplying 5 with the existing power of 5, 5⁴,

⇒ 5n² = 3² x 5⁵ x x⁶

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Answer:

[tex] \large{ \boxed{ \tt{answer : \boxed{ \tt{ k = 73 \degree}}}}}[/tex]

Please see the attached picture for full solution!

--------- Enjoy Learning<3---------

The order of numbers from Greatest to Least is 5.385, 2.714, 1.538, 0.612.

Arranged in a series that begins with the greatest or largest and ends with the least or smallest.

We can also call it Greatest to Least.

To order the number from greatest to least first we have to find the value of  given square root,

√29 = 5.385

√6/4 = 0.612

19/7 = 2.714

Now, we have the numbers :

5.385, 0.612, 2.714, 1.538

So, we will arrange the above numbers greatest to least

1) 5.385

2) 2.714

3) 1.538

4) 0.612

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Answer: -2, 2

Step-by-step explanation:

The derivative of a function, f(x), at a point where f(x) has a sharp turn (or cusp) does not exist.

The derivative of a function, f(x), at a point where f(x) has a vertical tangent line does not exist.

Using this information, we can see that f(x) is not differentiable when x=3 since there is a vertical tangent line. We can also see that f(x) is not differentiable when x=-1 since there is a cusp.

Answer:

tyyyy is my final answer

Step-by-step explanation:

please find attached file for the problem. hope it will help you , let me know if you have any further query

Answer:

67

Step-by-step explanation:

Each time the number goes up by 7. After 9 moretimes 4 will increase by 63.

4+63=67.

The 10th term should be 67

Answer:

1. m ∠ 1 = 86°

  m ∠ 2 = 4°

- Problem in the picture

2. m ∠ 1 = 6°

   m ∠ 2 = 84°

Step-by-step explanation:

I'm confused, so I'll just solve both problems (assuming that they are the same type of angle)

1.

m Z1 = (x+84)° and m2 = 2xº.

m ∠ 1 = (x + 84)°

m ∠ 2 = 2x°

Complementary angles are equal to 90°

(x + 84) + 2x = 90

x + 84 + 2x = 90

3x + 84 = 90

      -84    -84

----------------------

3x = 6

÷3  ÷3

-----------

x = 2°

m ∠ 1 = (x + 84)°

m ∠ 1 = (2 + 84)°

m ∠ 1 = 86°

m ∠ 2 = 2x°

m ∠ 2 = 2(2)°

m ∠ 2 = 4°

2. (Problem in the picture)

m ∠ 1 = (x - 6)°

m ∠ 2 = 7x°

Complementary angles are equal to 90°

(x - 6) + 7x = 90

x - 6 + 7x = 90

8x - 6 = 90

     +6    +6

---------------------

8x = 96

÷8    ÷8

----------------

x = 12

m ∠ 1 = (x - 6)°

m ∠ 1 = (12 - 6)°

m ∠ 1 = 6°

m ∠ 2 = 7x°

m ∠ 2 = 7(12)°

m ∠ 2 = 84°

I hope this helps!