10, 15, 22.5, 33.75.... what’s next?
.

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Here are two key characteristics of the polar coordinate system:

1. Radial Distance (Radius): In the polar coordinate system, the location of a point is determined first by its distance from a fixed point, called the pole, analogous to the origin in the Cartesian coordinate system. This distance is often denoted as \( r \), and it can be thought of as the radius of a circle centered at the pole, with the point lying on the circumference of this circle.

2. Angular Coordinate (Angle): The second characteristic of a point's location in the polar coordinate system is the angle [tex]\( \theta \)[/tex] (theta), which is measured from a fixed direction, typically the positive x-axis of the corresponding Cartesian coordinate system. This angle, usually measured in degrees or radians, determines the direction of the line from the pole to the point.

These two values, [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex], are called polar coordinates, and they provide an alternative to the Cartesian (rectangular) coordinate system for representing points on a plane, particularly useful in scenarios where the geometry or the nature of the problem is radially symmetric, such as in the cases of circular motion or fields (gravitational, electric, etc.).

Answer: The actual distance is 40 miles.

Step-by-step explanation:

First, it’s always easier for the first unit to be 1, so it’s easier to convert. To do get one from 1/4, you would multiply by 4.

1/4 x 4 = 1

However, we all know that if you do something to one side, you must do it to the other side, so we multiply 5 by 4.

5 x 4 = 20.

Your equation know looks like this:

1 inch = 20 miles.

Now, we just multiply both sides by 2, since that the amount of inches we need.

1 x 2 inches = 20 x 2 miles

2 inches = 40 miles

Therefore, the actual distance is 40 miles.

Answer:

The correct answer is a) R = = - [tex]\frac{1}{5}[/tex] [tex]x^{2}[/tex] + 30x; b) $ 1120; c) Maximum quantity is 75 units with maximum revenue being $1125; d) p = $15.

Step-by-step explanation:

Demand equation: p = - [tex]\frac{1}{5}[/tex]x + 30 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 150 ; where p is the price of the product and x is the quantity sold.

a) Revenue function by the problem is given to be R= p × x = - [tex]\frac{1}{5}[/tex] [tex]x^{2}[/tex] + 30x.

b) Revenue at x = 70 is given by 2100 - 980 = $ 1120.

c) For maximizing the R we differentiate it with respect to x and equate it to zero.

⇒ - [tex]\frac{2}{5}[/tex] x + 30 =0

⇒ x = 75.

As the second order derivative is negative at this point, this is the value of x that maximizes the revenue.

Maximum Revenue is at x = 75 and is equal to $1125.

d) Price charged by the company for maximum revenue is $15.

0.8‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

o.8

Step-by-step explanation:

trust me im doing it

Answer:

a subscript n=4.3(n-1)+3.9

Step-by-step explanation:

Answer:

yes

[tex] - \frac{4}{3} p + ( - \frac{2}{5} ) = - \frac{4}{3} p - \frac{2}{5} [/tex]

Step-by-step explanation:

Because ,

[tex]( + ) \times ( - ) = ( - )[/tex]

Answer:i think its 15 because if you take the km numbers and subtract them

Step-by-step explanation:

Answer:

Je pense que la réponse est 15 jours

Step-by-step explanation:

Answer:

The mode is 8

Step-by-step explanation:

Answer: 8 is the mode.

Step-by-step explanation:

Basically when finding the mode you have to find the number that was used the most. So I’m this case 8 was listed twice which makes it the mode!

Answer:

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg

the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon shape are a hexagonal floor tile, pencil cross-section, clock, a honeycomb, etc. It can be either regular (with 6 equal side lengths and equal angles) or irregular (with 6 unequal side lengths and angles).

According to the question,

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2)

                                             = 180(6 - 2)

                                             = 180 × 4

                                             = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 × 240/13 = 2160/13

[tex]\frac{2160}{13}[/tex]  = [tex]166\frac{2}{13}[/tex]

Hence, the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

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Answer: I believe it will take Bobby 2 more hours to hike 12 miles in total it’s 6 hours

Bobby will spend 6 hours hiking on Sunday.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that On Saturday, Bobby spent 4 hours hiking 8 miles. On Sunday, Bobby plans to hike 12 miles.

WE need to find the time he will spend hiking on Sunday.

Then 4 hours hiking =  8 miles.

12 miles = 4/8 x 12

= 1/2 x 12

= 6

Hence, it will take Bobby 2 more hours to hike 12 miles.

thus, he will spend 6 hours hiking on Sunday.

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Answer:

There are a total of  

✔ 12

strawberries.

There are a total of  

✔ 2

people.

The expression to find the mean, or balance point, is  

✔ 12/2

✔ Ona

should give 2 strawberries to  

✔ Barton

for the number of strawberries to be balanced.

Step-by-step explanation:

Barton only has four strawberries and needs two more, while Ona has eight and will share two.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Barton has 4 strawberries and Ona has 8 and they want to redistribute their strawberries so they each have an equal number.

We'll apply division by splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

In order for Ona and Barton to have the same number of strawberries, the total number of strawberries must be divided in two.

=(8 + 4) / 2

= 12 /2

= 6

Thus, Barton only has four strawberries and needs two more, while Ona has eight and will share two.

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Answer:

-2

Step-by-step explanation:

Set up the equation where the number is x

5x=x squared -14

minus the 5x to make a quadratic equation

[tex]x^{2}[/tex]-5x-14=0

factor the equation

(x-7)+(x+2)=0

then you can find the opposites of the consonants,and find the negative answer is -2

Answer: 24 miles

Step-by-step explanation: 12 mph is two times as fast as 6 mph so 6 hours round trip is 2 hours for bike and 4 hours for jogging. You can either plug 2 for 12 (bike) or 4 for 6 (jog) either way you get 24

Answer:

24 miles

Step-by-step explanation:

9514 1404 393

Answer:

  1/15

Step-by-step explanation:

The only area that is a multiple of 4 and 3 is the one marked with a 12. The probability that the spinner will land on any one of the 15 areas is 1/15.

The probability of landing on a number that is a multiple of both 4 and 3 when spinning a spinner with 15 equal areas numbered 1 through 15 is 1/15, since there is only one number that satisfies both conditions, which is the number 12.

To determine the probability that the result is a multiple of 4 and a multiple of 3 when spinning a spinner with 15 equal areas numbered 1 through 15, we first need to find the numbers on the spinner that meet both criteria.

A multiple of 4 and 3 is also a multiple of 12, since lcm(4,3) = 12. The multiples of 12 within the range of numbers 1 through 15 are just the number 12 itself. So there is only one number on the spinner that is a multiple of both 4 and 3.

The probability (P) of landing on that number is:

P = (Number of favorable outcomes) / (Total number of possible outcomes)

P = 1 / 15

Therefore, the probability is 1/15

Answer:

240 people

Step-by-step explanation:

According to the given data,

In each bus,there are total number of 36 students and 4 adults

So, total 40 people are in one bus so...

As, there are six Fields buses

=>40 x 6

=240

Answer: Total 240 people are going on the field trip.

To calculate the total number of people going on the field trip, multiply the number of students and adults by the number of buses and sum the result, resulting in 240 people.

The question relates to the calculation of the total number of people going on a field trip with a given number of students and adults per bus and a total number of buses. To find out how many people in total are going on the field trip, we need to multiply the number of students and adults by the number of buses and add up the results.

Each bus holds 36 students and 4 adults. With 6 buses on the field trip, we calculate the total number of people by multiplying the number of buses by the total capacity per bus (students plus adults): (36 students + 4 adults) × 6 buses.

So, the calculation is as follows:

40 people per bus × 6 buses = 240 people going on the field trip.

Answer:

-7/4

Step-by-step explanation:

We can find the slope of a line passing through two points by using

m = (y2-y1)/(x2-x1)

   = (-2 -5)/(1 - -3)

   = -7/ (1+3)

    = -7/4

Answer:

There are two possibilities for the number. They are 3531902 and 3135902

Step-by-step explanation:

(i) Given that the sum of the digits = 23

(ii) Largest digit is in the hundreds place (5th digit)

(iii) Smollest digit is in the tens place (6th digit)

(iv) Millions and tens thousands digits are the same, (1st and 3rd digit)

(v) Hundreds place is my only composit number(5th digit)

The composite numbers < 10 are 4, 6, 8, 9

(vi) Since the number is an even number, the 7th digit must be either 0,2,4,6,8.

It cannot be 4,6,8 due to case (v) and it cannot be 0 due to case (iii), hence 7th digit is 2 and the 6th digit has to be 0.

(vii) 5th digit has to be either 6,8 or 9, and by making it as 6 or 8, there are less options and it doesn't satisfy other conditions and so 9 is the 5th digit.

The 1 - 4 digits has to be filled by 1,3,5,7. By probability and case (i), there are 2 combinations, they are 3531902 and 3135902.

Answer:

1.25 cm

Step-by-step explanation:

Draw a radius line from the center to one of the top corners.  This forms a right triangle where the hypotenuse is r, the width is 1, and the height is 2−r.  Using Pythagorean theorem:

(2−r)² + 1² = r²

4 − 4r + r² + 1 = r²

5 − 4r = 0

r = 5/4

r = 1.25

Answer:

6800 toothpicks

Step-by-step explanation:

Capacity (how many can be held) is another word for volume.

The equation for volume is

V = lwh

And in the regular-sized box V = 850 toothpicks, so

850 = lwh

We need to double each dimension. Multiply length by 2, width by 2, and height by 2. 2*2*2 = 8, so multiply both sides by 8.

8* 850 = 8 * lwh

6800 = lwh

The jumbo box can hold 6800 toothpicks.

The jumbo box will hold 1700 toothpicks.

The volume of cylinder is given by -

V = πR²h

Given is that there are 850 toothpicks in a​ regular-sized box. A jumbo box is made by doubling all the dimensions of the​ regular-sized box.

The volume {V} cubic units of the box can hold 850 toothpicks.

The volume {1} cubic units of the box can hold (850/V) toothpicks.

The volume {2V} cubic units of the box can hold (850/V x 2V) toothpicks.

(850/V x 2V)

850 x 2

1700

Therefore, the jumbo box will hold 1700 toothpicks.

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Answer:

7231cm^2

Step-by-step explanation:

Please kindly check the attached file for explanation.

Answer:

The area of the octagon stop sign to the nearest square centimetres is 187 cm²

Step-by-step explanation:

The stop sign is in the shape of a regular octagon, therefore, the area is given by the following relation;

Area of regular octagon = 2 × (Side Length)² × (1 + √2)

Where:

Side Length = 38.7 cm

Area of regular octagon = 2 × 38.7 × (1 + √2) = 186.86 cm²

The area of the octagon stop sign = 186.86 cm²

The area of the octagon stop sign to the nearest square centimetres = 187 cm².

Answer:

L = 9

Step-by-step explanation:

Translating this into symbols, we get L = W + 1 and A = 72 = W * L.

Substituting W + 1 for L in the latter equation, we get:

72 = W(W + 1), or:

W^2 + 1W - 72 = 0

This factors into (W + 9)(W - 8) = 0, so that W must be either -9 or +8.

Since W represents width, a physical measurement, we eliminate the negative result and conclude that W = 8 units.  Then L = W + 1 = 9 units.

Note that (8)(9) = 72, as we already know.

The length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Let's denote the width of the rectangle as \( w \) and the length of the rectangle as \( l \).

According to the problem, the length \( l \) is given by:
[tex]\[ l = w + 1 \][/tex]

The area of the rectangle is given by:
[tex]\[ \text{Area} = l \times w = 72 \][/tex]

Substituting the expression for \( l \) into the area formula:
[tex]\[ (w + 1) \times w = 72 \][/tex]

This can be rewritten as:
[tex]\[ w^2 + w - 72 = 0 \][/tex]

We now have a quadratic equation. To solve this, we can use the quadratic formula:
[tex]\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\where \( a = 1 \), \( b = 1 \), and \( c = -72 \).\\[/tex]
Plugging in these values:
[tex]\[ w = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-72)}}{2 \cdot 1} \]\[ w = \frac{-1 \pm \sqrt{1 + 288}}{2} \]\[ w = \frac{-1 \pm \sqrt{289}}{2} \]\[ w = \frac{-1 \pm 17}{2} \][/tex]

This gives us two potential solutions for \( w \):
[tex]\[ w = \frac{16}{2} = 8 \]\[ w = \frac{-18}{2} = -9 \][/tex]

Since a width cannot be negative, we discard \( w = -9 \) and take \( w = 8 \).

Therefore, the width \( w \) is 8 units. Using the relationship \( l = w + 1 \), we find:
[tex]\[ l = 8 + 1 = 9 \][/tex]

So, the length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Answer:

8 units

Step-by-step explanation:

[tex] {(x + 6)}^{2} + {(y - 4)}^{2} = 16 \\ {(x + 6)}^{2} + {(y - 4)}^{2} = {4}^{2} \\ equating \: it \: with \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ {r}^{2} = {4}^{2} \implies \: r = 4 \\ d = 2r = 2 \times 4 = 8 \: units[/tex]

Hence, diameter of the circle is 8 units.

Answer:

1.  [tex]\( f\circ g(x)=0.05x-150[/tex]

2. [tex]\( g\circ f(x)=0.05x-3000[/tex]

3. The first one represents Dale's commission

Explanation:

1. The composition of the function

                                                             [tex]\( f\circ g(x)=f(g(x)) \)[/tex]    

means that you first apply the function g(x) and then f(x) on the output of g(x).

That is:

       [tex]f(g(x)=0.05(x - 3000)[/tex]

       [tex]f(g(x))=0.05x-150[/tex]

2. The composition of the function

                                                             [tex]\( g\circ f(x)=g(f(x)) \)[/tex]                                                                  

means that you first apply the function f(x) and then g(x) on the output of f(x).

That is:

      [tex]g(f(x))=((0.05x)-3000)=0.05x-3000[/tex]

3. Which one represents Dale's commission

To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).

Therefore, you first use g(x).

Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.

Therefore, the composition that represents Dale's commission is the first one:

  [tex]f(g(x)=0.05(x - 3000)[/tex]

       [tex]f(g(x))=0.05x-150[/tex]

Answer:

One centimeter is equal to 10 millimeters. It is also equal to 0.1 decimeter and 0.01 meter. One kilometer contains 100,000 centimeters.

Step-by-step explanation:

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Answer: 100x centimeters

Step-by-step explanation:

We know that 100 centimeters are in every meter. To find the number of centimeters in X amount of meters, we multiply X by 100. Take for example 4 meters. 4 times 100 equals 400. We then know that there are 400 centimeters in 4 meters.

Answer:

10,50,250

Step-by-step explanation:

multiply by 5 each time

Answer: 2, 10, 50, 250, 1250

Step-by-step explanation:

The given sequence is a geometric sequence. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 2

n = 5

T5 = 1250

The 5th term, T5 is expressed as

1250 = 2 × r^(5 - 1)

1250/2 = r^4

625 = r^4

5^4 = r^4

r = 5

The second term is

2 × 5 = 10

The third term is

10× 5 = 50

The fourth term is

50 × 5 = 250