Points A and B are on a circle with centre O and radius n so that AOB = (360/n). Sector AOB is cut out of the circle. Determine all positive integers n for which the perimeter of sector AOB is greater than 20 and less than 30

Answer:

85,100

Step-by-step explanation:

85 <= (81 + 89 + x) / 3 <=90

255 <= 81 + 89 + x <=270

255 <= 81 + 89 + x <=270

174 <= 89 + x <= 189

85 <= x <= 100

x = 85, 100

To find the greatest common factor of a polynomial, find a number that all of its coefficients are divisible by, for example, the GCF of an 8x 2 + 4x + 2 is 2 because all of the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x2 + 2x + 1).

A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. The GCF of 12, 20, and 24 is 4 because it is the largest.

To find the greatest common factor of a polynomial,  find a number that all the coefficients of the polynomial are divisible by i.e. the GCF of a 8x^2 + 4x + 2  is 2 because all the coefficients (8, 4, 2) are divisible by 2 and the expression simplifies to 2(4x^2 + 2x + 1).

The GCF can be smaller than the smallest coefficient, for example 20x^2 + 15x + 10 (GCF is 5, smallest coefficient is 10) and 5 < 10. However it cannot be larger than the smallest coefficient.

Therefore the smallest coefficient should be larger than or equal to the GCF in order to be divisible.

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The measure of angles JKL and LKM are 100° and 40° respectively.

A supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles JKL, LKM and JKM are not supplementary angles:

m∠JKL + m∠LKM = m∠JKM

Substituting the given parameters into the formula, we have;

4x° + (2x − 10)° = 140°

6x° − 10 = 140°

6x° = 140° + 10°

6x° = 150°

x° = 150/6

x = 25°

For angle JKL, we have:

m∠JKL = 4x

m∠JKL = 4(25)

m∠JKL = 100°.

For angle LKM, we have:

m∠LKM = 2x − 10

m∠LKM = 2(25) − 10

m∠LKM = 50 − 10

m∠LKM = 40°

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Answer: 3.14 * 3^2 = 28.26

Answer:28.26

Step-by-step explanation:

Answer: 22, 12 or 33

Step-by-step explanation:

11cm is the base and 4 is the height your answer is 22 if 6cm is the base and 4 is the height your answer is 12 and if 6 is your height and 11 is your base your answer is 33

The actual length of surfboard based on the information is 6 3/8 feet.

From the information illustrated, the drawing of a surboard in a catalog shows it's length as 8 1/2 inches.

The actual length of surfboard if 1/2 inch length on the drawing correspond to 3/8 foot of actual length will be illustrated thus:

Let the actual length be x.

1/2 / 3/8 = 8 1/2 / x

0.5 / 0.375 = 8.5 / x

Cross multiply

0.375 × 8.5 = 0.5x

x = (0.375 × 8.5) / 0.5

x = 6.375 = 6 3/8 feet

The length is 6 3/8 feet.

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The width of prism is 9yards.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.

Given Data

Rectangular prism:

Volume = 990 yd³

Length = 10 yards

Height = 11 yards

Volume of rectangular prism = Length× Height× Width

990 = 10 ×11× width

Width = [tex]\frac{990}{10(11)}[/tex]

Width = 9

The width of prism is 9yards.

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The worth of the horse is 1800 dollars

Given that a cowboy worked for one year for 19,200 plus a horse.

After 7 months, he quit and was paid 10,450 but got to keep the horse.

We need to find the worth of the horse.

Here, the horse is part of the payment in total, so it has to be used as a variable when setting up the proportion.

Let us consider the net worth of the horse to be H

solving for H,

[19,200 + H] / 12 = [10,450 + H] / 7

Now, cross multiply

134,400 + 7H = 125,400 + 12H

134,400 - 125,400 = 12H - 7H

9,000 = 5H

H = 9,000 / 5

H = $1,800

Hence, the net worth of the horse, H is $1,800.

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Answer:

[tex]\frac{(x+3)(x-1)}{x}[/tex]

Step-by-step explanation:

So the first thing you want to do is factor out the polynomials.

[tex]x^2+4x+3 ; (x+3)(x+1)[/tex]

[tex]x^2+x; x(x+1)[/tex]

[tex]2x^2-3x+1; (2x-1)(x-1)[/tex]

Once you have factored these out, you can write out the division using keep-change-flip;

[tex]\frac{(x+3)(x+1)}{2x-1}*\frac{(2x-1)(x-1}{x(x+1)}[/tex]

Before trying to multiply all of the factors, rule out factors that appear both in the numerator and the denominator;

[tex]\frac{(x+3)}{1}*\frac{(x-1)}{x}[/tex]

Now you can multiply the fractions and receive [tex]\frac{(x+3)(x-1)}{x}[/tex]

Answer:

$75.6

Explanation:

If the original cost was $70 and it was marked up 20%, the price after this is calculated as:

$70 + $70(0.2) = $70 + $14 = $84

Where $70(0.2) = $14 is the amount added to the original when it is marked up 20%.

Then, it was discounted 10%, we get that the selling price is

$84 - $84(0.1) = $84 - $8.4 = $75.6

Where $84(0.1) = $8.4 is the discount made on the initial price.

Therefore, the answer is $75.6

The inequality that represents the problem "6 less than a number greater than four" is x - 6 > 4.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Consider the statement,

6 less than a number greater than four.

Let x be the number.

The symbol " > " can be represented as a number greater than another.

Then 6 less than a number greater than 4 can be represented as:

x - 6 > 4

The inequality x - 6 > 4 can be represented for the problem " 6 less than a number greater than four".

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The conference room is 21 feet long and 14 feet wide.

Given that, in a blueprint of a building, a conference room is 6 inches long and 4 inches wide.

Scale factor is a number by which the size of any geometrical figure or shape can be changed with respect to its original size. It is used to draw the enlarged or reduced shape of any given figure and to find the missing length, area, or volume of an enlarged or reduced figure.

Here, the scale factor is 2 inches : 7 feet.

Now, length = 6 inches

= 2 inches + 2 inches + 2 inches

= 7 feet + 7 feet + 7 feet

= 21 feet

Width = 4 inches

= 2 inches + 2 inches

= 7 feet + 7 feet

= 14 feet

Therefore, the conference room is 21 feet long and 14 feet wide.

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H   E

2   18

4   36

6   54

8   72

10  90

H = Hours

E = Earned

These are all equivalent.

If you want to do this on your own, write out the multiplication then remove odd ones, that's exactly what I did.

The solution are

The answer is B and D.

The probability that a randomly chosen item from this assembly line is defective is 0.125.

Probability simply means the likelihood of the occurence of an event.

From the information, the review of her record reveals that she accepts only 8% of all defective items and it was also found that 1% of all items from the assembly line are both defective and accepted by the inspector.

Therefore, the probability will be:

= Percentage of detectives / Percentage of defective accepted

= 1% / 8%

= 0.01 / 0.08

= 0.125

The probability is 0.125.

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[tex]\displaystyle\\Answer:\ 119\ \boxed{\frac{4}{7} }[/tex]

Step-by-step explanation:

[tex]\displaystyle\\P=10\frac{1}{7}+12\frac{2}{7}+15\frac{3}{14} +24\frac{1}{14} +12\frac{2}{7} +10\frac{1}{7}+35\frac{3}{7} \\\\P=(10\frac{1}{7}+12\frac{2}{7}+12\frac{2}{7} +10\frac{1}{7}+35\frac{3}{7})+(15\frac{3}{14} +24\frac{1}{14}) \\\\P=(\frac{71}{7} +\frac{86}{7} +\frac{86}{7}+\frac{71}{7} +\frac{248}{7} )+(\frac{213}{14}+\frac{337}{14})\\\\[/tex]

[tex]\displaystyle\\ P=\frac{71+86+86+71+248}{7} +\frac{213+337}{14} \\\\P=\frac{562}{7} +\frac{550}{14} \\\\P=\frac{562}{7}+\frac{2(275)}{2(7)} \\\\P=\frac{562}{7} +\frac{275}{7}\\\\P=\frac{562+275}{7} \\\\P=\frac{837}{7}\\\\P=119\frac{4}{7}[/tex]

let's firstly convert the mixed fractions to improper fractions and then add them up.

[tex]\stackrel{mixed}{10\frac{1}{7}}\implies \cfrac{10\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{71}{7}} ~\hfill \stackrel{mixed}{12\frac{2}{7}}\implies \cfrac{12\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{86}{7}} \\\\\\ \stackrel{mixed}{15\frac{3}{14}}\implies \cfrac{15\cdot 14+3}{14}\implies \stackrel{improper}{\cfrac{213}{14}} ~\hfill \stackrel{mixed}{24\frac{1}{14}}\implies \cfrac{24\cdot 14+1}{14}\implies \stackrel{improper}{\cfrac{337}{14}}[/tex]

[tex]\stackrel{mixed}{35\frac{3}{7}}\implies \cfrac{35\cdot 7+3}{7}\implies \stackrel{improper}{\cfrac{248}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{71}{7}+\cfrac{71}{7}+\cfrac{86}{7}+\cfrac{86}{7}+\cfrac{213}{14}+\cfrac{337}{14}+\cfrac{248}{7}\hspace{5em}\textit{so we have an LCD of 14} \\\\\\ \cfrac{(2)71+(2)71+2(86)+2(86)+(1)213+(1)337+2(248)}{14} \\\\\\ \cfrac{1674}{14}\implies \cfrac{837}{7}\implies 119\frac{4}{7}[/tex]

Answer: 3 4/25

Step-by-step explanation:

The equation of line that passes through the point (-1,4) and slope = -3 , in slope intercept form is  y = (-3)x + 1 .

The Slope Intercept Form of the line is represented by

y=mx+c

where , m is the slope

and

c is the y-intercept

In the question ,

it is given that

the slope of the line is = -3 .

So, the equation of line becomes

y = (-3)x+c    ...(i)

As this line passes through (-1,4) , it will satisfy the equation of line

Substituting the values x as -1 , y as 4 , in equation(i) ,

we get

4 = (-1)(-3) + c

4 = 3 + c

c = 4-3

c = 1

So, the y intercept(c)  is 1 .

Hence the equation of line becomes y = (-3)x + 1 .

Therefore , the equation of line that passes through the point (-1,4) and slope = -3 , in slope intercept form is  y = (-3)x + 1 .

The given question is incomplete , the complete question is

write the equation of line in slope intercept form that passes through the point (-1,4) and has slope as -3 .

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The publisher should produce and sell 2356 books so that the production costs will equal the money from sales.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $24,149. The variable costs will be $11.50 per book. The publisher will sell the finished product to bookstores at a price of $21.75 per book.

Assume the number of books to be printed be [x].

Then, we can write -

24149 + 11.50x = 21.75x

21.75x - 11.5x = 24149

10.25x = 24149

x = 2356 books

Therefore, the publisher should produce and sell 2356 books so that the production costs will equal the money from sales.

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The domain is a set tht contains all possible x-values in a relataion or a function. In this problem, we just need to know what the x-coordinates are to be able to identify the domain.

Let us first list down the coordinates of the given points. We have:

The x-coordinates are: -3, -1, 1, 3, and 6.

So the domain is: {-3, -1, 1, 3, 6}. The answer is option C.

Answer: 3.86

Step-by-step explanation:

Here we will show you how to calculate 9 divided by 7/3. We will give you the answer in fraction form and decimal form.

Here is 9 divided by 7/3 displayed mathematically:

9

 ÷    

7

3

The numbers in 9 divided by 7/3 are labelled below:

9 = whole number

7 = numerator

3 = denominator

To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:

9 x 3

7

 =  

27

÷

7

Thus, the answer to 9 divided by 7/3 in fraction form is:

27

÷

7

To make the answer to 9 divided by 7/3 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

27 / 7 = 3.86

The answer is rounded to the nearest two decimal points if necessary.

27/7 is an improper fraction and should be written as 3 6/7.

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9 divided by 7/3 is equal to 27/7 or 3 6/7.

To divide 9 by 7/3, we can rewrite the division as a multiplication by the reciprocal of the divisor.

The reciprocal of 7/3 is obtained by flipping the fraction, which means interchanging the numerator and denominator.

Therefore, the reciprocal of 7/3 is 3/7.

So, we can rewrite the division as:

9 ÷ (7/3) = 9 × (3/7)

To multiply fractions, we simply multiply the numerators together and the denominators together.

So, multiplying 9 and 3 gives us 27, and multiplying 7 and 1 gives us 7.

Therefore:

9 ÷ (7/3) = 27/7

The result, 27/7, is an improper fraction. It means we have 27 parts divided into 7 equal parts.

However, if you prefer, we can also express the result as a mixed number, which consists of a whole number and a proper fraction.

To convert 27/7 into a mixed number, we divide the numerator (27) by the denominator (7).

The quotient is the whole number part, and the remainder becomes the numerator of the proper fraction.

27 ÷ 7 = 3 remainder 6

So, the mixed number representation of 27/7 is:

27/7 = 3 6/7

Therefore, 9 divided by 7/3 is equal to 27/7 or 3 6/7.

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No height value is given, thus the volume cannot be found. The equation is:

1/3πr²h, r = d/2
1/3π(d/2)²h
1/3(3.14)(3.5/2)²h
1/3(3.14)(1.75)²h
1/3(3.14)(3.0625)h
1.053(3.0625)h
3.22h

The volume of the cone is approximately 3.22h.

Answer: A

Step-by-step explanation:

First you multiply 138 x 14 =1932 then divide 28 then you have 69 then add 209 then you have 278.

sorry if its wrong.

Answer:

A) 278

Step-by-step explanation:

Use PEMDAS for order of operations:

Start with anything in parentheses, and then operations are performed on any exponents (also called powers). Next, perform operations on multiplication or division from left to right. Finally, operations on addition or subtraction are performed from left to right.

The value of V illustrated in the ratio V : 33= 7 : 11 is 21.

It should be noted that a ratio is simply used to show the relationship between the variables and illustrate the comparison.

In this case, the value of V can be illustrated as:.

V/33 = 7/11

Cross multiply

11V = 33 × 7

V = (33 × 7) / 11

V = 21

Therefore, V is 21.

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From the statements that are provided in the question, the statement that best describes when the plans  is Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

A word problem are sentences describing a real-life scenario where a problem needs to be solved by mathematical calculation.

Ideally, for the best health benefits, such as increasing strength and aerobic and reduction in heart diseases, it is suggested to do a combination of strength training and aerobic training for at least five times a week.

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week. is the correct statement

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David and Daniel were given $12 each in the beginning as the given condition.

What are conditions?

Let david and daniel were given = $x each as per statement.

at the end david had = 2x

and daniel had= x+12

Condition is given that : in the end,  the boys still have the same amount of money.

Therefore, equating both what David and Daniel had

2x=x+12

x=12

David and Daniel were given $12 each in the beginning as the given condition.

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