Using prime factorization what is the GCF 3y 2 squared, 24y 3 cubed

Answer:

[tex] {4}^{3} [/tex]

Step-by-step explanation:

your are taking 4 and multiplying it by itself three times hence 4 to the third power

Answer:

4³

Step-by-step explanation:

Answer:

No, the two ratios are not the same.

Step-by-step explanation:

When we are saying "apples to oranges", mathematically it means:

[tex]\frac{Apples}{Oranges}[/tex],

Which could be 2:3 or 3:2, which in fractional from are written as [tex]\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] respectively.

We see that

[tex]\frac{2}{3} \neq \frac{3}{20}.[/tex]

In words the ratio 2:3  says "for every two apples there are three oranges", and 3:2 says "for every three apples there are two oranges". Again we see that  the two sentences are not saying the same thing, therefore the ratio 2:3 is not same as 3:2.  

Final answer:

The ratio 2:3 is not the same as 3:2 because they represent different relationships between the quantities of apples and oranges in a comparative scenario or barter trade. These ratios suggest different terms of trade and would result in different exchange outcomes.

Explanation:

The question is whether the ratio 2:3 is the same as 3:2 when comparing apples to oranges. To understand this, we must recognize that a ratio represents a relationship between two quantities, expressing how many times one value contains the other or is contained within it. In the context of a fruit bowl, a ratio of 2:3 would mean for every 2 apples, there are 3 oranges, while the ratio 3:2 means for every 3 apples, there are 2 oranges. Therefore, these two ratios are not the same as they represent different relationships between the quantities of apples and oranges.

Considering ratio comparisons like in barter trading, the terms of trade are critical. If 2 bushels of apples can be traded for 3 bushels of oranges, that is a 2:3 apple-to-orange trade ratio. On the other hand, if we reverse the ratio to 3:2, it would mean something quite different for trade or value comparisons. Specifically, you'd need 3 bushels of apples to get 2 bushels of oranges.

It's essential to compare apples to apples; comparative statistics are only useful when the comparison is logical and applicable. The ratios 2:3 and 3:2 convey different terms and thus would yield different outcomes in any exchange or comparative scenario.

Answer:

x² - 8x + 12 = 0

(x - 6)(x - 2) = 0

x = 2, 6

f(4) = -4

Plot (0, 12), (2, 0), (4, -4), (6, 0), and (8, 12) on the graph. Then draw a smooth curve that goes through these points.

Answer:3

Step-by-step explanation:

Answer:

x= -3 and x= -2

Step-by-step explanation:

(x+3)(x+2)

Hence, the zeroes are:

-3 and -2

Hoep this helps!

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Answer:

x=-12

Step-by-step explanation:

-18=x-6

-18+6=x--6+6

-12=x

p - 62%p = %=$159.60

p - 62p/100 = $159.60

100p - 62p = $15960

38p = $15960

p = $15960/38

p = $420

Area of a regular pentagon with a side of 10in  is 172

Step-by-step explanation:

Given:

Side of the regular pentagon = 10in

To Find:

Area of the regular pentagon=?

Solution:

We know that ,

[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)

Step 1: Finding the Area of the triangle

we know that in a right angle triangle, there are base, height and hypotenuse  [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]

So, from the above equation,  

[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]

[tex]height=\frac{5}{tan(36)}=6.88[/tex]

area of right angle triangle

=> [tex]\frac{1}{2}\times base \times height[/tex]

=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]

=> 17.20

Area of the triangle =2 x area of right angle triangle

Area of the triangle =2 x  17.20

Area of the triangle= 34.40

Step 2: Finding the Area of the pentagon

Substituting the values in (1)

[tex]Area of Pentagon = 5\times 34.40 [/tex]

Area of Pentagon= 172

Answer:

Yes the mean is greater than the median

Step-by-step explanation:

To find the mean of numbers, you add all of them and divide them by how many there are in total.

75+80+81+96+100= 432

There are five numbers so divide the total by 5.

432÷5= 86.4

That is your mean.

The median is the one in the middle. There are five numbers, so the one in the middle is 81.

The mean is 86.4 and the median is 81.

Answer:

the mean is greater

Step-by-step explanation:

well mean is average so lets do that first

to find the mean, you add all of the percentages up and divide it by the amount of percentage

75 + 80 + 81 + 96 + 100 = 155 + 177 + 100 = 432

and now you divide 432 by 5 to get 86.4

so the mean is 86.4

and the median is the middle:

75 80 81 96 100

           ↑

81 is the median since its in the middle

86.4 > 81

so the mean is greater than the median

Answer:

p=ak^t

p1=491272*k^0

p2=782341*k^10

782341/491272 = k^10

k=1.047629

growth rate is 4.7629%

2012: predicted population is 491272*1.047629^12=858,642 people

1245863=491272*1.047629^t

1.047629^k=2.5363599

ln both sides is k ln 1.0476=ln 2.5363

t=20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272*1.0476^17 or 1083552, or more than actual, so the rate of growth is slowing down.

The required exponential growth rate, k is 4.7629%

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function will be as

p=a[tex]k^t[/tex]

p₁=491272*k⁰

p₂=782341*k¹⁰

782341/491272 = k¹⁰

k = 1.047629

So, the growth rate is 4.7629%

2012: the predicted population is 491272 × 1.047629¹² =858,642 people

1245863=491272 × [tex]1.047629^t[/tex]

[tex]1.047629^k[/tex] = 2.5363599

ln both sides is k ln 1.0476 = ln 2.5363

t = 20.000 years.

Rule of 72 would say 72/4.76 or 15.12 years for doubling

14.90 years

2017 predicted is 491272 × 1.0476¹⁷ or 1083552, or greater than the real rate of increase, hence the rate of growth is decreasing.

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The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

Step-by-step explanation:

Let us revise some facts about parallel lines

The equations of two parallel lines have:

The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept

The given line has equation 5x - 2y = 10

Put it in the form of y = m x + b to find its slope

∵ 5x - 2y = 10

- Subtract 5x from both sides

∴ -2y = 10 - 5x

- Divide to sides by -2

∴ y = -5 + [tex]\frac{5}{2}[/tex] x

∴ y =  [tex]\frac{5}{2}[/tex] x - 5

- The value of m is the coefficient of x

∴ m = [tex]\frac{5}{2}[/tex]

∴ The slope of the given line is [tex]\frac{5}{2}[/tex]

∵ Parallel lines have same slopes

∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]

- Substitute the value of m in the form of the equation

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + b

To find b substitute x and y in the equation by the coordinates of any point lies on the line

∵ The parallel line passes through point (3 , -5)

- Substitute x and y by the coordinates of the point (3 , -5)

∵ x = 3 and y = -5

∴ -5 = [tex]\frac{5}{2}[/tex] (3) + b

∴ -5 = [tex]\frac{15}{2}[/tex] + b

- Subtract [tex]\frac{15}{2}[/tex] from both sides

∴ b = [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]

∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

The equation of the parallel line in slope-intercept form is;

y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]

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Answer:

C. Parallel

D. Segment

F. Ray

Explaination:

Answers A, E, & G (line, point, & plane) are undefined terms.

Answer:

A

Step-by-step explanation:

The transformation performed on triangle 1 to create triangle 2 is a translation by the vector (-4, -4), which means each point was moved 4 units to the left and 4 units down.

The transformation used can be determined by observing the differences between corresponding coordinates in the two triangles. If we subtract the coordinates of A′(2,2) from A(6,6), for instance, we get a change of -4 in the x-direction and -4 in the y-direction. Similarly, subtracting B′(4,3) from B(12,9) and C′(3,2) from C(9,6) results in changes of -8 and -6 in the x-direction and -6 and -4 in the y-direction, respectively.

This means that every point on triangle 1 was moved 4 units to the left and 4 units down to create triangle 2. Thus, the transformation that took place is called a translation by the vector (-4, -4).

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Answer:

a = 108° and b = 144°

Step-by-step explanation:

The opposite angles of a rhombus are the same and the sum of all the angles of the rhombus is 360°.

So, from the given diagram of the rhombus we can write  

2b + 2× 36 = 360

⇒ 2b = 360 - 72 = 288

⇒ b = 144° (Answer)

Again, the each angles of a pentagon is given to be a.

Hence, we can write 3a + 36 = 360

⇒ 3a = 324

⇒ a = 108° (Answer)

Answer:

-216

Step-by-step explanation:

Negative times positive is negative.

27 * 8 = 216

Answer is negative, so

-27 * 8 = -216

Answer:

-216

Step-by-step explanation:

Write the problem as a mathematical expression. ( − 27 ) ⋅ ( 8 )

multiply -27 by 8

Answer:

4^5x-5

Step-by-step explanation:

4^5x-7/4^-2

=4^5x-5

The expression 4⁵ × 4⁻⁷ divided by 4⁻² simplifies to 1 by using the properties of exponents. First, add the exponents in the numerator, then subtract the exponents for division, resulting in 4⁰, which equals 1.

We need to simplify the expression:

4⁵ times 4⁻₇ ext{ divided by } 4⁻²

To simplify, let's first combine the powers of 4 in the numerator:

= 4⁵ times 4⁻⁷

= 4⁽⁵⁺⁽⁻⁷⁾⁾

= 4⁻²

= 4⁻² ext{ divided by } 4⁻²

= 4⁽⁻²⁻⁽⁻²⁾⁾

= 4⁽⁻²⁺²⁾

= 4⁰

4⁰ = 1

Therefore, the given expression simplifies to 1.

Let n be the current term and n+1 be the next term

Then the pattern is: n+1 = n * 5

Step-by-step explanation:

Given series is:

0.13, 0.65, 3.25, 16.25

We can find the ratio between consecutive numbers to find the pattern

So,

[tex]Ratio = \frac{0.65}{0.13}\\=5[/tex]

We can see that multiplying the previous term with 5 gives us the next term

0.13 * 5 = 0.65

0.65 * 5 = 3.25

3.25 * 5 = 16.25

Let n be the current term and n+1 be the next term

Then the pattern is: n+1 = n * 5

Keywords: Pattern, Sequence

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Answer:

2

Step-by-step explanation:

Because the # ends in a even number, it can be divisible by 2

Answer:

[tex]x^{2} =1, then\ x=1[/tex] is NOT true.

Step-by-step explanation:

1.

[tex]If\ x=1, then\ x^{2} =1[/tex] ......True

( 1 )² = 1

2.

If [tex]x^{2} =1, then\ x=1[/tex] ........ NOT True

∴ x =± 1     .........this is correct

3.

[tex]If\ x=-1, then\ x^{2} =1[/tex] ......True

( -1 )² = 1

4.

x2 = 1 if and only if x = 1 or x = -1. .........True

( 1 )²  = 1

( -1 )² = 1

Answer:

9

Step-by-step explanation:

It saying 3 times to the power of 2

or

3 squared

so basically it's saying

3^3=9

Answer: 12.69 miles approx

Step-by-step explanation:

let x represent the number of miles traveled

1.75 + 0.65x = 10

0.65x  = 8.25

x = 12.69 miles approx

5,998.7714 ft

Step-by-step explanation:

Well find x in the illustration;

First To find the opposite side of the right-angled triangle we'll using tangent of the given angle

Tangent Ф = Length of the opposite side / Length of the adjacent side

Tan 43 = h / 6390

h = Tan (43) * 6390

h = 5,958.7714 ft

Then we'll add the height of the beacon which is 40 ft above ground;

x = 5,958.7714 ft + 40 ft

x = 5,998.7714 ft

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Answer:

44

Step-by-step explanation:

20 percent less than 220

Answer:

The answer to this question is S=44

Step-by-step explanation:

Answer:

The monthly payment for the loan amount for 20 years is $806.167

Step-by-step explanation:

The principal loan amount= $ 50,000

The rate of interest = 7 %

the time period of loan = 20 years = 20 × 12 = 240 months

let the amount after 20 years = $ A

From Compounded method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm Time}[/tex]

or, A = 50,000 × [tex](1+\dfrac{\textrm 7}{100})^{\textrm 20}[/tex]

or, A = 50,000 × [tex](1.07)^{20}[/tex]

Or, A = 50,000 × 3.8696

∴ Amount = $ 193,480

So, The amount after 20 years = $ 193,480

The monthly payment amount = $ [tex]\frac{193480}{240}[/tex] = $ 806.167

Hence The monthly payment for the loan amount for 20 years is $806.167 Answer

Answer:

x = 7

Step-by-step explanation:

x + 7 = 14

Subtract 7 from both sides

x = 14 - 7 = 7

Answer: the answer is 7

Step-by-step explanation:

Answer:

y = -x + 0

slope intercept: 0

Step-by-step explanation:

You would start at the origin, since your slope intercept is 0. The slope, -1 (since -x is the same as -1x), is telling us the line will be negative, so the line you are graphing will be heading up one space at a time towards the left, up 1 and sideways 1. Rise over Run.

Answer:

C, because

-32 x seconds since she jumped + 14000

because 14000 would be 14000 units above 0, and -32 represents the seconds she had jumped, which would basically be -32+14000, which is the same as saying 14000 - 32.

Answer:14 and 5

Step-by-step explanation:

Simplifying

4(0.2x + -5) = 12

Reorder the terms:

4(-5 + 0.2x) = 12

(-5 * 4 + 0.2x * 4) = 12

(-20 + 0.8x) = 12

Solving

-20 + 0.8x = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20' to each side of the equation.

-20 + 20 + 0.8x = 12 + 20

Combine like terms: -20 + 20 = 0

0 + 0.8x = 12 + 20

0.8x = 12 + 20

Combine like terms: 12 + 20 = 32

0.8x = 32

Divide each side by '0.8'.

x = 40

Simplifying

x = 40

Answer:

6000

Step-by-step explanation:

Each mp3 sells at $120 per mp3 player multiply that by 100 its $12000

It cost them $45 per mp3 to be made multiply that by 100 its $4500 then add the $1500 for the week and its $6000

$12000-$6000=$6000

They make a profit of $6000 in a week

The company would make a profit of $6,000 from selling 100 MP3 players in one week after subtracting the total costs of $6,000 from a total revenue of $12,000.

The company's profit when selling 100 MP3 players in one week can be calculated by subtracting the total costs from the total revenue. First, we calculate the total revenue by multiplying the selling price of $120 per MP3 player by the number of players sold, which is 100. This results in a total revenue of $12,000 (120 x 100).

Next, we calculate the total costs, which include a fixed overhead of $1,500 per week and a variable cost of $45 per MP3 player. For 100 players, the variable cost sums up to $4,500 (45 x 100). Therefore, the total costs amount to $6,000 ($1,500 + $4,500).

To find the profit, we subtract the total costs from the total revenue:

Total Revenue = 100 x $120 = $12,000

Total Costs = $1,500 (fixed) + 100 x $45 (variable) = $6,000

Profit = Total Revenue - Total Costs = $12,000 - $6,000 = $6,000

Therefore, the company would make a profit of $6,000 if it sold 100 MP3 players in one week.