Factor the expression using the greatest common factor.
-12z+16z4 - 3z²

they are called perfect square numbers

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196 heres some hope that helps!

Function representing number of followers for different situation are:

a. Number of followers in 't' years N = 500,000 ( 1 + 19/100 )^t.

b. Number of people following in 2019 are 1,690,000 ( nearest thousand )

Total number of followers of social media website in 2012 = 500,000

Followers increases by 19% every year.

let 'N' represents the number of followers.

a. Function to represents the number of follower in 't' years after 2012 is:

N = 500,000 ( 1 + 19/100 )^t

b. Number of people following website in 2019 is:

t = 2019 -2012

 = 7

N = 500,000 ( 1 + 19/100 )^7

⇒ N = 500,000 ( 1.19 )^7

⇒ N = 500,000 × 3.379

⇒ N= 1689657.7

⇒ N = 1,690,000 ( nearest thousand )

Therefore, the number of followers represented for different condition are:

a. Function to represent number of followers in 't' years is

N = 500,000 ( 1 + 19/100 )^t

b. Number of followers in 2019 are 1,690,000 ( nearest thousand )

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1) The slope of the regression line is 35
2) The correlation coefficient is 0.95
3) Employees’ annual earnings are strongly related to their tenure
4) Employee earnings increase with tenure.

The slope of the regression line in this data set is close to 35. In order to determine the slope, two points must be identified that are either on or near the line.

We have the following two points;

(1, 175) and (2.5, 225)

slope = (change in y) / (change in x)        

          = (225-175)/(2.5-1) = 33.33

This is close to 35.

2) The correlation coefficient of the annual earnings and tenures of employees at Stan & Earl Corp is almost 0.95. This value, known as the coefficient of correlation, shows the level of connection between two variables and the direction of their linear relationship. The scatter-plot demonstrates a strong positive relationship between the employees' annual earnings and their tenure.

Hence the correlation coefficient is close to 0.95.

3) The data suggests a strong connection between an employee's annual earnings and their tenure. The correlation coefficient was estimated to be close to 0.95, which represents a significant positive relationship between the two variables. As a result, it can be concluded that there is a clear relationship between an employee's annual earnings and the length of time they have been with the company.

4) As employees' tenure with the company increases, their annual earnings also increase. This can be deduced from the slope of the regression line which was calculated to be close to 35, indicating a positive relationship between the two variables. The positive correlation coefficient supports this

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The regression line for this data set has a slope close to m = (5.5,35,-50,-2.5) , and the correlation coefficient is close to (0.20,0.40,0.75,0.95) .

Based on this information, we can conclude that employees’ annual earnings are (strongly related, moderately related, weakly related, not related) to their tenure. Employee earnings (increase with, decrease with, are not affected by) tenure.

It takes 3.9 years long the person have to leave the money in the bank until it reaches 11300 dollars

Suppose that the initial amount of something is P.

Let after one unit of time, it increases by R% [per unit time] end compounds on the resultant total of that quantity, then, after T such units of time, then the quantity would increase to:

[tex]A=P\left(1+\frac{R}{100}\right)^{nT}[/tex]

A person invests 7000 dollars in a bank. The bank pays 6.25 % interest compounded semi-annually.

Given that:

Principal =7000

Interest (r) = 6.25 % compounded semi annually

As compounded semi annually n = 2

Calculate time, t, if final amount A = 11300

Using the compound interest formula

[tex]A=P\left(1+\frac{R}{100}\right)^{nT}[/tex]

A = Final amount

n = number of times interest is applied per period

11300 = 7000 [tex](1+0.0625)^{2t[/tex]

113 = 70 [tex](1.0625)^{2t[/tex]

1.614 =  [tex](1.0625)^{2t[/tex]

Take the log of both sides

log 1.614 = 2t log 1.0625

0.2079 = 2t (0.0263)

0.2079 = 0.0526 t

t = 3.9

Time period will be 3.9 years.

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The associative property works with addition and multiplication, but not division and subtraction because the grouping of terms affects the result of the operation.

A mathematical concept known as the associative property governs the addition and multiplication of three or more terms. It claims that the way the phrases are grouped has no bearing on how the operation turns out.

This implies that the same result may be obtained by adding or multiplying three or more terms in any sequence. Nevertheless, division and subtraction are not covered by the associative property.

We should take a gander at the accompanying cases to show how expansion and increase are connected:

Example 1: Addition

(2 + 3) + 4 = 2 + (3 + 4)

5 + 4 = 2 + 7

9 = 9

Example 2: Multiplication

(2 × 3) × 4 = 2 × (3 × 4)

6 × 4 = 2 × 12

24 = 24

We can observe from both cases that the word grouping has no impact on the operation's outcome. The associative characteristic, therefore, applies to both addition and multiplication.

The associative characteristic, however, does not apply to division and subtraction. For instance:

(8 ÷ 4) ÷ 2 ≠ 8 ÷ (4 ÷ 2)

2 ÷ 2 ≠ 8 ÷ 2

1 ≠ 4

We can observe from this example that the term grouping has an impact on the operation's outcome. The associative property does not, therefore, apply to division.

The associative property does not also hold for subtraction. For instance:

(8 - 4) - 2 ≠ 8 - (4 - 2)

4 - 2 ≠ 8 - 2

2 ≠ 6

In this example, we can again see that the grouping of terms affects the result of the operation. Therefore, the associative property does not apply to subtraction.

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The ordered pair (5,200) represent in this situation is a straight line passing through y = 20x.

Having zero width and extending on all sides, a line is a geometry object. An unbent line is, to put it simply, a straight line. A straight line is one that doesn't curve and extends indefinitely on both sides.

We have ordered pair (5,200),

x = 5

so y = 200

so y = 5 x 40

so we have  y = 40x

This is a straight line passing through the origin on the point  (5,200), through any point.

An ordered pair consists of two items. Because the ordered pair differs from the ordered pair unless a = b, the order of the objects in the pair is important. Other names for ordered pairs include 2-tuples and 2-length sequences.

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Complete question:

What does the ordered pair (5, 200) represent in this situation?

Answer: 8.5 L

Step-by-step explanation: I looked it up l o l

Answer:

Your answer is: 8.51718

Step-by-step explanation:

There's 1.057 quarts in a liter. You multiply that by 9 to get 8.51718.

The optimal solution amount will increase by the amount that the additional 10 units of the second constraint can be used to benefit the overall solution.

The optimal solution amount will increase with the addition of 10 units to the second constraint. This is because the additional 10 units can be used to benefit the overall solution by providing more of the resources that are necessary to reach the optimal solution. For example, if the second constraint is a limit on the amount of a certain resource that can be used, then the additional 10 units can be used to increase the amount of resources available, which can lead to a better overall solution. In addition, the additional 10 units can also be used to increase the efficiency of the solution, by allowing the solution to use the same amount of resources more efficiently.

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Answer:

10x+15y-10

Step-by-step explanation:

5(2x+3y-2)

=10x+15y-10

Answer:

[tex]y=\dfrac{1}{8}x^2[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

Given that the vertex of the parabola is (0, 0):

Substitute the values of h and k into the formula:

[tex]y=a(x-0)^2+0[/tex]

[tex]y=ax^2[/tex]

Given that the parabola passes through the point (12, 18), substitute this into the equation and solve for a:

[tex]18=a(12)^2[/tex]

[tex]18=144a[/tex]

[tex]a=\dfrac{18}{144}[/tex]

[tex]a=\dfrac{1}{8}[/tex]

Therefore, the equation of the parabola in vertex form is:

[tex]y=\dfrac{1}{8}x^2[/tex]

Answer: 42 = 8w + 15

Step-by-step explanation:

Multiplying the length and width together, we get 3m x 4m = 12m². This means that the area of the rectangle is 12 square meters.

Area = Length x Width

Area = 3m x 4m

Area = 12m²

To solve for the area of a rectangle, you will need to use the formula Area = Length x Width. In this example, the length of the rectangle is 3 meters and the width is 4 meters. To calculate the area of the rectangle, you will need to multiply the length and width together. 3m x 4m = 12m². Therefore, the area of the rectangle is 12 square meters.

The area of a rectangle is calculated by multiplying the length and width of the rectangle together. The formula used to calculate the area of a rectangle is Area = Length x Width. To put this formula into practice, lets use the example of a rectangle that is 3 meters long and 4 meters wide. Multiplying the length and width together, we get 3m x 4m = 12m². This means that the area of the rectangle is 12 square meters. This formula can be used for any rectangle, as long as the length and width are known. Knowing the area of a rectangle can be useful for many purposes, such as calculating the amount of paint or carpeting needed to cover the surface area of the rectangle.

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Answer:

1. rest

2. dynamics

3.  measure

4. chord

5. staff

6. double bar line

7. bar line

8. mezzo-piano

9. fermata

10. allegro

11. articulation

12. moderato

13. tenuto

14. larghetto?

15. accent

16. crescendo

17. diminuendo

18. time signature

19. accelerando

20. slur

The cost for sending the parcel with each company is £72 via WeGoFast and £80 by ParcelsFly.

In product, exploration, retail, and account, a cost is the value of plutocrat that has been used up to produce commodity or deliver a service, and hence isn't available for use presently. In business, the cost may be one of accession.

Hector needs the parcel to be send.

Dimension for his cuboid parcel is given by 10 cm by 10 cm by 40 cm.

10cm x 10cm x 40cm

Sum of the three dimension in cm

= (10 + 10 + 40) cm

= 60 cm.

Volume of the parcel in  = (10 × 10 × 40)  = 4000 cm³

Price charge by WeGoFast

= Sum of the three dimensions in cm × £1.20

= £ (60 × 1.20) = £72.

Price charged by ParcelsFly

= Volume measured in  × £0.02

= £ (4000 × 0.02) = £80

Therefore, The cost of sending the parcel with each company is £72 by WeGoFast and £80 by ParcelsFly.

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The value of y in the given proportion is 1/13.

In mathematics, a proportion is a statement that two ratios are equal. A ratio is a comparison of two quantities, typically written as a fraction. For example, if we have two quantities, a and b, then the ratio of a to b is written as a/b.

A proportion is written in the form a/b = c/d, where a, b, c, and d are numbers. This means that the ratio of a to b is equal to the ratio of c to d. We can also write this as a:b = c:d.

To solve the proportion:

                   (4y+5):3=(y+7):4

We can cross-multiply and simplify:

                  4(4y+5) = 3(y+7)

                  16y + 20 = 3y + 21

Subtracting 3y from both sides:

                  3y + 20 = 21

Subtracting 20 from both sides:

                  13y = 1

Dividing both sides by 13:

                  y = 1/13

Therefore, the value of y that satisfies the proportion is y = 1/13.

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Answer:

A)7y-4xy

Algebraic expressions are just that expressions. No inequality signs or equations. That's what makes them special

Step-by-step explanation:

The income tax for each household are:

Let's evaluate each household income tax cases:

Household 1

Taxable income = $400,000

Tax rate = $45,210 + 35%  over $204,100

Income tax = $45,210 + 35% ($400,000 - $204,100)

Income tax = $45,210 + $68,565

Income tax = $113,775

Household 2

Taxable income = $10,954

Tax rate = 10% income

Income tax = 10% ($10,954)

Income tax = $1,095.40

Household 3

Taxable income = $108,962

Tax rate = $12,962 + 24% over $84,200

Income tax = $12,963 + 24%($108,962 - $84,200)

Income tax = $12,963 + $5,942.88

Income tax = $19,804.88

Household 4

Taxable income = $209,850

Tax rate = $45,210 + 35% over $204,100

Income tax = $45,210 + 35% ($209,850 - $204,100)

Income tax = $45,210 + $2,012.50

Income tax = $47,222.50

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Answer:

There were 8 student who went on a trip.

Step-by-step explanation:

Let's call the original number of students "x". The total cost of the trip was $80, so the cost per student was $80/x.

When four more students decided to go, the new number of students became x + 4, and the cost per student was reduced by $1, to $80/x - $1.

We can set up an equation to solve for x:

$80/x = $80/(x + 4) - $1

Expanding the right side:

$80/x = $80/x + $80/4 - $1

Combining like terms:

$80/x = $80/4 + $80/x - $1

Solving for x:

$80/4 = $80/x - $1

$80/4 + $1 = $80/x

$20 + $1 = $80/x

$21 = $80/x

Finally, solving for x:

x = 80/$21 = 80/21 = 3.81 (rounded to nearest whole number)

So, there were 4 students on the original trip.

There were 4 students on the original trip and 4 more students joined, so in total, there were 4 + 4 = 8 students who went on the trip.

Answer: 8 student

Step-by-step explanation:

Check the picture below.

As a result, 315 pupils attended the school play.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The first equation in the system is given by the total number of attendees:

c + a = 330

The second equation is given by the number of children being 21 times the number of adults:

c = 21a

We can use substitution to find the value of a and then find the value of c. Substituting the second equation into the first equation, we get:

21a + a = 330

Combining the two terms on the left-hand side, we have:

22a = 330

Dividing both sides by 22, we have:

a = 15

So there were 15 adults in attendance at the school play. To find the number of children, we can use the second equation:

c = 21a = 21 * 15 = 315

So there were 315 children in attendance at the school play.

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Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism is a valid and useful approach.

What is Surface area?

The surface area of a solid item is a measurement of the total area occupied by the object's surface.

Yes, Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism makes sense.

A box can be thought of as a combination of a triangular prism and a rectangular prism because a box is made up of six faces, with three rectangular faces and three triangular faces. By finding the surface area of the triangular prism and the rectangular prism separately, and then adding them together, one can find the total surface area of the box.

This method can make finding the surface area of a box faster and easier because one can use formulas that are specifically designed for finding the surface area of triangular prisms and rectangular prisms. By breaking down the box into its constituent parts, one can simplify the calculation and avoid having to use a more complex formula for finding the surface area of a box.

In summary, Chris's method of finding the surface area of a box by thinking of it as a combination of a triangular prism and a rectangular prism is a valid and useful approach.

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Answer:

The answer to the classification of the statements is:

1.True

2.False

3.False

4.True

Answer:

True

False

False

True

Step-by-step explanation:

The sum of the interior angles of a regular hexagon is S = 720° and each angle of the regular hexagon x = 120°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of the interior angles of the hexagon be S

Now , the number of sides for a hexagon = 6

And ,Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

Substituting the values in the equation , we get

6θ = 180 ( 6 - 2 )

On simplifying the equation , we get

6θ = 180 x 4

6θ = 720°

Therefore , the sum of angles is 720°

And , the value of x = 720 / 6 = 120°

Hence , the sum of interior angles of hexagon is 720°

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Answer:

Here's the exponential equation to model the card's value:

y = 98.70 * 2^x

where x is the number of years after Mr. Olsen purchased the card.

To find the value of the card after 5 years:

x = 5

y = 98.70 * 2^5 = 98.70 * 32 = $3162.40

So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

m

The bacteria's population increases exponentially, and its equation is

P(t) = P[tex]_{0}[/tex]e[tex]^{kt}[/tex]

Where,

P[tex]_{o}[/tex] is the initial population t is the number of hours.

k is the growth rate.

It is given that the population of the bacteria after one hour triples itself. i.e

P(1)=3P[tex]_{o}[/tex]

3P[tex]_{o}[/tex]=Pe[tex]k^{(l)}[/tex]

3=e[tex]^{k}[/tex]

In 3 = In e[tex]^{k}[/tex]

In 3=k ln e

In 3 = k(1)

k = ln (3)

Thus, the rate of growth is k= ln (3)

Substitute k = ln (3) in the equation P(t) = P[tex]_{o}[/tex]e[tex]^{kt}[/tex].

P(t) = P[tex]_{o}[/tex]e[tex]tln^{(3)}[/tex]

It is given that there are 1 million bacteria after 5 hours. i.e. P(5)=10,00,000

P(5) = P[tex]_{o}[/tex]e[tex]^{(5)} ln^{(3)}[/tex]

10,00,000 Pe[tex]^{(5)}ln^{(3)}[/tex]

10,00,000 = P[tex]_{o}[/tex]e[tex]ln^{(3)^{5} }[/tex]

10,00,000 = P[tex]_{o}[/tex][tex](3)^{5}[/tex]

P[tex]_{o}[/tex] = 10,00,000 / [tex]3^{5}[/tex]

P[tex]_{o}[/tex] = 10,00,000 / 243

Thus, the formula for any t is P(t) = (10,00,000 / 243) e[tex]ln^{(3)^{t} }[/tex]

Find the doubling time for the bacteria population.

Let X= 10,00,000 / 243 then the equation for the doubling time for the bacteria is

2X = Xe[tex]ln^{(3)t[/tex]

2 = e[tex]ln^{(3)t}[/tex]

t= ln (2) / ln (3) ≈ 0.63094 hours

Or t=37.8564 minutes.

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The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

To find the dimensions of the wall find the dimensions of the rectangles given in the figure. Calculate the area of the rectangle and factorize the resultant equation for the value of 'x'. Calculate the dimensions of the wall by using the number of panels along the height and top.

Here we have  

A wall has paneling made up of rectangles

Area of the rectangle = 30 square feet  

Given that the edge of each rectangle in the paneling is (2x+3) feet in width and (4x+2) feet in height.  

Area of the rectangle = (2x + 3)(4x +2) = [ 8x²+ 16x + 6 ]  

Given that area of the rectangle = 30 ft²  

=> 8x²+ 16x + 6 = 30

=> 8x²+ 16x - 24 = 0  

=> x² + 2x - 3 = 0

=> x² + 3x - x - 3 = 0

=> x(x + 3) - (x + 3) = 0

=> (x + 3)  (x - 1) = 0

=> x = -3 and  x = 1  

We need to x = 1  [ since height can't be taken in negative ]

Dimensions of the rectangle,

Width, 2x + 3 = 2(1) + 3 = 5 feet

Height, 4x + 2 = 4(1) + 2 = 6 feet

Given that there are 4 rectangles along the height

Height of the wall = 4 × 6 = 24 feet

There are 3 rectangles along the top.

Width of the wall = 3 × 5 = 15 feet

Therefore,

The value of 'x' is 1. The height of the wall is 24 feet and the width of the wall is 15 feet.

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option B is correct, the equation or function of the graph is y≥3/4x-3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The line passing through points (4,0) and (0,3)

Slope=3/-4=-3/4

Now let us find y intercept

0=-3/4(4)+b

0=-3+b

b=3

Hence, option B is correct, the equation or function of the graph is y≥3/4x-3.

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Answer: 2,4,6

Step-by-step explanation: All of these have x=3 as a solution.

Answer:

Step-by-step explanation:

6=2x

x^2=9

x-3=0

Grade 4N usually has physical education on a Wednesday at 1:43 pm and ends at 2:13 pm. with the new mandated change, at  2:28 pm Grade 4N PE will now end

The new regulations require physical education classes to be a minimum of 30 minutes long. Allowing for an extra 15 minutes to the existing PE class brings the end time to 2:28 pm.  This is an important change because it ensures that all students receive the recommended amount of physical activity each week.

Physical education is a vital part of a student’s development, as it provides the opportunity for students to become more active, and socially engaged, and learn about the importance of a healthy lifestyle.  The extra 15 minutes of physical education also allows for more time for students to learn about safety procedures and the proper way to use the equipment, which is important for the overall well-being of the students.

Additionally, the extra time allows for more time for individual instruction, which can be beneficial for students who need extra help or who may be struggling with a certain skill.

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Answer:

3 bags of leaves each weekday

Step-by-step explanation:

5b + 11 = 26

Subtract 11 from both sides.

5b = 15

Divide 5 on both sides.

b = 3

Grace filled 3 bags of leaves each weekday.