g a farmer has 24002400 feet of fencing and wants to fence off a rectangular field that boarders a straight river. he needs no fence along the river. what are the dimensions of the field that has the largest area? (list the smallest dimension first)

Answers

Answer 1

Answer:

  600 ft by 1200 ft

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.

Perimeter

Let x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...

  x + 2y = 2400

Solving for y gives ...

  y = (2400 -x)/2

Area

The area is the product of the two dimensions:

  A = xy = x(2400 -x)/2

We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.

The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:

  x = (0 +2400)/2 = 1200

  y = (2400 -x)/2 = (2400 -1200)/2 = 600

The dimensions of the field that has the largest area are 600 ft by 1200 ft.

__

Additional comment

As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.


Related Questions

Write the equation of the line that passes through the points (3, -8) and(9, 9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.​

Answers

I’m pretty sure the answer is y+8=17/6(x-3)

8. You are selling concessions at a local swim meet. Hot dogs are being sold for
$1.00 and soda is being sold for $0.50. At the end of the day you made $150.
Let x represent the number of hotdogs sold and y represent the number of
sodas sold. Write an equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.

a. Standard Form:

b. Slope-Intercept Form:

c. If you sold 40 hot dogs how many sodas did you sell?

d. Using the Standard Form, identify the x-intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.

e. Using the Standard Form, identify the y-intercept of the graph and explain
how the y-intercept relates to the number of hot dogs and sodas sold.

Answers

The equation  that can be used to find the number of hotdogs

and sodas sold at the swim meet.

a)x+0.50y=150

b)  y=-2x+300

c)Number of soda sold y =220 if hot dog is 40.

d)  x intercept=150. It is related to the total earnings of soda and hot dogs sold.

f) y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

What is x-intercept and y-intercept?

An equation's or a function's graph that contacts the x axis is said to have a "X intercept." This is comparable to a point having a value of zero. Given that it is located on the horizontal axis, this is sometimes referred to as the horizontal intercept. The y value at the point where the line meets the y axis is known as the y intercept. By examining the graph and identifying the point that crosses the y axis, we may determine the y intercept. This point's x coordinate will always be 0. It will be recorded as (0,y). Given that it is on the vertical axis, this is also referred to as a vertical intercept.

Let us take number of hot dogs sold as x and number of soda sold as y.

Cost of one hot dog = $1.00

Cost of one soda = $0.50

Then , cost of x number of hot dogs sold = 1x

cost of y number of soda sold = 0.50y

Then, . At the end of the day you made $150.

=> 1x+0.50y= 150

a) standard form of the equation is ,

=> x+0.50y=150 ------->1

b) x+0.50y=150

=> x+[tex]\frac{1}{2}[/tex]y=150

=>2x+y=150*2

=>2x+y=300

Then slope intercept form is  y=-2x+300------->2

c) Number of hot dogs sold x=40 and put into 2 ,

then ,  y=-2(40)+300

=> y=-80+300

=>y=220

Number of soda sold y =220

d) To find x intercept put y=0 into 1 , then

=> x+0=150

=>x=150

Here x intercept=150. It is related to the total earnings of soda and hot dogs sold.

e)To find y intercept put x=0 into 1,

=> 0+0.50y=150

=> y = 150/0.50

=> y =300

Here y intercept = 300 . It is related to the 2 times of the total earnings of soda and hot dogs sold.

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which statement can you use to conclude that quadrilateral xyzw is a parallelogram

Answers

The statement can you use to conclude that quadrilateral xyzw is a parallelogram

The statement to conclude that quadrilateral XYZW is a parallelogram is

XY = WZ and XW = YZ

Quadrilateral :

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points.

Parallelogram :

A parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other , where the pair of parallel sides are equal in length.

So we can conclude that :

XY is parallel to WZ  and XW is parallel to YZ .

so ,

XY = WZ and XW = YZ is the conclusion .

Hence , the answer is XW = YZ and XY = WZ

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what is the reciprocal of 5 1/3

Answers

Answer:

Step-by-step explanation:

reciprocal of 51/3 is 3/16

Hi you need to change 5 1/3 from mixed number to improper fraction 51/3=(5x3)+1  /3 =16/3

The  reciprocal   of 16/3 is 3/16

The shapes below are mathematically similar.
X
9 cm
Calculate the length of side x.
8 cm
12 cm
Not drawn
to scale

Answers

The length of side x is 6cm

We need to find the scale factor of the shapes below are mathematically similar.

it can be found using the two bases given.

The base of the smaller triangle is 9  and that of large triangle is 12

9/12 = 3/4

The smaller triangle is 3/4 of the larger one.

Multiply the known side by 3/4

X = 8 x 3/4 = 6

X= 6

Therefore, the length of side x is 6cm

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Simplify
1-(cos^2)theta/(sin^2 )theta
A. 1
B. sin^2 theta
C. cos^2 theta
D. tan^2 theta

Answers

Answer:
A) 1



Explination:
1 because cos^2 theta + sin^2 theta = 1
So 1-cos^2 = sin^2
Which means you now have sin^2 theta/sin^2 theta
Which =1

What is the y-intercept of g(x) = -|x +6|+ 4

Answers

Answer: -2

Step-by-step explanation:

since g(x) is a function, x needs to be 0 in order to find the y-intercept. so we plug in 0 to the function. -|0+6|+4=-2 so the y-intercept is -2

What is the equation of a parabola that passes through the points (−5, −10), (−3, 2), and (2, −3)?.

Answers

The equation of the parabola is y = -x² - 2x + 5

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The equation of the parabola with the points

A ( -5 , -10 ) , B ( -3 , 2 ) and C ( 2 , -3 )

So , from the equation of parabola ,we get

y = ax² + bx + c


Substituting the values of x and y , in the equation of point A , we get

-10 = a ( -5 )² - 5b + c

-10 = 25a - 5b + c   be equation (1)

Substituting the values of x and y , in the equation of point B , we get

2 = a ( -3 )² - 3b + c

2 = 9a - 3b + c   be equation (2)

Substituting the values of x and y , in the equation of point C , we get

-3 = a ( 2 )² + 2b + c

-3 = 4a + 2b + c   be equation (3)

By the method of brute force , we can solve the equations and derive the equation for the parabola

So , the equation for the parabola will be

y = -x² - 2x + 5

Now , substituting the values of x and y from the points , we get

For point A ( -5, -10 )

-10 = - 25 + 10 + 5

-10 = -10

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point B ( -3, 2 )

2 = -9 + 6 + 5

2 = 2

Therefore , the equation is TRUE

Now , substituting the values of x and y from the points , we get

For point C ( 2 , -3 )

-3 = -4 - 4 + 5

-3 = -3

Therefore , the equation is TRUE

Hence , the equation of the parabola is y = -x² - 2x + 5

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cos²x + 2 cosx - 3=0

Answers

The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

In the question ,

it is given that ,

the quadratic equation is cos²x + 2 cosx - 3 = 0 ,

let cosx = a ,

So , the equation becomes , a² + 2a - 3 = 0

writing the factors using the splitting the middle term method ,

we get ,

a² [tex]+[/tex] 3a -a - 3 = 0

a(a + 3) -1(a [tex]+[/tex] 3) = 0

(a - 1)(a [tex]+[/tex] 3) = 0

which means a - 1 = 0      or    a + 3 = 0

a [tex]=[/tex] 1    or     a [tex]=[/tex] -3 ,

Substituting a = cosx , we get

cosx [tex]=[/tex] 1   or cosx [tex]=[/tex] -3 ,

Therefore , The Solution for the given quadratic equation is Cosx = 1 and Cosx = -3 .

The given question is incomplete , the complete question is

Solve the given quadratic equation for Cosx , cos²x + 2 cosx - 3 = 0 .

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a 2013 study by pediatricians investigates whether it is better to give children the diphtheria, tetanus and pertussis (dtap) vaccine in the thigh or the arm. the pediatricians collected the data from two different random samples. the first random sample was collected from children who were given the vaccine in the thigh. the second random sample was collected from children who were given the vaccine in the arm. pediatricians recorded whether the children had a severe reaction or not. no severe reaction severe reaction thigh observed expected 4758 4750.9 30 37.1 arm observed expected 8840 8853.1 76 68.9 reference: jackson, l.a., peterson, d., nelson, j.c., et al. (13 co-authors). 2013. vaccination site and risk of local reactions in children one through six years of age. pediatrics 131: 283-289. pediatricians conducted a chi-square test of independence. the chi-square test statistic for this datais 2.0609 with a p-value of 0.1511. what can the pediatricians conclude? group of answer choices there is a statistically significant association between vaccine location and severe reaction. pediatricians have strong evidence that the severe reactions to vaccine depend on location of the vaccine. there is not enough evidence to conclude that there is an association between vaccine location and severe reaction. the pediatricians cannot make a conclusion. the conditions for use of the chi-square test are not met.

Answers

Ther right option is that there is not enough evidence to conclude that there is enough association between vaccine location and severe reaction.

Given that,

Children who received the vaccine in the thigh received the first random sample. Children who received the immunization in the arm provided the second random sample.

The chi-square test yields a chi square is 2.0609 with a P value of 0.1511 meaning, the chi square test is not statistically significant.

A,B is therefore out.

C is not also right.

D is what we get when we cannot reject null hypothesis.

Therefore, We cannot conclude that there is dependence.

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the garden table and a bench cost $582 combined. the garden table costs $68 less than the bench. what is the cost of the bench?​

Answers

Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

what is 10 + 10 i need some help

Answers

Answer:20

Step-by-step explanation: my man

Answer:

20

Step-by-step explanation:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

= 20

This graph shows the height in inches, h, of a bamboo plant t months after it had been planted

4.1 Write an equation that describes the relationship between t and h.

4.2 After how many months will the Bamboo plant be 66 inches tall?

Answers

The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

A linear function is a function that varies linearly with respect to the changing variable.

4.1)

The linear equation is given as y = mx + c

Here, m is the slope while c is the y-intercept.

Given line has a y-intercept of 12.

Slope m = (12 - 24)/(0 - 4) = 3

Thus, h = 3t + 12

4.2)

Time is taken to bamboo to 66 inches tall,

66 = 3t + 12

3t = 54

t = 3 months.

Hence "The linear function or equation represents the height of the bamboo h with respect to time t is y = 3x + 12 and the time taken to reach 66 inches is 3 months".

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Jo flips a coin {h, t}; then rolls a 6-sided die {1, 2, 3, 4, 5, 6}. How many possible outcomes are in the sample space of this experiment?.

Answers

The possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

Jo flips a coin sample space for a coin = {h, t}

and rolls a 6-sided die sample space for a die = {1,2,3,4,5,6}

at a time coin is tossed and the die is rolled

the possible outcomes in the sample space of this experiment are

{(h,1),,(h,2),(h,3),(h,4),(h,5),(h,6),(t,1),(t,2),(t,3),(t,4),(t,5),(t,6)}

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3
What is the area of the composite figure?
12.5cm
20cm
500
490.62
245.31
745.31
25cm
4
27

Answers

Answer: 745.31 cm²

Total area of the figure can be obtained by adding area of the semi circle and rectangle.

The radius of the semi circle is given as 12.5cm and it's area is equal to (πr²)/2

I hope you understand It's simple!

you are synthesizing a chip composed of random logic with an average activity factor of 0.1. you are using a standard cell process with an average switching capacitance of 450 pf/mm2 . estimate the dynamic power consumption of your chip if it has an area of 70 mm2 and runs at 450 mhz at vdd

Answers

The dynamic power consumption of your chip if it has an area of 70 mm² and runs at 450 MHz at vdd = 0.9V is 1.08 W.

It is given that,

The average activity factor = 0.1

The Average switching capacity = 450 pF/mm²

We know that,

              p = aCV²f

putting the values in the above equation:

   = 0.1× (450e⁻¹² × 70) × (0.9)² × 450e⁶

   = 1.08 W

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[tex]3x-8\geq 7[/tex]

Answers

Answer:

x ≥ 5

Step-by-step explanation:

3x - 8 ≥ 7 ( add 8 to both sides )

3x ≥ 15 ( divide both sides by 3 )

x ≥ 5

8. Angles x and y are located in the first quadrant
such that sin x=5/3 and cos y=5/13
a) Determine an exact value for cosx.
b) Determine an exact value for siny.

Answers

sin y =12/13 but can't find cos x as sin x can't exceed from 1.

It can be solved by using identities of trigonometry.

What are the  trigonometric identities?

These are the equivalent ways to define trigonometric functions.

Basic identities are:

sin²x + cos²x = 1

1 + tan²x = sec²x

1 + cot²x = cosec²x

For cos x:
cos²x = 1 - sin²x

          = 1 - (5/3)²

          = 1- (25/9)

          = -16/9

i.e. not possible

For sin y:

sin²y = 1 - cos²y

         = 1 - (5/13)²

         = 1 - 25/169

         = 144/169

So, sin y = ±(12/13)

but as mentioned x and y are in 1st quadrant ,

so, sin y = 12/13.

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The sum 691 + 208 is closest to the sum
A. 600 + 200
B. 700 + 200
C. 700 + 300
D. 900 + 200

Answers

Answer:

B. 700+200

Step-by-step explanation:

691+208=899

A. 600+200=700

B.700+200=900

C.700+300=1000

D.900+200=1100

B is closest to 899

Answer:

700+200

Step-by-step explanation:

we round these numbers to the closest hundreds by looking at the tenth place

5 or more we round up

4 or less we let it rest and round down

691 since it is 9 in the tenths place we round up to 700

208 since the tenths place is 0 we round down to get 200

700+200 is the answer hopes this helps please mark brainliest

The 3rd term of a a G.P is 18 and the 7th term is 32/9. Find the G.P​

Answers

The G.P. of a term is 256/243.

To find out the G.P. for the 3rd term:

Let us consider the 1st term to be 'a'.

So, [tex]ar^{2}=18[/tex] ....... Equation (1)

Also [tex]ar^{6} = \frac{32}{9}[/tex] .....  Equation (2)

Dividing (2) by (1), we get,

[tex]\frac{ar^{6}}{ar^{2}} = \frac{32}{162}[/tex]

[tex]r^{4}[/tex] = 16/81.

r = 2/3.

Putting r in equation (1) than we will get

a = 81/2.

So, 10th term = [tex]ar^{9}[/tex]

= (81/2) ×(512/19683)

= 256/243.

Hence the answer is the G.P. of a term is 256/243.

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the annual rainfall in a certain region is approximately normally distributed with mean 41.4 inches and standard deviation 5.5 inches. round answers to the nearest tenth of a percent. a) what percentage of years will have an annual rainfall of less than 43 inches?

Answers

The probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

How to calculate the probability?

Given

μ = 41.4

σ = 5.5

First, we need to find the z score when the rainfall 43 inches. So:

z = (x - μ) / σ

z = (43 - 41.4) / 5.5

z = 0.2909

Then, to find out the probability we need to find P(z < 0.2909) in the z score table. So, we get 0.6141 or in percentage is 61.41%.

Thus, the probability percentage the year will have an annual rainfall less than 43 inches is 61.41%.

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at gumdrops galore candy store, miguel and his sister each fill a bag with gumdrops. miguel's bag of black gumdrops weighs 3 8 of a pound. miguel pays for both his gumdrops and his sister's red gumdrops. in all, miguel buys 7 8 of a pound of gumdrops. he wants to know how much his sister's red gumdrops weigh. use an equation to find the weight of his sister's red gumdrops. to write a fraction, use a slash ( / ) to separate the numerator and denominator.

Answers

Miguel's sister's red gumdrops weigh 0.5 pounds.

Formulate based on the conditions stated: [tex]\frac{3}{8} + x = \frac{7}{8}[/tex]

Unknown terms should be moved to the left side of the equation: [tex]x = \frac{7}{8} - \frac{3}{8}[/tex]

Numerators written over common denominator: [tex]x = \frac{7-3}{8}[/tex]

Determine the total or difference: [tex]x = \frac{4}{8}[/tex]

Remove the connecting element: [tex]x = \frac{1}{2}[/tex]

get the outcome: or x = 0.5 or 50%

A fraction is a mathematical symbol representing any quantity of equal parts, and it also represents a portion of a whole. In common English, the word "fraction" is used to describe the quantity of parts of a particular size. Fractions speed up and simplify calculations by making it easier to divide and evaluate numbers.

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Hello! Can someone please help me. I am in trouble, hope ypu help me guys, with complete answer! THANK YOU​

Answers

Answer:

[tex]\textsf{1.} \quad (x-1)^2=12(y+2)[/tex]

     See attachment 1.

2.  See attachment 2.

Step-by-step explanation:

Question 1

Given values:

Vertex:  (1, -2)Focus:  (1, 1)

As the x-value of the vertex and focus is the same, the parabola has a vertical axis of symmetry.

The focus is always on the inside of the parabola.

Since p represents the distance from the vertex to the focus, and the distance from the vertex to the focus is 1 - (-2) = 3, then p = 3.

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.  Therefore, as p > 0, the parabola opens upwards.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a vertical axis of symmetry)\\\\$(x-h)^2=4p(y-k)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h,k+p)$\\ \phantom{ww}$\bullet$ Directrix: \; $y=(k-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $x=h$\\\end{minipage}}[/tex]

Therefore:

h = 1k = -2p = 3

Substitute the values into the formula:

[tex]\implies (x-h)^2=4p(y-k)[/tex]

[tex]\implies (x-1)^2=4\cdot 3(y-(-2))[/tex]

[tex]\implies (x-1)^2=12(y+2)[/tex]

See attachment 1 for the graph of the parabola.

Question 2

Given equation of a parabola:

[tex](y-4)^2=8(x+2)[/tex]

As the y-variable is contained within the squared part of the equation, the parabola has a horizontal axis of symmetry.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Standard form of a parabola}\\(with a horizontal axis of symmetry)\\\\$(y-k)^2=4p(x-h)$\\\\where:\\ \phantom{ww}$\bullet$ $p\neq 0$\\ \phantom{ww}$\bullet$ Vertex: \;$(h,k)$\\ \phantom{ww}$\bullet$ Focus:\; $(h+p,k)$\\ \phantom{ww}$\bullet$ Directrix: \; $x=(h-p)$\\ \phantom{ww}$\bullet$ Axis of symmetry: \; $y=k$\\\end{minipage}}[/tex]

Therefore:

h = -2k = 44p = 8 ⇒ p = 2

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.   Therefore, as p > 0, the parabola opens to the right.

Find the y-intercepts of the graph by substituting x = 0 into the equation:

[tex]\implies (y-4)^2=8(0+2)[/tex]

[tex]\implies (y-4)^2=16[/tex]

[tex]\implies y-4=\pm4[/tex]

[tex]\implies y=4\pm4[/tex]

[tex]\implies y=0, y=8[/tex]

To sketch the graph of the parabola, plot:

Vertex = (-2, 4)Focus = (0, 4)Axis of symmetry:  y = 4y-intercepts:  (0, 0) and (0, 8)

Draw a curve through the vertex and y-intercepts, opening to the right.

Use the axis of symmetry to ensure the curve is symmetric.

See attachment 2 for the graph of the parabola.

PLEASE HELP, NEEDED ASAP

Answers

Answer:

a) x=5

b) x=4

Step-by-step explanation:

4x-3=2x+7

-2x.  -2x

2x-3=7

   +3. +3

2x=10

x=5

2x+6=7x-14

-2x.   -2x

6=5x-14

+14. +14

20=5x

/5. /5

4=x

Hopes this helps please mark brainliest

Solve all 3 and maybe I will give brainlest

Answers

C) for No. 1
B) for No. 2
D) for No. 3

Hope this helps! Please, if I am correct, let me know and reward me by giving me 1 heart, 5 stars and brainliest, it would help a ton. Thank you!

Have an AWESOME day everyone! :)

PLEASE HELPPPPP ASAPPPP I NEED THIS MATH DONE! WILL GIVE BRAINLIST

Answers

Answer: __________________________________________

3x + 9

Answer: 3x + 9

Step-by-step explanation:

Two similar bottles are shown. The smaller bottle can hold 500 ml of water. How much water can the larger bottle hold?

Smaller bottle length=15cm
Larger bottle length=21cm

Answers

The larger bottle will be able to hold a volume of 1372ml

What is Volume of similar object?

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

This shows that the ratio of the cube of length of the bottle is equal to the the ratio of their volumes

the length of the smaller bottle = 15, the cube of the length= 15^3= 3375

the length of the larger volume = 21, the cube of the length is 21^3=9261

therefore 3375/9261= 500/x

x is the volume of the larger bottle

therefore x= 500×9261/3375

x= 1372ml.

therefore the volume of the larger bottle is 1372ml

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Graph equations that represent the growth rates of hamburgers sold
and wraps sold in the same coordinate plane. Compare the steepness
of the graphs. What does this mean in the context of the problem?

Answers

(a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

In the question ,

it is given that

the rate at which the hamburgers are selling = 160 hamburgers per hour ,

we need to find the rate at which the wraps are selling

From the table ,

we can see that the wraps are sold in an Arithmetic Progression ,

So , at 60 minutes the wraps sold = 2.5 + (n-1)d

= 2.5 + 59×2.5

= 2.5 + 147.5

= 150

So , after one hour , number of wraps sold is 150 and the number of hamburgers sold is 160 .

Similarly , after 2 hours , the number of wraps sold will be 300 and number of hamburgers sold will be 320 .

So, the hamburgers sells faster than wraps .

the slope(steepness)  of the hamburgers = (number of hamburgers sold)/60

= 160/60

= 2.667

the slope(steepness) of the wraps = (number of wraps sold)/60

= 150/60

= 2.5

from the above data , we can see that the steepness of hamburgers is more ,

which means that the hamburgers sells faster than wraps .

the equation that denotes the number of hamburgers sold is y = 2.667x

the equation that denotes the number of wraps sold is y = 2.5x

where x is time in minutes .

The graph that represents the growth rate of hamburger and wraps is shown below .

Therefore , (a) Hamburgers sells faster than Wraps ,

(b) The graph of the equations that represents the Hamburgers and Wraps sold are shown below .

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question is in the pic .

Answers

The set of ordered pairs that represent dilation factor of -3 is

c. A' (-3, -18) B' (-18, -18) C' (-3, -6)

How to find the coordinates of the image

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

From the graph the coordinates are read and following the given transformation rule we have

preimage                           image

A (1, 3)   → (2 * -3, 4 * -3) →   A' (-3, -8)

B (6, 6)  → (4 * -3, 4 * -3) →    B' (-18, -18)  

C (1, 6)  → (3 * -3, 2 * -3) →    C' (-3, -6)

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19) Over the past 4 hours the temperature fell 37.5°F. On average, how much did the temperature fall per hour?​

Answers

Answer:

if you don't mind is there a starting number or a chart so i can calculate and solve this for you!

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