PROBLEM SOLVING Volunteers work for six hours to clean up litter in a park. The graph represents
the time x (in hours) and the number y of garbage bags filled.
Garbage bags

(6, 69)
(5, 57.5) (4, 46)
(2, 23)
10 (1, 11.5)
(3, 34.5)
Write an equation that represents the garbage bags filled as a function of time

Interpret the slope and the y intercept
The domain is____ the range is____

How many garbage bags could the volunteers fill in 12 hours
____ garbage bags

Explain.

The dimensions that will minimize the cost, obtained from the cost function are;

Width = [tex]\sqrt[3]{\frac{45}{11} }[/tex] feet

Length = [tex]2\cdot \sqrt[3]{\frac{45}{11} }[/tex] feet

Height = [tex]\dfrac{20}{\left(\sqrt[3]{\frac{45}{11} }\right)^2 }[/tex]

A function is a rule, or law or expression that provides the definition between an input variable and an output variable.

Base length of the box = 2 × The base width of the box

Cost of the material used to build the top and the bottom = $11 per square feet

Cost of the material used to build the sides = $3 per square feet

Volume of the box = 40 cubic feet

Let x represent the width of the base of the box, and let y represent the height of the box

The information from the question indicates;

The length of the base of the box = 2·x

The volume of the box, V = x × 2·x × y = 2·x²·y = 40

V = 2·x²·y = 40

[tex]y = \dfrac{40}{2\cdot x^2} = \dfrac{20}{x^2}[/tex]

The cost of the box which can be obtained from the surface area of the box can be found as follows;

Cost of the top and the bottom = 2 × x × 2·x × 11 = 44·x²

Cost of the material for the sides = (2 × x × y + 2 × 2·x × y) × 3 = 18·x·y

Cost of the box, C = 44·x² + 18·x·y

[tex]C = 44\cdot x^2 + 18\cdot x \times \dfrac{20}{x^2} = \dfrac{44\cdot x^2+360}{x}[/tex]

To minimize the cost of the box, we get;

[tex]C' =\dfrac{d}{dx}\left( \dfrac{44\cdot x^2+360}{x}\right) = 0[/tex]

[tex]\dfrac{d}{dx}\left( \dfrac{44\cdot x^3+360}{x}\right) = \dfrac{x\times 44\times 3 \times x^2 - \left(44\times x^3+360\right)}{x^2} = \dfrac{88\cdot x^3-360}{x^2} =0[/tex]

At the minimum cost, [tex]\dfrac{88\cdot x^3-360}{x^2} =0[/tex]

Therefore; 88·x³ - 360 = 0

88·x³ = 360

[tex]x = \sqrt[3]{\dfrac{360}{88} } =\sqrt[3]{\dfrac{45}{11} }[/tex]

The width of the base of the box that minimizes the cost is; [tex]x =\sqrt[3]{\dfrac{45}{11}}[/tex]

The length of the base of the box that minimizes the cost is; [tex]2\cdot x =2\times \sqrt[3]{\dfrac{45}{11}}[/tex]

The height of the box that minimizes the cost is; [tex]\dfrac{20}{x^2} = \dfrac{20}{\sqrt[3]{\dfrac{45}{11} } }[/tex]

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If two points on the map measures 10 cm, with a scale of 1 : 1000 the actual distance is 10 000 cm

information gotten from the question

a scale of 1:1000

2 points on the map 10 cm = ?

Scale factors refer to the amount or the factor the image on a map was increased or reduced in comparison with the actual dimension of the image

A map has a scale of 1 : 1000

the scale factor is 1/1000 then 10/?

1/1000 = 10/?

cross multiplying gives

? = 10 000 cm

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Answer: (3, 1)

Step-by-step explanation:

Plug in each coordinate and see if the equation holds true:   

[tex](13, 2)\\13+2(7)=13+14=27\neq 10[/tex]

[tex](2, 1)\\2+7(1)=2+7=9\neq 10[/tex]

[tex](4, 1)\\4+7(1)=4+7=11\neq 10[/tex]

[tex]3+7(1)=3+7=10[/tex]

Answer:

7.1032,7.209,7.23,7.3.

so we can not put the dot and imagine like 71032 72090 we not put the 0 but it's can not be with no 0 72300 and we not put 0 73000 it most greatest so

i write answer on the top!

The customer have to pay $87.9 for the watch.

A customer at the store wanted to buy a different watch that was listed at $88 but had a 15% discount.

Given the information is

Watch is listed at $88 and had a discount of 15%

The customer had to pay a sales tax of 5%

Than, by reducing the discount from the price listed

= $88 - 15%

= 88 - [tex]\frac{15}{100}[/tex]

= 87.85

Now we have to add 5% tax to the discounted price

= 87.85+5%

= $87.9

Hence the answer is the customer have to pay $87.9 for the watch.

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If no withdrawals were made from the accounts. The total interest earned at the end of 1 year is $230 and the percent interest for the total deposited is 5.75%.

a. Total interest earned  :

Total interest earned  = (0.02)($1000)+(0.07)($3000)

Total interest earned =$20+$210

Total interest earned =$230

b. Percent interest amount deposited

Percent interest amount deposited = Total interest earned / Total amount deposited

Percent interest amount deposited = $230 /( $1,000 + $3,000)

Percent interest amount deposited = $230 / $4000

Percent interest amount deposited = 0.0575 × 100

Percent interest amount deposited =5.75%

Therefore $230 is the interest earned and 5.75 is the percent interest.

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The equation of the given line is y = 2x + 4

The equation y = mx + c is the general equation of any straight line, where m is the slope of the line and c is the y -intercept.

Given a line passing through points (-1, 2) and (-3, -2)

We know (y - y1) = [(y2−y1)/(x2−x1)](x - x1).

Therefore, y - 2 = [(-2-2)/(-3+1)](x+1)

y-2 = 2x + 2

y = 2x + 4

Hence, The equation of the given line is y = 2x + 4

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115.5  is the total amount of interest paid by this investment at the end of 5 years

What is the Percentage?

percentage, a relative value indicating the hundredth parts of any quantity.

Given,

Samantha invested $660 into an account that paid 3.5% interest compounded annually.

We need to find the total amount of interest paid by this investment at the end of 5 years

A=P(1+rt)

A is the final amount

P is the principal amount

r is the rate of interest

t is time

A=?,P=660,r=3.5%=0.035, t=5

A=660(1+0.035(5))

=660(1+0.175)

=660(1.175)

A=775.5

To check the total amount of interest paid by this investment at the end of 5 years

We need to find the difference between the initial amount and the final amount

775.5-660 =115.5

Hence 115.5  is the total amount of interest paid by this investment at the end of 5 years

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The overall weighted average grade for this student in the class is 83.5%.

The weighted average grade is a function of the multiplication of each rate by the average score for each grading category.

The class grades are added to obtain the total grade that the student received for the different categories, involving class participation, classwork/homework, and tests/projects.

                                      Grade   Average    Class Grade

Participation                    10%        100          10% (10% x 100%)

Classwork/Homework   30%         95          28.5% (30% x 95%)

Test/projects                  60%         75          45% (60% x 75%)

Total grade in class                                      83.5%

Thus, from the student's participation, classwork/homework, and tests/projects, we can summarize that they scored an average weighted grade of 83.5%.

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If you want easy access to your money for paying bills, eating out, etc, it is best to use a checking account.

A checking account is a sort of bank account that enables simple deposits and withdrawals of cash for everyday use.

For instance, you may use your debit card to withdraw cash, deposit a check you receive, or set up direct deposit to get your paychecks.

It is advisable to utilize a checking account if you want quick access to your money for things like paying bills and dining out.

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The gallons of water and gallons of the premium antifreeze solution that must be mixed are 60 gallons and 120 gallons respectively.

In order to solve this word problem, we would assign a variable to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:

Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:

w + p = 180      ....equation 1.

0.60p = 0.40(180)    ....equation 2.

From equation 2, we have:

0.60p = 0.40(180)

0.60p = 72

Premium antifreeze, p = 72/0.60

Premium antifreeze, p = 120 gallons.

For the gallons of water, we have:

w + p = 180

Water, w = 180 - p

Water, w = 180 - 120

Water, w = 60 gallons.

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The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

In the question ,

it is given that ,

a member of hiking club paid $51 for 4 months ,

let the number of months be represented on x coordinate , and

the amount paid be represented on y coordinate .

So , the point becomes (4 , 51).

also given that you pay a total of $105 after 10 months ,

the second point becomes (10 , 105).

to find the equation in slope intercept form , we need slope ,

So , Slope = (105-51)/(10-4)

= 54/6

= 9

So , the equation having the point (4,51) and slope as 9 , in slope intercept form is

(y - 51) = 9(x - 4)

y - 51 = 9x - 36

y = 9x - 36 + 51

y = 9x + 15

Therefore , The linear equation in the slope intercept form that models this situation is y = 9x + 15 .

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The function of f(0) =7.0710.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x) = 2(x)² +5√(x+2)

f(0) = 2*0 +5√2

f(0) =  7.0710

Hence the value will be 7.0710.

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Answer:

[tex]16a^6x^4y^2[/tex]

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., [tex](x^2)^2 = x^{2 \cdot 2} = x^4[/tex])

Using that rule, we get:

[tex](-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}[/tex].

This can be simplified to

[tex]16 \cdot x^4 \cdot y^2 \cdot a^6[/tex],

which can be written as:

[tex]16a^6x^4y^2[/tex]

using the commutative property of multiplication.

Step-by-step explanation:

x = price per muffin

21 × x = 30

x = 30/21 = 10/7 = $1.428571429... ≈

≈ $1.43

she needs to charge $1.43 per muffin.

According to the given distance, the dog can run on 22.5 miles

Distance:

Distance refers the the length of the line joining the two points. Here the two points lie on the same horizontal or same vertical line, the distance can be found by subtracting the coordinates that are not the same.

Given,

On his trip to meet Clare, Kiran brought his dog with him.

Here at the same time Kiran and Clare started walking, the dog started running 6 miles per hour.

When they got to Clare it turned around and ran back to Kiran. And when it got to Kiran, it turned around and ran back to Clare, and continued running in this fashion until Kiran and Clare met.

Here we know that they meet after 3.75 hours.

And we know that the dog was running 6 miles per hour

So, for 3.75 hours, it can be calculated as,

=> 3.75 x 6

=> 22.5

Therefore, then the dog can ran 22.5 miles.

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The hopper will empty all of the grain in approximately 48.2 seconds .

Total amount of grain in the hopper = 2024.5 cubic feet

Rate at which the grain is emptied = 42 cubic feet /second.

Time taken to empty the grain

= 2024.5 / 42

= 48.202...

≈ 48.2 seconds

The ratio of two related quantities represented in several units is known as a rate. The numerator of something like the ratio expresses the rate of change for the other dependent variable if the denominator of both ratios is expressed as a single unit of each of these quantities and it is assumed that even this quantity can also be changed in a predictable way.

Hence the hopper will empty all the grain in about 48.2 seconds.

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Answer:

The costs are equal at 3 miles.  It coest $8 for either company

At 8 miles the green cost 13 and the red cost 18.

My advice would be to use the Red compnay if traveling less than 3 miles and the green company is traveling more than 3 miels.  At 3 miles the costs are the same.

Step-by-step explanation:

The slopes and the y-intercepts of two equations are different.

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

From the information provided, we have the following equations:

2x + y = 3       ....equation 1.

−2y = 14 − 6x    ....equation 2.

In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:

2x + y - 2x = 3 - 2x

y = 3 - 2x

y = -2x + 3

Therefore, m = -2 and c = 3.

For the second equation, we would divide both sides by -2 as follows:

−2y/-2 = 14/-2 − 6x/-2

y = -7 + 3x

y = 3x - 7

Therefore, m = 3 and c = -7.

In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.

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Answer:

y = -2x + 3

y = 3x + -7

The slopes and the y-intercepts are different.

The system represents lines that Intersect at one point

Exactly one solution

Step-by-step explanation:

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The ending inventory cost on December 31 for 21 units, under the three inventory methods, is as follows:

a) first-in, first-out (FIFO) method: $719

b) last-in, first-out (LIFO) method: $661

c) weighted average cost method: $690

The ending inventory cost is the difference between the cost of goods available for sale and the cost of goods sold determined by the various inventory methods.

Some of the inventory methods include:

Date       Activities         Units     Unit Cost   Total

Jan. 1      Inventory           16            $31       $496

Aug. 13   Purchase           14           $33         462

Nov. 30  Purchase           13           $35         455

Available for sale            43                       $1,413

Average cost = $32.86 ($1,413 ÷ 43)

Ending inventory             21

Units sold =                     22 (43 - 21)

a) FIFO:

Ending inventory = $719 (13 x $35 + 8 x $33)

Cost of goods sold = $694 ($1,413 - $719)

b) LIFO:

Ending inventory = $661 (16 x $31 + 5 x $33)

Cost of goods sold = $752 ($1,413 - $661)

c) Weighted Average:

Ending inventory = $690 (21 x $32.86)

Cost of goods sold = $723 (22 x $32.86)

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Answer:

D

Step-by-step explanation:

The slope of the function A which is presented as an equation and the slope of function B presented as a table are presented as follows;

The slope of function A is 4

The slope of function B are;

Between f(0) and f(1), the slope is 1

Between f(1) and f(2), the slope is 3

Between f(2) and f(3), the slope is 5

The slope is found by the ratio of the rise to the run of the graph.

The function A is; y = 4·x - 5

Function A is of the form y = m·x + c

Where;

m = The slope of the function = 4

Therefore;

The slope of function A is 4

The first difference of the values of function B is not a constant.

The value of f(0) in function B is 0

The value of f(1) in function B is 1

The slope between f(0) and f(1) is m = (f(1) - f(0))/(1 - 0)

Which indicates that m = (1 - 0)/(1 - 0) = 1

The slope of function B between f(1) and f(2) is found as follows;

f(2) = 4, f(1) = 1, from which we get;

m = (4 - 1)/(2 - 1) = 3

The slope between f(2) and f(1) is 3

The slope of the function B between f(2) and f(3) is found as follows;

f(2) = 4, f(3) = 9, from which we get;

m = (9 - 4)/(3 - 2) = 5

The slope of the function B between f(2) and f(3) is 5

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Answer:

[tex]-1.7f+-25[/tex]

Step-by-step explanation:

1 ) To simplify combine like terms...

[tex]=-2.5f+0.8f+-16+-9[/tex]

[tex]=(-2.5f+0.8f)+(-16+-9)[/tex]

[tex]=-1.7f+-25[/tex]

Hope this helps! :)

Answer:

Step-by-step explanation:

The price of the car before tax was $18,560.3

Let the price of the car be x. Then,

x + 6% of x = $19,674

106x/100 = $19,674

x = $ 19,673*100/106

with BODMAS, we get

x= $18560.3

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Answer:

1,200 pennies

Step-by-step explanation:

The median of the data collected from a track meet  is 2 meters.

The median is the middle number in a sorted, ascending or descending list of numbers.

To calculate the median of the given date, we folloe the steps below.

Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2

Step 1: Rearreange the date in accending order.

Step 2: Pick the middle of the number in the arranged data

Hence, the median of the data collected is 2 meters.

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Answer:

2.5

Step-by-step explanation:

The observation I can make of the pattern is that the sequence always increase by 10.

The sequence above shows an arithmetic pattern. Therefore, the arithmetic formula can be used to solve the next sequence.

7, 17, 27, 37, 47, 57..

Therefore,

aₙ = a + (n - 1)d

where

Therefore,

a = 7

d = 17 - 7 = 10

Hence, the arithmetic formula is as follows:

aₙ = 7 + (n - 1)10

aₙ = 7 + 10n - 10

aₙ = 10n - 3

The sequence always increase by 10.

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Answer: unit rate

Step-by-step explanation:

its obvious

Answer:

I believe it is a unit rate