1. Jin fills up a 510-gallon pool in the backyard for her children. She fills it with the garden hose at a rate of 17 gallons per minute. After it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. The children then get in and have fun for an hour. The pool loses about _1_ gallon of water each minute due to Time (minutes) Amount of Water (gallons) 0 5 20 30 45 60 80 100 120 150 200 2 their splashing and playing. At the end of the hour, they tear the pool while getting out, which causes a leak. The pool then begins to lose water at a rate of 2 gallons per minute. a. Complete the table to show the amount of water in the pool after each minute. b. Create a graph to model the problem situation. Include when the pool will be empty. c. Write a piecewise function that models this problem situation. Explain your reasoning for each piece of the function. d. Identify the x- and y-intercept. Explain what they mean in terms of the problem situation. e. Determine when the pool will have 470 gallons of water in it. Identify the piece(s) of function you used. Explain your reasoning. 2. Jin asks her children to pay her back for the damaged pool. They must give her $15 per week. Together they have $165 in a savings account. a. Write a function to represent the amount of money they have after x weeks. Describe the domain and range of this function in terms of the problem situation. b. To rebuild their account, the children will receive a combined $15 per week in allowances. They start saving the week after their account is depleted and save for another 11 weeks. What are the domain and range of this function and what do they mean in terms of the problem situation? Write a function to represent this part of the graph. c. Graph the equations on the same grid. Is the graph continuous or discrete? Explain your reasoning. d. Write a function to represent the entire graph.

Answer:

107/21

Step-by-step explanation:

re - phrase the question algebraically:

-14/3 + y = 3/7

LCM of 3 and 7  = 21

-98/21 + y = 9/21

what should be added to -98 to make 9?

answer: 107

therefore answer: 107/21

Hope this helps.

Good Luck

Answer:

Here we have two inequalities.

P is price of the gallon,we have that:

$2.40 ≤ P ≤ $2.65

C is the amount of gallons that Ricardo buys each week.

8,5 ≤ C ≤ 11

Now, with this you can find the maximum and minimum amount that he can spend on a week.

The minimum is when he buys only 8.5 gallons and the price per gallon is $2.40

Cost = 8.5*$2.40 = $20.4

The maximum cost is when he buys 11 gallons, and the price of the gallon is $2.65

Cost = 11*$2.65 = $29.15

So the amount that he spends per week in gas, S, is:

$20.4 ≤ S ≤  $29.15

Answer:

442

Step-by-step explanation:

Answer:

The translation rule of the tile floor is T -3,2 (x,y)

From the complete question, the tile floor is shifted left by 3 units, and shifted up by 2 units.

This is represented as:

(x,y) -> (x - 3, y + 2)

This can also be written as:

T -3,2 (x,y)

Hence, the translation rule is T -3,2 (x,y)

Read more about translation at:

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Answer:

A: T-3, 2(x, y)

Step-by-step explanation:

Answer:

She needs to order 12 cars

Step-by-step explanation:

To find the total number of models, we just need to multiply the number of options for each choice:

body style: 2 options

interior package: 3 options

drive train: 2 options

So the number of different models is:

2 * 3 * 2 = 12 different models

So in order to have all the possible models, she needs to order 12 cars.

Answer:

Y greater than or equal to 6

Step-by-step explanation:

I can't do the sign so I just said it

Combine like terms

Answer:

Y Greater Than Or Equal To   Number 6

Hopes This Helps

Answer:

y = -2x + 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

x= -5,1,4,6 y=9,0,-7,-1

the range of a given function equals to the value of y in order

range = -7,-1,0,9

Answer:

See below.

Step-by-step explanation:

Alexi originally has $43 in his bank account and deposits $7 per week.

Week 1: $50

Week 2: $57

Week 3: $64

Week 4: $71

Week 5: $78

The pattern is that it increased $7 every week starting from $43.

A pattern rule would be: y = 7x + 43 where x represents the number of weeks.

Answer: The equation can be written as 8n = 99.2.

Step-by-step explanation:

In my answer, I used the variable n to distinguish itself as one side of the stop sign. 99.2 is the final perimeter in inches.

A stop sign is an octagonal shape (otherwise, it is made up of 8 equal sides). Therefore, with this information, you can interpret that the length of one side would be equal to the length of all of the other sides.

Hence, the answer can be represented as 8n = 99.2.

Answer:

6-Sided Figure.

Step-by-step explanation:

A 6 - sided figure is called a Hexagon.

What is Line segment?

A line segment is a part of line having two endpoints and it is bounded by two distinct end points and contain every point on the line that is between its endpoint.

Given that;

The polygon is a Hexagon.

Now,

Since, A hexagon is made up with 6 - sided.

And, A polygon is called a Hexagon when it has 6 sides, 6 angles and 6 vertices.

Thus, A 6 - sided figure is called a Hexagon.

Learn more about the hexagon visit:

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Answer:

C.

Step-by-step explanation:edge2020

Answer:

i  said c yea it is

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given

V = πr²h

Isolate h by dividing both sides by πr²

[tex]\frac{V}{\pi r^2}[/tex] = h → C

Answer:

-9

Step-by-step explanation:

9=b-2b

9=-b

divide both sides by -

b=-9

Answer:

[tex] \boxed{b = 9} [/tex]

Step-by-step explanation:

[tex] = > 2b + 9 = b \\ \\ = > 2b - b + 9 = 0 \\ \\ = > b + 9 = 0 \\ \\ = > b = - 9[/tex]

Answer:

area- 36.07 cm^2

perimeter- 28cm

Step-by-step explanation:

1) we could break the composite shape into 2 seperate shapes:

1 shape- measuring 3.1 by 3.4 cm

2nd shape- measuring (3.1)+(3.8)cm by 3.7 cm

since both shapes are rectangles we can find area by multiplying length and width

so 3.1*3.4=10.54

and 3.1+3.8=6.9

6.9*3.7=25.53

we can add both areas up to get TOTAL area of figure:

25.53+10.54=36.07

area- 36.07 cm

to find perimeter: there are 2 unknown sides in this figure, the bottom side length can be found out by adding 3.1 and 3.8, which is 6.9 and the side adjacent to the bottom one can be found by adding 3.4 and 3.7, which is 7.1

now we add up all the numbers: 3.1+3.4+3.8+3.7+6.9+7.1= 28

28 cm

Answer:

Step-by-step explanation:

[tex]\frac{(12a - 6bc - 3)}{20ab-5c)} \\\\\frac{3 . (4a - 2bc - 1)}{5 . (4ab - c)}\\\\[/tex]

Answer:

18, if im correct...

Step-by-step explanation:

I'm pretty sure you would multiply the 6 options (for each die side) by the 3 options (rock, paper, or scissors) together.

so 6*3=18

the right answer is √68 units...

please see attached picture for full solution

hope it helps

good luck on your assignment

Stay safe

Answer:

Area = 370 m²

Cost to paint = £105

Step-by-step explanation:

Area of the wall of a cinema hall = Area of a trapezoid (1)+ Area of a rectangle (2) + Area of a trapezoid (3)

Area of a trapezoid = [tex]\frac{1}{2}(b_1+b_2)h[/tex]

where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel sides and h is the distance between these sides.

Area of trapezoid (1) = [tex]\frac{1}{2}(11+12)\times 6[/tex]

                                  = 69 m²

Area of the rectangle (2) = Length × Width

                                         = 12 × 15

                                         = 180 m²

Area of the trapezoid (3) = [tex]\frac{1}{2}(12+10)\times 11[/tex]

                                         = 121 m²

Now area of the wall = 69 + 180 + 121

                                   = 370 m²

One tin covers the area = 25 m²

Number of tins required to paint the wall = [tex]\frac{\text{Total area}}{\text{Area covered by one tin}}[/tex]

= [tex]\frac{370}{25}[/tex]

= 14.8

Therefore, number of tins to be purchased = 15

Cost to paint the complete wall = 15 × £7

                                                       = £105

Answer: 4

Step-by-step explanation: a is three units away from o and a’ is 9 units away from o. you add 9+3 to get the total distance and divide that number by 3 to get the scale factor. 12/3=4

The scale factor for the given dilation is 3

Dilation is a transformation of an object which changes its size. if the dilated image is larger then it is called enlargement. If the dilated image is smaller it is called reduction.

If the dilation has the origin as the center of dilation, we can find points on the image formed by dilation by multiplying the coordinates of the original geometric object like triangle multiplying by the scale factor. For scale factor k, the transformation of the dilation is written as :  (x, y) → (k x, k y).

The scale factor ,k  = coordinate of image / coordinate of original

Given that Triangle ABC is dilated to create triangle A’B’C’ using point O as the center of dilation as shown in the figure

Scale Factor = coordinate of image / coordinate of original

                    = OA' / OA = 9/3 = 3

Therefore, the scale factor for the given dilation is 3.

Also, Learn more about dilation from the link given below:

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Answer:

A= 78.5 sq. in

Step-by-step explanation:

Step by step

1: A = pi * r^2

2: A = 3.14 * 25

In words.

1: Times the pi by r^2

2: The answer will come out as 3.14

3: Times the Answer that is 3.14 by 25

Answer: A= 78.5 sq. in

Hope this helps.

Answer:

C=43.988cm

Step-by-step explanation:

r=d/2=14cm/2=7cm

C=2πr

C=2×3.142×7cm

C=6.284×7cm

C=43.988cm

Answer:

39.0953=39cm2

Step-by-step explanation:

Minor arc =70

Angle of arc=70

Then this sector =70/360=7/36 of the circle

Then area = 7/36x3.14x8x8=39cm2 approximatly

Answer:

x = -2/3

Step-by-step explanation:

27^x=1/9

writing 27 as 3^3  and 1/9 as 3 ^-2

3^3^x = 3^-2

We know that a^b^c =a^(b*c)

3^(3x) = 3^-2

Since the bases are the same the exponents need to be the same

3x = -2

x = -2/3

Answer:

0.965925826

0.258819045

Step-by-step explanation:

→If you were to calculate [tex]sin(75)[/tex], you would have a total of:

0.965925826

→If you were to calculate [tex]cos(-75)[/tex], you would have a total of:

0.258819045

Answer: He scored 7 marks

Step-by-step explanation:

Correct answer gets +5, so 5 * 3 = 15

Incorrect answer gets -2 so -2 * 4 = -8

So he scored 15 - 8 = 7

Answer:

-39 is less than or equal to C

Step-by-step explanation:

39 is greater or equal to -C

-39 is less than or equal to C

Answer:

~62%

Step-by-step explanation:

Let n(A) be the number of students signed up for Algebra II.

Given that n(A) = 298

Let n(B) be the number of students signed up for Chemistry.

Given that n(B) = 328

n(A [tex]\cup[/tex] B) will be the number of students who have signed up for either one or both of two subjects.

n(A [tex]\cup[/tex] B) = 386

Formula for n(A [tex]\cup[/tex] B):

n(A [tex]\cup[/tex] B) = n(A) + n(B) - n(A [tex]\cap[/tex] B)

Where n(A [tex]\cap[/tex] B) is the number of students signed up for both the courses.

Putting the values in the formula above:

386 = 298 + 328 - n(A [tex]\cap[/tex] B)

n(A [tex]\cap[/tex] B) = 240

Formula for Probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(A \cap B) = \dfrac{n(A \cup B) }{n(A \cap B)}[/tex]

[tex]\Rightarrow P(A \cap B) = \dfrac{240 }{386}\\\Rightarrow P(A \cap B) = 62.17\%[/tex]

Hence, the required probability is ~62%

The probability that a student chosen at random from the 386 will be signed up for both of the courses should be 62%.

Since total of 386 students are taking either one or both of the two courses. If 298 students signed up for Algebra II and 328 have signed up for Chemistry

So here the no of students that signed up for both subjects should be

= 298 + 328 - 386

= 240

Now the probability is

[tex]= 240\div 386[/tex]

= 62%

Hence, The probability that a student chosen at random from the 386 will be signed up for both of the courses should be 62%.

Learn more about probability here: https://brainly.com/question/16923992

Answer:

2 times

Step-by-step explanation: