Jon filled a bucket with 2.7 gallons of water. He used 0.98 gallons for watering his tomato plants and 0.76 gallons for watering his peppers. How much water did he have left in his bucket?

Graphs and functions can be used to illustrate real life events.

The table is given as:

[tex]\left[\begin{array}{cccccccccc}Time&0&1&2&3&4&5&6&7&8\\P_1&90.0&76.5&65.0&55.3&47.0\\P_2&39&37&35&33&31\end{array}\right][/tex]

(a) The pattern in each population

Population 1

This population follows a geometric pattern.

The common ratio (r) is calculated by dividing the subsequent values of population 1.

We have:

[tex]r = \frac{P_1(1)}{P_1(0)}[/tex]

This gives

[tex]r = \frac{76.5}{90.0}[/tex]

[tex]r = 0.85[/tex]

Express as percentage

[tex]r = 85\%[/tex]

Next, we calculate the scale factor (k)

[tex]k = 1 - r[/tex]

[tex]k = 1 - 85\%[/tex]

[tex]k = 15\%[/tex]

Hence, the pattern of population 1 is: the population decreases by 15% each year

Population 2

This population follows an arithmetic pattern.

The common difference (d) is calculated by subtracting the subsequent values of population 1.

We have:

[tex]d = P_2(1) - P_2(0)[/tex]

[tex]d = 37 - 39[/tex]

[tex]d = -2[/tex]

-2 indicates that the population reduces, each year by 2000

(b) Complete the table

For population 1, we keep multiplying current population by 85%.

So, we have:

[tex]P_1(5) = 47.0 \times 85\% = 40.0[/tex]

[tex]P_1(6) = 40.0 \times 85\% = 34.0[/tex]

[tex]P_1(7) = 34.0 \times 85\% = 28.9[/tex]

[tex]P_1(8) = 28.9 \times 85\% = 24.6[/tex]

For population 2, we keep adding -2 to the current population

So, we have:

[tex]P_2(5) = 31 -2 = 29[/tex]

[tex]P_2(6) = 29 -2 = 27[/tex]

[tex]P_2(7) = 27 -2 = 25[/tex]

[tex]P_2(8) = 25 -2 = 23[/tex]

So, the complete table is:

[tex]\left[\begin{array}{cccccccccc}Time&0&1&2&3&4&5&6&7&8\\P_1&90.0&76.5&65.0&55.3&47.0&40.0&34.0&28.9&24.6\\P_2&39&37&35&33&31&29&27&25&23\end{array}\right][/tex]

(c) The graph of the two populations

First, we determine the equations of both populations

Population 1

We have:

[tex]P_1(0) = 90.0[/tex]

[tex]r = 0.85[/tex]

The nth term of a geometric sequence is:

[tex]P_1(n) = P_1(0) \times r^n[/tex]

This gives

[tex]P_1(n) = 90.0 \times 0.85^n[/tex]

Population 1

We have:

[tex]P_2(0) = 39[/tex]

[tex]d = -2[/tex]

The nth term of an arithmetic sequence is:

[tex]P_2(n) = P_1(0) + nd[/tex]

This gives

[tex]P_2(n) = 39 -2 \times n[/tex]

[tex]P_2(n) = 39 -2n[/tex]

See attachment for the graphs of:

[tex]P_1(n) = 90.0 \times 0.85^n[/tex] and [tex]P_2(n) = 39 -2n[/tex]

(d) Determine if both populations ever have the same value

From the attached image, the graph of both populations intersect at:

[tex](8.891,21.218)[/tex] and [tex](16.337,6.327)[/tex]

This means that both populations have equal values, twice

Read more about graphs and functions at:

https://brainly.com/question/18806107

Answer:

Step-by-step explanation:

Given the equation 3x-4y = 24,

The solution of the equation of the equation will be gotten at the point where x = 0 and y = 0 as shown;

when x = 0

3(0)-4y = 24

0-4y = 24

y = 24/-4

y = -6

Also when y = 0

3x-4(0) = 24

3x = 24

x = 24/3

x = 8

Hence the solution of the equation (x, y) are (8, -6)

b) The standard from of equation of a line is y = mx+c where m is the slope. To get the slope of the line, we will need to rewire the equation in slope intercept form first.

Given 3x-4y = 24

-4y = 24-3x

-4y = -3x+24

Divide through by -4

-4y/-4 = -3x/-4 + 24/-4

y = 3/4 x - 6

Comparing

m = 3/4

Hence the slope of the line is 3/4

c) This has been done in (b) above. The equation in slope-intercept form is

y = 2/4 x - 6

Answer:

I think it is B.

Step-by-step explanation:

They don't tell where the fraction will be placed and other people got it wrong when they thought they put the fraction in the greatest spot.

The value of x could be 1 and one-sixth, or StartFraction 8 Over 5 EndFraction options (A) and (B) are correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

The fractions are:

8/7, 1 2/5, x, 1 2/3, 2

Or

8/7, 7/5, x, 5/3, 2

1.142, 1.4, x, 1.667, 2

x could be

x = 1 1/6 = 1.166

Thus, the value of x could be 1 and one-sixth, or StartFraction 8 Over 5 EndFraction option (A) and (B) are correct.

Learn more about the fraction here:

brainly.com/question/1301963

#SPJ6

Answer:

61.50 pounds

Step-by-step explanation:

10.25 x 6

Answer:

135 rats

Step-by-step explanation:

first do 5 x 3 (because it triples every week) that equals 15 then triple that witch is 45, then triple that one more time, 135 (because you are supposed to do 3 weeks) so its 135 rats! hoped this helped ;)

Answer:

r = 2.7 cm

Step-by-step explanation:

From the figure attached,

To find the value of 'r' we will apply the sine rule in ΔRST,

sin(m∠R) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

sin(20)° = [tex]\frac{r}{SR}[/tex]

sin(20)° = [tex]\frac{r}{8}[/tex]

r = 8sin(20)°

r = 8(0.34202)

r = 2.736

r ≈ 2.7 cm

Answer:

b2= a2-c2. that is the formula while making b2 subject

Answer:

[tex]b=\sqrt{c^2-a^2}[/tex]

Step-by-step explanation:

a² + b² = c²

~Subtract a² to both sides

b² = c² - a²

~Take square root of both sides

b = ±√c²-a²

Best of Luck!

Answer:

C

Step-by-step explanation:

2 * 3 is 6

4 * 3 is 12

8 * 3 is 24

Answer:

C

Step-by-step explanation:

2,6 4,12 and 8,24 are all simplified to the fraction 1/3 so the relationship is proportional.

Also in each of the x column every number is always three times the amount.

Hope this helps! :) Plz mark as brainliest

Answer: No. The pool frame she choose will not fit into the 216 foot cubed hole. She should have picked a frame of 6ft.

Step-by-step explanation:

From the question, we are informed that Mrs. Dillard is installing a cubed swimming pool in her backyard and that the hole that her husband dug in her backyard is 216 feet cubed.

We are further told that she went to the pool store to pick out a pool frame. She chose a pool frame that had a length, width, and height of 7ft.

Since the height is 7ft, the volume will be: = 7ft × 7ft × 7ft = 343 feet cubed.

This shows that the pool frame she choose will not fit in the hole dug. She should have picked a frame of 6feet since (6ft × 6ft × 6ft) = 216 ft cubed.

Answer:

y+4= -16(x-9)

Step-by-step explanation:

point slope form is y-y1=m(x-x1)

substitute y-(-4)= -16(x-9)

simplify y+4= -16(x-9)

Answer:

Here we want to find all the possible combinations that we can make,

First, let's define the selections that we have, and the number of options for each one of these selections. (Remember that each option can be selected only once)

we have 3 flavors and 2 toppings, so let's analyze this case:

First flavor ----- here we have 10 options

Second flavor ---- because we already selected one before, now we have 9 options.

Third flavor ---- because we already selected two before, now we have 8 options.

First topping --- here we have 5 options,

Second topping --- because we already selected one before, here we have 4 options.

Now the total number of possible combinations will be equal to the product between the number of options for each selection:

C = 10*9*8*5*4 = 14,400

Answer:

21.6 km

Step-by-step explanation:

Given that,

The distance covered by a horse is 19.33 km and the distance covered by the train is 2.27 km.

Time taken during entire journey is 26.48 minutes

We need to find the total kilometers of Vanessa's journey in total. It can be calculated by simply adding distance covered by a horse and by train.

Total distance = 19.33 km+2.27 km

D = 21.6 km

So, the total distance covered by Vanessa's journey is 21.6 km.

Answer:

the answer is no solution

Step-by-step explanation:

when u solve you end up with 0= -22

Answer:

77

Step-by-step explanation

add

Answer:

its 130

Step-by-step explanation:

Answer: SEE EXPLANTION!

Step-by-step explanation:

In rolling a die once, you do have a 1/6 chance of getting 6. In rolling a die once (for the second roll), you do have a 1/2 chance of getting an odd number (getting 1, or 3 or 5).

Thank you!

Answer:

1/2.

Step-by-step explanation:

There are 3 odd numbers on the die (1, 3, 5) and 3 even numbers (2, 4, 6). So, the probability would be 3/6 (3 odd out of a total 6 numbers), which simplfies  to 1/2.

Answer:

y=3x +5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Hope this helped!

Happy Halloween!

Answer:

She used 1,136 fabrics in her third quilt

Step-by-step explanation:

For the first quilt, the number of fabrics used is 142

second quilt is 4 times this = 142 * 4 = 568 quilts

For the third quilt, she doubled the number of fabrics used

That will be 2 * 568 = 1,136 quilts

Answer:

<3 = 40 degrees

Step-by-step explanation:

90 + 58 + <1 = 180

148 + <1 = 180

<1 = 32

<1 = <2

32 = <2

<2 + <3 + 108 = 180

32 + <3 + 108 = 180

<3 + 140 = 180

<3 = 40

Answer:

its 21/40

Step-by-step explanation:

Answer:

m=1/6, point: (-1,-7)

Step-by-step explanation:

the point slope form is y-y1=m(x-x1) and m is the slope and x1 is 1 and y1 is -7 so it will be y-(-7)=1/6(x-(-1)) then when you simplify it, it will be y+7=1/6(x+1)

Answer:

The answer is below

Step-by-step explanation:

A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field position after the 3 plays.

Solution:

Number line is a straight line on which numbers are marked and are separated at regular intervals. A number line can be used for both addition and subtraction. Addition is done by counting to the right while subtraction is done by counting to the left.

Given that the football team lost 5 yards in each of their three downs, this is the same as 3(-5) = (-5) + (-5) + (-5)

Hence since it is negative we move to the left. Starting from 0, we move 5 units to the left 3 times, this gives -15

Answer:

b^itch as^s do ur own work

Step-by-step explanation:

Answer:

not enough info

Step-by-step explanation:

unless there is a way to confirm the other 90° angle, u cant say anything. it would be asa if u could. not sure if this is 100% correct, the lines are perpendicular, so it would be 90, but idk lol

Answer: i think it is (A

Step-by-step explanation:

Answer:

10 sessions

Step-by-step explanation:

let s be the number of gym session

and let y be the cost

the cost can be represented as

y=ms+c

given data

Green's Gym

c=$50

m=$30

y=30s+50------------1

Breakout Gym

c=$250

m=$10

y=10s+250------------2

equating 1 and 2 we can find s, which is the number of session

30s+50=10s+250

30s-10s=250-50

20s=200

s=200/20

s=10

     therefore the number of session is 10

Answer:

4/6 or in simplest form 2/3.

Step-by-step explanation:

2-(-2)/4-(-2)= 4/6