100 PTS PLEASE HELP!!!!

The graph below shows the height of a tunnel f(x), in feet, depending on the distance from one side of the tunnel x, in feet:

Graph of quadratic function f of x having x-intercepts at ordered pairs 0, 0 and 36, 0. The vertex is at 18, 32.

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height? (6 points)

Part B: What is an approximate average rate of change of the graph from x = 5 to x = 15, and what does this rate represent? (4 points)

Answer:

The solution to the differential equation

y' = 1 + y²

is

y = tan x

Step-by-step explanation:

Given the differential equation

y' = 1 + y²

This can be written as

dy/dx = 1 + y²

Separate the variables

dy/(1 + y²) = dx

Integrate both sides

tan^(-1)y = x + c

y = tan(x+c)

Using the initial condition

y(0) = 0

0 = tan(0 + c)

tan c = 0

c = tan^(-1) 0 = 0

y = tan x

In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:

[tex]y = tan x[/tex]

Then say the differential equation as:

[tex]y' = 1 + y^2[/tex]

then rewriting as:

[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]

Integrate both sides, we have that:

[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]

So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:

[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]

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Answer:

20,158 cases

Step-by-step explanation:

Let [tex]t=0[/tex] represent year 2010.

We have been given that since 2010, when 102390 Cases were reported, each year the number of new flu cases decrease to 85% of the prior year.

Since the flu cases decrease to 85% of the prior year, so the flu cases for every next year will be 85% of last year and decay rate is 15%.

We can represent this information in an exponential decay function as:

[tex]F(t)=102,390(1-0.15)^t[/tex]

[tex]F(t)=102,390(0.85)^t[/tex]

To find number of cases in 2020, we will substitute [tex]t=10[/tex] in our decay function as:

[tex]F(10)=102,390(0.85)^{10}[/tex]

[tex]F(10)=102,390(0.1968744043407227)[/tex]

[tex]F(10)=20,157.970260446597\approx 20,158[/tex]

Therefore, 20,158 cases  will be reported in 2020.

Answer:

Distance = 44 m

Change in position = 0 m

Step-by-step explanation:

Given:

Running around the house covering a total length of 44 m and reaching the same position where you started.

So, initial position is same as final position.

Change in position is given as:

Change = Final position - Initial position

Now, since, final position = Initial position.

So, Change in position = 0 m

Now, distance is the total length of the path covered. So, you started from your initial position and ran around the house covering a path length of 44 m before reaching the same starting position.

Therefore, the distance is equal to the path length and hence is equal to 44 meters

Answer:

Option A:    [tex]$ \frac{\textbf{2}}{\textbf{9}} $[/tex]

Step-by-step explanation:

Given there are 10 cards viz: 1, 2, 3, 4, . . . , 10

We find the probability of drawing two cards less than six, without replacing the first card.

Draw 1:

There are 5 cards with value less than 6. 1, 2, 3, 4, 5

The total number of cards is 10.

The probability of the number being less than 6 = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} cards \hspace{1mm} less \hspace{1mm} than \hspace{1mm} 6}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $[/tex]

[tex]$ = \frac{5}{10} $[/tex]

Draw 2:

We are again drawing a card without replacing the card that was drawn earlier. This makes the total number of cards 9.

Also, the number of cards less than 6 will now be: 4.

Therefore, probability of drawing a number less than 6 without replacing

[tex]$ = \frac{4}{9} $[/tex]

Since, both draw 1 and draw 2 are happening we multiply the two probabilities. We get

[tex]$ \textbf{P} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{10}} \hspace{1mm} \times \hspace{1mm} \frac{\textbf{4}}{\textbf{9}} $[/tex]

[tex]$ \therefore P = \frac{\textbf{2}}{\textbf{9}} $[/tex]

Hence, OPTION A is the required answer.

Answer:

The answer is x = -6.6

Step-by-step explanation:

Answer:

X= -6.6

Step-by-step explanation:

Just do 13.8 - 20.4. It will equal -6.6.

Answer:

Step-by-step explanation:

It would take them 8 hours to complete the painting task if they worked together.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

If painter A can paint the area in 3 hours, and painter B can paint the same area in 5 hours, then it would take them a total of 3+5=8 hours to paint the area together.

It's worth noting that this assumes that both painters are able to work at their full capacity while working together and that they are able to divide the work between them in an efficient manner. If either of these conditions is not met, it could take them longer than 8 hours to complete the job.

Hence, working together, it would take them 8 hours to complete the painting job.

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Answer:

  sin(13π/40)

Step-by-step explanation:

The given expression matches the pattern ...

  sin(a)cos(b) +cos(a)sin(b) = sin(a+b)

Then ...

  sin(pi/5)cos(pi/8) + cos(pi/5)sin(pi/8) = sin(π/5 +π/8)

  = sin(13π/40)

_____

  π/5 +π/8 = π(1/5 +1/8) = π(8/40 +5/40) = π(13/40)

The trigonometric expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 can be simplified to sin(13π/40) by using the sine addition formula.

The expression sinπ/5 cosπ/8 + cosπ/5 sinπ/8 resembles the formula for the sine of a sum, sin(a+b) = sin(a)cos(b) + cos(a)sin(b). By applying this trigonometric identity, we can rewrite the expression as the sine of a single angle. Therefore, sinπ/5 cosπ/8 + cosπ/5 sinπ/8 is equivalent to sin(π/5 + π/8). To simplify it further, we must find a common denominator for the two angles, π/5 and π/8, which is 40. Thus, we get sin((8π + 5π)/40), which simplifies to sin(13π/40).

Answer:

1. Yes, the lines are perpendicular.

2. [tex]y=\frac{5}{4}x+6[/tex]

Step-by-step explanation:

The first equation of Exercise 1 is incomplete. Let's assume that it is:

[tex]2x + 3y =n[/tex]

Where "n" is a number.

First, it is important to remember that the equation of a line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

By definition, the slopes of perpendicular lines are negative reciprocals.

1 . If you solve for "y" from the first equation, you get:

[tex]2x + 3y =n\\\\3y=-2x+n\\\\y=-\frac{2}{3}x+\frac{n}{3}[/tex]

You can identify that the slope is:

[tex]m=-\frac{2}{3}[/tex]

The second equation of the line is:

[tex]y=\frac{3}{2}x+4[/tex]

And its slope is:

[tex]m=\frac{3}{2}[/tex]

Since the slopes are negative reciprocals, the lines are perpendicular.

2. Given the first equation of the line:

[tex]y= -\frac{4}{5}x+6[/tex]

You can identify that:

[tex]m=-\frac{4}{5}\\\\b=6[/tex]

Since the first line and the second one are perpendicular, you know that the slope of the other line is:

[tex]m=\frac{5}{4}[/tex]

According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:

[tex]y=\frac{5}{4}x+6[/tex]

Answer: p=11

Step-by-step explanation:

12p+7)139

-7 -7

12p)132

÷12 ÷12

P)11

Answer:

p= 11

Step-by-step explanation:

1 2p + 7 > 1 39​

collection of like term

12p > 139 - 7

12p > 132

Divide both side by the coefficient of p

12p/12 > 132/12

p = 11

If they were to win $30 they would expect to get $27 in profit.

If they were to win $10 they would expect $7.

If they were to win $0 they would expect $-3 in profit, so technically if they win nothing they lose money.

Hope I could help! :D

If player expect to get out of this game every time he/she plays then they would loose money.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30.

and, If they were to win $30, they would anticipate making a profit of $27.

Also, if they would anticipate $7 if they were to win $10.

So, if they were to win nothing, they would lose money because they would expect to make $-3 in profit.

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Answer: B. 33%

Step-by-step explanation:

Given : Response  - Frequency

          Not satisfied - 20

              Satisfied - 40

         Highly satisfied - 60

Total customers = (Number of customers  Not satisfied) +  (Number of customers satisfied) + ( (Number of customers  Highly satisfied) )

= 20+40+60=120

Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]

[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]

Hence, the percentage of the responses indicated that customers were satisfied = 33%

Thus , the correct answer is B. 33%

To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.

To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.

Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.

To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.

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It's 1.25 seconds, I just took the test and got 100% Good Luck!!! :)

6.60 would be the total cost for both 3 pounds and two pounds :D

Answer:

$6.60

Step-by-step explanation:

multiply 1.20 (red apples) by 3 (lbs) = 3.6

and 1.50 (green apples) times 2 (lbs) = 3

then add the two totals = $6.60

Answer: 25/36

Step-by-step explanation:

A die has six faces, therefore its sample space S is 6

Since we are rolling a die twice(at different times), the probability of one turning up the first time is 1/6(i.e expected outcome/total outcome)

Similarly, if we throw the die the second time, the probability of one turning up the second time is also 1/6

The probability of having number greater than 1 land at each time will be (1- 1/6) which is 5/6.

Therefore the probability of having number greater than 1 land at "both times" will be 5/6×5/6 = 25/36

Answer:

79 years old

Step-by-step explanation:

Let his age be x

400-3x=163

400-163=3x

237=3x

Divide both side by 3

237/3 =3x/3

79=x

The man's age (x) =79 years old

Answer:

the answer is c

Step-by-step explanation:

i took the test and got a 100

The range of the function is all real numbers less than or equal to 0.

A function is an expression that shows the relationship between two or more variables or numbers.

The domain of a function is the set of input values while the range is the set of output values.

From the graph, The range of the function is all real numbers less than or equal to 0.

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Answer:

Influencer

Step-by-step explanation:

An influencer is a person who has the power affect purchase decisions of others because of his ability such as knowledge, position with audience.

Final answer:

A person acting as a specifier in the buying center provides product specifications and may influence the purchase decision by setting requirements, interacting with both customer and seller but not making final purchasing decisions.

Explanation:

Depending on the product, there may be a person who acts as specifier in the buying center, often by providing specifications for the product being purchased or the vendor being considered.

A specifier plays a crucial role in the procurement process, ensuring that the product or service meets the organization's needs and standards. In a buying center, this individual might not have the authority to make final purchase decisions but is influential by setting the requirements that the potential products or suppliers must meet.

A specifier may interact closely with both the customer and seller to ensure that the right features, quality, and functionalities are captured in the procurement specifications.

This person may also assess the long-term reliability of supplier relationships, such as through exclusive dealer agreements, to safeguard the company's interests. The role of the specifier is analogous to that of a product consultant, providing insights without directly engaging in sales or price negotiations.

The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).

To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).

Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.

Using the combination formula, C(27, 8) is calculated as:

27! / (8! * (27-8)!)

= 27! / (8! * 19!)

Factor out the common terms from the numerator and denominator

The remaining terms give us the total number of combinations

The probability is therefore: 1 / C(27, 8).

Answer:

x=-5 and x=-1.5

Step-by-step explanation:

The given function is

[tex]v(x) = \frac{{x}^{2} - 25}{2 {x}^{2} + 13x + 15} [/tex]

The points of discontinuity occurs at where the denominator is zero.

[tex]2 {x}^{2} + 13x + 15= 0[/tex]

We solve by factoring.

We first split the middle term:

[tex]2 {x}^{2} + 3x + 10x + 15= 0[/tex]

We factor by grouping:

[tex]x(2x + 3) + 5(2x + 3)= 0[/tex]

[tex](x + 5)(2x + 3) = 0[/tex]

The points of discontinuity occur at x=-5, and x=-1.5

Final answer:

The function v(x) has discontinuities at x = -3 and x = -5/2.

Explanation:

A point of discontinuity in a mathematical function refers to a location where the function fails to be continuous. In other words, it's a point at which the function exhibits a break or abrupt change in its behavior.

The point of discontinuity for the function [tex]v(x) = (x^2-25)/(2x^2+13x+15)[/tex] can be found by setting the denominator equal to zero and solving for x. In this case, the denominator factors to (x+3)(2x+5), indicating discontinuities at x = -3 and x = -5/2. These are the points where the function is not defined.

Points of discontinuity are essential to understanding the behavior and properties of functions, particularly in areas like calculus and real analysis. They are critical in identifying where a function fails to meet the criteria for continuity and in analyzing the behavior of functions in various contexts.

Answer:

Line ED

Explanation:

Opposite side is EF (because its opposite to the angle)

Hypotenuse side id FD (opposite of right angle)

Adjacent is the line leftover

Answer:

B

Step-by-step explanation:

Adjacent is the one with 90° and the angle, theta

ED in this case

Answer:

The vertex of the function is at point (-4,-1).

Step-by-step explanation:

Given function:

[tex]f(x)=(x+4)^2-1[/tex]

Solution:

The vertex form of a function is given by:

[tex]f(x)=a(x-h)^2+k[/tex]

where [tex](h,k)[/tex] is the vertex of the function. At this point the function has the maximum or minimum value.

Writing the given function in the vertex form.

[tex]f(x)=(x-(-4))^2+(-1)[/tex]

On comparing the above function with the standard form we find that:

[tex]a=1\\h=-4\\k=-1[/tex]

Thus, the vertex of the function is at point (-4,-1)

The vertex of the function f(x)= (x + 4)² - 1 is at the point (-4,-1) by comparing it with the vertex form of a quadratic function f(x) = a(x - h)² + k.

The function given is in the vertex form of a quadratic function, which is f(x) = a(x - h)² + k. In this form, the vertex of the graph of the function is at the point (h, k). For f(x)=(x + 4)² - 1, you can see that h is -4 and k is -1. Therefore, the vertex of the graph of the function is at the point (-4,-1).

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Answer:

We have: b = 823 foot

h = 534 Ft ,

Substitute their values,

A = 823 * 534

A = 439482 Ft² briefly, Your Answer would be: 439482 Ft²

~

For a fraction;

49 and 10/12

 multiply 8 and 2/3 by 5 and 3/4!

Answer:

k  = 0.0916

Step-by-step explanation:

T(t) = [tex]T_{s} + ( T_{o} - T_{s} )e^{-kt}[/tex]

from question; t = 12 mins , [tex]T_{s}[/tex] = 50 C , [tex]T_{o}[/tex] = 80 C , T = 60 C

60 = 50 + (80 - 50) [tex]e^{-12k}[/tex]

60-50 = 30 [tex]e^{-12k}[/tex]

10/30 =  [tex]e^{-12k}[/tex] (Taking natural Log of both sides)

In(0.3333) = In [tex]e^{-12k}[/tex]

-1.0986 = -12k

k = 0.0916

Answer:

Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Step-by-step explanation:

Given:

Goal of Total number of hours of biking in park =20 hours.

Number of hours rode on first day = [tex]5\frac34 \ hrs.[/tex]

So we will convert mixed fraction into Improper fraction.

Now we can say that;

To Convert mixed fraction into Improper fraction multiply the whole number part by the fraction's denominator and then add that to the numerator,then write the result on top of the denominator.

[tex]5\frac34 \ hrs.[/tex] can be Rewritten as [tex]\frac{23}{4}\ hrs[/tex]

Number of hours rode on first day = [tex]\frac{23}{4}\ hrs[/tex]

Also Given:

Number of hours rode on second day = [tex]6\frac45 \ hrs[/tex]

[tex]6\frac45 \ hrs[/tex] can be Rewritten as [tex]\frac{34}{5}\ hrs.[/tex]

Number of hours rode on second day = [tex]\frac{34}{5}\ hrs.[/tex]

We need to find Number of hours she need to ride on third day in order to achieve the goal.

Solution:

Now we can say that;

Number of hours she need to ride on third day can be calculated by subtracting Number of hours rode on first day and Number of hours rode on second day from the Goal of Total number of hours of biking in park.

framing in equation form we get;

Number of hours she need to ride on third day = [tex]20-\frac{23}{4}-\frac{34}{5}[/tex]

Now we will use LCM to make the denominators common we get;

Number of hours she need to ride on third day = [tex]\frac{20\times20}{20}-\frac{23\times5}{4\times5}-\frac{34\times4}{5\times4}= \frac{400}{20}-\frac{115}{20}-\frac{136}{20}[/tex]

Now denominators are common so we will solve the numerator we get;

Number of hours she need to ride on third day =[tex]\frac{400-115-136}{20}=\frac{149}{20}\ hrs \ \ Or \ \ 7\frac{9}{20}\ hrs.[/tex]

Hence Rebecca and Dan need to ride [tex]7\frac{9}{20}\ hrs.[/tex] on the third day in order to achieve goal of biking.

Final answer:

Rebecca and Dan need to ride for 7 9/20 hours on the third day to reach their goal of biking a total of 20 hours in the national park, having already biked 5 3/4 hours on the first day and 6 4/5 hours on the second day.

Explanation:

Rebecca and Dan are biking in a national park and want to achieve a goal of biking a total of 20 hours over three days. They biked 5 3/4 hours on the first day and 6 4/5 hours on the second day. To find the time they need to bike on the third day, we first convert the hours they biked into improper fractions:

Next, we add these two amounts together:

(23/4) + (34/5) = (23×5 + 34×4) / (4×5) = (115 + 136) / 20 = 251/20 hours.

Now we convert 251/20 hours to a mixed number:

251/20 = 12 11/20 hours

They have biked a total of 12 11/20 hours over the first two days. Their total goal is 20 hours, so we need to subtract the time already biked from the total goal:

20 hours - 12 11/20 hours = (20×20 - 12×20 - 11)/20 = (400 - 240 - 11)/20 = 149/20 hours.

Finally, we convert 149/20 hours back to a mixed number to find out how long they need to ride on the third day:

149/20 hours = 7 9/20 hours.

So, Rebecca and Dan need to ride for 7 9/20 hours on the third day to meet their goal of biking a total of 20 hours in the park.

To figure this out, use the acronym SOHCAHTOA to determine which trigonometric function to use.

8 is opposite to <R and 3 is adjacent to <R so we use tangent.

Set up the following equation: tan(x)=8/3

Find the inverse (aka. tan^-1): x=69.44

So your answer is <R=69.4 degrees

Hope this helped!

Answer:

x = 28.5 minutes

Step-by-step explanation:

Let x be the time taken for finishing the bike race.

Given:

Ella finished a bike race = 37.6 minutes

Miranda finished the race sooner than Ella = [tex]9\frac{1}{10} = \frac{91}{10} = 9.1\ minutes[/tex]

We need to find the minutes did it take Miranda to finish the race.

Solution:

From the statement, Miranda finished the race 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.

So, time taken by Miranda to finish the race:

[tex]Mirianda\ finshed\ a\ bike\ race = (Ella\ finshed\ a\ bike\ race) - 9.1[/tex]

[tex]x=37.6-9.1[/tex]

x = 28.5 minutes

Therefore, Miranda finished the bike race in 28.5 minutes.

Answer:

Hence,

The measure of ∠A is 60.065°

[tex]\m\angle A= 60.065[/tex]

Step-by-step explanation:

Given:

ΔABC is a Right Angle Triangle at ∠ B = 90°

BC = Opposite side to ∠A = 13 unit

AC = Hypotenuse  = 15 unit  

To Find:

m∠A = ?  

Solution:

In Right Angle Triangle ABC ,Sine Identity,

[tex]\sin A= \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]

Substituting the values we get

[tex]\sin A= \dfrac{BC}{AC}=\dfrac{13}{15}=0.8666\\\angle A=\sin^{-1}(0.8666)\\m\angle A= 60.065\°[/tex]

Hence,

The measure of ∠A is 60.065°

[tex]\m\angle A= 60.065[/tex]

Answer:

X+y=237Litres

Step-by-step explanation:

Let a be mixture of milk and water.

Let x =milk

Let y= water

z = x+y

Final volume of mixture =63litres + z

5/12(3+z))+60=8/15(63-z)

z =x+y= 237litres

The value of [tex]x+y[/tex] is 237 liters.

Given information:

A 63 liter mixture contains milk and water in a ratio of 4:5.

Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].

The initial mixture can be written as,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]

The initial amount of water and milk will be,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]

x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.

The mixture, now, can be written as,

[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]

60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.

Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.

The final mixture can be written as,

[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]

Solve for x and y as,

[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]

So, the value of [tex]x+y[/tex] will be,

[tex]x+y=147+90\\=237[/tex]

Therefore, the value of [tex]x+y[/tex] is 237 liters.

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