The Hamptons family has a fish tank holding 10,450 ml of water.The water is leaking at a rate of 270 ml per minute.

Part A: Define the input and output in the given scenario.


Part B: Write a function to model this situation.


Part C: How many liters of water will be left in the tank after 10 minutes.?

Answer:

13 1/3 miles = 40/3 miles

Step-by-step explanation:

1 1/8 gallons of gasoline  = 9/8 gallons of gasoline

(40/3) / (9/8)

= 40/3 x 8/9

= 320 /27

= 11 23/27 miles gallon of gasoline

Answer:

Yes, one box of Oaties is enough for everyone.

Explanation:

To find out if one box of Oaties is enough for everyone, let's calculate the total amount of cereal needed for each group and then sum them up.

For the younger children:

Number of younger children = 11

Amount of cereal needed for each younger child = 1/3 cup

Total cereal needed for younger children = Number of younger children × Amount of cereal needed for each younger child

Total cereal needed for younger children = 11 × 1/3 = 11/3 cups

For the older children:

Number of older children = 10

Amount of cereal needed for each older child = 3/4 cup

Total cereal needed for older children = Number of older children × Amount of cereal needed for each older child

Total cereal needed for older children = 10 × 3/4 = 30/4 = 7.5 cups

Now, let's sum up the total cereal needed for both groups:

Total cereal needed = Total cereal needed for younger children + Total cereal needed for older children

Total cereal needed = 11/3 + 7.5

To add fractions, we need a common denominator, which is 3 in this case:

Total cereal needed = (11/3) + (7.5 × 3/3)

Total cereal needed = (11/3) + (22.5/3)

Total cereal needed = (11 + 22.5) / 3

Total cereal needed = 33.5/3

Now, 33.5/3 cups of cereal are needed for everyone.

Since one box of Oaties contains 12 cups of cereal, let's check if it's enough:

1 box = 12 cups

So, 12 cups > 33.5/3 cups

Yes, one box of Oaties is enough for everyone.

Answer:

$33,856

Step-by-step explanation:

We have been given that in 1980, when the consumer price index (CPI) was 82.4, Ivan purchased a house for $71,900. The CPI in 1970 was 38.8. We are asked to find the cost of house in 1970.

[tex]\text{Past dollars in terms of recent dollars}=\text{Dollar amount}\times \text{Ending-period CPI}\div\text{ Beginning-period CPI}[/tex]

Substitute the given values:

[tex]\text{Cost of house in 1970}=\$71,900\times 38.8\div 82.4[/tex]

[tex]\text{Cost of house in 1970}=\$71,900\times 0.470873786407767[/tex]

[tex]\text{Cost of house in 1970}=\$33,855.825242718[/tex]

[tex]\text{Cost of house in 1970}\approx \$33,856[/tex]

Therefore, the cost of house in 1970 was $33,856.

The equation representing the Manuel's situation is -

y = 10x + 5

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following problem -

Manuel builds and sells wooden crates. He made this table to show how much his crates cost in dollars -

Number of crates (n)    2       4       6       8

Cost ($)                       $25   $45   $65   $85

We can write the equation as -

y = mx + c

y = {(45 - 25)/(4 - 2)}x + c

y = 10x + c

c = 25 - 10 x 2

c = 5

Therefore, the equation representing the Manuel's situation is -

y = 10x + 5

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Answer:

its -5 just took the test

Step-by-step explanation:

Answer:

The correct answer is option B, - 5

Step-by-step explanation:

Answer:

−5x − 7 < −22 and −5x − 7 ≥ −3 (the first one)

Step-by-step explanation:

22 is bigger than -5x and 7

-5x-7 is equal to or less than 22

and negative 3 is just negative 3

hope this helps!

The equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 is -5x - 7 < -22 and -5x - 7 ≥ -3.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

We can subtract 7 from all parts of the inequality to get:

-29 > -5x ≥ -10

Then we can divide all parts by -5 (and remember to reverse the direction of the inequality signs because we are dividing by a negative number) to get:

5.8 < x ≤ 2

So, an equivalent form of the compound inequality -22 > -5x - 7 ≥ -3 is:

-5x - 7 < -22 and -5x - 7 ≥ -3

Therefore, the equivalent form of the compound inequality −22 > −5x − 7 ≥ −3 is -5x - 7 < -22 and -5x - 7 ≥ -3.

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To estimate the length of one wall of the square kitchen, take the square root of the area of 500 square feet, which gives approximately 22.4 feet, rounded to the nearest tenth.

The student is asking how to estimate the length of one wall in a square kitchen that has an area of 500 square feet. To find the length of the wall, you need to take the square root of the area because the area of a square is equal to the side length squared. Using a calculator, the square root of 500 is approximately 22.36 feet. Therefore, the length of one wall of the square kitchen is approximately 22.4 feet, rounded to the nearest tenth of a foot.

The question is about comparing the ratios or rates of the number of cans to cost. This mathematical analysis can help you determine which option offers the best value for money. The same method can be used to compare prices of different types of fruits.

The subject of the problem concerns the unit cost for purchasing cans or apples, bananas, grapes, and raspberries. It's essentially a comparison between two ratios or rates in mathematics. In this case, we have the ratio of cans to cost (either 5 cans for $6 or 8 cans for $10). For the first ratio, the price per can is $6 ÷ 5 cans = $1.2 per can. In the second scenario, the price per can is $10 ÷ 8 cans = $1.25 per can. Therefore, the option of 5 cans for $6 has a lower cost per can compared to the option of 8 cans for $10.

With the same method, you can compare prices of different types of fruits (apples, bananas, grapes, and raspberries), determining which fruit gives you the best value for your money based on the price per unit.

Through this kind of mathematical analysis, you can make informed decisions about value for money, which is a useful skill not only in performing school assignments but also in real-world situations such as grocery shopping.

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Answer:

The answer should be A) v-z w-x

Step-by-step explanation:

Answer: It is a rational number.

Step-by-step explanation:

Sine we know that Rational numbers are those numbers which can be written in the form of p/q where, q is not equal to zero.

Here p denotes the numerator and q denotes the denominator.

So, According to question,

p = 19 and q = 7

Hence, it is written in p/q form.

Therefore, it is a rational number.

If Mr.Ramirez divides 12 frogs equally into 6 groups for students each group will have 2 frogs.

Unitary method is a mathematical technique for first obtaining the value of a single unit then deriving the required units by multiplying it with the single unit.

This type of question can be solved using the unitary method where we can obtain how many frogs each group gets.

Given, Mr.Ramirez divides 12 frogs equally into 6 groups for students to study.

∴ Each group will have the total number of frogs upon the total number of groups which is,

= (12/6).

= 2 frogs.

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To find out how long Marsha and Sílvio practiced, we set up the equation x + 2x = 90, where x is the time Sílvio practiced. Solving the equation, we found that Sílvio practiced for 30 minutes and Marsha for 60 minutes.

The question asks us to solve for the amount of time Marsha and Sílvio each practiced their instruments given that Marsha practiced for twice the time that Sílvio did and together they practiced for a total of 90 minutes.

Let's denote the time Sílvio practiced as x minutes. This means Marsha practiced for 2x minutes. We know that the sum of their practice times is 90 minutes, which gives us the equation:

x + 2x = 90

Combining like terms, we have:

3x = 90

Dividing both sides by 3 to solve for x gives:

x = 30

Therefore, Sílvio practiced for 30 minutes and Marsha practiced for 60 minutes (double the time of Sílvio).

Answer:

81..........................................................................................

Step-by-step explanation:

To find the number of bowling pins equal in mass to one bowling ball, divide the mass of the ball by the mass of one pin. Approximately 4 pins are equal in mass to a 5.54 kg bowling ball.

To find how many bowling pins are equal in mass to one bowling ball, we divide the mass of the bowling ball by the mass of a single pin. This gives us the number of pins that would have a combined mass equal to the mass of the ball.

Mass of bowling ball = 5.54 kg
Mass of one pin = 1.58 kg

We calculate the number of pins as follows:

Number of pins = Mass of bowling ball / Mass of one pin
Number of pins = 5.54 kg / 1.58 kg
Number of pins ≈ 3.51

Since the number of pins must be a whole number, we would say that approximately 4 pins are equal in mass to one bowling ball.