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. Define the input and output in the given scenario

An array can be utilized to represent the multiplication of two numbers in Mathematics. In this representation, the number 12 can be depicted by a 3x4 or 2x6 arrays. There can be various arrays to represent a number such as 12.

In mathematics, specifically in multiplication, arrays are often used to represent and visualize the multiplication of two numbers. The number 12 can be represented by an array in multiple ways, here we will use two ways:

Remember, for any number, there can be multiple arrays that represent it. For the number 12, for instance, other arrays such as 1 row by 12 columns (1x12) or 12 rows by 1 column (12x1) are possible as well.

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By setting up an equation based on the fact that K is between J and L, we found that x = 6. Substituting this value back into the expression for KL, we determined that KL = 8.

To find the value of x and KL, we'll first set up an equation using the fact that K is between J and L, which means JL = JK + KL. Substituting the given expressions:

5x - 10 = 2x + (x + 2)

Now, solve for x:

[tex]\[5x - 10 = 2x + x + 2\][/tex]

[tex]\[5x - 10 = 3x + 2\][/tex]

[tex]\[5x - 3x = 2 + 10\][/tex]

[tex]\[2x = 12\][/tex]

[tex]\[x = 6\][/tex]

Now that we have found the value of [tex]\(x\)[/tex], we can find [tex]\(KL\)[/tex] by substituting \(x = 6\) into the expression for KL:

[tex]\[KL = x + 2 = 6 + 2 = 8\][/tex]

So, x = 6 and KL = 8.

The question probable maybe:

Find the value of x and KL if K is between J and L. JK=2x, KL=x+2, and JL=5x-10.

sum = 10000(10000-1)/2

sum = 10000(100001)/2

sum = 100010000/2

sum = 50,005,000

Answer:

(-12)^2 = -12 * -12 = 144

The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

The statement is given as: "the difference of two numbers less than the greater number"

Let the numbers be x and y, where x > y.

So, the interpretation of the statement is:

x - y < x

Add x to both sides

-y < 2x

Rewrite as:

y > -2x

This means that the statement is true only when the smaller number is greater than twice the additive inverse of the greater number

Hence, the counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

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Answer:121

Step-by-step explanation:

The surface area to volume ratio for a cube with sides of 5 cm can be calculated using the formulas for surface area and volume of a cube. After calculating, the ratio is found to be 1.2 cm^-1.

The concept you're asking about relates to both geometry and biology, particularly cell biology. The surface area to volume ratio is important in determining how substances move in and out of cells.

To calculate the surface area and volume of a cube with sides measuring 5 cm, we use these two formulas:

Substituting 5 cm into these formulas, we get:

Finally, to get the surface area to volume ratio, divide the surface area by the volume:

So, the surface area to volume ratio for a cube with sides of 5 cm is 1.2 cm^-1.

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It’s 83

Step-by-step explanation:

Lorraine earned $2970 in simple interest over the 9 years.

We can use the formula for simple interest, which is:

[tex]\[ I = P \times r \times t \][/tex]

where:

[tex]\( I \)[/tex] is the interest earned,

[tex]\( P \)[/tex] is the principal amount (the initial amount of money),

[tex]\( r \)[/tex] is the annual interest rate (in decimal form), and

[tex]\( t \)[/tex] is the time the money is invested for, in years.

Given:

[tex]\( P = \$5500 \)[/tex] (the principal amount),

[tex]\( r = 6\% \)[/tex] per year (which we convert to a decimal by dividing by 100.

[tex]\( r = 0.06 \)[/tex]

[tex]\( t = 9 \)[/tex] years (the time period).

Now, we can calculate the simple interest:

[tex]\[ I = \$5500 \times 0.06 \times 9 \][/tex]

[tex]\[ I = \$5500 \times 0.54 \][/tex]

[tex]\[ I = \$2970 \][/tex]

Answer:

circle, line segment, and parallel lines

Step-by-step explanation:

A circle is the set of all points a given distance from a fixed point called a center.  This only uses the undefined term "point."

A line segment is a portion of a line with two distinct endpoints.  This uses the undefined terms "line" and "point."

Parallel lines are lines that never intersect.  This uses the undefined term "line."

An angle is two rays joined at a common point called the vertex.  While this does use the undefined term "point," it also uses the defined term "ray."  This is not one of our options.

An arc is a portion of the circumference of a circle.  This uses the term "circle," so it is not one of our options.

The required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

A company added a new oil thank that holds 350 barrels of oil than its old oil tank . Together they hold 3650 barrels of oil.

According to given question we have

Let the  Capacity of old oil tank = x barrels

Let the Capacity of New oil tank = x + 350 barrels

So,

x + x + 350 = 3650

2x = 3300

x = 1650 barrels

∴Capacity of old oil tank = 1650 barrels

Capacity of New oil tank

=  x + 350

=1650 +350

=2000 barrels

Therefore, the required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

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The value of x, which is the time delay between the two stones' projections, is 1.4 seconds. The velocity of the second stone 6 seconds after the first stone's projection (so 1.4 seconds after its own projection) is 11.32 m/s.

This question involves physics concepts, particularly with motion under gravity, velocity, and displacement. We need to use these principles of Physics to solve the problem.

First, let's calculate the displacement of the first stone 6 seconds after it is thrown. Since the stone is thrown downwards, its final displacement (S1) is given by the equation of motion:

S1 = ut + 0.5gt2, where u is initial velocity (8 m/s), g is acceleration due to gravity (9.8 m/s2), and t is the time (6 seconds).

Therefore, S1 = 8*6 + (1/2)*9.8*6*6 = 48 + 176.4 = 224.4 m.

The first stone is thrown from a tower of height 248 m, so its displacement from the base of the tower is

248 - S1 = 248 - 224.4 = 23.6 m.

The second stone is thrown upwards from the base of the tower, Therefore, after t=x seconds, it travels upward by S2 = ut - 0.5gt2 (=25x - 0.5*9.8*x2).

At t=6 seconds, it must be at a the same height as the first stone (23.6 m). So we set 25x - 0.5*9.8*x2 = 23.6, and solve this quadratic equation to find x = 1.4 seconds.

The second part of the question asks for the velocity of the second stone at this instant. The velocity of an object thrown upward-moving object is given by

v = u - gt, here u = initial velocity = 25 m/s, g = 9.8 m/s2 and t=x=1.4 seconds. Plugging in these values, we find that v = 25 - 9.8*1.4 = 11.32 m/s.

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To frame a cabin:

Lee will take 6.47 days and Ron will take 10.47 days.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

Lee can frame a cabin in 4 days less than Ron.

Ron can frame,

= 1 cabin/(x+4) days.

Lee can frame,

= 1 cabin/(x) days.

When they work together, they will do the job in 4 days.

That means,

4/x+4 + 4/(x) = 1

4(x+4+x)/x(x+4) = 1

x²-4x-16 = 0

Solving the quadratic equation,

x = 2 ± 2√5

Then,

x = -2.47 and x = 6.47.

Therefore, Lee can frame a cabin in  6.47 days and Ron will take 10.47  days.

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The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

Here,

The number is 633,248.

We have to compare the values of each 3 in the number 633,248.

What is Place value?

The value represented by a digit in a number on the basis of its position in the number is called the place value.

Now,

The number is 633,248.

From right the first 3 has place in Thousand place.

So, place value of this 3 is thousands place.

And, From right the second 3 has place in Ten thousands place.

The difference of each 3 is that they have different place values.

Therefore, The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

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A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]

B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]

Step 1: Understanding the conversion

Step 2: Converting microseconds to seconds

First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]

Step 3: Converting seconds to standard form

Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.

Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]

Answer:16 3/10

Step-by-step explanation: