Adding fractions with uncommon denominators

Answer:

B is the correct answer , B. 10,24,26

Step-by-step explanation:

Answer:

If a unit fraction has a repeating decimal, its multiples will also have repeating decimals. Division by the same divisor generates the same repeating pattern. Thus, multiples cannot avoid repetition.

Explanation:

If the decimal form for a unit fraction (a fraction where the numerator is 1) is a repeating decimal, then its reciprocal (the fraction obtained by flipping the numerator and denominator) will also be a repeating decimal. This is a consequence of the way division works.

For example, if [tex]\( \frac{1}{3} \)[/tex] is a repeating decimal (0.333...), then [tex]\( \frac{3}{1} \)[/tex] (which is [tex]\( 3 \times \frac{1}{3} \)[/tex] ) will also be a repeating decimal because dividing 3 by 1 will result in the same repeating pattern.

So, no matter how you multiply a unit fraction that has a repeating decimal representation, the resulting decimal will still be repeating. Therefore, it is not possible for a multiple of that fraction to have a decimal form that is not a repeating decimal.

The given equation is a linear equation in standard form. It can be solved for 'y' by isolating 'y' on one side. The resulting 'y' expression represents a straight line in a 2D coordinate system.

The equation 3/5 x + 1.4 y = 2/5 is a linear equation in the standard form a*x + b*y = c. In this equation, 'x' and 'y' are variables, '3/5' is the coefficient of 'x', '1.4' is the coefficient of 'y', and '2/5' is a constant.

To solve this equation, we can neatly isolate 'y' by subtracting '3/5 x' from both sides of the equation which would give us 1.4*y = -3/5*x+2/5. Then, we could further simplify by dividing both sides by '1.4', giving the equation for 'y' in terms of 'x'.

Note that this equation represents a straight line in a coordinate system. The value of 'x' and 'y' would depend on the specific problem's constraints or where this line intersects with another line in a system of linear equations.

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25*2 = 50

80-50 =30

30 /2 = 15

Answer is B

40 x 5280 = 211200 feet per hour

211200 / 3600 = 58.666 = 59 feet per second

Answer:

40%

Step-by-step explanation:

The second ten natural (counting) numbers are:

11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Out of these, the prime numbers are:

11, 13, 17, 19

This is 4 numbers out of 10; this makes

4/10 = 0.4 = 40%

In the second ten natural numbers (11-20), the prime numbers are 11, 13, 17, and 19, making 4 out of 10 numbers or 40% of numbers in this range, prime.

The second ten natural numbers are 11 through 20. To figure out what percent of these are prime numbers, we must first identify the primes in this set. The prime numbers between 11 and 20 are 11, 13, 17, 19. That's four prime numbers. Then, to find the percentage, we take the number of primes (4) and divide it by the total numbers in the set (10). So, 4/10 = 0.4. Multiply this by 100% to convert to a percentage and we have 40%.

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The the function represented by f(x) = mx + b is called a linear function.

A straight line can be written in the form of equation as, y = mx + c.

Two straight lines intersect each other only at one point.

When two straight lines are parallel to each other the angle between them is zero.

The given function is as below,

f(x) = mx + b

This function is equivalent to the point-slope function of a straight line where m represents the slope of the line and c is the y-intercept.

The degree of the given function is one.

Thus, it is a linear function.

Hence, a function of the form f(x) = mx + b, where m and b are real numbers, is called a linear   function.

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The equation of the line L is : y = -5x - 10..or 5x + y = -10

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

Given; The point A(-3,5) and the point B(1,-15) lie on the line L.

The slope = (-15 - 5) / (1 - (-3)

= -20/4

m = -5

Therefore, y = mx + b

The slope(m) = -5

Now use either of ur points...(-3,5)...x = -3 and y = 5

Thus, we subtract and find b, the y value,

5 = -5(-3) + b

5 = 15 + b

5 - 15 = b

-10 = b

Thus the equation is : y = -5x - 10..or 5x + y = -10

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The equation of the circle will be x² + (y + 3)² = 4. Then the correct option is C.

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at the (h,k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x - h)² + (y - k)² = r²

The center of the circle is at (0, -3) and the radius of the circle is 2 units. Then the equation of the circle will be

(x - 0)² + (y - (-3))² = 2²

         x² + (y + 3)² = 4

Then the correct option is C.

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To calculate the time it takes to fill a tank using a well pump that pumps at 8.4 gallons per minute, divide the tank's volume (in gallons) by the pump's output rate (8.4 gallons per minute). For example, for a tank with a volume of 84 gallons, it would take about 10 minutes to fill.

The time it takes to fill the tank with a well pump pumping at a rate of 8.4 gallons per minute depends on the size of the tank, which wasn't specified in your question. However, to calculate this, you would use the formula: Time = Volume / Rate. If 'Volume' is the size of your tank in gallons and 'Rate' is the rate the well pump can pump water in gallons per minute (8.4 in this case), you would divide the 'Volume' by the 'Rate' to get the time it would take to fill the tank in minutes.

For example, if your tank has a volume of 84 gallons, using our formula: Time = Volume / Rate, it would translate to Time = 84 / 8.4. This gives us a duration of 10 minutes.

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After the addition of sand in the sandbox the total amount of sand in the sandbox will be equal to 21900 grams.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Total amount of sand in the sandbox = 14,500 grams

Then, James adds 7400 grams more to the sandbox.

So,

The total amount of sand in the sandbox will be,

= 14500 + 7400

= 21900 grams.

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Your questions seem incomplete, so the complete question may be:

Jim has 19,700 g of sand in his sandbox. He brings home another 6,300 g of sand from the beach to add to his sandbox.

How many kilograms of sand does Jim have in his sandbox now?

Answer:

  In the US: 14,560,000

  In Britain: 1.456×10⁷

Step-by-step explanation:

On the European side of the Atlantic, "standard form" for a number is the form called "scientifc notation" on the American side of the Atlantic.

Answer:

  B.  0.0000000861

Step-by-step explanation:

The exponent of -8 tells you the leading digit (8) goes in the 8th spot to the right of the decimal point. The number is ...

[tex]0.0000\,0008\,61[/tex]

To divide 65 by 26 and give the answer as a mixed number, find how many times 26 can go completely into 65 to give the whole number part, with the remainder being your numerator and 26 the denominator. This gives 2 13/26. Simplifying the fraction, 65 divided by 26 equals 2 1/2.

To divide 65 by 26 and represent the answer as a mixed number, we first determine how many times 26 can go into 65 without going over. This figure is our whole number. 26 goes into 65 two times completely (2x26 equals 52), with a remainder of 13 (65 - 52 equals 13) left over. Therefore, the whole number part of our mixed number result is 2 and the remainder becomes the numerator in our fraction, with 26 being the denominator. Hence, 65 divided by 26 equals 2 13/26. To simplify this fraction, we can see that 13 and 26 share a common factor of 13. Dividing both by 13, our simplified fraction is 1/2. Therefore, 65 divided by 26 as a mixed number is 2 1/2.

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The fraction 9/4 can be written as a decimal by performing the division, resulting in 2.25. As this is already to three decimal places, the answer is 2.250.

To write the fraction 9/4 as a decimal, you simply need to perform the division operation. Dividing 9 by 4 will give you the decimal. Using a calculator or long division, the result is 2.25.

However, your question asks for the answer to be rounded to three decimal places. Since 2.25 already falls within that criteria, there's no need for further rounding. Therefore, 9/4 as a decimal, rounded to three decimal places, is 2.250.

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