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A function has a constant halving time. What type of function does this represent?

48:3= 16  36:2=18  96:6= 16

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.

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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Answer:

Average height increase for each additional centimeter of armspan is 0.93cm

What is height increase ?

Change in height from the last one is the increase of height .

Given , height y = 6.4 + 0.93x

            For x=1

              y1 = 6.4+ 0.93

            For x=2

              y2 = 6.4 + 0.93*2

            For x=3

              y3 = 6.4 + 0.93*3

   Here height increase

              y2-y1 = 0.93

              y3-y2 = 0.93

Hence,  average height increase for each additional centimeter of armspan is 0.93cm.

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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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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?

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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Final Answer:

La cantidad de agua que se debe agregar para que haya 20 gramos de cal por litro es de aproximadamente 0.625 litros. Esto se calcula ajustando la proporción actual de 250 gramos de cal en 8 litros de agua. La nueva proporción será de 20 gramos de cal por litro.

Step-by-step explanation:

Para resolver este problema, podemos usar una regla de tres simple. La relación actual es de 250 gramos de cal por 8 litros de agua. Queremos saber cuántos gramos de cal habría en 1 litro de agua.

Primero, calculemos cuántos gramos de cal hay por litro de agua en la situación actual:

[tex]\( \frac{250 \, \text{gramos de cal}}{8 \, \text{litros de agua}} \)[/tex]

Ahora, queremos encontrar cuántos gramos de cal habría en 1 litro de agua, así que multiplicamos la cantidad actual por 1/8:

[tex]\( \frac{250 \, \text{gramos de cal}}{8 \, \text{litros de agua}} \times \frac{1 \, \text{litro de agua}}{8} \)[/tex]

Esto nos dará la cantidad de gramos de cal por litro de agua en la nueva situación. Ahora, queremos que esta cantidad sea de 20 gramos:

[tex]\( \frac{250 \, \text{gramos de cal}}{8 \, \text{litros de agua}} \times \frac{1 \, \text{litro de agua}}{8} = x \, \text{gramos de cal por litro} \)[/tex]

Queremos que ( x ) sea igual a 20 gramos:

[tex]\( x = 20 \, \text{gramos de cal por litro} \)[/tex]

Entonces, puedes resolver esta ecuación para encontrar cuántos litros de agua se necesitan:

[tex]\( \frac{250 \, \text{gramos de cal}}{8 \, \text{litros de agua}} \times \frac{1 \, \text{litro de agua}}{8} = 20 \, \text{gramos de cal por litro} \)[/tex]

Resolviendo esta ecuación, obtendrás la cantidad de litros de agua necesarios para lograr que haya 20 gramos de cal por litro.

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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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.

Answer:

96

Step-by-step explanation:

All you gotta do is multiply 7 by a high number like say 80 you wont get 672 just keep on multiplying it by higher numbers till you get 672 i hope i helped

Answer: [tex]p(x)= 13x-20[/tex]

Step-by-step explanation:

Given: The revenue for mowing x lawns is [tex]r(x) = 18x[/tex] .

Becca's cost for gas and the mower rental is c(x) = 5x + 20

The profit from mowing x lawns is given by :-

[tex]p(x)=(r-c)(x)[/tex]

The above  function can be written as

[tex]p(x)=(r-c)(x)=r(x)-c(x)\\\\\Rightarrow p(x)= 18x-(5x+20)\\\\\Rightarrow p(x)= 18x-5x-20\\\\\Rightarrow p(x)= 13x-20[/tex]

Answer with explanation:

The function for which we have to find , the intervals on which the polynomial is entirely negative and those on which it is entirely positive.

 f(x)= -x²+6 x -10

 If you will find the root of the function, there is no real root.

To find the root we will use Discriminant formula

For a Quadratic function, ax²+b x+c=0,

 [tex]x=\frac{-b+\sqrt{D}}{2a}\\\\D=b^2-4ac\\\\x=\frac{-6\pm \sqrt{6^2-4 *(-1)*(-10)}}{2*(-1)}\\\\x=\frac{-6\pm\sqrt{-4}}{-2}[/tex]

→So,there is no interval in which  the polynomial is entirely negative and those on which it is entirely positive, which can be represented in interval notation using Ф.

   [tex]f(x)= -(x^2-6x+10)\\\\= - [(x-3)^2-9+10]\\\\=-(x-3)^2-1[/tex]

For, any value of x,the value of f(x) will be always Negative.

To find the vertex, put ,x-3=0

 x=3

And, by putting , x= 3 ,in the equation we get

y = -1

So,Vertex = (3, -1)

⇒If you will try to find the intervals in which the function is increasing , means the curve is moving up is from (-∞, 3) and the intervals in which the function is decreasing , means the curve is moving downward is from , (3, ∞).

Answer:  The required solution for b is [tex]b=\dfrac{2c+4}{3}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for b :

[tex]\dfrac{3b-4}{2}=c~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for b, we must take b on one side of the equation and all other terms on the other side.

From equation (i), we get

[tex]\dfrac{3b-4}{2}=c\\\\\Rightarrow 3b-4=2c\\\\\Rightarrow 3b=2c+4\\\\\Rightarrow b=\dfrac{2c+4}{3}.[/tex]

Thus, the required solution for b is [tex]b=\dfrac{2c+4}{3}.[/tex]

The interpretation of v(4) = 64 for a cube's volume means a cube with 4-unit sides has a 64 cubic unit volume. Doubling the sides to 8 units leads to a volume of 512 cubic units, resulting in a volume ratio of 8:1 because volume scales with the cube of the side length increase.

The statement v(4) = 64 indicates that a cube with side length 4 units has a volume of 64 cubic units. When each side of the cube is doubled, the new side length becomes 8 units. The volume of a cube is calculated as the cube of its side length (s³). So, the new volume is 8³ or 512 cubic units.

The ratio of the new volume to the old volume is 512:64, which simplifies to 8:1. This ratio is not simply 2 because the volume of a cube increases by the cube of the factor by which the side is increased. Since the sides are doubled (a factor of 2), the volume increases by 2³ or 8 times, not 2 times.

This reasoning outlines why the ratio of the volumes of two cubes, when one cube has sides twice as long as the other, is not 2 but 8:1. The surface area to volume ratio is also affected by changes in the side length, which is significant not only in geometry but also in disciplines such as biology.

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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