A family went on vacation and used 5.4 gallons of gasoline to travel 150 miles. How many total gallons of gasoline will they need to travel 200 more miles?

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.

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%.

https://brainly.com/question/35915729

#SPJ2

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.

To learn more about finding average , click :

brainly.com/question/33677379

#SPJ5

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, ∞).

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.

48:3= 16  36:2=18  96:6= 16

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.

https://brainly.com/question/35412502

#SPJ2

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]

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]

To find the product of the expression (a-3/7) divided by (3-a/21), multiply (a-3/7) by the reciprocal of (3-a/21), yielding the simplified expression ((21a - 9)/ (21a - 7)) valid for all values of 'a' except when 'a' equals 8/3.

The student is asking for the product of the expression (a-3/7) divided by (3-a/21). To simplify this expression, we need to apply the division of fractions rule, which states that to divide by a fraction, you multiply by its reciprocal. The reciprocal of (3-a/21) is (21/(3a-1)). So our new expression is (a-3/7) × (21/(3a-1)).

We can multiply the numerators and denominators separately: (a-3/7) × 21 = (a× 21 - 3× 3) and 7 × (3a-1) = 21a-7. Simplified, we get ((21a - 9)/ (21a - 7)) as the product.

However, we should also check if the expression is defined for all values of 'a' as there may be values for which the denominator becomes zero. Specifically, we need 'a' to not be such that (3a-1) equals 7, which simplifies to a = 8/3. So for all values of 'a' except when 'a' equals 8/3, the product of the given expression is ((21a - 9)/ (21a - 7)).

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