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The total cost for gas when driving 113 km per day in Europe for a week, with gas at 1.10 euros per liter and a mileage of 39.0 mi/gal, would be approximately $66.19 after converting euros to dollars at the given exchange rate of 1 euro = 1.26 dollars.

To calculate the cost of gas for driving 113 km per day over a week in Europe, where gas costs 1.10 euros per liter and the car has a gas mileage of 39.0 mi/gal, a series of conversions and calculations need to be done:

Step-by-step this would be:

Therefore, if the car is driven 113 km per day in Europe, the total cost for gas over one week, given the parameters listed, would be approximately $66.19 when converted into dollars.

48:3= 16  36:2=18  96:6= 16

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.

To clear fractions in the given equation 1/4x-2/5=1/2x+2, multiply each term by the least common denominator (LCD) of the fractions to eliminate the fractions. Simplify the equation and solve for x.

To clear fractions in the given equation 1/4x-2/5=1/2x+2, we can find the least common denominator (LCD) of the fractions. The LCD is the least common multiple (LCM) of the denominators, which in this case is 20. To clear the fractions, we can multiply each term in the equation by 20:

So, the value that can be used to clear fractions in the given equation is x = -48/5.

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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]

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 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:

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]

9.1 has 2 significant digits so to have 1 you need to round it to a whole number,

in 1 significant digit would be 9

To solve for sinθ when θ is in Quadrant II and cosθ = -2/3, use the Pythagorean identity sin2θ + cos2θ = 1. Since sinθ will be positive in Quadrant II, after calculations, sinθ equals √5/3.

To find the sine value for an angle θ in Quadrant II, where the cosine of θ is given to be cosθ = -2/3, we can use the Pythagorean identity: sin2θ + cos2θ = 1. We already know that cosθ = -2/3, so we can solve for sinθ:

Since we are in Quadrant II, where sine values are positive, we take the positive square root:

So the value of sinθ when cosθ = -2/3 in Quadrant II is √5/3.

Answer:

213 euros per month

Step-by-step explanation:

1dollar = 0.7306euros

thus $3,500 dollars can be found by a rule of three

dollar             euro

1             ⇒  0.7306

3500     ⇒        x

we find x as follows:

[tex]x=\frac{0.7306*3500}{1} = 2,557.1[/tex] euros

She will pay 2,557.1  euros per year.

Dividing between the 12 months of the year:

[tex]\frac{2,557.1}{12}=213.1[/tex]

Rounding to the nearest whole euro she will pay 213 euros per month.

Answer:

A

Step-by-step explanation:

I just took the test