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Dmitrij [34]
3 years ago
11

A mixture is made with 45 ounces of a 10% saline solution and $x$ ounces of a 70% saline solution. The resulting mixture is a 25

% saline solution. What is the value of $x$
Mathematics
1 answer:
solmaris [256]3 years ago
7 0

Answer:

x = 15 ounces

Step-by-step explanation:

A mixture is made with two types of solutions.

Solution A - 45 ounces of 10% saline solution

Solution B - x ounces of 70% saline solution

Resulting mixture - (x + 45) ounces of 25% saline solution

To get the value of x, equation will be,

(45 × 0.10) + (x × 0.70) = (x + 45) × 0.25

4.5 + 0.70x = 0.25x + 11.25

0.25x - 0.70x  = 4.5 - 11.25

-0.45x = -6.75

x = \frac{6.75}{0.45}

x = 15 ounces    

You might be interested in
Two college roommates have each committed to donating to charity each week for the next year. The roommates’ weekly incomes are
schepotkina [342]

Answer:

C. 5 weeks.

Step-by-step explanation:

In this question we have a random variable that is equal to the sum of two normal-distributed random variables.

If we have two random variables X and Y, both normally distributed, the sum will have this properties:

S=X+Y\\\\\ \mu_S=\mu_X+\mu_Y=30+60=90\\\\\sigma_S=\sqrt{\sigma_X^2+\sigma_Y^2}=\sqrt{10^2+20^2}=\sqrt{100+400}=\sqrt{500}=22.36

To calculate the expected weeks that the donation exceeds $120, first we can calculate the probability of S>120:

z=\frac{S-\mu_S}{\sigma_S} =\frac{120-90}{22.36}=\frac{30}{22.36}=1.34\\\\P(S>120)=P(z>1.34)=0.09012

The expected weeks can be calculated as the product of the number of weeks in the year (52) and this probability:

E=\#weeks*P(S>120)=52*0.09012=4.68

The nearest answer is C. 5 weeks.

6 0
2 years ago
Which of the following sets shows all the numbers from the set {1, 2.5, 3, 4.5, 5} that make the inequality 3a + 4 ≥ 13 true?
zmey [24]
3(1)+4<span>≥ 13
7</span><span>≥ 13 
No

3(2.5)+4</span><span>≥ 13
11.5</span><span>≥ 13
No

3(3)+4</span><span>≥ 13
13</span><span>≥ 13
Yes

{3, 4.5, 5}</span>
3 0
3 years ago
Read 2 more answers
Two square are congruent ,if they have same ______​
OverLord2011 [107]

Two squares are congruent if they have the same side length.

3 0
3 years ago
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If you had to add two fractions with denominators of 4 and 5. What might the denominator of the sum be? Show more than one possi
Fiesta28 [93]

Answer:

9

Step-by-step explanation:

4 0
3 years ago
5x minus 4 equals x squared minus 4x plus 4. What is x
Sauron [17]

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((0 -  5x2) -  4x) -  4  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  -5x2 - 4x - 4  =   -1 • (5x2 + 4x + 4)

Trying to factor by splitting the middle term

3.2     Factoring  5x2 + 4x + 4

The first term is,  5x2  its coefficient is  5 .

The middle term is,  +4x  its coefficient is  4 .

The last term, "the constant", is  +4

Step-1 : Multiply the coefficient of the first term by the constant   5 • 4 = 20

Step-2 : Find two factors of  20  whose sum equals the coefficient of the middle term, which is   4 .

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step  3  :

 -5x2 - 4x - 4  = 0

Step  4  :

Parabola, Finding the Vertex :

4.1      Find the Vertex of   y = -5x2-4x-4

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is  -0.4000  

Plugging into the parabola formula  -0.4000  for  x  we can calculate the  y -coordinate :

 y = -5.0 * -0.40 * -0.40 - 4.0 * -0.40 - 4.0

or   y = -3.200

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = -5x2-4x-4

Axis of Symmetry (dashed)  {x}={-0.40}

Vertex at  {x,y} = {-0.40,-3.20}

Function has no real roots

Solve Quadratic Equation by Completing The Square

4.2     Solving   -5x2-4x-4 = 0 by Completing The Square .

Multiply both sides of the equation by  (-1)  to obtain positive coefficient for the first term:

5x2+4x+4 = 0  Divide both sides of the equation by  5  to have 1 as the coefficient of the first term :

  x2+(4/5)x+(4/5) = 0

Subtract  4/5  from both side of the equation :

  x2+(4/5)x = -4/5

Add  4/25  to both sides of the equation :

 On the right hand side we have :

  -4/5  +  4/25   The common denominator of the two fractions is  25   Adding  (-20/25)+(4/25)  gives  -16/25

 So adding to both sides we finally get :

  x2+(4/5)x+(4/25) = -16/25

Adding  4/25  has completed the left hand side into a perfect square :

  x2+(4/5)x+(4/25)  =

  (x+(2/5)) • (x+(2/5))  =

 (x+(2/5))2

Things which are equal to the same thing are also equal to one another. Since

  x2+(4/5)x+(4/25) = -16/25 and

  x2+(4/5)x+(4/25) = (x+(2/5))2

then, according to the law of transitivity,

  (x+(2/5))2 = -16/25

Note that the square root of

  (x+(2/5))2   is

  (x+(2/5))2/2 =

 (x+(2/5))1 =

  x+(2/5)

Now, applying the Square Root Principle to  Eq. #4.2.1  we get:

  x+(2/5) = √ -16/25

Subtract  2/5  from both sides to obtain:

  x = -2/5 + √ -16/25

Since a square root has two values, one positive and the other negative

  x2 + (4/5)x + (4/5) = 0

  has two solutions:

 x = -2/5 + √ 16/25 •  i

  or

 x = -2/5 - √ 16/25 •  i

Note that  √ 16/25 can be written as

 √ 16  / √ 25   which is 4 / 5

Solve Quadratic Equation using the Quadratic Formula

4.3     Solving    -5x2-4x-4 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                   

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     -5

                     B   =    -4

                     C   =   -4

Accordingly,  B2  -  4AC   =

                    16 - 80 =

                    -64

Applying the quadratic formula :

              4 ± √ -64

  x  =    —————

                   -10

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written  (a+b*i)

Both   i   and   -i   are the square roots of minus 1

Accordingly,√ -64  =

                   √ 64 • (-1)  =

                   √ 64  • √ -1   =

                   ±  √ 64  • i

Can  √ 64 be simplified ?

Yes!   The prime factorization of  64   is

  2•2•2•2•2•2

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 64   =  √ 2•2•2•2•2•2   =2•2•2•√ 1   =

               ±  8 • √ 1   =

               ±  8

So now we are looking at:

          x  =  ( 4 ± 8i ) / -10

Two imaginary solutions :

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

 or:

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

Two solutions were found :

x =(4-√-64)/-10=2/-5+4i/5= -0.4000-0.8000i

x =(4+√-64)/-10=2/-5-4i/5= -0.4000+0.8000i

<em>hope i helped</em>

<em>-Rin:)</em>

6 0
3 years ago
Read 2 more answers
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