A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is
95% salt. She wants to obtain 60 ounces of a mixture that is 85% salt. How many ounces of each solution should she use?

Answers

Answer 1

we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.

likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.

[tex]\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}[/tex]


Related Questions

what has a fraction in numerator, denominator or both???

Answers

a fraction that has a numerator and a denominator, is called a Complex fraction, i’m not sure if this is what you were asking for though.

Find the missing measurements

Answers

Answer:

O = 16.7 degrees

A = 73.3 degrees

Step-by-step explanation:

used a triangle calculator

Consider the figures below. Which of the following statements are true, given <S is congruent to <J and <N is congruent to <E? Select all that apply.

<A is congruent to <O

Triangle SAN~TriangleJOE

Triangle SAN is congruent to Triangle JOE

SN is congruent to JE

The perimeter of Triangle JOE is half the perimeter of Triangle SAN

There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN

There exists a sequence of rigid and non-rigid motions that maps Triangle SAN onto Triangle JOE

Answers

Answer:

<A is congruent to <O

Triangle SAN~TriangleJoe

There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN

Step-by-step explanation:

So sorry if i am wrong!! I hope this can help!

Answer:

A

B

G

Angle A is congruent to angle O

Triangle SAN ~ Triangle JOE

There exists a sequence of rigid and non-rigid motions that maps triangle SAN onto triangle JOE

Step-by-step explanation:

Just got the question wrong, this was the correct answer

Grace and Jackie are both accountants. They each charge their customers an hourly fee for their service, as described below. Grace charges $540 for 18 hours of service. Jackie charges $40 per hour. Who charges more per hour?

Answers

Answer:

Jackie

Step-by-step explanation:

Since Grace charges 30 an hour (540 divided by 18 is 30) and Jackie charges 40 and hour, so Jackie would charge more.

Which expression is equivalent to 4 (5X + 3y)

Answers

Answer:

20x + 12y

Step-by-step explanation:

=> 4(5x + 3y)

=> 20x + 12y

Since we can't simplify this further, 20x + 12y is out answer.

Hoped this helped.

Write an equation with slope of -2 and goes through the point (-3,7)

Answers

Answer:

y = -2x + 1

Step-by-step explanation:

Substitute  the slope and the given point into y = mx + b and solve for "b".

y = mx + b

7 = -2(-3) + b

7 = 6 + b

1 = b       the y-intercept is 1

The equation of the line is y = -2x + 1

Rewrite as equivalent rational expressions with denominator (c- 9) (c+9)(c + 6):

Answers

Answer:

Step-by-step explanation:

as (c + 9)(c - 9) = c² - 81

and (c - 9)(c + 6) = c² - 3c - 54

    8(c + 6)        =         8c + 48        

(c² - 81)(c + 6)       (c - 9)(c + 9)(c + 6)

            10c(c + 9)     =     10c² + 90c        

(c² - 3c - 54)(c + 9)       (c - 9)(c + 9)(c + 6)

The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;

1.  8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expressions are,

1. 8 / (c² - 81)

2. 10c / (c² - 3c - 54)

Now,

Solve the expressions for the denominator (c- 9) (c+9)(c + 6) as;

1. 8 / (c² - 81) = 8 / (c² - 9²)

                   = 8 / (c + 9) (c - 9)

Thus, 8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c² - (9- 6)c - 54)

                               = 10c / (c² - 9c + 6c - 54)

                               = 10c / [c(c-9) + 6(c - 9)]

                               = 10c / (c + 6) (c - 9)

Thus, 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

Therefore, The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;

1.  8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

4. Sale of Mathematics and English books in the year 2005, 2006, 2007 and 2008 are given below : Years Mathematics English 2005 200 100 2006 300 250 2007 400 200 2008 500 500 Question 1. In which year is the difference in the sale minimum? (a) 2008 (b) 2007 (c) 2006 (d) 2005 Question 2.​

Answers

Step-by-step explanation:

2008because there is no difference between the number of sold notebooks

help me out guys I don't get this ?!​

Answers

Answer:

B: (-2,-3)

Step-by-step explanation:

The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.

Relatively Simple Math, pls lend a hand. 50 points and Brainliest

Answers

I think the answer is A

Answer:

B. 192 miles in 3 hours

Step-by-step explanation:

Mr. Anderson's rate is:

480 / 7.5 = 64 mph

Given options, find rates and compare with the above number:

A. 120/2 = 60 mph, NoB. 192/3 = 64 mph, YesC. 100/1.5 = 66.66 mph, NoD. 240/3.25 = 73.85 mph, No

The length of a rectangular rug is 6 ft. more than the width. The perimeter is 40ft. find the length and the width of the rug.

Answers

width = 7ft
length = 13ft
Width is 7ft
Length is 13ft

Which is the better deal? $39.55 for 7 pairs of jeans OR $22.48 for 4 pairs of jeans

Answers

Answer:

I will say %39.56 for 7 pairs because you'll have 7 pair of jeans so you don't have to buy more if some of your jeans rips or something happens so yeah.

Answer:

$39.55 for 7 pairs of jeans

Step-by-step explanation:

The LCM of 7 and 4 is 28, so I decided to use that as an example.

4×7=28

22.48×8=179.84

So if you wanted 28 jeans, you'd be paying $179.84

- - - - -

Now the first deal.

7×4=28

39.55×4=158.2

For 28 jeans, you'd be paying $158.20

For 28 jeans, the first choice offers a better deal than the other.

Mind you, I know the word problem isnt about 28 jeans. But since 28 was the LCM of 4 and 7, I decided to use it as an example

-5/8 - (-4/3)
Pls help

Answers

Answer:

Step 1 of 2: Subtract.  

Subtract

(

negative 5 over 8  

−  

5

8

) − (

negative 4 over 3  

−  

4

3

) =  

17 over 24  

17

24

Step 1 of 2: Subtract, sub-step a: Subtract a negative.  

Subtract a negative

negative 5 over 8  

−  

5

8

− (

negative 4 over 3  

−  

4

3

) =  

negative 5 over 8  

−  

5

8

+  

4 over 3  

4

3

Subtracting a negative is the same as adding a positive.

Step 1 of 2: Subtract, sub-step b: Find common denominator.  

Find common denominator

negative 5 over 8  

−  

5

8

+  

4 over 3  

4

3

= −

( 5 × 3 ) over ( 8 × 3 )  

5 × 3  

8 × 3  

+  

( 4 × 8 ) over ( 3 × 8 )  

4 × 8  

3 × 8  

=  

negative 15 over 24  

−  

15

24

+  

32 over 24  

32

24

24 is the least common multiple of denominators 8 and 3. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Subtract, sub-step c: Add.  

Add

negative 15 over 24  

−  

15

24

+  

32 over 24  

32

24

=  

(  

negative 15  

−15 + 32 ) over 24  

negative 15  

−15 + 32  

24

=  

17 over 24  

17

24

Answer:

The answer would be 17/24

Step-by-step explanation:

1. Common denominator is going to be 24. 3(-5/8) - 8(-4/3)

2. Next multiply. -15/24 + 32/24

3. After addition you get 17/24 or 0.7

You pay a real estate agent a 4% commission for selling your
house. After paying the commission, you receive $302,900. What
was the actual selling price of the house?
Yes

Answers

Answer:

Step-by-step explanation: 56

need help with this i don't understand

Answers

Answer:

7see below5the rule is not one-to-one

Step-by-step explanation:

Applying the squaring rule to each of the elements of the domain, we get ...

  [tex]\begin{array}{cc}\text{Domain}&\text{Range}\\1&1\\-3&9\\-\frac{1}{2}&\frac{1}{4}\\3&9\\2&4\\\frac{1}{4}&\frac{1}{16}\\0.5&\frac{1}{4}\end{array}[/tex]

__

1. There are 7 different numbers in the Domain list.

2. See above

3. There are 5 different numbers in the Range list.

4. The rule "square me" is not "one-to-one" Two different values in the domain can result in the same value in the range. -3 and 3 both result in 9. -1/2 and 0.5 both result in 1/4.

Natural numbers are ? Integers

Answers

Answer:

natural numbers are the positive numbers that begins from 1 ...

but integers include natural numbers , it's negative and zero

Help my first time learning this it’s an easy problem

Answers

Answer:

I don't know but I I would just say C maybe?

Answer:

I say do B

Step-by-step explanation:

B and C look approximately the same but B look smaller

If I’m wrong I’m srry :<

Which of the following is the graph of f(x) = |x|?

Graph 1
Graph 2
Graph 3
Graph 4

Answers

Answer:

i think its the second graph

Step-by-step explanation:

i have most important question what is 2+2 ?

Answers

Answer:

4

Step-by-step explanation:

Answer:

When I look at -2^2 I see two operations, a negation and a power (square). The convention in mathematical expressions is that powers are performed before negations (also before additions, multiplications and divisions) so to evaluate -2^2 you first square the 2 to get 4 and then apply the negation to arrive at -4.

With (-2)^2 the parentheses tell you to consider -2 as a single quantity and square it so (-2)^2 = (-2) × (-2) = 4.

I hope it's help

What is 55% of 20?!?!?!

Answers

Answer:

11

Step-by-step explanation:

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

use the method:

is/of and %/100

plug in 55 for the percent, and 20 for 'of'

should be: x/20 and 55/100

cross multiply to get 11.

 

1%of 20 is 0.2 0.2x5=1         5% of 20 is 1

10% of 20 is 2 2x5=10          50% of 20 is 10

1+10=11

That is just how i do it to make it easier for others, and sometimes for me.

Please take a look at the picture

Answers

Answer:

A) -3/-11

Step-by-step explanation:

-3/-11-3/11

-3/-11

Reduce the fraction with -1.

3/11

Hope this help :)

Please helpp for 17 points......
a. -4
b. -1
c. 1
d. 4

Answers

Answer: -4

Explanation: subtract 4 then 8 and so on

Answer:

Step-by-step explanation:

d

solve pls brainliest

Answers

Answer:

40

Step-by-step explanation:

LCD = 40
9/8 and 1/10 = 45/40 and 4/40

Complete the equation of the line whose y-intercept is (0,-1) and slope of 4

y=(answer)

Answers

y=4x-1 is the answer

2x.67 find the product draw a picture

Answers

Answer:

1.34

Step-by-step explanation:

2x67/100

= 134/100

= 1.34

a lamp post cast a Shadow 15 feet long while a 6 foot man standing nearby cast a shadow 5 ft long. what proportion can be used to determine the hight of the lamp post

Answers

Answer:

6/5=x/15

Step-by-step explanation:

6/5=x/15,where x is hight of the lamp post

x=18

Someone pls help me with these worksheets >.<



(Please answer properly, if u don't know, just ignore so someone who knows can answer)

Answers

Answer:

gsdddddddddddddddddddddddddddd

Step-by-step explanation:

Tara's pool is 50 yards in length and 20 feet in width. How many square feet is the pool? How many square yards in the pool? Show your work.

Answers

1 yard = 3 feet 3 x 50 = 150 ft. L x W = Area

150’x 20’ = 3,000 sq. ft. 3,000 sq ft. divided by 3 = 1,000 sq. yd.

What is the output, or dependent variable or
quantity?
Х
f(x)
у
DONE

Answers

Answer:

x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.

Step-by-step explanation:

If the values of a variable depends on the other variable, then it called dependent variable.

If the value of a variable does not depend on the other, then it is called independent variable.

If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.

The given function is

Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.

The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.

Substitute x=2 in the given function.

The value of f(2) is 2.

Answer:

f(x)

Step-by-step explanation:

Find the equation of a line that passes through the point (2,5) and has a gradient of 2. Leave your answer in the form y = m x + c

Answers

Answer:

y=2x+1

Step-by-step explanation:

y-5/x-2=2

2x-4=y-5

y=2x+1

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