Solve
3x + 4y = 8
-2X + 5y = 3

Answer:

The answer is 6.

Step-by-step explanation:

In the question it is stated that Lisa has designed a "within-group" or "within-subject" experiment using three categories with 2 subject in each category.

Within-group / within-subject experiments mean that every participant is tested for each condition of the experiment, so everyone goes through the same process.

Considering these informations, we can calculate that each participant was in 6 cells because there are 3 categories and 2 subjects for each of the categories.

I hope this answer helps.

Answer:

Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]  

Part B)  [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]

Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the  median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]

[tex]M(-1,-1)[/tex]

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

N(3, 2) and M(-1,-1)

substitute the values

[tex]m=\frac{-1-2}{-1-3}[/tex]

[tex]m=\frac{-3}{-4}[/tex]

[tex]m=\frac{3}{4}[/tex]

step 3

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{3}{4}[/tex]

[tex]point\ N(3, 2)[/tex]

substitute

[tex]y-2=\frac{3}{4}(x-3)[/tex]

step 4

Convert to slope intercept form

Isolate the variable y

[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]

[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]

[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]  

Part B) Find the equation of the  right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]

[tex]M(-1,-1)[/tex]

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]m=\frac{-8-6}{1+3}[/tex]

[tex]m=\frac{-14}{4}[/tex]

[tex]m=-\frac{14}{4}[/tex]

[tex]m=-\frac{7}{2}[/tex]

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=-\frac{7}{2}[/tex]

so

[tex]m_2=\frac{2}{7}[/tex]

step 4

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{7}[/tex]

[tex]point\ M(-1,-1)[/tex] ----> midpoint LP

substitute

[tex]y+1=\frac{2}{7}(x+1)[/tex]

step 5

Convert to slope intercept form

Isolate the variable y

[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]

[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]

[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]  

we have

L(-3, 6) and P(1, -8)

substitute the values

[tex]m=\frac{-8-6}{1+3}[/tex]

[tex]m=\frac{-14}{4}[/tex]

[tex]m=-\frac{14}{4}[/tex]

[tex]m=-\frac{7}{2}[/tex]

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

we have

[tex]m_1=-\frac{7}{2}[/tex]

so

[tex]m_2=\frac{2}{7}[/tex]

step 3

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{2}{7}[/tex]

[tex]point\ N(3,2)[/tex]

substitute

[tex]y-2=\frac{2}{7}(x-3)[/tex]

step 4

Convert to slope intercept form

Isolate the variable y

[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]

[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]

[tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]

The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.

We know that, the volume of square base pyramid is a²h/3

Now, x²(x+2)/3

= (x³+2x²)/3

Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.

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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.

The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.

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Answer:

4.847 cups

Step-by-step explanation:

Let's say x is number of cups of orange juice originally in the container.

The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups.  So the new concentration in the container is:

(x − 1) / x

Next, he takes another cup out, but this time, it isn't 100% orange juice any more.  So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x.  The total volume is still x cups, so the new concentration is:

[x − 1 − (x − 1) / x] / x

Repeating this logic, after he replaces the third cup with water, the final concentration is:

{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x

This final concentration is equal to 1/2.

1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x

1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x

1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]

1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x

1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x

1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)

1/2 x³ = x³ − x² − 2x² + 2x + x − 1

0 = 1/2 x³ − 3x² + 3x − 1

0 = x³ − 6x² + 6x − 2

Using a calculator to solve this:

x = 4.847

There are originally 4.847 cups in the container.

Answer:

It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx

Step-by-step explanation:

Given function is a trignometric one

y = tanx

we have tanx has values 0 for all multiples of pi.

i.e. tan x =0 whenever [tex]x = 2n\pi[/tex] for all integers n.

Also tanx has a period of pi.

It is a discontinuous graph extending in one period from -pi/2 to pi/2.

Hence the mid point of each period is the x intercept.

It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx

Final answer:

The x-intercepts of the function y=tan(x) are at integer multiples of π. The concept of 'center points' for y=tan(x) is not well-defined due to the nature of the function having no central axis and being periodic.

Explanation:

The student is inquiring about the x-intercepts and center points of the function y=tan(x). The x-intercepts of the tangent function occur wherever y=0, which happens at values of x that are integer multiples of π, as the tangent function has a period of π.

On the other hand, the concept of center points is not well-defined for the tangent function since it does not have a central axis like an ellipse or a bounded pattern. The tangent function is periodic and continuous between its vertical asymptotes, which occur at odd multiples of π/2.

Answer:No, he doesn't have enough wood for the roof.

Step-by-step explanation:

Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be

1.75 - 0.8 = 0.95 meters

He used 0.4 of what is left for the floor. This means that the length of the board left would be

0.95 - 0.4 = 0.55 meters

He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.

Answer:

$62.54  

Step-by-step explanation:

     12 cans dog food = 12 × 1.89  = $22.68

2 bags dental chews = 2 × 12.69 =   25.38

                                              1 toy =   10.25

                                       Subtotal =    58.31

         Sales tax = 0.0725 × 58.31 =      4.23

                                         TOTAL = $62.54

Suzie's total cost for June was $62.54.

The complement of 'rain today' is 'no rain today'. Its probability is 1 - the probability of 'rain today', which calculates to 35%.

In probability theory, the complement of any event A represents 'not A'. In this context, the event is 'rain today', therefore the complement of the event would be 'no rain today'.

Probability of an event and its complement always add up to 1. Therefore, you can calculate the probability of the complement by subtracting the probability of the event from 1. So, the probability of the complement of the event 'rain today' is 1 - 0.65 which equals 0.35 or 35%.

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Answer:

  A.  neither even nor odd

Step-by-step explanation:

The equation is that of a parabola whose line of symmetry is x=-5. Even functions are symmetrical about the line x=0, so this is not an even function. It has terms of even degree, so is not an odd function.

The function is neither even nor odd.

Answer:

Option A - neither even nor odd

Step-by-step explanation:

Given : [tex]f(x)=(x+5)^2[/tex]

To find : Determine whether the function below is an even function, an odd function, both, or neither ?

Solution :

We know that,

1) If f(-x)=f(x) it is an even function.

2) If f(-x)=-f(x) it is a odd function.

[tex]f(x)=(x+5)^2[/tex]

[tex]f(x)=x^2+10x+25[/tex]

Substitute x with -x in the function,

[tex]f(-x)=(-x+5)^2[/tex]

[tex]f(-x)=x^2-10x+25[/tex]

The function does not comply with the definitions.

The function is neither even  nor odd.

Therefore, option A is correct.

Answer:

b

Step-by-step explanation:

Answer: Kelvin has 39 cards

Dustin has 42 cards

Mike has 54 cards

Step-by-step explanation: please see attachment for explanation

Answer:

Step-by-step explanation:

The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.

To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows

Hypotenuse^2 = opposite ^2 + adjacent ^2

AC = hypotenuse

Opposite = 3

Adjacent = 3

AC^2 = 3^2 + 3^2 = 9 + 9 = 18

AC = √18 = 4.24

BX = AX = 3(they are both radii)

BC = AC = 4.24

The perimeter of triangle ABC would be

3 + 3 + 4.24 + 4.24 = 14.48

Answer:the boat will travel about 20.62 miles

Step-by-step explanation:

Since the boat travelled from dock A to dock B without passing and stopping at dock C along the way. The number of miles travelled would be the hypotenuse of the right angle triangle shown. To determine the number of miles travelled, we would apply Pythagoras theorem which is expressed as

Hypotenuse^2 = opposite side^2 + adjacent side^2

Looking at the triangle,

Opposite side = 13 miles

Adjacent side = 16 miles

Hypotenuse^2 = 13^2 + 16^2 = 425

Hypotenuse = √425 = 20.62 miles

Answer:

cos x (2 sin x − 1)

Step-by-step explanation:

sin(2x) − cos x

Use double angle formula.

2 sin x cos x − cos x

Factor.

cos x (2 sin x − 1)

Final answer:

The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).

Explanation:

Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:

sin 2x - cos x = 2 sin x cos x - cos x

Factoring out the common factor cos x, we get:

sin 2x - cos x = cos x (2 sin x - 1)

So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).

Answer:

The cost of a bag of chips is [tex]c=\$0.85[/tex]

Step-by-step explanation:

Let

c ----> the cost of a bag of chips

we know that

The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05

The cost of 3 bags of chips is equal to multiply 3 by its cost c

so

The linear equation that represent this situation is

[tex]2.50+3c=5.05[/tex]

solve for c

Subtract 2.50 both sides

[tex]3c=5.05-2.50[/tex]

[tex]3c=2.55[/tex]

Divide by 3 both sides

[tex]c=2.55/3[/tex]

[tex]c=\$0.85[/tex]

Using probability concepts and the information given, it is found that there is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.

The percentages given are:

Hence:

[tex]p = 0.07(0.25) + 0.93(0) = 0.0175[/tex]

There is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.

A similar problem also involving probabilities. is given at https://brainly.com/question/14398287

The probability that a randomly selected student gets a GED is 0.0175, or 1.75%.

To find the probability that a randomly selected student gets a GED, we need to multiply the probability of a student dropping out (0.07) by the probability of a dropout getting a GED (0.25). This can be calculated using the formula:

Probability of getting a GED = Probability of dropping out * Probability of getting a GED if dropped out = 0.07 * 0.25 = 0.0175

Therefore, the probability that a randomly selected student gets a GED is 0.0175, or 1.75%.

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Answer:

Solid

Step-by-step explanation:

Rewriting for the sake of clarity:

1) For the following inequality, indicate whether the boundary line should be dashed or solid.  x ≤ 5

2)  Since it is a closed interval which includes the number 5 then this can also be written as:

[tex](-\infty,5][/tex]

3) Hence, we can graph it as a solid line crossing the point (5,0). For the x coordinate 5, is within the interval.

Answer: the amount by which her lunch account would have been impacted is $45

Step-by-step explanation:

Each day Valerie charges her lunch account for her lunch. If the cost of lunch is $3 then, it means that Valerie charges the lunch account with $3 daily. It means that in x days, she would have charged her lunch account with 3×x = $3x

If she charged her account for a period of 15 days, it means that x = 15. Therefore, the amount by which her lunch account would have been impacted is 3×15 = $45

Answer:

57

Step-by-step explanation:

Answer:

There are 520 sheep on Farm B.

Step-by-step explanation:

Let the Number of sheep on farm B be x

Given:

On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B.

It means Number of sheep on farm A multiplied by 4/5 is equal to 1/2 multiplied by Number of sheep on farm B.

framing the equation we get;

[tex]\frac{4}{5}\times \textrm{Number of  sheep on Farm A} = \frac{1}{2} \times x[/tex]

Number of  sheep on Farm A = [tex]\frac{x}{2}\times\frac{5}{4}  = \frac{5x}{8}[/tex]

Now Given:

Total Number of sheep =845.

We know that Total Number of sheep is equal to sum of sheep at farm A and sheep at farm B.

Framing equation we get;

[tex]\frac{5x}{8}+x=845[/tex]

Taking L.C.M we get;

[tex]\frac{5x\times 1}{8\times1}+\frac{x\times8}{8} =845\\\\\frac{5x}{8}+\frac{x}{8} =845\\\\\frac{5x+8x}{8}=845\\\\\frac{13x}{8}= 845\\\\13x=845\times8\\\\x=\frac{845\times8}{13} = 520[/tex]

Number of sheep on Farm B = 520 sheep

Number of sheep on Farm A = [tex]\frac{5}{8}\times 520 = 325\ sheep[/tex]

Hence There are 520 sheep on Farm B.

Answer: B) x = negative 1 plus-or-minus StartRoot 17 EndRoot

Step-by-step explanation:

The given equation is x squared + 2 x + 1 = 17. It is written as

x^2 + 2x + 1 = 17

It is a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c

Rearranging the given equation, it becomes

x^2 + 2x + 1 - 17 = 0

x^2 + 2x - 16 = 0

We will apply the general formula for quadratic equation. It is expressed as

x = [-b ± √(b^2 - 4ac)]/2a

From the equation,

a = 1

b = 2

c = -16

x = [-2 ± √(2^2 - 4×1×-16)]/2×1

x = [-2 ± √(4 + 64)]/2

x = (-2 ± √68)/2

x = (-2 ± 2√17)/2

x = (-2 + 2√17)/2 or x = (-2 - 2√17)/2

x = -1 + √17 or x = -1 - √17

Answer:

B) x = negative 1 plus-or-minus StartRoot 17 EndRoot i hope this was help

Step-by-step explanation:

Answer:

8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.

9. APY means annual percentage yield.

Explanation:

8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.

Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.

Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.

9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.

Answer:

Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Step-by-step explanation:

No. of hardcover book = x

No. of paperback book = y

Cost of one hardcover book = $8

Cost of one paperback book = $5

We are given that:

x+y=7 (Equation 1)

8x+5y=41 (Equation 2)

We can find out value of x and y by solving both equations simultaneously.

[tex]Multiplying Equation 1 by 5:\\5x+5y=35\\8x+5y=41\\Subtracting both equations\\-3x=-6\\x=2\\\\According to Equation 1:\\x+y=7\\Putting value of x=2\\2+y=7\\y=5[/tex]

Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE

Answer:

Step-by-step explanation:

The standard form for the equation of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5).  We will use these to solve for r-squared, then plug back in what we need to write the equation.

[tex](2-5)^2+(5-(-3))^2=r^2[/tex] which simplifies to

[tex](-3)^2+(8)^2=r^2[/tex] and

[tex]9+64=r^2[/tex] so

[tex]r^2=73[/tex]

Filling in the equation:

[tex](x-5)^2+(y+3)^2=73[/tex]

Answer:

26°

Step-by-step explanation:

An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

An isosceles triangle is a triangle that has two equal sides and angles.  

Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).

Given:

The three angles of the triangle are given to be x°, x°  and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°

The sum of angles in a triangle is 180°

∴  x° + x° + 128° = 180°

2x° = 180° - 128°

2x° = 52°

x° = 52° / 2

x° = 26°

The measurement of one of the acute angles is 26°

Answer:

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

Step-by-step explanation:

Lets the number of men's shoes he sells be x and women's shoes be y.

For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .

He needs to sell atleast 10 women's shoes and 5 men's shoes.

Also he needs to make atleast $60 per week.

x ≥ 5

y ≥ 10

3x + 2.3y ≥ 60

These are are the 3 required inequalities.

Now we will see an example.

If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.

He will make a total profit = [tex]2.3\times 20 + 3\times 10[/tex] =$76

Answer:

4 cm

Step-by-step explanation:

we know that

The scale drawing is

[tex]\frac{1}{4}\ \frac{cm}{ft}[/tex]

That means ----> 1 cm in the drawing represent 4 ft in the mural

so

To find out the dimensions in the drawing, multiply the actual dimension by the scale drawing factor

so

[tex](16\ ft)(\frac{1}{4}\ \frac{cm}{ft})=4\ cm[/tex]

Answer:

Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.

Step-by-step explanation:

Given:

Total pizza = 1

Pizza ate at First time = [tex]\frac{1}{4}[/tex]

Pizza ate at Second time = [tex]\frac{3}{8}[/tex]

Pizza ate at Final time = [tex]\frac{1}{16}[/tex]

We need to find find the amount of pizza left.

Now to find the Amount of Pizza left is equal to Total Pizza minus Pizza ate at First time minus Pizza ate at second time minus Pizza ate at Final time.

Framing in the equation form we get;

Amount of Pizza left = [tex]1- \frac{1}{4} -\frac{3}{8} -\frac{1}{16}[/tex]

Now Taking the LCM we get;

Amount of Pizza left = [tex]\frac{1\times16}{16}- \frac{1\times4}{4\times 4} -\frac{3\times2}{8\times2} -\frac{1\times1}{16\times1}= \frac{16}{16}- \frac{4}{16} -\frac{6}{16} -\frac{1}{16}= \frac{16-4-6-1}{16}= \frac{5}{16}[/tex]

Hence Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.

Answer:

She lost $15 on her 50 dollar credit card.

Step-by-step explanation:

Kendra received a gift card in the mail from her grandparents. The gift card was worth $50.

Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.

Kendra loses $5 each month,

She forget the card for 3 months.

So, Multiply the $5 by 3 months

$5×3=$15

Hence, she lost $15.

Answer:

16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution.

Step-by-step explanation:

Let amount of 30% ounces be 'x' and that of 15% ounces by 'y'.

Given:

Total amount on mixing both the solution = 24 oz

∴ [tex]x+y=24\\x=24-y------------ 1[/tex]

Also, the total acid content in the resulting 25% solution is equal to the sum of the acid contents in 30% and 15% solutions.

∴ [tex]0.30x+0.15y=0.25(24)\\0.30x+0.15y=6-------2[/tex]

Now, plug in 'x' from equation (1) into equation (2). This gives,

[tex]0.30(24-y)+0.15y=6[/tex]

[tex]7.2-0.3y+0.15y=6[/tex]

[tex]-0.3y-0.15y=6-7.2[/tex]

[tex]-0.15y=-1.2[/tex]

[tex]y=\frac{1.2}{0.15}=8[/tex] ounces

Therefore, [tex]x=24-8=16[/tex] ounces

Hence, 16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution