Which expression is equivalent to RootIndex 4 StartRoot x Superscript 10 Baseline EndRoot? x squared (RootIndex 4 StartRoot x squared EndRoot) x2.2 x cubed (RootIndex 4 StartRoot x EndRoot) x5

Answer:

Constant of proportionality = 24

Equation: [tex]y=24x[/tex]

Step-by-step explanation:

Given:

'x' and 'y' are proportional to each other.

At [tex]x=3,y=72[/tex]

Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.

Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:

[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]

Therefore, the constant of proportionality is 24.

Now, a proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Now, plug in the given value of 'k' and complete the equation. This gives,

[tex]y=24x[/tex]

Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]

Simple sampling - A method where individuals are chosen randomly from a larger set.

Convenience sampling - The sample is being chosen as per ease of access thus it is not a random sampling.

Systematic sampling - Probability method where elements are chosen from a target population.

Stratified sampling - Method where population were divided into different groups called strata and the sample is then drawn from each group.

Cluster sampling - Population is where population were divided into different groups known as clusters. The clusters were then chosen randomly as the samples.

Answer: D (cluster sampling) - The service centers refer as the clusters and it is chosen randomly.

Final answer:

The Daimler - Chrysler survey method is an example of cluster sampling, where random groups (service centers) are selected and all members within these groups are surveyed.

Explanation:

The type of sampling used by Daimler - Chrysler when they randomly select 110 service centers during a certain week and survey all customers visiting those service centers is cluster sampling. In cluster sampling, the overall population is divided into groups, or clusters, and a random selection of these clusters is chosen.

All members (or customers, in this case) within these selected clusters are surveyed. This method is often more practical and cost-effective than surveying the entire population. It is important that the clusters themselves are representative of the population to ensure that data obtained is not biased.

Answer:

Step-by-step explanation:

the answers c.

Answer:

11/92

Step-by-step explanation:

G = 11

R = 7

B = 6

P(b) = 6/24 = 1/4

P(g) = 11/23

P(blue first and then green(without replacement)) = 1/4 * 11/23

= 11/92

The probability of randomly selecting a blue marble followed by a green marble from a jar of 24 marbles (6 blue, 7 red, 11 green) is 11/92.

The number of outcomes considered favorable or desired is compared to the total number of outcomes possible. In this situation, we're interested in choosing a blue marble first, then a green marble. The total number of marbles is 11 green + 7 red + 6 blue = 24 marbles.

Initially, the probability of selecting a blue marble is 6/24 = 1/4

because there are 6 blue marbles out of a total of 24.

After taking one marble out (assuming it's blue), you have 23 marbles left, with 11 of them being green. So, the probability of selecting a green marble next is 11/23.

Therefore, the probability of both of these events happening (selecting a blue marble followed by a green marble) is found by multiplying these two probabilities together, which gives (1/4) * (11/23) = 11/92.

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Final answer:

To find the year when the record became 19.68 seconds, substitute the value of R into the equation. Solve for t and add 1920 to get the year.

Explanation:

To find the year when the record became 19.68 seconds, we need to substitute the value of R into the equation:

R = -0.028t + 20.8

19.68 = -0.028t + 20.8

Solving for t:

Subtract 20.8 from both sides: -0.028t = -1.12

Divide both sides by -0.028: t = 40

Since t represents the number of years since 1920, we add 1920 to the result to get the year:

t + 1920 = 40 + 1920 = 1960

Therefore, the record became 19.68 seconds in the year 1960.

Step-by-step explanation:

[tex] \because \: a_n = - 1 + 3(n - 1) \\ \\ \therefore \: a_{55} = - 1 + 3(55 - 1) \\ \\ \therefore \: a_{55} = - 1 + 3 \times 54 \\ \\ \therefore \: a_{55} = - 1 + 162\\ \\ \huge \blue { \boxed{\therefore \: a_{55} = 161}}\\ \\ [/tex]

Hence, the 55th term of the sequence is 161.

Answer:

A) g is increasing, and the graph of g is concave up.

Step-by-step explanation:

g'(x) = ∫₀ˣ e^(-t³) dt

Since e^(-t³) is always positive, ∫₀ˣ e^(-t³) dt is positive when x > 0.  So the function is increasing.

Find g"(x) by taking the derivative using second fundamental theorem of calculus:

g"(x) = e^(-x³)

g"(x) is always positive, so the function is always concave up.

Final answer:

To find the two numbers with a sum of 29 and product of 180, we set up a system of equations, solve for one variable in terms of the other, and then factor a quadratic equation to find that the two numbers are 20 and 9.

Explanation:

The student's question is about finding two numbers based on their sum and product. To solve this, we can set up two equations based on the given information: let's call our numbers x and y. The first equation based on their sum is x + y = 29, and the second equation based on their product is xy = 180.

We can find one number in terms of the other using the first equation: y = 29 - x. We then substitute this into the second equation to get x(29-x) = 180. Simplifying, we have x² - 29x + 180 = 0. Factoring the quadratic equation, we get (x - 20)(x - 9) = 0, which gives us two possible values for x: 20 or 9. Thus, the two numbers are 20 and 9.

Answer:

The correct option is B) Qualitative and discrete.

Step-by-step explanation:

Consider the provided information.

Quantitative variable is the variables that can be determined by counting or measuring something.

Qualitative variable is the variables that can't be determined by counting or measuring something.

If the value is obtained by counting then it is called discrete variable, If the value obtained by measuring then it is called continuous variable.

Since the relationship can't be measure by counting so it it qualitative variable.

We can calculate the regular contact days so it is discrete variable.

Therefore, the correct option is B) Qualitative and discrete.

Tens is the correct answer

answer is C: [tex]\frac{EF}{DF}[/tex]

Answer:option C is the correct answer

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle,

DF represents the hypotenuse of the right angle triangle.

With m∠θ as the reference angle,

EF represents the adjacent side of the right angle triangle.

DE represents the opposite side of the right angle triangle.

To determine Cos ∠θ, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos θ = EF/DF

Bob can buy 15 cupcakes for the price of 18 cookies.

Step-by-step explanation:

============================

Work Shown:

x = number of hours spent running

8x = distance he runs (since he runs at 8 mph)

y = number of hours spent walking

3y = distance he walks (he walks at a speed of 3 mph)

8x+3y = total distance = 16 miles

8x+3y = 16

This equation is in standard form Ax+By = C

--------

Extra Info

Solving for y will get

8x+3y = 16

3y = -8x+16

y = (-8x+16)/3

y = (-8x)/3+16/3

y = (-8/3)x+16/3

This is in slope intercept form y = mx+b

m = -8/3 is the slope

b = 16/3 is the y intercept

Answer:

29 buttons

Step-by-step explanation:

6 x 5 - 1

Answer:

Step-by-step explanation: 29

The unit price in dollars per ounce will be $0.4 per ounce.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Tony sells 50.5 ounces of lemonade for a total of $20.20.

The unit price in dollars per ounce will be calculated as,

Rate = $20.20 / 50.5

Rate = $0.4 per ounce

The unit price in dollars per ounce will be $0.4 per ounce.

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Tony's lemonade has a unit price of $0.40 per ounce.

Tony sells 50.5 ounces of lemonade for a total of $20.20.

To find the unit price in dollars per ounce, we divide the total cost by the total number of ounces.

The calculation looks like this: $20.20 ÷ 50.5 ounces = $0.40 per ounce.

Therefore, the unit price of Tony’s lemonade is $0.40 per ounce. If rounding is necessary, this answer is already precise to the nearest cent.

Final answer:

To find the three numbers, we determine 'a' and 'r' using a system of equations derived from the conditions that they form a geometric progression with 12 and an arithmetic progression with 9. By solving these equations, we obtain the three numbers in sequence.

Explanation:

The question requires us to find three numbers that form a geometric progression with the third being 12, and when the third number is changed to 9, the numbers form an arithmetic progression.

Let's denote the first number as 'a' and the common ratio of the geometric progression as 'r'. The three numbers in the geometric progression can be represented as 'a', 'ar', and 'ar^2'. Given that the third number is equal to 12, we have 'ar^2 = 12'.

When 12 is replaced with 9 to form an arithmetic progression, the common difference 'd' can be found by subtracting the first term from the second term. The three numbers in this sequence are 'a', 'a + d', and 'a + 2d'. Given that the third number is now 9, we have 'a + 2d = 9'.

To find 'a' and 'r', we can set up a system of equations using the fact that the second number in both progressions is the same. So 'ar = a + d'. We have the following system:

ar^2 = 12 (1)

a + 2d = 9 (2)

ar = a + d (3)

From equation (3), we can solve for 'd' in terms of 'a' and 'r': 'd = ar - a = a(r - 1)'. Substituting 'd' in equation (2), we get 'a + 2(a(r - 1)) = 9', which simplifies to 'a(2r + 1) = 9'.

Using this new equation along with equation (1), we solve for 'a' and 'r' to find the three numbers:

a(2r + 1) = 9 (4)

ar^2 = 12 (1)

From equation (1), 'a = 12/r^2'. Substituting this into equation (4) gives us a single equation: '12/r^2(2r + 1) = 9', which we can solve to find 'r', and subsequently, 'a'. After solving these, we find the three numbers that form both the geometric and arithmetic progressions.

I would say false.

B is on top of S.

I'm using common sense here but If you were to draw a line from B and C.

S would not be marked in between that line.

The claim "S is between B and C" is false.

S is between B and C only if the 3 points are collinear, and S is between the other poitns in that line.

In the triangle we can see that CS and SB are perependicular lines, so the 3 points are not collinear, and thus, the statement "S is between B and C" is false.

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Answer:

The length of the room in the drawing is 5 inches.

Step-by-step explanation:

Given:

Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet.

The actual length of a room in the hotel is 20 feet.

Now, to find the length of the room in the drawing.

Let the length of the room in the drawing be [tex]x.[/tex]

The actual length of the room = 20 feet.

The scale used in drawing is 1 inch = 4 feet.

As, 1 inch is equivalent to 4 feet.

Thus, [tex]x[/tex] is equivalent to 20 feet.

Now, to get the length of the room in the drawing we use cross multiplication method:

[tex]\frac{1}{4} =\frac{x}{20}[/tex]

By cross multiplying we get:

[tex]20=4x[/tex]

Dividing both sides by 4 we get:

[tex]5=x[/tex]

[tex]x=5\ inches.[/tex]

Therefore, the length of the room in the drawing is 5 inches.

Question is wrong; Correct question is given below;

A baker started out with 12 cups of flour she had 9 1/4 cups of flour left after the first bunch of batter she made she had 6 1/2 cups of flour left after the second bunch of batter she made if she makes two more batches of batter how many cups of batter will be left?

Answer:

Baker will be left with 1 cups of Flour.

Step-by-step explanation:

Given

Amount of flour baker started with = 12 cups

Amount of flour left after making first batter = [tex]9\frac14\ cups[/tex]

[tex]9\frac14\ cups[/tex] can be Rewritten as [tex]\frac{37}4\ cups[/tex]

Amount of flour left after making first batter = [tex]\frac{37}4\ cups[/tex]

Now we can say that;

Amount of flour used to make first batter is equal to Amount of flour baker started with minus Amount of flour left after making first batter

Thus, the Amount of flour she use to make first batter = [tex]20-\frac{37}{4}[/tex]

Now we will use LCM to make the denominator common we get;

Amount of flour she use to make first batter = [tex]\frac{20\times4}{4}-\frac{37\times1}{4\times1} = \frac{48}{4}-\frac{37}{4}[/tex]

Now denominator common so we will solve the numerator we get;

Amount of flour she use to make first batter = [tex]\frac{48-37}{4}=\frac{11}{4}\ cups.[/tex]

Now Given:

Amount of  flour left after the second batch of batter = [tex]6\frac12\ cups[/tex]

[tex]6\frac12\ cups[/tex] can be Rewritten as [tex]\frac{13}2\ cups[/tex]

Amount of  flour left after the second batch of batter = [tex]\frac{13}2\ cups[/tex]

Thus, the quantity she use to make second batter = [tex]\frac{37}{4}-\frac{13}{2}[/tex]

Now we will use LCM to make the denominator common we get;

Amount of flour she use to make Second batter = [tex]\frac{37\times1}{4\times1}-\frac{13\times2}{2\times2}=\frac{37}{4}-\frac{26}{4}[/tex]

Now denominator common so we will solve the numerator we get;

Amount of flour she use to make Second batter = [tex]\frac{37-26}{4}=\frac{11}{4}\ cups[/tex]

Thus, she use [tex]\frac{11}{4}\ cups[/tex]  of flour for each batter.

Amount of Flour used in making 2 more batter = [tex]2\times\frac{11}{4}= \frac{11}{2}\ cups[/tex]

Now we can say that;

Cups of flour left will be equal to Amount of  flour left after the second batch of batter minus Amount of Flour used in making 2 more batter.

framing in equation form we get;

Cups of flour left = [tex]\frac{13}{2}-\frac{11}{2}=\frac{13-11}{2}=\frac{2}{2}=1\ cup[/tex]

Hence Baker will be left with 1 cups of Flour.

Answer:

Total number of flat screen sold is 3/4

Step-by-step explanation:

Let the total number of the flat screen sold be y

y = number of flat screen sold in the morning + number of the flat screen sold in the afternoon.

Number sold in the morning = 5/15

Number sold in the afternoon = 1/3

Y = 5/12 + 1/3

Find the LCM of 12 and 3

Y = (5 + 4)/12

Y = 9/12

Y = 3/4

Total number of flat screen sold is 3/4

5/12

+1/3

=9/12

Reduce to 3/4

Step-by-step explanation:

Answer: It will take 7 days to use the inventory of shipping labels.

Step-by-step explanation:

Given : Total boxes shipped by warehouse worker per day = 25

Every box contains 3 shipping labels.

Inventory has 500 shipping labels.

Then, the total number of boxes can be made =  (Total  shipping labels) ÷ (labels in each box)

500 ÷ 3  =166.67≈166

Number of days it will take to use the inventory of shipping labels=  (total number of boxes can be made)  ÷  (Total boxes shipped  per day)

= 166÷ 25=6.64≈7

Hence, it will take 7 days to use the inventory of shipping labels.

It will take about 7 days to use the inventory of shipping labels.

To find how many days it will take to use the inventory of shipping labels, we need to divide the total number of shipping labels by the number of shipping labels used per day.

The total number of shipping labels is 500 and the worker ships 25 boxes each day, with each box containing 3 shipping labels.

So, the worker uses 25 x 3 = 75 shipping labels per day.

Dividing the total number of shipping labels (500) by the number of shipping labels used per day (75), we get 500 / 75 = 6.67.

Rounding to the nearest whole number, it will take about 7 days to use the inventory of shipping labels.

Answer:

2/10 of her income will go to these items

Step-by-step explanation:

29 +15 = 41

41/1900  equal 2/10

Final answer:

Ena plans to spend 29% of her income on entertainment and 15% on groceries, which is a total of  [tex]\(\frac{44}{100}\)[/tex]of her income. Simplifying this to its lowest terms gives us [tex]\(\frac{11}{25}\)[/tex] of her income spent on these two items together.

Explanation:

To find the fraction of Ena's income that is spent on entertainment and groceries together, we need to sum the fractions of income allocated to each category. Ena plans to spend 29% of her income on entertainment and 15% on groceries. In fractional terms, 29% is the same as 29/100 and 15% is equivalent to 15/100. Adding these fractions together:

[tex]\(\frac{29}{100} + \frac{15}{100} = \frac{44}{100}\)[/tex]

Now, we simplify the fraction to its lowest terms:

[tex]\(\frac{44}{100} = \frac{44 \div 4}{100 \div 4} = \frac{11}{25}\)[/tex]

Thus, Ena plans to spend  [tex]\(\frac{11}{25}\)[/tex]of her income on entertainment and groceries together.

Answer: Quantity of Dark Chocolate used = 15 lb

 Quantity of Milk Chocolate used  = 35 lb

Step-by-step explanation:

Let x = Quantity of Dark Chocolate.

y =  Quantity of Milk Chocolate.

As per given , we have the following system of equations:

[tex]x+y= 50-------------(1)\\\\ 4x+2y=50\times2.60\\\\ 4x+2y=130-----------(2)[/tex]

Multiply equation (1) by 2 , we get

[tex]2x+2y= 100-------(3)[/tex]

Eliminate equation (3) from equation (2) , we get

[tex]2x=30\\\Rightarrow\ x=15[/tex]

Put x= 15 in (1) , we get [tex]15+y=50[/tex]

⇒ y=35

Therefore , Quantity of Dark Chocolate used = 15 lb

 Quantity of Milk Chocolate used  = 35 lb

Answer:

[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]

[tex]Cos\ F = \frac{3}{4}[/tex]

[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]

Step-by-step explanation:

Given

EF = 8

FG = 6

We need to find the trigonometric ratios.

Solution:

First we will find the length of the third side.

Now we know that;

△EFG is a right angled triangle with right angle at G.

Now applying Pythagoras theorem which states.

"The sum of square of the two legs of the triangle is equal to square of the hypotenuse."

so we can say that;

[tex]FG^2=EF^2+EG^2\\\\EG^2=FG^2-EF^2[/tex]

Substituting the given values we get;

[tex]EG^2=8^2-6^2=64-36=28[/tex]

Taking square roots on both side we get;

[tex]\sqrt{EG^2} =\sqrt{28}=\sqrt{4\times7}\\ \\EG = 2\sqrt{7}[/tex]

Now we will find the trigonometric values.

[tex]secE=\frac{Hypotenuse}{Adjacent\ side}[/tex]

Here Hypotenuse = EF = 8

Adjacent side of E = EG = [tex]2\sqrt{7}[/tex]

[tex]secE=\frac{8}{2\sqrt{7}} =\frac{4}{\sqrt{7}}[/tex]

Now rationalizing the denominator by multiplying numerator and denominator by [tex]\sqrt{7}[/tex] we get;

[tex]secE=\frac{4\times \sqrt{7} }{\sqrt{7}\times \sqrt{7} }\\\\secE = \frac{4\sqrt{7} }{7}[/tex]

Now,

[tex]Cos F = \frac{Adjacent \ side}{Hypotenuse}[/tex]

Adjacent side to F =GF = 6

Hypotenuse = EF = 8

[tex]Cos\ F = \frac{6}{8}\\\\Cos\ F = \frac{3}{4}[/tex]

Now,

[tex]Tan F = \frac{opposite \ side}{adjacent\ side}[/tex]

Here Opposite side of F = EG = [tex]2\sqrt{7}[/tex]

Adjacent side of F = GF = 6

[tex]Tan\ F= \frac{2\sqrt{7}}{6}\\\\Tan\ F =\frac{\sqrt{7}}{3}[/tex]

Hence Below are required details.

[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]

[tex]Cos\ F = \frac{3}{4}[/tex]

[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]

The value of the trigonometric ratio of an angle of the triangle is;

[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]

Given

Right △EFG has its right angle at G, EF=8, and FG=6.

The Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.

In right-angle △EFG, in which E is a right angle.

[tex]\rm EF^2=FG^2-EG^2\\\\8^2=6^2-EG^2\\\\EG^2=8^2-6^2\\ \\EG^2=64-36\\\\EG^2=28\\\\EG = 2\sqrt{7}[/tex]

The value of the trigonometric ratio of an angle of the triangle is;

[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]

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Answer:

(x⁻¹)(x⁻⁵) = x⁻⁶

Step-by-step explanation:

When multiplying number with the same base, you add up their exponent.

(x⁻¹)(x⁻⁵) =

= x⁽⁻¹⁾ ⁺ ⁽⁻⁵⁾

= x⁻⁶

you can also write x⁻⁶ as 1/x⁶. The negative sign in the exponent just flip the numerator and denominator with each others.

Answer:

The answer to your question is   x⁻⁶ or 1/x⁶

Step-by-step explanation:

Multiplying exponents

-To multiply exponents they must have the same base and the result will be the base and the exponents will add.

Ex

              (a³)(a²)

base = a

exponents = 3 and 2

result     a³ ⁺ ²  = a⁵

In your question

             (x⁻¹)(x⁻⁵) = x⁻¹⁻⁵ = x⁻⁶ = 1/x⁻⁶

Answer:1)2804m^2=4s.f

2)84Km^3=2s.f

3)5.029m=4s.f

4)0.00003068m=4s.f

5)4.6×10^5m=2s.f

6)4.06×10^-5m=3s.f

7)750m=3s.f

8)75m=2s.f

9)75,000.0m=5s.f

10)75.00m=2s.f

11)75,000.00m=5s.f

12)10cm=2s.t

B) to four significant figures

1)3.682

2)860100

3)375.7

4)51150

5)4673

C to 1 decimal places

1)1.4

2)4735.0

3)687524.0

4)7.6

5)235.0

Dto 2d.p

1)22.49

2)25880.00

3)30623.00

4)412541.00

5)866323.00

E)

1)6.201cm+7.4cm+0.68cm+12.0cm=26.281cm

2)1.6km+1.62km+1200km=1203.22km

3)8.264g-7.8g=0.464g

4)10.4168m-6m=4.4168m

5)12.00m+15.001kg=12.00m+15.001kg

6)1.31cm×2.3cm=3.013cm^2

7)5.7621m×6.201m=35.7308m^2

8)20.2cm/7.41s=2.726cm/s

Step-by-step explanation:

S.f means significant figures or Digits.

2)cm +kg is impossible because they are unlike termsi.e they do not have any thing in common, hence 12.00m+15.001kg cannot be added up.

This detailed answer involves the concept of significant figures, rounding off significant figures, and performing calculations while maintaining the appropriateness of significant figures in measurement.

Number of significant digits

Significance figures involve the digits in a number that carry meaningful information about its precision.

Rounding off to Significant Figures

To round to a certain number of significant figures, start from the first non-zero number and count the number of digits required, rounding the last one if necessary. Here are your rounded numbers:

Performing Calculations

In adding or subtracting numbers, the result should retain the smallest number of decimal places in the input values. In multiplication or division, the result should retain the smallest number of significant figures in the input values. Here are your answers:

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Answer: basically it would be whatever side the x is one indicating x is greater than 1

Step-by-step explanation:

Answer:

The winner completed the race in 96 hours and 52 minutes.

Step-by-step explanation:

Given:

Distance of the cycling race = 2292 miles

Average speed of the winner = [tex]23.66\ mph[/tex]

We need to find time required by winner to complete the race.

Solution:

Now we know that;

Time required can be calculated by dividing Total Distance from the Average speed.

framing in equation form we get;

time required by winner to complete the race = [tex]\frac{2292}{23.66} = 96.87\ hrs[/tex]

Now converting [tex]0.87\ hrs[/tex] into minutes we get;

[tex]0.87\times 60= 52.2\approx 52\ mins[/tex]

Hence the winner completed the race in 96 hours and 52 minutes.

Answer:

300 programs

Step-by-step explanation:

Let’s work with cents to make this easier. We convert the $12 to cents, making 1200 cents

Let the number of copies Alden printed be x. His total printing cost would be x * 54 = 54x cents.

He sold at 75 cents each and still had left 100 copies. This means his total sale would be (x - 100)75

He lost $12 on the venture. This means his cost price minus his selling price is $12 since it’s a loss.

Computing this:

54x - 75(x - 100) = 1200

54x - 75x + 7500 = 1200

-21x = 1200 - 7500

-21x = -6,300

x = 6300/21 = 300 programs