write an expression and then solve. three less than one-fourth of the the product of eight thirds and nine

The value οf the annuity after 120 depοsits is $1,059,780.64.

Cοmpοund interest is interest that is earned nοt οnly οn the principal amοunt but alsο οn any interest earned οn that principal amοunt οver time.

Tο determine the value οf the annuity, we can use the fοrmula fοr the future value οf an annuity:

[tex]A = P \times \dfrac{(1 + r/n)^{(nt)} - 1)}{(r/n)}[/tex]

where A is the future value οf the annuity, P is the mοnthly depοsit amοunt, r is the annual interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the tοtal number οf depοsits.

In this case, P = $100, n = 2 (since interest is cοmpοunded semi-annually), t = 120, and r is the interest rate per year, sο we need tο find r. Tο dο this, we can use the fοrmula:

[tex]A = P\times (1 + r/n)^{(nt)[/tex]

where A is the future value of the annuity after t depοsits.

Substituting the given vaIues, we have:

[tex]\$100 \times (1 + r/2)^{(2\cdot120)[/tex] = A

SimpIifying, we get:

[tex](1 + r/2)^{240} = A/100[/tex]

Taking the natural lοgarithm of both sides, we get:

[tex]ln(1 + r/2)^{240} = ln(A/100)[/tex]

240*ln(1 + r/2) = ln(A/100)

ln(1 + r/2) = ln(A/100)/240

Solving for r, we get:

[tex]$r = 2 \times \frac{e^{(ln(A/100)}}{240) - 1}[/tex]

Substituting the given vaIues, we get:

r = 0.4902 or 49.02%

Now we can plug in all the values into the original fοrmula for the future value οf the annuity:

[tex]A = $100\times \dfrac{(1 + 0.4902/2)^{(2\cdot 120) - 1)}}{0.4902/2}[/tex]

SimpIifying, we get:

A = $1,059,780.64

Therefοre, the value οf the annuity after 120 depοsits is $1,059,780.64.

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Therefore , expression problem solution is during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

There is a need for mathematical operations like multiplying, splitting, combining, and now even deleting. If they were combined, it would be said that: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and mathematical operations like additions, subtractions, missteps, algebraic formulas, and divisions. It is possible to evaluate and analyse words and phrases.

Here,

Distance is determined by rate and duration.

for the distances that children and adults travel, two equations should be made up:

=> (d - 16) = 1t (for the youngsters) (for the kids)

=> d = 3t (for the males) (for the adults)

where "t" represents the amount of time that has elapsed since the competition began.

We can set the distances between the children and adults to be equal because we know that they were side-by-side at some time during the race:

=> d - 16 = 3t - 16

When we simplify this solution, we obtain:

=> d = 3t

When we add this to the prior solution, we obtain:

=> 3t - 16 = 1t

To solve for "t," we obtain:

=>  t = 8 sec.

Now that we know how far the grownups travelled:

D=3t=3x8=24 metres.

As a result, during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

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I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.

Answer:

Réponse :Explications étape par étapea) Le vecteur AC(xc-xa;yc-ya)vecteur AC(-6;-3

Step-by-step explanation:

Les coordonnées d'un vecteur dans un r.o.n. décrivent le déplacement qu'il représente. Ainsi, un déplacement de « 3 ...

The matrices A and B are given as:

A = [3/4 0]
[0 3/4]

B = [-4 0]
[0 -4]

2a) Compute AB:

AB = [3/4 0] * [-4 0]
[0 3/4] [0 -4]

= [3/4 * -4 + 0 * 0 3/4 * 0 + 0 * -4]
[0 * -4 + 3/4 * 0 0 * 0 + 3/4 * -4]

= [-3 0]
[0 -3]

2b) Compute BA:

BA = [-4 0] * [3/4 0]
[0 -4] [0 3/4]

= [-4 * 3/4 + 0 * 0 -4 * 0 + 0 * -4]
[0 * 3/4 + -4 * 0 0 * 0 + -4 * 3/4]

= [-3 0]
[0 -3]

2c) How did your answer in part (a) and (b) compare?

The answers in part (a) and (b) are the same. Both AB and BA resulted in the matrix [-3 0] [0 -3].

2d) Will this be true, in general, for any two matrices when you multiply them (assuming their dimensions line up so that they may be multiplied)? If so, explain your reasoning. If not, show an example of two matrices C and D such that CD≠DC.

No, this will not be true in general for any two matrices when you multiply them. The order in which matrices are multiplied matters, and in most cases, AB≠BA. Here is an example of two matrices C and D such that CD≠DC:

C = [1 2]
[3 4]

D = [5 6]
[7 8]

CD = [1 * 5 + 2 * 7 1 * 6 + 2 * 8]
[3 * 5 + 4 * 7 3 * 6 + 4 * 8]

= [19 22]
[43 50]

DC = [5 * 1 + 6 * 3 5 * 2 + 6 * 4]
[7 * 1 + 8 * 3 7 * 2 + 8 * 4]

= [23 34]
[31 50]

As you can see, CD≠DC.

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The correct equation is;

p = 4t + 1

The equation of a line is a mathematical expression that describes the relationship between the x and y coordinates of the points on the line. In general, the equation of a line can be written in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

We can get the slope of the graph from;

m = y2 - y1/x2 =x2 - x1

m = 1 - 0/0.25 - 0

m = 4

Since the y intercept is at y = 1 then we have;

p = 4t + 1

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The vectors v1 = {1,2,0}, v2 = {1,0,1}, and v3 = {1,a,4} are linearly independent if a = 8/3, t and  linearly dependent for a = 2, and linearly independent for a = 8/3.

For the vectors to be linearly independent, we need to check if the following system of equations has a unique solution:

c1v1 + c2v2 + c3v3 = 0

where c1, c2, c3 are constants, and 0 is the zero vector.

Substituting the given vectors, we get the following system of equations:

c1 + c2 + c3 = 0 (1)

2c1 + ac3 = 0 (2)

c2 + 4c3 = 0 (3)

If we can find values of a for which this system of equations has a non-trivial solution, then the vectors are linearly dependent. Otherwise, they are linearly independent.

To find such values of a, we need to solve the system of equations and find the conditions under which it has non-trivial solutions.

From equations (2) and (3), we get:

c2 = -4c3 (4)

2c1 + ac3 = 0 (5)

Substituting equations (1) and (4) into equation (5), we get:

2(-c2 - c3) + ac3 = 0

Simplifying, we get:

(-2 + a)c3 - 2c2 = 0

Substituting equation (4), we get:

(-2 + a)c3 + 8c3 = 0

Solving for c3, we get:

c3 = 0 if a = 2

c3 = 0 if a = 8/3

For a = 2, the system reduces to:

c1 + c2 = 0

2c1 = 0

c2 + 4c3 = 0

This system has a non-trivial solution: c1 = 0, c2 = 1, c3 = -1/4.

Therefore, the vectors are linearly dependent for a = 2.

For a = 8/3, the system reduces to:

c1 + c2 + c3 = 0

(8/3)c3 = 0

c2 + 4c3 = 0

This system has only the trivial solution: c1 = c2 = c3 = 0.

Therefore, the vectors are linearly independent for a = 8/3.

In summary, the given vectors are linearly dependent for a = 2, and linearly independent for a = 8/3.

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The coordinate of the other endpoint of the line segment is (-1, 2).

In geometry, a line segment is a part of a line that has two endpoints. It is the shortest distance between two points on a line. A line segment can be straight or curved, and can be vertical, horizontal, or diagonal.

The length of a line segment can be measured using units such as centimeters, inches, or feet. The midpoint of a line segment is the point that is exactly halfway between its endpoints, and it is located at the average of the x-coordinates and the y-coordinates of the endpoints.

Let (x, y) be the coordinate of the other endpoint of the line segment. Then, we know that the midpoint of the line segment is given by the formula:

midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the given values, we have:

(1, -2) = ((3 + x)/2, (-6 + y)/2)

Multiplying both sides by 2, we get:

(2, -4) = (3 + x, -6 + y)

Separating the x and y terms, we have:

2 = 3 + x -> x = -1

-4 = -6 + y -> y = 2

Therefore, the coordinate of the other endpoint of the line segment is (-1, 2).

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we can reject the null hypothesis

Null Hypothesis (H₀): μ ≥ 50

Alternative Hypothesis (H₁): μ < 50

Assumptions:
- A normal distribution for the population of LCBO stores
- A random sample of 20 stores
- A significance level of 0.05

Critical-value approach:

First, calculate the test statistic using the formula:

Test statistic = (Sample Mean - Population Mean) / (Standard Deviation / √Sample Size)

= (41.3 - 50) / (12.2 / √20)

= -2.6

Then, compare this test statistic to the critical-value.

The critical-value is the value that divides the acceptance and rejection regions of the distribution. The critical-value for a two-tailed test with a significance level of 0.05 is ±1.96.

Since -2.6 is less than -1.96, the test statistic falls into the rejection region and we reject the null hypothesis.

p-value approach:

Calculate the p-value using the formula:

p-value = 1 - CDF(test statistic)

Where CDF is the cumulative distribution function.

= 1 - CDF(-2.6)

= 0.004

Since 0.004 is less than 0.05, we reject the null hypothesis.

In conclusion, based on the critical-value approach and the p-value approach, we can reject the null hypothesis and conclude that the population mean sales increase is less than 50 cases.

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The following are solutions to the given problems given f(x)=x²- 5x+7 and g(x)=3x² + 4x - 2;

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = 4 x² - x + 5

A function can be defined as a relation between a set of inputs having one output each. In other words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain (range). A function is generally denoted by f(x) where x is the input.

here, we have,

The general mathematical representation of a function is y = f(x).

f(x)=x²- 5x+7

g(x)=3x² + 4x - 2

so, we get,

(f- g)(x) = x²- 5x+7 - (3x² + 4x - 2)

(f- g)(x) = x²- 5x+7 - 3x² - 4x + 2

(f- g)(x) = -2x² - 9x + 9

(g-f)(x) = 3x² + 4x - 2 - (x²- 5x+7)

(g-f)(x) = 3x² + 4x - 2 - x² + 5x - 7

(g-f)(x) = 2x² + 9x - 9

(f + g)(x) = x²- 5x+7 + 3x² + 4x - 2

(f + g)(x) = 4 x² - x + 5

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The graphs when classified are decay and growth functions

The complete solution is shown below

A graph that represents an exponential growth would increase as the input value (x) increases, while graphs of exponential decay would decrease with increment in x

This means that:

An exponential function is represented as

y = abˣ

If b > 1, then it is a growth function, otherwise it is a decay function

This means that:

For the equation y = abˣ, we have

Initial value = a

Decay rate (if b < 0) = 1 - b

Growth rate (if b > 0) = b - 1

This means that

Function (12) is unclear

13. f(x) = 11(0.4)ˣ:

Initial value = 11

Decay factor = 0.4

Decay rate = 6%

14. f(x) = (1/4)ˣ:

Initial value = 1

Decay factor = 1/4

Decay rate = 75%

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Answer:

B

Step-by-step explanation:

2 is hundred = 2x100

0 is tens =0x10

4 is unit =4 x 1

All numbers after the decimal point to the right are fractions

0 is tenth = 0/10 =0

1 is hundredth =1/100

7 is thousandth 7/1000

Now you can choose the right answer

The solutions to this 3x^(2)-4x=-2  are x=(2/3)+i*√(2/9) or x=(2/3)-i*√(2/9).

To solve this equation by completing the square, we need to first rearrange the equation and then complete the square for the x terms. Here are the steps:

1. Rearrange the equation:
3x^(2)-4x=-2 becomes 3x^(2)-4x+2=0

2. Divide the entire equation by the coefficient of the x^(2) term:
(3x^(2)-4x+2)/3=0/3 becomes x^(2)-(4/3)x+(2/3)=0

3. Complete the square by adding the square of half the coefficient of the x term to both sides of the equation:
x^(2)-(4/3)x+(2/3)+(4/3)^(2)/4=(4/3)^(2)/4 becomes x^(2)-(4/3)x+(4/9)=(4/3)^(2)/4-(2/3)

4. Simplify the right side of the equation:
(4/3)^(2)/4-(2/3)=(16/9)/4-(2/3)=(4/9)-(2/3)=(4/9)-(6/9)=-(2/9)

5. Factor the left side of the equation:
(x-(2/3))^(2)=-(2/9)

6. Take the square root of both sides of the equation:
x-(2/3)=+/-sqrt(-(2/9))

7. Solve for x:
x=(2/3)+/-sqrt(-(2/9)) becomes x=(2/3)+i*sqrt(2/9) or x=(2/3)-i*sqrt(2/9)

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The exponential function that is equivalent to the geometric sequence, aₙ = 9.5 × 5ⁿ is A. f(n) = (0.95)5ⁿ.

An exponential function is a mathematical function that calculates the exponential growth or decay of a data set.

There are two types of exponential functions: exponential growth and exponential decay.

The function f(x) = bx where b > 1 represents exponential growth function while f(x) = bx when 0 < b < 1, represents an exponential decay function.

Thus, the equivalent exponential function is Option A.

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For subspace (a.1) basis for Col(A) is the first four columns of A and dimension is 4. For (a.2) basis for Row(A) is the first four rows of A and dimension is 4. A basis for (a.3) Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0 and dimension is 7.

A basis for a subspace is a set of vectors that are linearly independent and span the subspace. The dimension of a subspace is the number of vectors in a basis for that subspace.

(a.1) Col(A) is the subspace of R^4 spanned by the columns of A. To find a basis for Col(A), we can reduce A to its reduced row echelon form (RREF) and find the columns of A that correspond to the pivot columns in the RREF. The RREF of A is:

1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0

The pivot columns are the first four columns, so a basis for Col(A) is the first four columns of A:

{[1, 1, 1, 1], [1, 1, -1, -1], [1, -1, 1, -1], [1, -1, -1, 1]}

The dimension of Col(A) is the number of vectors in the basis, which is 4.

(a.2) Row(A) is the subspace of R^11 spanned by the rows of A. To find a basis for Row(A), we can reduce A to its RREF and find the nonzero rows. The RREF of A is the same as above, so a basis for Row(A) is the first four rows of A:

{[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1, -3, 3, 0, 0]}

The dimension of Row(A) is the number of vectors in the basis, which is 4.

(a.3) Nul(A) is the subspace of R^11 consisting of all vectors x such that Ax = 0. To find a basis for Nul(A), we can reduce A to its RREF and find the solutions to the homogeneous equation Ax = 0. The RREF of A is the same as above, and the general solution to Ax = 0 is:

x1 = 0
x2 = 0
x3 = 0
x4 = 0
x5 = free
x6 = free
x7 = free
x8 = free
x9 = free
x10 = free
x11 = free

A basis for Nul(A) is the set of vectors obtained by setting one free variable to 1 and the others to 0:

{[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]}

The dimension of Nul(A) is the number of vectors in the basis, which is 7.

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Answer:

1+1= 2

Step-by-step explanation:

im a genuis

The highlighted part of circle shown below is known as segment.

A segment of a circle is a region of the circle that is bounded by a chord and the arc that it intersects. More specifically, a segment is the region between a chord and a minor or major arc of a circle.

The chord is the straight line that connects two points on the circumference of the circle, and the arc is the curved part of the circumference that lies between these two points. A segment is named according to its chord, for example, the segment determined by the chord AB is referred to as segment AB. The area of a segment of a circle can be calculated using the formula A = (1/2)r^2(θ-sinθ), where r is the radius of the circle, and θ is the central angle of the segment in radians.

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The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2

To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:

√(x + 3) + 2 > √(x - 4) + 12

Now, we can rearrange the terms and square both sides to get rid of the radicals:

√(x + 3) - √(x - 4) > 10

(√(x + 3) - √(x - 4))^2 > 10^2

x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100

2x - 2√(x + 3)(x - 4) > 101

Now, we can isolate the radical term and square both sides again:

-2√(x + 3)(x - 4) > 101 - 2x

4(x + 3)(x - 4) > (101 - 2x)^2

4(x^2 - x - 12) > 10201 - 404x + 4x^2

0 > 3x^2 - 403x + 10237

Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:

0 > 3(13^2) - 403(13) + 10237

0 > 507 - 5239 + 10237

0 > 4505

Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:

4(x^2 - x - 12) > (101 - 2x)^2

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For the given triangle ABC, the exact values of the three angles are: A = 50°, B = 60°, and C = 70°.

Let ABC be a triangle. The angles A, B, and C can be determined using the fact that the sum of the angles in any triangle is 180°.

We know that

A = 5x, B = 6x, and C = 7x, so:

A + B + C = 5x + 6x + 7x = 18x

Since the sum of the angles in a triangle is 180°, we can set

18x = 180°

and solve for x:

18x = 180°, x = 10°

Therefore, A = 50°, B = 60°, and C = 70°.

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The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

The Apothem of a regular octagon is 5 units. Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 4

tan 22.5° = n / 8

n = 3.3137

Then the perimeter is given as,

P = 8 x 3.3137

P = 26.51 units

The perimeter of the regular octagon with an apothem of 4 units will be 26.51 units.

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The correct answer to this question is 7/220. To calculate this answer, divide the number of students who preferred the turkey club (7) by the total number of seventh-grade students (220). The fraction form of this answer is 7/220, the decimal form is 0.0318, and the percentage form is 3.18%.

Proportion is a mathematical concept that compares two values, which can be the same or different, using division. It is used to identify the relationship between two or more values. It can also be used to compare the parts of a whole or to compare two different wholes. Proportions can be expressed as a fraction, a decimal, or a percentage.

This answer can be used to estimate the number of students who preferred the turkey club. To do this, multiply the total number of seventh-grade students (220) by the proportion (7/220). This calculation results in 7 students. In other words, approximately 7 of the 220 seventh-grade students preferred the turkey club.

The proportion 7/220 can also be used to estimate the number of students who preferred the turkey club if the total number of seventh-grade students changes. For example, if the total number of seventh-grade students increases to 250, the estimated number of students who preferred the turkey club can be calculated by multiplying the new total (250) by the proportion (7/220). This calculation results in 8 students.

Therefore, the correct answer to the question is 7/220.

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The 6th term of the sequence is -97.65625

From the question, we have the following parameters that can be used in our computation:

A(n) = -2.5^(n-1)

In the sixth term, we have

n = 6

Substitute the known values in the above equation, so, we have the following representation

A(6) = -2.5^(6-1)

Evaluate

A(6) = -97.65625

Hence, the 6th term is -97.65625

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The correct answer is d. 9.9498.

To find the standard deviation of a distribution, we use the formula:

Standard deviation = √[(∑(x - mean)2)/n]

First, we need to find the mean of the distribution. The mean is the sum of all the values divided by the number of values. In this case, the mean is:

mean = (35 + 250)/5 = 57

Next, we need to find the sum of the squared differences between each value and the mean. This is:

∑(x - mean)2 = (35 - 57)2 + (250 - 57)2 = 485 + 37249 = 37734

Finally, we divide this sum by the number of values and take the square root to get the standard deviation:

Standard deviation = √(37734/5) = √7546.8 = 9.9498

So the standard deviation of the distribution is 9.9498.

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Answer:

Let the base of the triangle and parallelogram be denoted by 'b' and their respective altitudes be denoted by 'h1' and 'h2'.

Given that the area of the triangle is equal to the area of the parallelogram, we have:

Area of triangle = (1/2)bh1 Area of parallelogram = b*h2

Since the areas are equal, we have:

(1/2)bh1 = b*h2

Simplifying the above equation, we get:

h1 = 2*h2

Substituting the given value of h2 as 100 m, we get:

h1 = 2*100 = 200 m

Therefore, the altitude of the triangle is 200 meters

This graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

Profit is the difference between a firm's total revenue and total expenses. It is the amount of money a business has earned after subtracting the cost of goods sold, operating expenses and taxes from its total revenue.

The graph reveals a few key pieces of information that can be used to assess the potential profitability of Tara’s prints. Firstly, the graph shows that there is a fixed cost associated with each print, regardless of how many prints are sold. This cost is represented by the straight line at the bottom of the graph. Additionally, the graph reveals that the cost of the prints increases exponentially as more prints are sold. This means that the more prints Tara sells, the more money she makes. Lastly, the graph shows that the revenue from selling prints is significantly higher than the cost of producing them, indicating that Tara can make a profit if she is able to sell enough prints. Overall, this graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.

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Step-by-step explanation:

We can solve for x in terms of y from the equation 3x - y = 12 as follows:

3x - y = 12

3x = y + 12

x = (y + 12)/3

Similarly, we can solve for y in terms of x:

3x - y = 12

-y = -3x + 12

y = 3x - 12

Now, we can substitute these expressions for x and y into the expression 8x/2y to get:

8x/2y = 4x/y

Substituting (y + 12)/3 for x, we get:

4x/y = 4((y + 12)/3)/y = 4(y + 12)/3y

Simplifying the numerator, we get:

4(y + 12) = 4y + 48

Substituting 3x - 12 for y, we get:

4y + 48 = 4(3x - 12) + 48 = 12x

Therefore, 8x/2y = 4x/y = 12x/4y = 12x/(3x - 12)

We cannot simplify this expression further without additional information. Therefore, the answer is (D) The value cannot be determined from the information given.

Answer: D, 912

Step-by-step explanation:

g(21) = 24 (21 + 17)

g(21) = 24 x 38

g(21) = 912 (Use your calculator for this part)

Answer: It is and answer that is not known yet

Step-by-step explanation: so 5x5=x x would be 25