Mrs. Morse's Class was washing cars to raise money for a fundraiser To wash each car it costs $3. 50 for water and soap if they make a profit of $1. 50 how much do they charge for each car washed?

The probability of the intersection of X and Y, (P(X ∩ Y)) is 1/18.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

Given that P(X|Y) = 1/3 and P(Y) = 1/6, we need to find P(X ∩ Y).

To find the probability of the intersection of X and Y (P(X ∩ Y)), you can use the formula:

P(X ∩ Y) = P(X|Y) * P(Y)

Now, plug in the given probabilities:

P(X ∩ Y) = (1/3) * (1/6)

Multiply the fractions:

P(X ∩ Y) = 1/18

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A construction company is designing a new playground. They plan to use a combination of rectangular and circular areas. The rectangular area will be used for a basketball court, while the circular area will be used for a play area.

The rectangular area will have a length of x + 5 meters and a width of x meters, while the circular area will have a radius of x meters. The combined area of the rectangular and circular areas will be 400 square meters.

The construction company needs to determine the value of x that will minimize the cost of constructing the playground. The cost of constructing the basketball court is $50 per square meter, while the cost of constructing the play area is $75 per square meter.

To solve this problem, we need to find the minimum cost of constructing the playground, which is given by a degree 3 polynomial equation.

Let C(x) be the cost of constructing the playground, then we have:

C(x) = 50(x + 5)x + 75πx^2

We need to find the value of x that minimizes C(x). To do this, we take the derivative of C(x) with respect to x and set it equal to 0:

C'(x) = 50(2x + 5) + 150πx = 0

Simplifying, we get:

4x + 10 + 3πx = 0

Rearranging and factoring out x, we get:

x(4 + 3π) = -10

Therefore, the value of x that minimizes the cost of constructing the playground is:

x = -10 / (4 + 3π)

This is the solution to the degree 3 polynomial equation. However, since x represents a length, it must be positive. Therefore, we reject the negative value and the final answer is:

x ≈ 2.9 meters

This means that the rectangular area will have a length of approximately 7.9 meters and a width of approximately 2.9 meters, while the circular area will have a radius of approximately 2.9 meters.

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The value of function f (x) is,

⇒ F (x) = 4x⁴ + 7x² + 7x - 22

We have to given that;

Function is,

⇒ F' (x) = 16x³ + 14x + 7

Now, We get;

Integrate both side;

F (x) = 16 x⁴ / 4 + 14x²/2 + 7x

F(x) = 4x⁴ + 7x² + 7x + c

Since, F (1) = - 5

Hence,

F (x) = 4 (1)⁴ + 7 (1)² + 7 (1) + c

- 5 = 4 + 7 + 7 + c

c = - 22

Thus, The function f (x) is,

⇒ F (x) = 4x⁴ + 7x² + 7x - 22

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Answer:

If x was 5 and x+u=15, then we can solve for u by subtracting 5 from both sides:

x+u = 15

5+u = 15

u = 10

Therefore, if x was 5 and x+u=15, then u would be 10.

Answer: u = 10

Step-by-step explanation:

x+u=15

x=5

5+u=15

5-5+u=15-5

0+u=10

u=10

We are 95% confident that the true mean length of action films over the past decade is between 110.49 minutes and 127.51 minutes.

We want to construct a 95% confidence interval for µ = the mean length of an action film over the past decade.

Name : Confidence interval for the mean

Conditions : The sample is random and comes from a population with a normal distribution or the sample is large (n≥30).

Random : Randomly select 30 action films.

10% : 30 is less than 10% of the population of all action films in the past decade.

Normal/Large sample : The sample size is 30, which is less than 30% of the population, but the standard deviation is known to be 21.5 minutes. Therefore, we can assume that the population is normally distributed and use a z-distribution.

95% confidence interval = X ± z*(σ/√n), where X = 119, σ = 21.5, n = 30, and z for 95% confidence level is 1.96

95% confidence interval = 119 ± 1.96*(21.5/√30)

95% confidence interval = (110.49, 127.51)

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Answer:

[tex]\\x \quad\quad \;\;\;f(x)\\\\-3 \quad\quad f(-3) -= - f(3) = -(-11) = \boxed{11}\\\\-1\quad\quad f(-1) = -f(1) = \boxed{-19}\\\\2\quad\quad\:\:\: f(2) = - f(-2) = \boxed{- 5}\\\\4\quad\quad\:\:\:f(4) = - f(-4) = - (-3) = \boxed{3}[/tex]

Step-by-step explanation:

A function is "even" when:

[tex]f(- x) = f(x) \textrm{\;for\;all\;x}[/tex]

In other words there is symmetry about the y-axis (like a reflection):

A function is "odd" when
[tex]f(-x) = -f(x) \textrm{ for all x}[/tex]
The symmetry is around the origin

Looking at the table and using the property of an odd function we can solve for the missing values

[tex]\\x \quad\quad \;\;\;f(x)\\\\-3 \quad\quad f(-3) -= - f(3) = -(-11) = \boxed{11}\\\\-1\quad\quad f(-1) = -f(1) = \boxed{-19}\\\\2\quad\quad\:\:\: f(2) = - f(-2) = \boxed{- 5}\\\\4\quad\quad\:\:\:f(4) = - f(-4) = - (-3) = \boxed{3}[/tex]

If a business had sales of $4,000,000, and a margin of safety of 25%, the break-even point was is c. $1,000,000.

The margin of safety is the difference between the actual or expected sales and the break-even point. In this case, if the margin of safety is 25%, it means that the business is generating sales that are 25% higher than the break-even point.

To calculate the break-even point, we can use the following formula:

Break-even point = Fixed costs / Contribution margin ratio

The contribution margin ratio is the difference between the sales price and variable costs, divided by the sales price. We don't have enough information to calculate it directly, but we can use the margin of safety to estimate it.

If the margin of safety is 25%, it means that the contribution margin ratio is 25% of the sales price. So, the variable costs must be 75% of the sales price, and the contribution margin ratio is 25%/100% = 0.25.

We know that the sales are $4,000,000, but we don't know the fixed costs. However, we can use the break-even formula to solve for it:

$1,000,000 = Fixed costs / 0.25

Fixed costs = $250,000

Therefore, the break-even point is $250,000 / 0.25 = $1,000,000.

Based on the given information, the break-even point for the business with sales of $4,000,000 and a margin of safety of 25% is $1,000,000.

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Pn has a smooth coordinate representation in terms of theta,Pn is a smooth map.

To show that the map Pn: S^1 -> S^1 given by Pn(z) = z^n is smooth, we need to show that it is well-defined and has smooth coordinate representations.

First, let's show that Pn is well-defined. We need to show that if z and w are two complex numbers with the same magnitude, then Pn(z) and Pn(w) also have the same magnitude. This is true because |z^n| = |z|^n = |w|^n = |w^n|, since z and w have the same magnitude. Therefore, Pn(z) and Pn(w) are both points on the unit circle, and Pn is well-defined.

Next, let's find a coordinate representation for Pn. We can represent a point on the unit circle using a complex number of magnitude 1, i.e., z = cos(theta) + isin(theta) for some angle theta. Then, Pn(z) = (cos(theta) + isin(theta))^n. Using the binomial theorem, we can expand this as a polynomial in cos(theta) and sin(theta):

Pn(z) = cos(ntheta) + isin(n*theta)

This shows that Pn has a smooth coordinate representation in terms of theta, which is a smooth coordinate on S^1. Therefore, Pn is a smooth map.

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The simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

The expression cos^2x sin^4x can be simplified by using the trigonometric identity that states sin^2x + cos^2x = 1.

We can rewrite cos^2x sin^4x as cos^2x (sin^2x)^2. Then, using the trigonometric identity sin^2x + cos^2x = 1, we can substitute (1 - cos^2x) for sin^2x.

This gives us cos^2x (1 - cos^2x)^2, which can be expanded using the binomial theorem to give cos^2x (1 - 2cos^2x + cos^4x).

Finally, we can simplify this expression further by distributing the cos^2x term and collecting like terms to get cos^2x - 2cos^4x + cos^6x.

Therefore, the simplified expression of cos^2x sin^4x is cos^2x - 2cos^4x + cos^6x.

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The arc length is 176 units.

To find the arc length of the curve r(t) = (1-9t)i + (5+2t)j + (6t-5)k, -10 ≤ t ≤ 6, we need to use the formula:

L = ∫[tex]a→b[/tex] |[tex]r'(t)[/tex]| dt

where a and b are the lower and upper limits of t, and r'(t) is the derivative of r(t).

First, we need to find the derivative of r(t):

r'(t) = -9i + 2j + 6k

Next, we need to find the magnitude of r'(t):

|r'(t)| = [tex]sqrt((-9)^2 + 2^2 + 6^2) = sqrt(121)[/tex] = 11

Now, we can substitute these values into the arc length formula and evaluate the integral:

L = ∫-[tex]10→6 |r'(t)|[/tex] dt

L = ∫[tex]-10→6 11[/tex] dt

L =[tex]11[t] from -10 to 6[/tex]

L = 11(6 - (-10))

L = 11(16)

L = 176

Therefore, the arc length of the curve r(t) = (1-9t)i + (5+2t)j + (6t-5)k, -10 ≤ t ≤ 6 is 176 units.

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The expression for the width of the rectangular room is (a² - 4a - 21)/(a+3) hence by performing polynomial division, we find that the width of the room is given by the expression: Width = a - 7

To find the expression for the width of the rectangular room, we need to use the formula for the area of a rectangle which is length multiplied by width. In this case, we are given that the area of the room is a² - 4a - 21 and the length is a+3. So, we can set up the equation:

a² - 4a - 21 = (a+3) * w

where w represents the width of the room. To solve for w, we need to simplify the equation by expanding the right-hand side:

a^2 - 4a - 21 = aw + 3w

Next, we can rearrange the terms to get w by itself:

w(a+3) = a² - 4a - 21

w = (a^2 - 4a - 21)/(a+3)

Therefore, the expression for the width of the rectangular room is (a² - 4a - 21)/(a+3).

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The band that De La Soul sampled and got sued for is The Turtles.

De La Soul is a hip-hop group from Long Island, New York that gained popularity in the late 1980s and early 1990s. Their music is known for its innovative sampling techniques and eclectic use of a wide variety of musical genres and sounds. One of their most famous songs, "Transmitting Live from Mars," features a sample from the 1968 song "You Showed Me" by The Turtles.

However, The Turtles and their record label, Flo & Eddie, sued De La Soul and their label, Tommy Boy Records, for copyright infringement. The Turtles claimed that De La Soul had used an unauthorized sample of their song without permission. The case went to court, and in 1991, a judge ruled in favor of The Turtles and Flo & Eddie, awarding them $1.7 million in damages.

The ruling had significant implications for the music industry and the use of sampling in hip-hop and other genres. It established a precedent that using even short samples of copyrighted material without permission could be considered infringement and could result in substantial financial penalties. This had a chilling effect on many artists, who became more cautious about using samples in their music.

In recent years, De La Soul has been outspoken about the negative impact the lawsuit had on their career and their ability to release their music. They have criticized the music industry for its treatment of artists and for its failure to adapt to the changing landscape of music distribution and consumption. Despite these challenges, De La Soul remains a highly respected and influential group in hip-hop history.

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There is sufficient evidence to conclude that more than 10% of homes in the city are not up to the current electrical codes when, in fact, there are no more than 10% that are not up to the current electric codes.

Explanation:

A Type I error occurs when we reject the null hypothesis (H0) when it is actually true. In this case, the null hypothesis (H0) states that the percentage of homes in the city that are not up to the current electric codes is no more than 10%. The alternative hypothesis (Ha) states that the percentage of homes in the city that are not up to the current electric codes is more than 10%.

A Type I error in this scenario would be to conclude that there is sufficient evidence to support the alternative hypothesis (Ha) that more than 10% of homes are not up to the current electrical codes, when in fact, the true percentage is no more than 10%.

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The right response is therefore: "There is sufficient evidence to conclude that more than 10% of homes in the city are not up to current electrical codes when, in fact, there are no more than 10% that are not up to current electrical codes."

In this hypothesis test, the type I error is the mistake of rejecting the null hypothesis even though it is true. In other words, it is the fallacy of assuming that more than 10% of homes do not meet the current electrical code while in fact, it is just 10%.

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Therefore, the correct inequality to find the domain is simply x - 3 < 0, which simplifies to x < 3.

To find the domain of a function, we need to determine all the values of the independent variable (usually represented by x) that the function is defined for. In this case, the function is defined as f(x) = x - 3, which means we can plug in any value of x into the expression x - 3 to get a corresponding value of f(x).

However, there are some values of x that would cause the expression x - 3 to be undefined. For example, if we were trying to find f(x) when x = 2, we would get f(2) = 2 - 3 = -1, which is a valid output. But if we were trying to find f(x) when x = 3, we would get f(3) = 3 - 3 = 0/0, which is undefined.

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The transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

The transformations are applied in the following order:

Horizontal translation: The function is shifted 9 units to the right by subtracting 9 from the input variable x.

f(x) → f(x - 9)

Horizontal scaling: The function is compressed horizontally by a factor of 1/3 by dividing the input variable x by 3.

f(x - 9) → f(1/3(x - 9))

Vertical reflection: The function is reflected about the x-axis by multiplying the output values of f by -1.

f(1/3(x - 9)) → -f(1/3(x - 9))

Vertical scaling: The function is stretched vertically by a factor of 8 by multiplying the output values by 8.

-f(1/3(x - 9)) → -8f(1/3(x - 9))

Therefore, the transformations are applied in the following order: horizontal translation, horizontal scaling, vertical reflection, and vertical scaling.

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The value of C is 1/9 for the probability density function using integration.

We know that the probability density function (pdf) integrates to 1 over the interval [0, a]:

∫[0,a] cx^n dx = 1

Substituting the given values for n and a, we get:

∫[0,3] cx^2 dx = 1

Integrating with respect to x:

c ∫[0,3] x^2 dx = 1

c [x^3/3] from 0 to 3 = 1

c (3^3/3 - 0) = 1

c = 1/9

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By inserting parentheses in the expression we obtained: A = 10: 4 + (2[tex]^2[/tex] * 3) - 5 * 2, (4 + 2[tex]^2[/tex]) * (3 - 5) * 2 & B = 14: (4 + 2[tex]^2[/tex]) * (3 - 5 * 2), 4 + (2[tex]^2[/tex] * (3 - 5)) * 2.

How we insert parentheses in the expression 4 + 2[tex]^2[/tex] * 3 - 5 * 2 in two ways so that the result is A = 10 and B = 14.

For A = 10, we have the following expressions and their corresponding results:

        - Calculation: 2^2 = 4, 4 * 3 = 12, 5 * 2 = 10, 12 - 10 = 2.

        - Calculation: 2[tex]^2[/tex] = 4, 4 + 4 = 8, 3 - 5 = -2, -2 * 2 = -4, 8 * (-4) = -32.

For B = 14, we have the following expressions and their corresponding results:

       - Calculation: 2[tex]^2[/tex] = 4, 5 * 2 = 10, 4 + 4 = 8, 3 - 10 = -7, -7 * 8 = -56.

       - Calculation: 2[tex]^2[/tex] = 4, 3 - 5 = -2, 4 * (-2) = -8, -8 * 2 = -16, 4 + (-16) = -12.

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P.S. sorry it's out of order >< i added arrows to show what corresponds to which of the two questions

The diameter of Cl atom has been 25,000 times larger than the diameter of the Cl nucleus.

To calculate the relationship between the diameter of Cl atom and nucleus, the diameter has to be calculated.

Diameter = 2 × radius

Diameter of Cl atom:

Cl atom = 2 × 100 pm

Cl atom = 200pm

1 pm = 10⁻¹²m

200 pm = 200×10⁻¹²m

Diameter of Cl nucleus:

Cl nucleus = 2 × 4 fm

Cl nucleus = 8 fm

1 fm  = 10⁻¹⁵m

8 fm  =8× 10⁻¹⁵m

The relationship between the Cl atom and the nucleus has been made by taking the ratio of the diameter of the Cl atom to the Cl nucleus.

Diameter of Cl atom/Diameter of Cl nucleus = 200×10⁻¹²/8×10⁻¹⁵

Diameter of Cl atom = 25000 Diameter of Cl nucleus.

Thus, the diameter of Cl atom has been 25,000 times larger than the diameter of the Cl nucleus.

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The radius of a Cl nucleus is 4.0 fm, and the radius of a Cl atom is 100 pm. (1 fm = 1x 10-15 m; 1 pm = 1 x 10-12 m).How many times larger is the diameter of the Chlorine atom than the diameter of the Chlorine nucleus?

A type I error occurs when we reject the null hypothesis (H0) when it is actually true.

b) The significance level (α) is the probability of making a type I error. Since the rejection region is {y ≤ 12} and the null hypothesis is p = 0.8, we need to find the probability of getting a sample proportion (y/20) less than or equal to 0.6 (12/20) under the null hypothesis. Using a normal approximation to the binomial distribution, we have:

z = (0.6 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -1.79

From a standard normal distribution table, we find that the area to the left of z = -1.79 is approximately 0.0367. Therefore, α = 0.0367 or 3.67%.

c) A type II error occurs when we fail to reject the null hypothesis (H0) when it is actually false.

d) To find β when p = 0.6, we need to find the probability of not rejecting the null hypothesis (H0: p = 0.8) when the true proportion is p = 0.6. Using a normal approximation to the binomial distribution, we have:

z = (0.6 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -1.79

We want to find the probability that z is greater than -1.79, which is the area to the right of z = -1.79 under the standard normal distribution. From a standard normal distribution table, we find that the area to the right of z = -1.79 is approximately 0.9637. Therefore, β ≈ 0.9637.

e) To find β when p = 0.4, we again need to find the probability of not rejecting the null hypothesis (H0: p = 0.8) when the true proportion is p = 0.4. Using a normal approximation to the binomial distribution, we have:

z = (0.4 - 0.8) / sqrt(0.8 * 0.2 / 20) ≈ -3.58

We want to find the probability that z is greater than -1.79, which is the area to the right of z = -3.58 under the standard normal distribution. From a standard normal distribution table, we find that the area to the right of z = -3.58 is approximately 0.9997. Therefore, β ≈ 0.9997.

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The rule for g(x) is g(x) = ln((x/8) - 3) + 1.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

To write a rule for g(x) that represents a translation 3 units right and 1 unit up, followed by a horizontal stretch by a factor of 8 of the graph of f(x) = ln(x), proceed as follows:

1. Translate 3 units right by replacing x with (x - 3) in the original function:

f(x - 3) = ln(x - 3).
2. Translate 1 unit up by adding 1 to the translated function:

f(x - 3) + 1 = ln(x - 3) + 1.
3. Apply a horizontal stretch by a factor of 8 by replacing x with x/8 in the translated function:

f((x/8) - 3) + 1 = ln((x/8) - 3) + 1.

The complete question is:

"What is the rule for g that represents a translation of 3 units to the right and 1 unit up, followed by a horizontal stretch by a factor of 8, applied to the graph of f(x) = ln x?"

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Answer:

648 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 27 cm

W = 24 cm

Let's solve

27 x 24 = 648 cm²

So, the area of the shape is 648 cm²

Answer: 80 + 2L*L = 26*L

Step-by-step explanation:

Answer:

To solve this problem, we can use the formulas for the perimeter and area of a rectangle:

Perimeter = 2 * (length + width) Area = length * width

Since we're dealing with a square in this case, we can simplify these formulas slightly:

Perimeter = 4 * side Area = side^2

where "side" is the length of one side of the square.

Given the perimeter and area of the map, we can set up two equations in terms of "side":

4 * side = 26 (since the perimeter is 26 feet) side^2 = 40 (since the area is 40 square feet)

From the first equation, we can solve for "side" by dividing both sides by 4:

side = 6.5

Substituting this value into the second equation, we get:

(6.5)^2 = 40.25

Since the area of the map is supposed to be 40 square feet, this means that the map's dimensions are not actually a square, but instead a rectangle with dimensions that are very close to 6.5 feet by 6.17 feet (since 6.5 * 6.17 = 40.05 square feet, which is very close to 40).

Therefore, to answer the question "What are the dimensions of the map?", we can say that the map's dimensions are approximately 6.5 feet by 6.17 feet.

Step-by-step explanation:

The statement is incorrect. The difference is said to be statistically significant if it is unlikely to have occurred by chance alone.

In statistical hypothesis testing, a p-value is calculated to determine the likelihood of observing a difference as extreme as the one observed, assuming that the null hypothesis is true. If the p-value is below a predetermined significance level (often 0.05), the difference is considered statistically significant, indicating that it is unlikely to have occurred due to random variation.

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The qualities of the given set are that it is closed and its interior is open.

The given set is the region between two concentric circles centered at the origin with radii of 3 and 4. To determine the qualities of this set, we can consider its boundaries, interior, and exterior. The boundaries of the set are the two circles of radius 3 and 4. These boundaries are included in the set, so the set is closed. The interior of the set consists of all points whose distance from the origin is between 3 and 4. Since the set contains no points on the boundaries, it is open. The exterior of the set consists of all points whose distance from the origin is either less than 3 or greater than 4. Since the complement of the set is the union of two open disks, the exterior of the set is also open. Therefore, the qualities of the given set are that it is closed and its interior is open.

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The angles and side of the parallelogram can be found as follows:

m∠E = 135°

FG = 10 units

A parallelogram is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the sum of the adjacent angles of a parallelogram is always supplementary. Opposite angles of parallelogram are equal.

Hence,

3x - 15 + 7x - 5 = 180

10x - 20 = 180

10x = 180 + 20

10x = 200

x = 200 / 10

x = 20

m∠G = M∠E = 7(20) - 5 = 140 - 5 = 135 degrees

Let's find the side FG as follows:

3y = y + 8

3y - y = 8

2y = 8

y = 8 / 2

y = 4

Therefore,

FG = 2(y + 1) = 2(4 + 1) = 10 units

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The z-score is a standardized score that tells us how many standard deviations a data point is away from the mean. It is calculated as:

z = (x - mu) / sigma

where x is the raw score, mu is the mean, and sigma is the standard deviation.

For a normally distributed set of data with a mean of 10 and a standard deviation of 3, the z-score for each of the following raw scores would be:

x = 7

z = (7 - 10) / 3 = -1

The z-score for a raw score of 7 is -1.

x = 12

z = (12 - 10) / 3 = 0.67

The z-score for a raw score of 12 is 0.67.

x = 16

z = (16 - 10) / 3 = 2

The z-score for a raw score of 16 is 2.

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If the car's base price is $22,760 and its factory-installed options total $1,230, the destination charge is $385, then the sticker price of Jill Stern's sedan is $24,375.

To find the sticker price, we need to add the base price, factory-installed options, and destination charge.

Base price: $22,760
Factory-installed options: $1,230
Destination charge: $385

Sticker price = Base price + Factory-installed options + Destination charge
Sticker price = $22,760 + $1,230 + $385
Sticker price = $24,375

Therefore, the sticker price of Jill Stern's sedan is $24,375.

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The Area of sector is 437.646 inch².

We have,

radius= 14 inch

Angle = 256 degree

So, area of sector

= ∅ / 360πr²

= 256/ 360 (3.14) (14)²

= 0.7111 x 3.14 x 196

= 437.646 inch²

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complete question:

Find the areas of the sectors formed by angle DFE . Round your answers to the nearest hundredth. A circle of radius 14 centimeters with center as point F. Two points E and D are marked on the circle such that measure of angle corresponding to major arc E D at the center, is 256 degrees. Point G is marked on major arc E D. The area of the red sector is about square centimeters and the area of the blue sector is about square centimeters.

The [tex](3,-3)[/tex]is a solution of the inequality [tex]y\leq -5x + 3[/tex].

We can test whether[tex](3,-3)[/tex]is a solution of the inequality [tex]y \leq -5x + 3[/tex] by substituting the values of x and y into the inequality and seeing if the inequality is true or false.

Substituting [tex]x=3[/tex] and [tex]y=-3[/tex] into the inequality, we get:

[tex]-3 \leq -5(3) + 3[/tex]

Simplifying the right side of the inequality, we get:

[tex]-3 \leq -15 + 3\\-3 \leq -12[/tex]

Since [tex]-3[/tex] is indeed less than or equal to [tex]-12[/tex], the inequality is true when [tex]x=3[/tex] and [tex]y=-3[/tex].

Therefore, [tex](3,-3)[/tex] is a solution of the inequality [tex]y \leq -5x + 3[/tex].

Learn more about Inequality  at

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