Jermaine did this work to solve an equation. Did he make an error?

Answer:

The inequality is given to be :

[tex]\frac{3x+8}{x-4}\geq 0[/tex]

The inequality will be greater than or equal to 0 if and only if both the numerator and denominator of the left hand side will have same sign either both positive or both negative.

CASE 1 : Both positive

3x + 8 ≥ 0

⇒ 3x ≥ -8

[tex]x\geq \frac{-8}{3}[/tex]

Also, x - 4 ≥ 0

⇒ x ≥ 4

Now, Taking common points of both the values of x

⇒ x ∈ [4, ∞)

CASE 2 :  Both are negative

3x + 8 ≤ 0

⇒ 3x ≤ -8

[tex]x\leq \frac{-8}{3}[/tex]

Also, x - 4 ≤ 0

⇒ x ≤ 4

So, Taking common points of both the values of x we have,

[tex]x=(-\infty,-\frac{8}{3}][/tex]

So, The solution of the equation will be the union of both the two solutions

So, Solution is given by :

[tex]x=(-\infty,-\frac{8}{3}]\:U\:[4,\infty)[/tex]

(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.

(b) The model predicts a score of 64 for 3 hours of homework.

(c) The number 40 represents the baseline test score when no homework is done, according to the model.

Analyzing the Scatter Plot and the Model

(a) Characterizing the Relationship

The scatter plot depicts test scores in relation to the hours of homework. Here’s how we can characterize the relationship:

- Positive Correlation: There is a general upward trend, indicating that as the hours of homework increase, the test scores also tend to increase.

- Strength: The points are not perfectly aligned, but there is a noticeable positive correlation, suggesting that more homework hours are associated with higher test scores.

- Outliers: Most points follow the trend, although there are a few variations. For example, there are a couple of points with low homework hours but relatively high test scores.

(b) Predicting the Score for 3 Hours of Homework

Paul uses the function [tex]\( y = 8x + 40 \)[/tex] to model the relationship, where [tex]\( y \)[/tex] represents the test score and [tex]\( x \)[/tex] represents the hours of homework.

To predict the score for 3 hours of homework:

[tex]\[y = 8(3) + 40 = 24 + 40 = 64\][/tex]

So, the model predicts a score of [tex]\( \boxed{64} \)[/tex] for 3 hours of homework.

(c) Meaning of the Number 40 in the Model

In the context of the situation, the number 40 in the equation [tex]\( y = 8x + 40 \)[/tex] represents the y-intercept. This implies:

- Baseline Score: If a student spends 0 hours on homework, the model predicts that they would score 40 on the test. This serves as a baseline score, indicating the minimum test score a student could achieve without any homework.

Summary

(a) The relationship between hours spent on homework and test scores is a positive correlation, where more homework is generally associated with higher test scores.

(b) The model predicts a score of 64 for 3 hours of homework.

(c) The number 40 represents the baseline test score when no homework is done, according to the model.

Peter needs approximately 34 inches of ribbon to create an 'X' across his 12-inch square flag, calculated using the Pythagorean theorem to find the length of the diagonals needed for the 'X'.

Peter is making an "X marks the spot" flag, which requires calculating the amount of ribbon needed to create the 'X'. The flag is a square with sides of 12 inches each. For an 'X', two ribbons will be needed, each stretching diagonally across the square. The diagonal length of a square can be determined using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the square has sides of 12 inches, making the formula for the diagonal:

d = √(12^2 + 12^2) = √(144 + 144) = √288 ≈ 16.97 inches.

Since Peter needs two diagonals to form the 'X', the total ribbon length will be 2 × 16.97 inches, which equals 33.94 inches. Therefore, Peter will need approximately 34 inches of ribbon to create the 'X' on his flag.

Answer:

-8.9%

Step-by-step explanation:

Answer:

The rate of change is - 8.89 %.

Step-by-step explanation:

Given,

The opening price = $ 3.15,

While closing price = $ 2.87,

Now,

[tex]\text{The rate  of change}=\frac{\text{closing price-opening price}}{\text{opening price}}\times 100[/tex]

[tex]=\frac{2.87-3.15}{3.15}\times 100[/tex]

[tex]=\frac{-0.28}{3.15}\times 100[/tex]

[tex]=-\frac{28}{3.15}=-8.8889\%\approx -8.89 \%[/tex]

Answer:

USD 3,508.16

Step-by-step explanation:

Hello

Let´s see what happens the first year when the car depreciates 13.75% of 20700 USD

[tex]depreciation=20700*\frac{13.75}{100} =2846.25 USD\\[/tex]

at the end of the first year the car will have a price of 20700-2486.25=17853.75 USD,  and this will be the price at the beginning of the second year.

completing the data for the 12 years with the help of excel you get

                                          depreciation           New Value

end of year 1  USD 20,700.00   USD 2,846.25   USD 17,853.75  

end of year 2  USD 17,853.75   USD 2,454.89   USD 15,398.86  

end of year 3  USD 15,398.86   USD 2,117.34   USD 13,281.52  

end of year 4  USD 13,281.52   USD 1,826.21   USD 11,455.31  

end of year 5  USD 11,455.31   USD 1,575.10   USD 9,880.20  

end of year 6  USD 9,880.20   USD 1,358.53   USD 8,521.68  

end of year 7  USD 8,521.68   USD 1,171.73            USD 7,349.94  

end of year 8  USD 7,349.94   USD 1,010.62   USD 6,339.33  

end of year 9  USD 6,339.33   USD 871.66           USD 5,467.67  

end of year 10 USD 5,467.67   USD 751.80       USD 4,715.87  

end of year 11  USD 4,715.87   USD 648.43     USD 4,067.43  

end of year 12 USD 4,067.43   USD 559.27   USD 3,508.16

after 12 years the car will ha a value of USD 3508.16

you can verify this by applying the formula

[tex]v_{2} =v_{1} (1-\frac{depreciatoin}{100} )^{n} \\\\v_{2} =20700 (1-\frac{13.75}{100} )^{12} \\v_{2} = 20700*0.1694\\v_{2} = 3508.16 USD[/tex].

Have a great day.

The value of a new car, originally priced at $20,700 and depreciating at 13.75% per year will be approximately $1446.63 after 12 years. This is calculated using a compound interest formula with a negative rate.

In order to solve this, we are going to use the formula for compound interest. Although we're actually dealing with depreciation, the calculation is the same as for interest, we just use a negative rate. The formula is P(t) = P0 * (1 + r) ^t, where P(t) is the value of the car after time t, P0 is the initial price of the car, r is the rate of depreciation, and t is time.

Here P0 = $20,700, r = -13.75% = -0.1375 (remember to convert rate from percentage to a proportion), and t = 12 years.

Substituting these values into the formula, we get: P(t) = 20700 * (1 - 0.1375)^12. Using a calculator, the value of the car after 12 years, to the nearest cent, is approximately $1446.63.

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Answer: No, the equation is not a good fit because the sum of the residuals is a large number.

Step-by-step explanation:

A residual is the difference on the scatter plot between the actual y-value and the predicted y-value from the regression line equation.

It is the vertical distance from the actual plotted point to the point on the regression line.

The residual is positive then the data point is above the graph.

The sum of the given residual values = [tex]4+(-1)+(-1)+1+(-1)+(-1)=1[/tex]

Since,  the sum of the residuals is greater than 0.

Therefore, The equation is not a good fit .

Answer:

A. No, the equation is not a good fit because the sum of the residuals is a large number.

Step-by-step explanation:

Answer : Distance will be 1507.2 feet .

Explanation :

Since we have given that

Radius of circle = 80 feet

So,

Circumference of circle is given by

[tex]2\pi r=2\times 3.14\times 80=502.4 \text{ feet}[/tex]

Since , a car travels 3 times around a traffic circle.

So,

[tex]\text{ Distance covered by the car will travel}= 3\times 502.4= 1507.2 \text{ feet }[/tex]

So, Distance will be 1507.2 feet .

Answer:

B) Area of triangle =  149.4 square units.

Step-by-step explanation:

Given : A triangle with sides 16 , 19, 27 .

To find : Area of a triangle.

Solution : We have given that triangle with sides 16 , 19, 27 .

Using heron's formula :

Area of triangle:  [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex].

Where, s = [tex]\frac{a+b+c}{2}[/tex] and a,b,c are sides of triangle.

Then s = [tex]\frac{16+19+27}{2}[/tex].

s = 31 units.

Area of triangle =  [tex]\sqrt{31(31-16)(31-19)(31-27)}[/tex].

Area of triangle =  [tex]\sqrt{31(15)(12)(4)}[/tex].

Area of triangle =  [tex]\sqrt{22320)}[/tex].

Area of triangle =  149.39 square units.

Area of triangle =  149.4 square units. ( nearest tenth)

Therefore, B) Area of triangle =  149.4 square units.

Ella sold 37 necklaces for $20 each at the craft fair. She is going to donate half of the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.

Solution:

Earning from 1 necklace=$20

Earning from 37 necklaces=$20*37

Half of the earnings= [tex] \frac{20*37}{2} =\frac{20}{2}*37=10*37 [/tex]

Half of the earnings=$10*37

Now, Applying Commutative Propert, a*b=b*a

So, Money she need to donate= Half of the earnings= 10*37 =37*10

So, Money she donates=$370

money she will donate=$370

Final answer:

To write a quadratic equation with roots −4 and 3 and a leading coefficient of 1, we start with the factored form (x - root1)(x - root2) = 0, substitute the given roots, and simplify to x² + x - 12 = 0.

Explanation:

The question asks us to write the quadratic equation whose roots are −4 and 3, and whose leading coefficient is 1. To find a quadratic equation given its roots, we can use the factored form of a quadratic equation, which is (x - root1)(x - root2) = 0, where root1 and root2 are the roots of the equation.

Given that the roots are −4 and 3, we substitute these values into the equation to get (x - (−4))(x - 3) = 0. Simplifying this, we first eliminate the double negative to get (x + 4)(x - 3) = 0. Multiplying these two binomials gives us the expanded form, which is x² + x - 12 = 0. This is the quadratic equation with roots −4 and 3, and a leading coefficient of 1.

Answer:

uses a visual representation of the logical flow of steps needed to reach a conclusion.  

Step-by-step explanation:

In a flowchart proof, there are boxes for the steps that lead us to the conclusion.  Below this are lines for the explanations of those steps.

Each box has an arrow pointing to the next box in the proof.

It helps us visualize the steps necessary to get from the given information to what we're asked to prove.

A flowchart proof contains a set of sentences explaining the steps needed to reach a conclusion uses  a visual representation of the logical flow of steps needed to reach a conclusion.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

A flowchart is a picture of the separate steps of a process in sequential order. It is a generic tool that can be adapted for a wide variety of purposes.

A flowchart proof uses a visual representation of the logical flow of steps needed to reach a conclusion. It contains a set of sentences explaining the steps needed to reach a conclusion and uses inductive reasoning to prove a statement.

Hence, A flowchart proof contains a set of sentences explaining the steps needed to reach a conclusion uses  a visual representation of the logical flow of steps needed to reach a conclusion.

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Locating -1.5 and 1.5 on a number line involves measuring 1.5 units from the origin, but in opposite directions; -1.5 is to the left and 1.5 is to the right.

Locating -1.5 on a number line is similar to locating 1.5 in that you measure the same distance away from the origin (0 point), which is 1.5 units. The main difference is the direction in which you measure from the origin. For -1.5, you would move 1.5 units to the left of the origin since negative numbers are represented to the left on a number line. On the other hand, for 1.5, you would move 1.5 units to the right of the origin because positive numbers are placed to the right.

Another perspective of understanding this concept comes from the coordinate system. If you stand on a straight line and choose a point as the origin, moving to the left will give you the negative coordinates, whereas moving to the right will give you the positive coordinates. Regardless of which side you choose, the absolute value of your position from the origin remains the same; only the sign changes to reflect the direction.

Answer:

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

Step-by-step explanation:

The given expression is

[tex]x^{3}+y^{3}[/tex]

This expression represents the sum of two perfect cubes, which is factorize as this product

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

We can demonstrate this factorization by multiplying the product

[tex](a+b)(a^{2}-ab+b^{2})=a^{3}-a^{2}b+ab^{2}+a^{2}b-ab^{2}+b^{3}=a^{3}+b^{3}[/tex]

Therefore, the answer is

[tex]x^{3}+y^{3}=(a+b)(a^{2}-ab+b^{2})[/tex]

Answer:

Area of triangle is 12 in.²

Step-by-step explanation:

we are given that:

The legs of a right triangle measure 4 and 6 inches.

(i.e. height and base of right angled triangle)

We have to find the area of this triangle.

area of triangle=[tex]\dfrac{1}{2}\times base\times height[/tex]

                        =[tex]\dfrac{1}{2}\times 4\times 6[/tex]

                       = 12 in.²

Hence, Area of triangle is 12 in.²

3+5 = 8

240/8 = 30

30*3 = 90 red cars

Answer:

I thing its B

Step-by-step explanation:

Just trust

Answer:

"Q and V" should be correct.

Step-by-step explanation:

The data points by themselves create a line formation, all the other choices no good.

In other-words~ "B"

o_o

The answer to your question is  A) 5.36

Hope this helps :)

Final answer:

To convert 2 2/3 to an improper fraction, multiply the whole number by the denominator and add the numerator, resulting in 8/3. The question lacks details to provide another specific quotient to compare this with. In dividing fractions, multiplication by the reciprocal is used to find equivalent quotients.

Explanation:

To find which quotient is equivalent to the mixed number 2 2/3, we must first convert the mixed number to an improper fraction. A mixed number is composed of a whole number and a fraction, which can be converted into an improper fraction by multiplying the denominator by the whole number and then adding the numerator to this product.

For the mixed number 2 2/3, we multiply the whole number 2 by the denominator 3, giving us 6, and then add the numerator 2, resulting in 8. Therefore, 2 2/3 as an improper fraction is 8/3.

However, without context, it's unclear what other quotient we are being asked to compare with the mixed number 2 2/3. Quotients can refer to the result of any division. Nonetheless, in contexts of dividing fractions, we use the multiplication of the inverse to find equivalent quotients. For example, if dividing by 3/1 (which is the same as dividing by 3), we would multiply by its reciprocal, 1/3.

In cases of conversion factors, we could use a factor that equals 1 to convert units without changing the value. For instance, 1 m / 100 cm is a conversion factor that equals 1, allowing us to convert meters to centimeters without changing the quantity.

Remember, multiplication and division in fractions can be seen as interconnected operations, where dividing by a number is the same as multiplying by its reciprocal.