According to the Rational Root Theorem, which statement about f(x) = 12x3 – 5x2 + 6x + 9 is true? Any rational root of f(x) is a multiple of 12 divided by a multiple of 9. Any rational root of f(x) is a multiple of 9 divided by a multiple of 12. Any rational root of f(x) is a factor of 12 divided by a factor of 9. Any rational root of f(x) is a factor of 9 divided by a factor of 12.

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

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.

3+5 = 8

240/8 = 30

30*3 = 90 red cars

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.

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:

(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.

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.

To learn more on Statistics click:

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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]

The answer to your question is  A) 5.36

Hope this helps :)

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.

The average amount of corn produced per acre represented in scientific notation can be found using the below formula:

[tex] The \;average\; amount\; of\; corn\; per\; acre=\frac{Bushels \; of\; corn\; produced\; in\; farm}{Area\; of\; farm\; in\; acres} [/tex]

We are given:

[tex] Area \; of\; FARM\; land= 4.2 \times 10^2 \; acres\\ \\ Amount \; of\; corn\; produced=6.72\; \times \; 10^4 \; bushels [/tex]

Substituting the above information in the formula, we get...

[tex] The \; Average\; amount\; of\; corn=\frac{6.72 \times 10^4}{4.2 \times 10^2} \\ \\ \frac{6.72}{4.2} \times \frac{10^4}{10^2}\; =\; 1.6 \times 10^{4-2}\; =\; 1.6 \times 10^2\\ \\ [/tex]

Conclusion:

[tex] The \; Average \; amount\; of \; corn \; is\; 1.6 \times 10^2 \; Bushes\; per\; corn [/tex]

The average amount of corn produced per acre represented in scientific notation is option B)[tex] 1.6 \times 10^2 [/tex]bushels per acre

Le answer is B 1.6 × 102 bushels per acre

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:

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

The answers to the dashed parts of the questions to prove that △ACO ≅ △BCO are respectively;

- All radii of the same circle are congruent

- Tangents to a circle that intersect are congruent

- Side CO is congruent to side CO

- SSS congruency theorem

The image of the Triangle and circle has been attached.

Now, from the attached image we can see that;

Thus, it means that AO ≅ BO because; All radii of the same circle are congruent

AC ≅ BC because; tangents to a circle that intersect are congruent.

AO ≅ BO

AC ≅ BC

CO ≅ CO

This means all three corresponding sides of both △ACO and △BCO are congruent. Thus, we can conclude that;

△ACO is congruent to △BCO by the "SSS Congruency theorem"

Read more about SSS Congruency theorem at; https://brainly.com/question/2102943

Answer:

Step-by-step explanation: edge2024

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.

To simplify the expression (3m⁻² n)⁻³/6mn⁻², follow the steps: apply the negative exponent rule, simplify by multiplying the exponents, and rearrange and combine like terms if necessary.

To simplify the expression (3m-2 n)-3/6mn-2 , let's break it down step by step:

Step 1: Apply the negative exponent rule. To do this, we can move any term with a negative exponent from the numerator to the denominator or vice versa. In this case, the term m-2 can be written as 1/m2.

Step 2: Simplify the expression by multiplying the exponents. The exponents in the expression can be added since they have the same base (m).

Step 3: Simplify further by rearranging and combining like terms if necessary.

Putting it all together, the expression is equivalent to (1/3m4n6)1/6mn-2.

Answer:

The answer is 327.08 i am in k12

Step-by-step explanation:

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