6 less than the product of 3 and a number. As an algebraic expression

To determine whether the series ∑(2n^3 – 6n^2 + 12) / (6 + 5n^4) converges or diverges, we can use the limit comparison test with the series ∑(1/\(n^4\)).

Let bn = 1/n^4, then we have:

lim n→∞ an/bn = lim n→∞ [(2n^3 – 6n^2 + 12) / (6 + 5n^4)] / (1/n^4)

= lim n→∞ [(2n^7 – 6n^6 + 12n^4) / (6n^4 + 5)]

= lim n→∞ [(2/n^3 – 6/n^4 + 12/n^6) / (6/n^4 + 5/n^8)]

= 2/6

Since 2/6 is a finite positive number, and ∑(1/n^4) is a convergent p-series, the limit comparison test implies that ∑(2n^3 – 6n^2 + 12) / (6 + 5n^4) also converges. Therefore, the given series converges.

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The probability sum of the dice is 2/11.

Let A be the event that the sum of dots is 5, then

A={(1,4), (2,3), (3,2), (4,1)}

n(A)=4

And, B is the event that one die shows a "one"

B={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (3,1), (4,1), (5,1), (6,1)}

n(B)=11

The Event that some of the dots are five and one of the die shows "one".

A intersection B = {(1,4), (4,1)}

Since n(A) = 36 (thirty-six possible samples of two dice)

P(A)=4/36

P(B)=11/36

P(A intersection B)=2/36

So, the required probability is

P(A|B)=P(A intersection B)/P(B) =2/11

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Answer:

V≈743.25

Step-by-step explanation:

V=5

12tan(54°)ha2=5

12·tan(54°)·4·182≈743.24624

By solving the inequality we get that the cheapest ticket is $29.

Here given,

If x is the number of $2 dollar increases required to meet her goal, then the minimum number of increases required is:

-100x² + 15,750x + 212,500 ≥ 243,600

- 100x² + 15,750x - 31,100 ≥ 0

x² - 157.5x + 311 ≥ 0

x = (157.5 ± \(\sqrt{157.5^{2} - (4*1*311 }\) ) / 2

x1 = 2

x2 = 155.5

The only conceivable value is x = 2 $2 increases

If the original cost was $25, the new rice needed to meet Amy's goal is:

P = 25 + 2 x 2

P = $29

The cheapest ticket is $29.

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Answer:

Step-by-step explanation:

The blanks get filled in like this:

Statement 3: m∠6 +m∠4 = 180°

Reason 3: Consecutive interior angles are supplementary

Statement 4: m∠6 +8·m∠6 = 180°

Statement 5: m∠6 = 20°, m∠4 = 160°

_____

You can see from the diagram that angles 4 and 6 are consecutive interior angles. You know the relation between those angles is that they are supplementary. The problem is asking you to state that relationship as Reason 3.

The given relation between the angles, m∠6 = 1/8·m∠4, can be recast as ...

  8·m∠6 = m∠4

This is the substitution that is used in statement 4.

Simplifying that statement gives 9·m∠6 = 180°   ⇒   m∠6 = 180°/9 = 20°. Then m∠4 = 8·m∠6 = 8·20° = 160°.

Answer:

59

Step-by-step explanation:

100/1.7=58.8

The ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape is 133 : 2.

What is  volume?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

We have,

the base radius of the cylinder, R=3 cm,

the height of the cylinder, H=5 cm,

the base radius of the conical hole, r=32 cm and

the height of the conical hole, h=89 cm

Now,

Volume of the cylinder, V=πR2H

=π×32×5

=45π cm3

Also,

Volume of the cone removed from the cylinder, v=13πr2h

=π3×322×89

=2π3 cm3

So, the volume of metal left in the cylinder, V'=V-v

=45π-2π3

=133π3 cm3

∴ The required ratio=V'v

=133π32π3

=1332

=133:2

So, the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape is 133 : 2.

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Answer:

$5

Step-by-step explanation:

The puck travelled a distance of 53.8 meters when the puck is 120 centimeters before the opponent's goal and puck travelled a distance of 56.2 meters when the puck is 120 centimeters after the opponent's goal.

Given that the distance to the opponent's goal from the player's current position is 55 meters. And after the shot, the puck is 120 centimeters from his opponent's goal.

We need to find out how many meters the puck travelled.

Also given there are 100 centimeters in 1 meter.

So, 55 meters = 55 × 100 centimeters

⇒ 55 metets = 5500 centimeters

Now, we are given that the puck is 120 centimeters from the opponent’s goal. It is not clear whether the puck landed before or after the goal post. So, considering both cases.

Case 1: the puck is 120 centimeters beyond the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters + 120 centimeters = 5620 centimeters

Divide 5620 by 100 to convert centimeters to meters.

The puck travelled a distance of 5620 cm or 56.2 meters.

Case 2: the puck is 120 centimeters before the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters - 120 centimeters = 5380 centimeters

Divide 5380 by 100 to convert centimeters to meters.

The puck travelled a distance of 5,380 cm or 53.8 meters.

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The equation that passes through the points (6, 3) and is parallel to the line x + 3y = 24 is [y = -1/3x + 5].

So, the equation will be:

Now, calculate as follows:

The gradient of the line: -1/3

Therefore, the equation that passes through the points (6, 3) and is parallel to the line x + 3y = 24 is [y = -1/3x + 5].

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Answer:

Step-by-step explanation:

409/5 is 1/8. then 81.8 and then check by multiplying 81.8 by 5 and that equals 409.

Answer: Positive correlation

Step-by-step explanation:

As you go up and along the graph the values go up.

Both have to be increasing basically.

5 half-dozens he should buy to make enough cookies.

What is an average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.

Here, we have

If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.

There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.

However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.

1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.

Since there are 6 eggs in a half dozen,

we need 30/6 = 5 half-dozens of eggs.

Hence, 5 half-dozens he should buy to make enough cookies.

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Answer:

f(-4)

Step-by-step explanation:

this is a lucky guess, hopefully u get it right :)

Answer:

A) there are no outliers in this distribution.

After the solution of the given equation 2.08(d - 9) = 0, the value of d is 9.

So, 2.08(d - 9) = 0 for d:

Therefore, after the solution of the given equation, the value of d is 9.

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Answer:

\({ \rm{y = - 3x + 5}}\)

Gradient = -3

• Parallel lines have the same gradient, therefore gradient, m is -3

\({ \rm{y = mx + c}}\)

• At point (0, -4)

\({ \rm{ - 4 = ( - 3 \times 0) + c}} \\ \\ { \rm{c = - 4}}\)

y intercept is -4

\({ \boxed{ \boxed{ \mathfrak{answer : }}{ \rm{\: \: y = - 3x - 4}}}}\)

Answer:

above answer is correct

mrk that braniliest

Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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Answer:

A = 1600π cm²

Step-by-step explanation:

We are given that a circle's radius increases 4 cm every second.

We want to know how large the area of the circle is after 10 seconds.

We first need to find how large the radius will be.

We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.

We can write this as a proportion:

\(\frac{4 cm}{1 s} = \frac{x}{10s}\)

We can cross multiply to get:

4 cm * 10 s = x * 1 s

Divide both sides by 1 s

(4 cm * 10 s) / (1 s) = 40cm = x

So, after 10 seconds, the radius will be 40cm.

We aren't done yet though, remember that the question wants us to find the area of the circle.

The area can be calculated using the equation A = πr², where r is the radius.

We can substitute 40 as r in the equation to get:

A = πr² = π * (40)² = 1600π cm²

Answer:

6,719.58

Step-by-step explanation:

The system of inequality y < 4x - 2 is represented by option B

An inequality graph represents the graphical representation of an inequality on a coordinate plane.

It visually represents the set of points that satisfy the given inequality. In the graph, the shaded region indicates the solution set of the inequality.

In the equation we watch out for dotted lines which is used to represent a less than of greater than without "equal to"

The graph is attached

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The measure of angle ∠3 and angle ∠6, which are alternate interior angles formed between the parallel lines m and n are;

m∠3 = 60°, m∠6 = 60°

Alternate interior angles are angles formed in the inside part of two lines that have a common transversal, and on opposite sides of the transversal.

The information are;

Line m is parallel to line n (m ║ n)

m∠3 = 7·x - 10

m∠6 = 5·x + 10

From the possible diagram in a similar question, we get;

∠3 and ∠6 are alternate interior angles formed between parallel lines therefore;

∠3 ≅ ∠6

m∠3 = m∠6 (definition of congruent angles)

7·x - 10 = 5·x + 10 (substitution property of equality)

7·x - 5·x = 10 + 10 = 20

2·x = 20

x = 20 ÷ 2 = 10

x = 10

m∠3 = 7 × 10 - 10 = 60

m∠3 = 60°

m∠3 = m∠6

Therefore;

m∠6 = 60°

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The magnitude of the vector QP is √73.

To find the component form of the vector QP, we need to subtract the coordinates of point P from the coordinates of point Q. The component form of a vector is represented as (x, y), where x and y are the differences in the x-coordinates and y-coordinates, respectively.

Given that P = (4, 1) and Q = (-4, 4), we can calculate the component form of the vector QP as follows:

x-component of QP = x-coordinate of Q - x-coordinate of P

                 = (-4) - 4

                 = -8

y-component of QP = y-coordinate of Q - y-coordinate of P

                 = 4 - 1

                 = 3

Therefore, the component form of the vector QP is (-8, 3).

To find the magnitude of the vector QP, we can use the formula:

Magnitude of a vector = √(\(x^2 + y^2\))

Substituting the x-component and y-component of QP into the formula, we get:

Magnitude of QP = √((\(-8)^2 + 3^2\))

              = √(64 + 9)

              = √73

Therefore, the magnitude of the vector QP is √73.

In summary, the component form of the vector QP is (-8, 3), and its magnitude is √73. The component form gives us the direction and the magnitude gives us the length or size of the vector.

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the answer is (D) 32.2

hopefully it help

Answer: d.) 32.2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Range = maximum value - minimum value

= 25 - 6 = 19

Option D is the correct answer

The solution to the given inequality  4(2x + 5) ≥ 4, are - 3, - 5, and - 10.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

The given inequality is - 4(2x + 5) ≥ 4.

- 8x - 20 ≥ 4.

- 8x ≥ 24.

8x ≤ - 24.

x ≤ - 3.

The solutions are, - 3, - 5, and - 10.

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In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.

For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.

The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.

The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.

In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.

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Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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