Find the dicontinuities of the function. f(x) = x2 12x 27 x2 4x 3 . there is a removable discontinuity at ( , ).

By the ratio test, the series converges for all [tex]x[/tex], since

[tex]\displaystyle \lim_{k\to\infty} \left|\frac{(k+1)^2 x^{k+4}}{(k+1)!} \cdot \frac{k!}{k^2 x^{k+3}}\right| = |x| \lim_{k\to\infty} \frac{(k+1)^2 k!}{k^2 (k+1)!} = |x| \lim_{k\to\infty} \frac1{k+1} = 0 < 1[/tex]

Then the radius of convergence is R = ∞, and the interval of convergence is the entire real line, -∞ < x < ∞.

The radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series. This can be obtained by using ratio test.  

Ratio test is the test that is used to find the convergence of the given power series.  

First aₙ is noted and then aₙ₊₁ is noted.

For  ∑ aₙ,  aₙ and aₙ₊₁ is noted.

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = β

Here aₙ = (n²/n!) xⁿ⁺³  and  aₙ₊₁ = ((n+1)²/(n+1)!) xⁿ⁺¹⁺³ = ((n+1)²/(n+1)!) xⁿ⁺⁴

Now limit is taken,

[tex]\lim_{n \to \infty} | \frac{a_{n+1} }{a_{n} } |[/tex] = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} /(n+1)!) x^{n+4} }{(n^{2} /n!) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((n+1)^{2} ) n!x^{n+4} }{(n+1)!(n^{2} ) x^{n+3} } |[/tex]

                      = [tex]\lim_{n \to \infty} | \frac{((1+1/n)^{2} ) x }{(n+1)} |[/tex]  

                      =   [tex]\lim_{n \to \infty} | \frac{ x }{(n+1)} |[/tex]  = 0 < 1

Since the limit is less than 1 the series is converging.

We get that,

interval of convergence = (-∞, ∞)

radius of convergence R = ∞

Hence the radius of convergence R is ∞ and the interval of convergence is (-∞, ∞) for the given power series.

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Answer:

11

Step-by-step explanation:

for this question we can look at the whole answer for the square root of 120 which equals 10.9544511501

[tex]\sqrt{120} = 10.9544511501[/tex]

now looking at our answer (10.9544511501) we want to find the nearest WHOLE NUMBER. in the current answer the whole number is 10, followed by many decimals.

10.9544511501

but to find the nearest whole number we have to round the place value BEFORE our whole number. (in this case the 9)

10.9544511501

we can now look at this highlighted section of our equation and think... is 10.9  closer to 11 or 10. well logically, to get to 11 from 10.9 we only have to go up by 0.1, rather than to get to 10, where you have to subtract 0.9.

10.9 + 0.1 = 11

10.9 - 0.9 = 10

But to make it easier, remember the rule:

the place value one place to the RIGHT of what you're rounding to, is what determines the new number. (in this case the .9)

and as any number 5 or above rounds up, we can say that our new number, rounded to the nearest whole number equals 11

10.9 rounded to the nearest whole number = 11

Answer:

Negative.

Step-by-step explanation:

b is above zero. So, it is positive.

c is below zero. So, it is negative.

A positive divided by negative number results in negative.

Answer:

B. negative

Step-by-step explanation:

-2 is negative. That's why.

The equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

Given the foci of ellipse is (±2,0) and vertices (±5,0).

We are required to find the equation of ellipse having foci (±2,0) and vertices (±5,0).

Equation is the relationship between two or more variables that are expressed in equal to form. Equation of two variables looks like ax+by=c.

Equation of ellipse is as under:

[tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex],where a is the semi major axis.

We have been given that a=5, c=2.

We know that [tex]c^{2} =a^{2} -b^{2}[/tex]

We have to find the value of b.

b=[tex]\sqrt{a^{2} -c^{2} }[/tex]

=[tex]\sqrt{5^{2} -2^{2} }[/tex]

=[tex]\sqrt{25-4}[/tex]

=[tex]\sqrt{21}[/tex]

Using the values of a and b in the equation [tex]x^{2} /a^{2} +y^{2} /b^{2} =1[/tex]

[tex]x^{2} /(2)^{2} +y^{2}/\sqrt{21} ^{2} =1[/tex]

[tex]x^{2} /4+y^{2} /21=1[/tex]

Hence the equation of the ellipse having foci  (±2,0) and vertices (±5,0) is [tex]x^{2} /4+y^{2} /21=1[/tex].

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The inequality to describe the possible temperature in Bismarck, North Dakota given that t represent temperature is t < 4°F

The inequality signs are;

Let

So

t < 4°F in Bismarck, North Dakota

This means, temperature in Bismarck, North Dakota is less than 4°F

Therefore, t < 4°F is the inequality to represent temperature in Bismarck, North Dakota.

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Answer:

x = 75

Step-by-step explanation:

Given information from the question:

x - 3y = 30

y = 15

We can substitute y = 15 into the equation to find x.

x - 3(15) = 30

x - 45 = 30

x - 45 + 45 = 30 + 45

x = 75

Answer:

75

Step-by-step explanation:

x-3y=30

x-3×15=30

x-45=30

x=30+45

x=75

The statements that are true regarding the angles formed by the transversal and parallel lines are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

Given the following angle measures formed when two parallel lines ( being cut by two transversals:

Using relevant theorems, let's determine which of the statements are true:

Angles 4 and 1 are vertical angles, therefore they are congruent based on the vertical angles theorem.

m∠4 = m∠1

m∠1 = 70°.

m∠2 = 180 - m∠4 [linear angles theorem]

m∠2 = 180 - 70

m∠2 = 110°

m∠6 = m∠4 [base on the alternate interior angles theorem]

m∠6 = 70°.

m∠9 = 180 - m∠12 [based on the linear angles theorem]

m∠9 = 180 - 130

m∠9 = 50°

m∠16 = m∠12 [based on the corresponding angles theorem]

m∠16 = 130°

The statements that are true are:

A. m∠1 = 70°.

B. m∠2 = 110°

C. m∠6 = 70°.

E. m∠9 = 50°

H. m∠16 = 130°

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The equation of the given parabola is y2=−20(x+3)

A parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

In general in a parabola, if we have

(y−n)2=4p(x−m),

then the vertex is (m,n)

The axis of symmetry is y=m

The focus is (p+m,n)

The directrix is x=m−p.

Hence, for the given case

p+m=−8

n=0

m−p=2

⇒n=0

m=−3

p=−5

So, the answer will be y2=−20(x+3)

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The inequality in the box has to be written as

x² + 2x - 80 ≤ - 65

We have

(10 + x)1 * (16-2x) ≥ 130

Next we would have to open the bracket

160 + 16x - 20x - 2x² ≥ 130

Then we would have to arrange the equation

- 2x² - 4x + 160 ≥ 130

Divide the equation by two

- x² - 2x + 80 ≥ 65

This is arranged as

x² + 2x - 80 ≤ - 65

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Answer:

  (a) 48, 52, 54

  (b) 6

  (c) b, c

Step-by-step explanation:

The sample mean is the mean of the sample. The range of sample means is the difference between the largest and smallest. As with all sampling processes, more data gives a better estimate.

The sample means are calculated in the attachment. For the different samples, they are ...

The range of the sample means is the difference between the largest and the smallest:

  range = 54 -48 = 6

More data is better, and the closer the estimates are to each other, the better confidence they offer. The true statements are ...

Answer:

x = -1

y = 1

Step-by-step explanation:

Given expressions

1) 2x + 3y - 1 = 0

2) 5x + 2y + 3 = 0

Add 1 on both sides of the 1) equation:

2x + 3y - 1 + 1 = 0 + 1

2x + 3y = 1

Subtract 3 on both sides of the 2) equation:

5x + 2y + 3 - 3 = 0 - 3

5x + 2y = -3

Current System

1) 2x + 3y = 1

2) 5x + 2y = -3

Multiply 2.5 on both sides of the 1) equation

(2.5) 2x + (2.5) 3y = (2.5) 1

5x + 7.5y = 2.5

Current System

1) 5x + 7.5y = 2.5

2) 5x + 2y = -3

Subtract 2) equation from 1) equation

(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)

Get rid of the parenthesis

5x + 7.5y - 5x - 2y = 2.5 + 3

Combine like terms

5x - 5x + 7.5y - 2y = 5.5

0 + 5.5y = 5.5

5.5y = 5.5

Divide 5.5 on both sides

5.5y / 5.5 = 5.5 / 5.5

[tex]\boxed{y=1}[/tex]

Substitute the y-value back to one of the equations to find the x-value

2x + 3y - 1 = 0

2x + 3(1) - 1 = 0

Combine like terms

2x + 3 - 1 = 0

2x + 2 = 0

Subtract 2 on both sides

2x + 2 - 2 = 0 - 2

2x = -2

Divide 2 on both sides

2x / 2 = -2 / 2

[tex]\boxed{x=-1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The number of cats is an illustration of inequalities and your neighbor has 4 cats before she bought the 2 new cats

Inequalities are expressions, numbers and mathematical statements that have unequal values when compared and/or evaluated

We start by representing the initial number of cats with x.

From the question, the new cats she bought are

New = 2

So, we have

x + New greater than 5

Rewrite properly as

x + New > 5

Substitute known values in the above inequality

x + 2 > 5

Subtract 2 from both sides

x + 2 - 2 > 5 - 2

Evaluate the right-hand side

x + 2 - 2 > 3

Evaluate the left-hand side

x > 3

The smallest integer number greater than 3 is 4

Hence, your neighbor has 4 cats before she bought the 2 new cats

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Answer:

Step-by-step explanation:

a. d^2 - 7d + 6 = 0

(d - 1)(d - 6) = 0

d - 1 = 0,  d - 6 = 0 therefore:

d = 1,  6.

b, x^2 + 18x + 81 = 0

(x + 9)(x + 9) = 0

x = -9  multiplicity 2.

c   u^2 + 7u - 60 = 0

(u + 12)(u - 5) = 0

u = -12, 5.

Answer:

Step-by-step explanation:

Opposite angles in a cyclic quadrilateral are supplementary.

  x° = 180° -105°

  x° = 75°

__

The value of the other angle is similarly found:

  w° = 180° -80°

  w° = 100°

__

Additional comment

This result comes from the inscribed angle theorem. That theorem tells you the measure of the inscribed angle is half the measure of the intercepted arc.

The opposite angles of a cyclic quadrilateral intercept the circle at the same two points, dividing the total 360° circle into two parts. Each angle has a measure equal to half its corresponding arc, so the total of the two angles is half the total of the two arcs: 360°/2 = 180°. The angles are supplementary.

Answer:

Rs 400 is the cost of an article for Ram.....

Step-by-step explanation:

X - cost of an article for Ram

120% = 1.2

1.2*X - Ram’s selling price

5% = 0.05

1.2*X*0.05 - Shyam selling price

1.2*X*0.05 = 504

X = Rs 400 is the cost of an article for Ram

Hope it Helps!!!!

The correct option is: (b)

                                =432.

By employing multiple processes, simplification refers to reducing the expression to a simpler form. Approximation is the process of making something less complicated and hence easier to accomplish or understand, or the object that arises from this process. The mathematical formula is simplified to its nearest value but is not exactly correct.

Therefore, we must follow the order listed above when simplifying expressions. In the example before, we divide 8 by 4 and then add the result to 12 because, according to BODMAS, division (D) comes before multiples (M).

[tex]$3 \cdot 2^{3} \cdot 2 \cdot 3^{2}Calculate exponents $2^{3}: 8$$$=3 \cdot 8 \cdot 2 \cdot 3^{2}$$Calculate exponents $3^{2}: 9$$$=3 \cdot 8 \cdot 2 \cdot 9$$ $3 \cdot 8 \cdot 2 \cdot 9= 432$$$=432$$[/tex]

So. the value will be = 432

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I understand that the question you are looking for is :

Simplify the expression to a single numerical value.

3*2^3*2*3^2

(a)144

(b)432

(c)900

(d)5,184

The star system is pictured is  open cluster

A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.

The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.

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I understand that the question you are looking for is :

| Will mark brainliest | Which type of star system is pictured? |

A. globular cluster

B. open cluster

C. binary

Answer:

B

Step-by-step explanation:

open cluster

Answer:

3 3/4 hour

Step-by-step explanation:

(3/4) ÷ (1/5) = (3*5) / (4*1)

= 15/4 hour

15/4 = 12/4 + 3/4 = 3 + 3/4 hour

= 3 3/4 hour

Answer:4:3

Step-by-step explanation: We can first calculate the wins. 24/7 is 4 and 4x4 = 16. So, they won 16 games and lost the rest. 28-16 = 12. 16:12 is equal to 4:3.

The given series is diverges according to the P Test.

According to the statement

we have given that the a series and we have to find that the those series is a converges or diverges.

So, For this purpose, we know that the

P-series test to say whether or not the series converges.

So, The given series is

[tex]1 + 1/\sqrt{32} + 1/\sqrt[3]{243 } + 1/\sqrt[4]{1024} + 1/\sqrt[5]{3125}[/tex]

And then

The value of  P becomes P = 5/6 < 1  when we find it using the p series test.

Hence, the p-series diverges

Because according to the p series test, The series converges if, and only if, the power satisfies p>1.

And diverges if, and only if, the power satisfies p<1.

So, The given series is diverges according to the P Test.

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Question:

Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.

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The number of classes Anna can take so the total cost for the month will be the same is 5.

The monthly cost would be  $37.50.

When the monthly cost is equal, both equations would be equal: 7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Monthly cost when the cost is the same: 7.5 x 5 = $37.50

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Answer:

5 classes

37.50

Step-by-step explanation:

got it right on edge

Answer:

6

Step-by-step explanation:

Original Equation

(n-1)!

Plug in 4 as n

(4-1)!

Subtract

(3)!

Rewrite using definition of factorial: [tex]a! = a*(a-1)*(a-2)....*1[/tex]

3! = 3*2*1

You don't really have to write the 1, since it doesn't change the value

6

Answer:

  334 in²

Step-by-step explanation:

The total surface area of the composite figure is the sum of the total area of the bottom cuboid and the lateral area of the top cuboid.

The area of a cuboid is given by the formula ...

  A = 2(LW +H(L+W))

For the bottom cuboid, the area is ...

  A = 2((9 in)(7 in) +(5 in)(9 in +7 in)) = 2(63 in² +5(16) in²) = 286 in²

The lateral area of a cuboid is the product of its perimeter and height. The perimeter is the sum of side lengths, or twice the sum of length and width.

  LA = Ph = (2(l +w))h

  LA = 2(5 in +3 in)(3 in) = 48 in²

The total surface area is the sum of the lateral area of the top cuboid and the total area of the bottom cuboid:

  SA = (48 in²) +(286 in²) = 334 in²

The surface area of the composite figure is 334 square inches.

__

Additional comment

The exposed area of the bottom cuboid is its total area less the area of the very top face.

The exposed area of the top cuboid is its lateral area plus the area of the very top face.

When we add these two exposed areas together, we find the area of the very top face is both subtracted and added from the sum of the total bottom area and the lateral top area. We skipped that step of adding and subtracting, because its net effect is zero.

Answer:

800÷100 = 8

65×8=520

[tex]\frac{520}{800}[/tex]

another way:

100%-65%=35%

35% = 0.35

800×0.35= 280

800-280=520

another way:

65% = 0.65

0.65×800=520

Hope it helped! :)

    Let's say you want to go on a vacation this summer because you finally saved enough money for it. While at the store to buy more hairbands (you just can't seem to figure out where they all went) you see something that you have been wanting for ages. The item is a bit on the more expensive side but you don't know when you will see it again. You decide to buy the item but you had to use some of the money planned for your trip to pay for it. But because you bought the item you now can't do all the activities you wanted on your trip.

The choice of buying the item affected your choices available on your trip.  

Answer:

dependent events

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

2^p = ⅛⁴

⅛ x ⅛ x ⅛ x ⅛ = 1/4096

2^p = 4096

log base 2 of 1/4096 = -12

The number of outcomes possible from flipping each coin is 2, therefore;

The possible outcome of flipping 4 coins is given by the sum of the possible combinations of outcomes as follows;

The number of possible outcome from flipping the first coin = 2 (heads or tails)

The outcomes from flipping the second coin = 2

The outcome from flipping the third coin = 2

The outcome from flipping the fourth coin = 2

The combined outcome is therefore;

Outcome from flipping the 4 coins = 2 × 2 × 2 × 2

The correct option is therefore;

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Answer:

  $0.04

Step-by-step explanation:

The cost per ounce is found by dividing the cost by the number of ounces.

In 2 gallons, there are 2×128 fl.oz. = 256 fl.oz. Then the cost per ounce is ...

  cost/ounces = $10.24/(256 fl.oz) = $0.04 /fl.oz.

The cost of the laundry detergent is $0.04 per fluid ounce.

__

Additional comment

Keeping the units with the numbers in a calculation can give you confidence that the calculated result has the units you want it to have.

The range of possible values should be (7,34), i.e 7 < x < 34.

The answer must be more noteworthy than 7, else the two sides are less than or rise to to the third. That triangle is outlandish. The reply must moreover be less than 34, since at that point the two other sides would rise to the third, making an impossible triangle.

By the property of triangle, Sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

To prove above propert, let us assume a  ΔABC

extend AB to D in such a way that AD=AC.

In ΔDBC, as the angles opposite to equal sides are always equal, so,

∠ADC=∠ACD

so,

∠BCD>∠BDC

As the sides opposite to the greater angle is longer, so,

BD>BC

AB+AD>BC

Since AD=AC, then,

AB+AC>BC

Hence, sum of two sides of a triangle is always greater than the third side.

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Answer:

7 < x < 34

Step-by-step explanation:

The output, y, when the input, x, is -5 is -2

The input is given as:

-5

This means that

x = -5

This is so because x represents the input

From the graph, we have the following highlight

The line of the graph passes through the point x = -5

On the graph;

When x = -5, the value of y is -2

This means that the output, y, when the input, x, is -5 is -2

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