Consider the following series. 1 5 1 10 1 15 1 20 1 25 Determine whether the series is convergent or divergent. Justify your answer. Converges; the series is a constant multiple geometric series. Converges; the limit of the terms, an, is 0 as n goes to infinity. Diverges; the limit of the terms, an, is not 0 as n goes to infinity. Diverges; the series is a constant multiple of the harmonic series.

Answer:

3/32

Step-by-step explanation:

9/16 × 3/4=27/144=3/16×1/2=3/32

Answer:

Area = 132 Square units

Step-by-step explanation:

Looking at the diagram, the top horizontal chord distance that's missing is calculated as;

21 - (9 + 3) = 9 units

Total distance of top horizontal chord = 9 + 3 = 12 units

Now, formula for area of trapezium is;

Area = ½(a + b)h

Where h is height = 8 units

The parallel sides are a & B.

In this case; a = 12 units

b = 21 units

Thus;

Area = ½(12 + 21)8

Area = 4 × 33

Area = 132 Square units

It will take 50 minutes!

-378/7=-54

2700/-54=-50

Answer and Step-by-step explanation:

When it says (f + g)(x), it means that it wants you to add the functions together.

So, let's add them.

[tex](2x^2 + 6x - 4) + (5x^3 -6x^2-3)\\\\\\5x^3 - 4x^2 + 6x - 7\\\\\\\\\\\\\\5x^3 - 4x^2 + 6x - 7[/tex]is the answer. (Answer choice B.)

#teamtrees #PAW (Plant And Water)

Answer:

2 whole and 1/8

Step-by-step explanation:

Find out the total pounds of strawberries for the 4 containers.

4/8 + 2/8 + 5/8 + 6/8 = 17/8

17/8 = 2 whole and 1/8

Answer:

2 1/8

Step-by-step explanation:

4/8+2/8+5/8+6/8=17/8

17/8 as a mixed number is 2 1/8

Answer:

Solution Set: (-2,5)

Step-by-step explanation:

Answer:

y = 6x + 8?

Step-by-step explanation:

The starting equation was unclear but if its perpindecular, flip the given slope. For example, if the slope was 3/4, its perpindecular slope would be 4/3.

Answer:

26904

Step-by-step explanation:

Answer:

$1,500

Step-by-step explanation:

Income - Expenses = Savings

     Income = 2 × 10,000 = $20,000

     Expenses = 3,500 + 10,000 + 5,000 = $18,500

$20,000 - $18,500 = $1,500 left for Savings

Answer:

Step-by-step explanation:

224 sq in.

Answer:

Step-by-step explanation:

If diameter is 6 then the radius is half of that or 3.

A = pi * r^2

A = pi * 3^2

A = 9pi ft^2

Answer:

81989970383

Step-by-step explanation:

Answer:

pros:Affordability,Known technologies,Safety.

cons:Greenhouse gas emissions,Mining destruction,Emission of harmful substances.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The pros of using coal as an energy souse is have alot of electicity and the con s of using coal as an energy souse is globlal warming, pollued air limited supply of coal in Earth

Pls Comment

Answer:

[tex]F\ or\ G= \{5,6,7,8,9,10,11,12\}[/tex]

[tex]P(F\ or\ G) = \frac{2}{3}[/tex]

Step-by-step explanation:

Given

[tex]S= \{7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18\}[/tex]

[tex]E=\{9, 10, 11, 12, 13, 14, 15, 16\}[/tex]

[tex]F=\{5, 6, 7, 8, 9\}[/tex]

[tex]G=\{9, 10, 11, 12\}[/tex]

[tex]H=\{2, 3, 4\}.[/tex]

Solving (a): Outcomes of F or G

F or G is the list of items in F, G or F and G.

So:

[tex]F=\{5, 6, 7, 8, 9\}[/tex]

[tex]G=\{9, 10, 11, 12\}[/tex]

[tex]F\ or\ G= \{5,6,7,8,9,10,11,12\}[/tex]

Solving (b): P(F or G)

The general addition rule is:

[tex]P(F\ or\ G) = P(F) + P(G) - P(F\ and\ G)[/tex]

Where:

[tex]P(F) = \frac{n(F)}{n(S)} = \frac{5}{12}[/tex]

[tex]P(G) = \frac{n(G)}{n(S)} = \frac{4}{12}[/tex]

[tex]P(F\ and\ G) = \frac{n(F\ and\ G)}{n(S)}[/tex]

[tex]F\ and\ G = \{9\}[/tex]

So:

[tex]P(F\ and\ G) = \frac{1}{12}[/tex]

[tex]P(F\ or\ G) = P(F) + P(G) - P(F\ and\ G)[/tex]

[tex]P(F\ or\ G) = \frac{5}{12} + \frac{4}{12} - \frac{1}{12}[/tex]

[tex]P(F\ or\ G) = \frac{5+4-1}{12}[/tex]

[tex]P(F\ or\ G) = \frac{8}{12}[/tex]

[tex]P(F\ or\ G) = \frac{2}{3}[/tex]

Answer:

5)

y= x+8

table:

you must sum 10, 11 ecc... to 8 to to get all the y

10+8= 18

19

20

21

22

23

6:)

y=x+50

It's the same as above

10. 20. 30. 40. 50

60. 70. 80. 90. 100.

i can't make the graph here sorry :(

The statements to determine the area of the polygon by division into triangles are evaluated as follows;

From the given description;

The polygon given can only be divided into two triangles if divided into triangles; GHK and HIK.

Hence, it follows that the area of triangle GHK plus the area triangle HIK is equivalent to the area of the given polygon.

Read more on Area of polygons;

https://brainly.com/question/17589084

Answer:

p(f)=5f-200

Step-by-step explanation:

----------------

Answer:

a) The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).

b) The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).

c) A sample size of 12 is needed.

d) A sample size of 125 is needed.

Step-by-step explanation:

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.78}{\sqrt{15}} = 0.39[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.39 = 4.46

The upper end of the interval is the sample mean added to M. So it is 4.85 + 0.39 = 5.24

The 95% CI for the true average porosity of a certain seam if the average porosity for 15 specimens from the seam was 4.85 is (4.46, 5.24).

(b) Compute a 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.327\frac{0.78}{\sqrt{11}} = 0.55[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 4.56 - 0.55 = 4.01

The upper end of the interval is the sample mean added to M. So it is 4.56 + 0.55 = 5.11

The 98% CI for true average porosity of another seam based on 11 specimens with a sample average porosity of 4.56 is (4.01, 5.11).

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.46?

95% CI means that [tex]z = 1.96[/tex]

A sample of n is needed, and n is found when M = 0.46. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.46 = 1.96\frac{0.78}{\sqrt{n}}[/tex]

[tex]0.46\sqrt{n} = 1.96*0.78[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.78}{0.46})^2[/tex]

[tex]n = 11.05[/tex]

Rounding up

A sample size of 12 is needed.

(d) What sample size is necessary to estimate true average porosity to within 0.18 with 99% confidence?

99% CI means that [tex]z = 2.575[/tex]

A sample of n is needed, and n is found when M = 0.18. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.18 = 2.575\frac{0.78}{\sqrt{n}}[/tex]

[tex]0.18\sqrt{n} = 2.575*0.78[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*0.78}{0.18})^2[/tex]

[tex]n = 124.5[/tex]

Rounding up

A sample size of 125 is needed.

Answer:

0.00043 is the answer

Step-by-step explanation:

10^-4=1/10000

43*1/10000= 0.00043

if the figure is a rectangle the answer is 473

Answer:

473

Step-by-step explanation:

First you need to make the fractions mixed numbers

27 1/2= 55/2

17 1/5= 86/5

Then you multiply across

55/2*86/5= 4730/10

then you divide 4730 by 10 to make it an improper fraction.

(because the denominator is 10 just take the 0 out of the end of 4630, this trick only works if the last number in the numerator is 0.)

And your anwser should be 473

I hope this helps!!!!!

well if she payed 40% and an average baseball glove costs $120 – $300

and a bat costs $75-$185. that would mean she spent around $197 or $485

which would mean

40% out of 197 is 78.8

and 291

i believe is the correct answer

Answer:

true

Step-by-step explanation:

Answer:

5x^2 - 2x + 4

Step-by-step explanation:

Answer:

In mathematics, a rational number is a number such as −3/7 that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number: for example, 5 = 5/1.

In mathematics, the irrational numbers are all the real numbers which are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers.

Step-by-step explanation:

hope it helps :)))

Answer:

11 maybe

Step-by-step explanation:

cant recheck the test

Answer:

a=3; (3,5) and (4,0) for the graph  

Step-by-step explanation:

ax-y=4

x=3, y=5 so...

a(3)-5=4

3a-5=4

+5 +5

3a=9

/3 .  /3

a=3

For the graph, use (3,5) and substitute x and y for anything:

ax-y=4

if x=0...

a(0)-y=4

-y=4

y=4

a=3; (3,5) and (4,0) for the graph!

Complete question is;

A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 144 feet of fencing, what is the largest area the farmer can enclose?

Answer:

A_largest = 2592 ft²

Step-by-step explanation:

Let the width which is going to be perpendicular to the already existing fourth wall be denoted by y. Since there will be 2, it means total width = 2y.

Since the farmer has 144 ft of fencing and the total width is 2y,it means that the length of the fence will be expressed as;

Length = 144 - 2y

Area of rectangular fencing is;

A = y(144 - 2y)

A = 144y - 2y²

To find the largest area, we will find the first derivative and the equate to 0 after which we plug the value of y back into the area equation to get it.

dA/dy = 144 - 4y

At dA/dy = 0;

144 - 4y = 0

y = 144/4

y = 36 ft

Thus, largest area is;

A_largest = 144(36) - 2(36)²

A_largest = 2592 ft²

    The largest area the farmer can enclose with the fence with him will be 2592 square feet.

      Let the length of the field = [tex]x[/tex] feet

      And the width of the field = [tex]y[/tex] feet

Therefore, area of the rectangular field = Length × Width

                                                              A = [tex]x\times y[/tex] square feet

Since, length of the fence = 144 feet

And the farmer has to enclose three sides of the rectangle as shown in the figure attached.

Therefore, length of the fence = length + 2(width)

                                                   = [tex](x+2y)[/tex] feet

Hence, [tex](x+2y)=144[/tex]

[tex]x=144-2y[/tex]

By substituting the value of 'x' in the expression for the area of the rectangular field.

[tex]A=(144-2y)y[/tex]

[tex]A=-2y^2+144y[/tex]

Find the derivative of the expression with respect to [tex]y[/tex],

[tex]A'=-4y+144[/tex]

Now equate it to zero to get the value of y,

[tex]A'=-4y+144=0[/tex]

[tex]y=36[/tex]

Now substitute the value of 'y' in the expression of area to get the maximum area enclosed.

[tex]A=-2(36)^2+144(36)[/tex]

   [tex]=-2592+5184[/tex]

   [tex]=2592[/tex] square feet

   Therefore, maximum area the farmer can enclose with the 144 feet of fencing will be 2592 square feet.

Learn more,

https://brainly.com/question/16880549

Answer:

El conjunto finito de pares ordenados son;

(1, 1), (1, 1/9), (1, 1/49), (1, 1/121), (1, 1/169)

Step-by-step explanation:

si f (X) = 1 / X2, determine el conjunto finito de pares ordenados para X = {1,3,7,11,13}

Dado que f (X) = 1 / X²

Para X = {1, 3, 7, 11, 13}

Tenemos;

f (X) = 1 / X²

f (1) = 1 / 1² = 1, Por lo tanto, tenemos el primer par ordenado, (1, 1)

f (3) = 1 / 3² = 1/9, por lo tanto, tenemos el segundo par ordenado (1, 1/9) ≈ (1. 0.11)

f (7) = 1 / 7² = 1/49, por lo tanto, tenemos el tercer par ordenado (1, 1/49) ≈ (1. 0.02)

f (11) = 1 / 11² = 1/121, por lo tanto, tenemos el cuarto par ordenado (1, 1/121) ≈ (1. 0083)

f (13) = 1 / 13² = 1/169, por lo tanto, tenemos el quinto par ordenado (1, 1/169) ≈ (1. 0.006)

Answer:

74.94×103= 3

because the number 10³ has

zeros when it is written without an exponent.

Step-by-step explanation:

74.94×103=

because the number 10³ has

zeros when it is written without an exponent.

3 zeros