Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If an answer does not exist, enter DNE.) 2 + 0.6 + 0.18 + 0.054 + ...

Answer: El número es 902 en el sistema decimal.

Step-by-step explanation:

Supongo que tenemos el número:

32012 en base 4, y lo queremos representar en base decimal.

Entonces, usando la regla general, podemos escribir este número como:

unidades*base^0 + decenas*base^1 + centenas*base^2......  

Es decir, acá tenemos:

2*4^0 + 1*4^1 + 0*4^2 + 2*4^3 + 3*4^4 = 902

El número es 902 en el sistema decimal.

This is not the complete question, the complete question is:

P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)

Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.

1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.

2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.

INSTRUCTION

a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.

b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).

Answer:

Step-by-step explanation:

(A)

Date        Particulars                               Debit                     Credit

2-Jan-19        Cash                                        3600  

                      Unearned Service Revenue                               3600

40 * 90 = 3600

services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.

(B)

Date           Particulars                                    Debit           Credit

31-Dec-19 Unearned Service Revenue            2413  

                       Service revenue                                             2413

internet = 300, price = 550, connection service = 500

(300/550) * 500 = 273

so

Original internet service contract = 40 * 273 = 10,920

Revenue recognized in 1st two years = 10,920 * 2/3 = 7280

Remaining service at original rates = 10920 - 7280 = 3640

Extended service = 3600

3640 + 3600 = $7240  

7240 / 3 = $2413

Step-by-step explanation:

We know that

14^2=196, and

15^2=225

so we know that sqrt(215) is between 14 and 15.

How do we know if it is between 14.5 and 15?

we need to know the value of 14.5^2, which we can calculate in the head as follows:

The square of all numbers ending in 5 such as 15 can be calculated by breaking up the 5 and the preceding digit(s),

The preceding digit is 1.  We multiply 1 by the next integer, 2 to get 2.

Attach 25 to 2 gives us 225 (as we saw above.

Example, 145*145 = 14*15 | 25 = 210 | 25 = 21025

so

14.5^2 = 210.25, which gives the more precise answer that

14.5^2 < 215 < 15^2, or

14.5 < sqrt(215) < 15  (fourth choice)

Since the third choice says sqrt(215) is between 14 and 1.5 (not 15), so the third choice is incorrect.

Note: if we eliminated the third choice, i.e. discard the likelihood of typo in the question, the only one left is the fourth choice.

Step-by-step explanation:

Log T = 11.8 + 1.5.M (with T is the amount of energy released by the earthquake, Log refers to the logarithm to the base 10)

-->T = [tex]10^{11.8 +1.5*6.5}[/tex] ≈3.458 *[tex]10^{21}[/tex]

Answer:  2.00 x 10¹⁰⁹

Step-by-step explanation:

log T = 11.8 + 1.5M

Given: M = 6.5

log T = 11.8 + 1.5(6.5)

log T = 11.8 + 9.75

log T = 21.55

      T = 10²¹⁻⁵⁵

      T = 1.995 x 10¹⁰⁹

      T = 2.00 x 10¹⁰⁹       rounded to the nearest hundredth

Answer:

240 m^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh

The base is 16 and the height is 30

A =1/2 ( 16*30)

240 m^2

Answer:

negative

Step-by-step explanation:

The slope of the line is negative because it goes from the upper corner down to the lower corner.

I remember it as negative because a rock would roll down it, if I would have to push it, it is positive.

Answer:

Hey there!

3/2= 1.5, which is good.

2/3=0.666666666666... no

3/4=0.75, which is good.

5/7= 0.71428... no

Answer:

these sequences are limited

you can try it in a calculator

Answer:

Midpoint of segment AB= (-0.5, 0)

Step-by-step explanation:

The midpoint coordinates of the midpoint has the x coordinate on .5 and the y coordinate on 0.

Answer:

  (-2.497, -6.860)

Step-by-step explanation:

For any magnitude r and direction θ, the translation to rectangular coordinates is ...

  (r, θ) ⇒ (x, y)

  (r, θ) ⇒ (r·cos(θ), r·sin(θ))

Your coordinates translate to ...

  (7.3, 250°) ⇒ (7.3·cos(250°), 7.3·sin(250°)) ≈ (-2.497, -6.860)

Answer:

729m³

Step-by-step explanation:

To find the length of one side find the cube root of 1728m³

³√1728=12metres

To find the length of the smaller cube

ratio 3:4.

4/7=12m

3/7=?

3/7×12 = 3/7×12×7/4

4/7

=9metres

To find volume of the small cube

volume=9×9×9

=729m³

Answer:

a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).

D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.

b. The 99% confidence interval would be wider than a 95% confidence interval.

As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.

Step-by-step explanation:

We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.8241.

[tex]p=X/n=581/705=0.8241[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8241*0.1759}{705}}\\\\\\ \sigma_p=\sqrt{0.000206}=0.0143[/tex]

The critical z-value for a 99% confidence interval is z=2.5758.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.5758 \cdot 0.0143=0.0369[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.8241-0.0369=0.7872\\\\UL=p+z \cdot \sigma_p = 0.8241+0.0369=0.8610[/tex]

The 99% confidence interval for the population proportion is (0.7872, 0.8610).

We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.

Answer:

17) 53.2

18) 17

Step-by-step explanation:

In similar triangles theorem, the ratio of the corresponding sides of two triangles are equal.

17) To determine x, ratio of the sides of 1st triangle/Ratio of the sides of 2nd triangle.

Ratio of base to the missing side:

7.6/x = 13.6/95.2

7.6/x = 13.6/95.2

7.6/x = 0.1428

7.6= 0.1429x

x = 53.2

18) ratio of shortest side/ longest side

3.4/7.9 = x/39.5

x = 3.4/7.9 × 39.5

x = 17

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24  

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24  

(b) The​ P-value is 0.004.

(c) Reject Upper H 0 because the​ P-value is less than the alpha = 0.01 level of significance.

(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Step-by-step explanation:

We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.

Let [tex]\mu[/tex] = population mean

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24      {means that the population mean is 24}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24     {means that the population mean is different from 24}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 18.3

            s = sample standard deviation = 6.3

            n = sample size = 15

So, the test statistics =  [tex]\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                    =  -3.504

The value of t-test statistics is -3.504.

(b) Now, the P-value of the test statistics is given by;

               P-value = P( [tex]t_1_4[/tex] < -3.504) = 0.002 or 0.2%

For the two-tailed test, the P-value is calculated as = [tex]2 \times 0.002[/tex] = 0.004 or 0.4%.

(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.

(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.

Hey there! I'm happy to help!

You haven't provided any answer choices but I can show you a trick to find any number between two numbers. This is will give you an instant answer to one being greater than one number and less than another.

What you do is you add the two numbers and divide by two!

2/5+3/5=1

1÷2=1/2

Therefore, 1/2 is a possible answer here.

I hope that this helps! Have a wonderful day!

Answer:

48

Step-by-step explanation:

16*3=48

Answer:

Speeds of car 1 and car 4 are same.

Step-by-step explanation:

Speed of an object = [tex]\frac{\text{Distance traveled}}{\text{Time}}[/tex]

For car 1,

Speed of car 1 = [tex]\frac{350}{5}[/tex]

                        = 70 miles per hour

For car 2,

Speed of car 2 = [tex]\frac{240}{4}[/tex]

                         = 60 miles per hour

For car 3,

Speed of car 3 = [tex]\frac{320}{5}[/tex]

                        = 64 miles per hour

For car 4,

Speed of car 4 = [tex]\frac{420}{6}[/tex]

                         = 70 miles per hour

Therefore, speeds of car 1 and car 4 are same.

Answer:

The angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Step-by-step explanation:

Denote Darius's camp site as C, the ranger station as R and the tree as T.

Consider the triangle CTR.

TX is the altitude of the right angled triangle TXR.

The altitude of a right angled triangle forms two triangle that similar to each other.

So, ΔTXC [tex]\sim[/tex] ΔTXR.

Compute the measure of TX as follows:

[tex]\frac{CX}{TX}=\frac{TX}{RX}\\\\TX^{2}=CX\times RX\\\\TX=\sqrt{CX\times RX}[/tex]

      [tex]=\sqrt{18\times 32}\\\\=24\ \text{yd}[/tex]

The angle d represents the angle of depression formed by Darius's sight line to the ranger station.

Compute the value of d as follows:

[tex]tan\ d^{o}=\frac{RX}{TX}\\\\d^{o}=tan^{-1} [\frac{RX}{TX}][/tex]

    [tex]=tan^{-1} [\frac{32}{24}]\\\\=53.13[/tex]

Thus, the angle of depression formed by Darius's sight line to the ranger station is 53.13°.

Answer:

The leg measures 2 I believe

Step-by-step explanation:

Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.

The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

Let the length of the perpendicular be x.

Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]

Hence, the length of one leg of the triangle is 2√2 cm.

Learn more about Pythagoras Theorem:

https://brainly.com/question/14461977

#SPJ2

Answer:

A corda deve ter um comprimento mínimo de 80 cm.

The string should have a minimum length of 80 cm.

Step-by-step explanation:

Espera-se que a corda seja colada em todo o contorno da moldura quadrada.

Isso significa que a cadeia precisa cobrir pelo menos todo o perímetro da moldura quadrada pelo menos uma vez.

Perímetro de um quadrado = 4L

L = comprimento lateral do quadrado.

O comprimento lateral da moldura quadrada = 20 cm

Comprimento mínimo da corda necessária = Perímetro da moldura quadrada = 4 × 20 = 80 cm.

Espero que isto ajude!!!!

English Translation

Sofia is going to glue a piece of string to the outline of a square frame 20 cm from the side. How long should this string be?

Solution

The string is expected to be glued all around the outlne of square frame.

This means the string needs to at least cover the whole perimeter of the square frame a minimum of one time.

Perimeter of a square = 4L

L = side length of the square.

The side length of the square frame = 20 cm

Minimum length of the string required = Perimeter of the square frame = 4 × 20 = 80 cm.

Hope this Helps!!!!

Answer:

a. 75,000

b. 50,000

c. 75,000

Step-by-step explanation:

The computation of allocating the joint cost using the physical units method is shown below:

[tex]Allocation\ rate = \frac{Joint\ costs}{Total\ number\ of\ products}[/tex]

[tex]= \frac{\$200,000}{300 + 200 + 300}[/tex]

[tex]Allocation\ rate = \frac{200,000}{800}[/tex]

= 250

For face cream

[tex]= Unit\ produced\times Allocation\ rate[/tex]

= [tex]300\times 250[/tex]

= 75,000

For body lotion

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 200\times 250[/tex]

= 50,000

For Liquid soap

[tex]= Unit\ produced\times Allocation\ rate\\\\ = 300\times 250[/tex]

= 75,000

hence, we simply applied the above formula by multiplying the units produced with the allocation rate so that each one allocation cost could come

Answer:

When you multiply a difference of squares, two terms cancel each other out and result in a binomial instead of a trinomial. To understand this, you can use an example.

When you multiply (x-3) and (x+3), you can use FOIL to expand them. By doing this, you get x^2-3x+3x-9. As you can see, -3x and 3x cancel each other out, so this results in a binomial instead of a trinomial.

Answer:

when you multiply them the two terms cancel each other out which will result in a binominal

Step-by-step explanation:

Answer:

  384.6 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...

  Tan = Opposite/Adjacent

  tan(7.5°) = (300 ft)/(distance to car 1)

  tan(9°) = (300 ft)/(distance to car 2)

Solving for the distances, we have ...

  distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft

  distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft

Then the separation between the cars is ...

  distance apart = 2278.73 ft - 1894.13 ft

  distance apart = 384.6 ft

Answer:

x = 4 or x = -13/4 = -4.33

Step-by-step explanation:

log (3x - 2) + log (x + 1) = 2 - log 2

Note 2 is also equals to log 100

log (3x - 2) + log (x + 1) = log 100 - log 2

log (3x - 2)(x + 1) = log (100/2)

log 3x² + 3x - 2x - 2 = log 50

log 3x² + x - 2 = log 50

3x² + x - 2 = 50

3x² + x - 2 - 50 = 0

3x² + x - 52 = 0

find the number to multiply that will give you -52 × 3 = -156 and add to give you 1. The numbers are -12 and 13.

3x² - 12x + 13x - 52 = 0

3x(x - 4) + 13( x - 4) = 0

(3x + 13)(x - 4) = 0

x = 4 or x = -13/4 = -4.33

If you insert 4 in the logarithm equation you will see that the left side is equal to the right

log (3x - 2) + log (x + 1) = log 100 - log 2

log 10 + log 5 = log 50

log 50 = log 50

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

[tex]p=X/n=370/559=0.6619[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02[/tex]

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948[/tex]

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

Answer:

  [tex]\textbf{J. }\dfrac{1}{x^2-x}[/tex]

Step-by-step explanation:

Factor the denominator and cancel the common factor.

  [tex]\dfrac{x+1}{x^3-x}=\dfrac{x+1}{x(x^2-1)}=\dfrac{x+1}{x(x-1)(x+1)}=\dfrac{1}{x(x-1)}\\\\=\boxed{\dfrac{1}{x^2-x}}[/tex]

Answer:

f(2) = 5

Step-by-step explanation:

Simply plug in 2 for x:

f(2) = 2(2) + 1

f(2) = 4 + 1

f(2) = 5

Answer:

20

Step-by-step explanation:

do 9/12 = 15/?

you do 12 times 15 divided by 9

hope this helps

Answer:    ∡PRS=61°

Step-by-step explanation:

As known the following equity is valid for the rhombus:

∡PQR+∡QRS = 180°

So  ∡QRS=180°- ∡PQR

∡QRS=180°- 58°= 122°

From another hand we know that PR is bisector of ∡QRS.

So ∡PRS=∡QRS:2= 122°:2=61°

∡PRS=61°