Joseph has 48 comic books. He sold one-fourth of his collection to his friend. He brought twice the number of comic books as he has now.how many comic books does he have now?

The series ∑n=1∞8n+19−n∑n=1∞​−n8n+19​ is convergent, but the sum does not exist (divergent).

To determine whether the series ∑n=1∞8n+19−n∑n=1∞​−n8n+19​ is convergent or divergent, we can analyze its behavior.

By observing the terms of the series, we can see that the general term 8n+19−n−n8n+19​ can be simplified to −8−19n−8−n19​. As nn approaches infinity, the term tends towards −8−8.

To further confirm this, we can evaluate the limit of the general term as nn approaches infinity:

lim⁡n→∞(−8−19n)=−8−0=−8limn→∞​(−8−n19​)=−8−0=−8

Since the limit of the general term is a finite value (-8), the series is convergent.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S=a1−rS=1−ra​

where aa is the first term and rr is the common ratio. In this case, the first term is −8−8 and the common ratio is 11. Plugging in these values, we get:

S=−81−1=−80S=1−1−8​=0−8​

The denominator is zero, which means the sum does not exist. Therefore, the series diverges.

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Answer:

Step-by-step explanation:

I answer for what I understand

280 : 70 = 28 : 7

4 = 4

true

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

I don't think so.

Step-by-step explanation:

1/2p-(1/4p-4)

1/2p-(1-16p/4p)

(2p-1+16p)/4p

(18p-1)/4p

2(9p-1)/4p

9p-1/2p

The solutions of the equation 81x³-192=0 are x=-2, x=2, and x=0. We can solve the equation by factoring 81x³-192. The first step is to factor out a 81 from the left side of the equation.

This gives us 81x³-192 = 81(x³-2). The next step is to factor x³-2. We can do this by using the difference of cubes factorization. This gives us x³-2 = (x-2)(x²+2x+1). Finally, we can equate each factor to 0 and solve for x. This gives us x=2, x=-2, and x=-1/2.

81x³-192 = 81(x³-2)

= 81(x-2)(x²+2x+1)

(x-2)(x²+2x+1) = 0

x-2 = 0 or x²+2x+1 = 0

x = 2 or x = -2 or x = -1/2

The first step is to factor out a 81 from the left side of the equation. This gives us 81x³-192 = 81(x³-2).

The second step is to factor x³-2 using the difference of cubes factorization. This gives us x³-2 = (x-2)(x²+2x+1).

The third step is to equate each factor to 0 and solve for x. This gives us x=2, x=-2, and x=-1/2.

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Answer:

418.00 cm³

Step-by-step explanation:

The volume of a cylinder is given by πr²h (r being the radius and h being the height)

The radius is half of the diameter: 6.4/2 is 3.2.

The height shown here is 13.

Instead of pi, the question says to use 3.14 instead of pi.

Putting these all together, you get 3.14×(3.2)²×13.

This can be expanded to 3.14×10.24×13.

From there, multiplying it all together gives you 417.9968 cm³.

The problem says to the nearest hundredth, so you want to round it to 2 decimal places. Since the 6 is above 5, it gets rounded up, leaving you with 418.00 cm³.

Step-by-step explanation:

top left picture

\(m = (1 - 0) \div ( - 3 - ( - 2)) \\ = - 1\)

top right

\(m = (3 - ( - 3)) \div ( - 1 - ( - 3)) \\ = 3\)

button left

\(slope = (2 - ( - 1)) \div (1 - 0) \\ = 3 \\ \)

y intercept=( 0 , -1)

button right

\(slope = ( - 1 - 2) \div (2 - 0) \\ = \frac{ - 3}{2} \)

y intercept= (0,2)

Answer:

1. m = -1

2. m = 2

3. slope = 3, Y - intercept = (0,-1)

4. slope = -3/2, Y - intercept = (0,2)

Step-by-step explanation:

for the first line we choose points (-2,0) and (0,-2)

slope= ∆y/∆x

= -2 - 0/0- -2

= -1

for the second graph we pick the point (-3,-3) and (-1,3)

slope = 3+3/-1 +3

= 6/2

= 3

for the third graph we pick (0,-1) and (1,2) as our points

slope = 2+1/1-0

= 3

pick point (0,-1) and and (X,y) to write the equation

3 = y+1/X

3x = y+ 1

y = 3x - 1

for the fourth graph (2,-1) and (0,2) are the points we pick to use

Slope = 2+1/0-2

= -3/2

we pick point (0,2) and (X,y) to write the equation

-3/2 = y-2 /X

-3x = 2y - 4

2y = -3x + 4

y = -3/2x + 2

The Diwali occurred on 0.408 or 40.8% of the year in 2017.

To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.

Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.

There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.

So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408

So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.

Therefore, Diwali occurred on 0.408 or 40.8%

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The hydrogen emission spectrum provides strong evidence for energy levels in atoms.

The hydrogen emission spectrum refers to the set of wavelengths of light emitted by hydrogen atoms when excited by energy. These wavelengths are discrete and can be precisely measured. The unique set of wavelengths emitted by hydrogen can be explained by the Bohr model of the atom.

According to the Bohr model, the electrons in an atom occupy specific energy levels or shells. When an electron absorbs energy, it jumps to a higher energy level, or excited state. As it returns to its original energy level, it emits the excess energy in the form of light or radiation. The energy of the emitted light is directly related to the energy difference between the two levels.

The emission spectrum of hydrogen consists of several distinct lines of different wavelengths, each corresponding to the transition of an electron from a higher energy level to a lower energy level. The wavelengths of these lines are given by:

λ = R(1/n₁² - 1/n₂²)

where λ is the wavelength of the emitted light, R is the Rydberg constant (a physical constant), n₁ is the initial energy level, and n₂ is the final energy level.

This equation shows that the wavelengths of the emitted light are directly related to the energy difference between the two energy levels. Therefore, the hydrogen emission spectrum provides strong evidence for the existence of quantized energy levels in atoms.

In conclusion, the discrete wavelengths of light emitted by hydrogen can be explained by the quantized energy levels predicted by the Bohr model. This fundamental concept of quantization has far-reaching implications in modern physics, and its understanding is crucial in many areas of science and technology.

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Answer:

x = 6

Step-by-step explanation:

3(3r - 8) = 4х + 6

9r - 24 = 4x + 6

5x - 24 = 6

5x = 30

x = 6

Answer:

x+y=-1

2x+2y=8

the correct answer is B

The piece of meat has a weight of 1,800g.

So, as the question says allow 30 minutes of cooking to each 450g.

Similarly,

Therefore, the piece of meat has a weight of 1,800g.

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Answer:

1800

Step-by-step-explanation:

Answer:

18 servings

Step-by-step explanation:

If one serving is 1/3 cup, one cup is 3 servings. Therefore, we can multiply 3 x 6 for an answer of 18 servings

Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.

To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:

Price = Dividend / (Required rate of return - Dividend growth rate)

In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.

First, let's calculate the present value of the future dividends:

PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3

PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3

PV = 0.877 + 0.769 + 0.675

PV = 2.321

Next, let's calculate the price:

Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV

Price = (1 / (0.14 - 0.06)) + 2.321

Price = (1 / 0.08) + 2.321

Price = 12.5

Therefore, the price of Lohi Corp. should be $12.50.

To calculate the expected capital gains yield over the next year, we need to use the formula:

Capital gains yield = (Dividend growth rate) / (Price)

Capital gins yield = 0.06 / 12.5

Capital gains yield = 0.0048

Convert to percentage:

Capital gains yield = 0.0048 * 100

Capital gains yield = 0.48%

Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

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Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

To determine the price of lohi corp., we need to calculate the present value of its future dividends. First, we estimate that the company will skip the next three annual dividends. This means that we will start receiving dividends from the fourth year. The first dividend to be paid is $1.00, and subsequent dividends will grow at a constant rate of 6 percent per year. The required rate of return on lohi corp. is 14 percent per year. This is the rate of return that investors expect to earn from investing in the company.

To calculate the price of Lohi Corp., we need to use the dividend discount model (DDM). The DDM formula is:

\(Price = Dividend / (Required rate of return - Dividend growth rate)\)

In this case, we know that Lohi Corp. will skip its next three annual dividends and then resume paying a dividend of $1.00. The dividend growth rate is 6% per year, and the required rate of return is 14% per year.

First, let's calculate the present value of the future dividends:

\(PV = (1 / (1 + Required rate of return))^1 + (1 / (1 + Required rate of return))^2 + (1 / (1 + Required rate of return))^3\)

\(PV = (1 / (1 + 0.14))^1 + (1 / (1 + 0.14))^2 + (1 / (1 + 0.14))^3\)

\(PV = 0.877 + 0.769 + 0.675\)

PV = 2.321

Next, let's calculate the price:

\(Price = (Dividend / (Required rate of return - Dividend growth rate)) + PV\)

\(Price = (1 / (0.14 - 0.06)) + 2.321\)

Price = (1 / 0.08) + 2.321

Price = 12.5

Therefore, the price of Lohi Corp. should be $12.50.

To calculate the expected capital gains yield over the next year, we need to use the formula:

\(Capital gains yield = (Dividend growth rate) / (Price)\)

\(Capital gins yied = 0.06 / 12.5\)

Capital gains yield = 0.0048

Convert to percentage:

Capital gains yield = 0.0048 * 100

Capital gains yield = 0.48%

Therefore, Lohi Corp.'s expected capital gains yield over the next year is 0.48%.

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The remaining 50.4% of the variance has not been accounted for, and it could be due to other factors that are not captured by the two variables being studied.

If the correlation between two variables is .496, it means that 49.6% of the variance has been accounted for. This is because the correlation coefficient measures the strength and direction of the linear relationship between the two variables, and it ranges from -1 to 1.

A correlation of 1 indicates a perfect positive linear relationship, while a correlation of -1 indicates a perfect negative linear relationship. In this case, a correlation of .496 indicates a moderate positive linear relationship.

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Answer:

Step-by-step explanation:

Area of the shape of the table = Length * Breadth (Rectangular in nature)

Area of the study table = 2m * 1.25m

Converting the units to cm

Since 100cm is equivalent to 1m, hence;

Area of the study table = 200cm * 125cm

Area of the study table = 25000cm²

If the study table is decorated with square design of size 10cm x 10cm, then the area of one square of such design will be 100 cm².

The number of square designs = Area of the study table/area of one square design

= 25000/100

= 250

Hence the number of such design on the study table is 250

Complete question :

Suppose the average yearly salary of an individual whose final degree is a master's is $55 thousand less than twice that of an individual whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn ?$116 thousand. Find the average yearly salary of an individual with each of these final degrees.

Answer:

Average salary of a bachelor's degree holder = $57,000

Average salary of a master's degree holder = $59,000

Step-by-step explanation:

Let:

Average salary of a bachelor's degree = b

Salary of a master's holder = 2b - 55000

Combined salary of both degrees :

b + (2b - 55000) = 116000

b + 2b - 55000 = 116000

3b = 116000 + 55000

3b = 171000

Divide both sides by 3

3b/3 = 171000/3

b = 57000

Hence,

Average salary of a bachelor's degree holder = $57,000

Average salary of a master's degree holder = 2(57000) - 55000 = 59,000

Answer:

since the decay rate constant of0.0 250 min.

hence the time required for the sample to decay to one forth of it's initial value is

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hyperkalemia is a medical condition that refers to an elevated level of potassium in the blood.

This condition can be caused by several factors, including kidney disease, certain medications, and hormone imbalances. Symptoms of hyperkalemia can range from mild to severe, depending on the level of potassium in the blood.

In a 60-year-old female diagnosed with hyperkalemia, the most likely symptom that would be observed is muscle weakness. This is because high levels of potassium can interfere with the normal functioning of muscles, leading to weakness, fatigue, and even paralysis in severe cases.

Other symptoms that may be observed in hyperkalemia include nausea, vomiting, irregular heartbeat, and numbness or tingling in the extremities. Treatment of hyperkalemia typically involves addressing the underlying cause of the condition, as well as managing symptoms through medication and lifestyle changes.

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The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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The weight of the chimney is approximately 2883.62 short tons.

To find the weight of the chimney, we need to calculate the volume of the frustum of the pyramid and then multiply it by the weight per cubic foot.

First, let's calculate the dimensions of the frustum of the pyramid:

Height of the frustum (h) = 186.3 ft

Side length of the upper base (a) = 10 ft

Side length of the lower base (b) = 16 ft

Next, we can calculate the side lengths of the upper and lower sections of the frustum:

Upper section side length (a1) = a = 10 ft

Lower section side length (b1) = b = 16 ft

The volume of a frustum of a regular pyramid can be calculated using the formula:

Volume = (1/3) × h × (\(a^2\) + a × a1 + a\(1^2\) + \(b^2\) + b × b1 + b\(1^2\))

Let's plug in the values:

Volume = (1/3) × 186.3 × (\(10^2\) + 10 * 10 + \(10^2\) + \(16^2\) + 16 × 10 + \(10^2\))

= (1/3) × 186.3 × (100 + 100 + 100 + 256 + 160 + 100)

= (1/3) × 186.3 × 816

= 51032.64 \(ft^2\)

Now, we can calculate the weight of the chimney by multiplying the volume by the weight per cubic foot:

Weight = Volume × Weight per cubic foot

= 51032.64 × 112.8 lb/\(ft^3\)

= 5767243.392 lb

To convert the weight to short tons, we divide it by 2000 (since there are 2000 lb in a short ton):

Weight in short tons = 5767243.392 lb / 2000

= 2883.62196 short tons (rounded to the nearest short ton)

Therefore, the weight of the chimney is approximately 2883.62 short tons.

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Answer:

1255 short tons

Step-by-step explanation:

Volume of a truncated pyramid (frustum) =

V = 1/3h(a² + b² + ab)

a = 16

b = 10

h = 186.3

V = 1/3(186.3)(16² + 10² + 16·10) = 62.1(256 + 100 + 160) = 32, 043.6

Subtract the volume of the flue:

V = 7.25 x 7.25 x 186.3 = 9792.4

V-total = 32043.6 - 9792.4 = 22,251.2

Weight = volume x density = 22,251.2 x 112.8 = 2.51 x 10⁶ lb

convert lb to short tons:

2.51 x 10⁶ lb / 2000 = 1254.97 ≈ 1255 short tons

Answer:w=−8

Step-by-step explanation:Step 1: Simplify both sides of the equation.

−2(w+3)=10

(−2)(w)+(−2)(3)=10(Distribute)

−2w+−6=10

−2w−6=10

Step 2: Add 6 to both sides.

−2w−6+6=10+6

−2w=16

Step 3: Divide both sides by -2.

−2w

−2

=

16

−2

w=−8

Answer:

Hi there!

Your answer is:

w= -8

Step-by-step explanation:

-2(w+3) = 10

First, distribute -2 to the parentheses

-2w -6 = 10

Next, isolate x by adding 6 to both sides

-2w = 16

Finally, divide both sides by -2

w = 16/-2

Simplify!

w= -8

Hope this helps

If 09 people can complete the job in 75 days then 25 people needs 45 days to complete the job.

Let T be the time and L be the Labor (Number of people working on the bridge).

T ∞ 1/√L  (Inverse relationship)

T = K/√L                   ----------------------------- (1)

Since, Constant "K" is introduced once the variation sign (∞) changes to equality (=) sign.

According to the question,

Time (T) = 75 days    and

labor (L) = 09

From the equation (1), we get,

    T = K / √L

⇒ 75   = K/√9

⇒ 75= K/3

⇒ K= 225

First, the relationship between these variables is:

                       T = 225/√L

Therefore, how long it will take 25 people to do it means that we should look for the time.

                           T=225/√L

                      ⇒  T= 225/√25

                      ⇒  T= 225/5

                      ⇒  T= 45 days.

therefore, 25 people needs 45 days to complete the job.

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Answer:

Area of the triangle = 12.92 cm²

Step-by-step explanation:

Area of a triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

From the figure attached,

Length of base of the triangle = 7.6 cm

Length of the height of the triangle = 3.4 cm

Area of the triangle = \(\frac{1}{2}(7.6)(3.4)\)

                                 = 12.92 square cm

Answer:

34

Step-by-step explanation:

hope this helps :)

Answer:

34

Step-by-step explanation:

First, plug in numbers and then solve...

Answer:

$7,507

Step-by-step explanation:

The (x-4) is not factor of f(x) =  because f(4)≠0.

What is factorization?

To factorise an algebraic statement, we first identify the terms' highest common factors and then arrange the terms into groups in accordance with those groups. In plain English, factorization is the process through which an algebraic expression gets expanded in the opposite direction.

To determine if (x - 4) is a factor of f(x) = x^3 - 2x^2 + 5x + 1, we need to check if f(4) equals zero. If f(4) equals zero, then (x - 4) is a factor of f(x), otherwise, it is not a factor.

So let's evaluate f(4):

\(f(4) = 4^3 - 2(4^2) + 5(4) + 1\\f(4) = 64 - 32 + 20 + 1\\f(4) = 53\)

Since f(4) is not equal to zero, we can conclude that (x - 4) is not a factor of f(x).

Here f(4)≠0 , then (x-4) is not factor of f(x) =  because f(4)≠0.

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

The area of the square 45 \(meters^{2}\)

Step-by-step explanation:

Width 3 meters

3x5=15

Length 15 meters

3x15=45