Find each sum 5/7+1/2

The sequence converges as the degree of the numerator and denominator are the same.

In this question we have the case of a rational equation representing a sequence, of which we must determine if the sequences converges and diverges. An useful form to prove the convergence of rational equations is using limit and algebra properties:

(5 · n - 1) / (n + 1)

[(5 · n - 1) / (n + 1)] · 1

[(5 · n - 1) / (n + 1)] · (n / n)

[(5 · n - 1) · n] / [(n + 1) · n]

[(5 · n - 1) / n] / [(n + 1) / n]

(5 - 1 / n) / (1 + 1 / n)

As n → + ∞, then 1 / n → 0 and the limit of (5 · n - 1) / (n + 1) is 5. Thus, the sequence converges as the degree of the numerator and denominator are the same.

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Answer:

x = 3, y = -9

Step-by-step explanation:

plug y=4x-21 into 7x+y=12 to get

7x + (4x-21) = 12 -> 11x -21 = 12 -> 11x = 33 -> x = 3

plug x=3 into y=4x-21 to get

y = 4(3) - 21 = 12 - 21 = -9

The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

So, given zeroes are -1, 3+3i.

Similarly,

So, the polynomial has the function: (x+1)x²

Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².

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Answer:

Options 2-5

Step-by-step explanation:

1. False, since the designs aren't identical.

2. True, both circles have a radius of 1.

3. True, you can translate the circles in Diego's design up to that they are all tangent to each other to make Elena's design.

4. True, both circles have diameter 10.

5. True, simlar logic to 2 and 4

Answer:

steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts

So, The numbers on a distance of 2.2 units from −3 on a number line are

-3 - 2.2 and -3+2.2

= - (3+2.2)  and - (3-2.2)

= -5.2 and - 0.8

Answer:

x = 11

m<H = 39°

Step-by-step explanation:

m<G = 6x - 15

m<H = 3x + 6

complementary angles = angles that add up to 90

6x - 15 + 3x + 6 = 90

9x = 99

x = 11

m<H = 3x + 6, plug in 11 as x

3 * 11 + 6

= 33 + 6

m<H = 39°

Answer:√16 and 6.39 are rational numbers because they can be expressed as a ratio and a fraction.

Answer: 27.185

Step-by-step explanation:

Hi there!

If you just want to add 27+0.185, the answer is 27.185.  

You just have to add 27+0.185 (what I think of for this question is just adding the 27 to it).

Hope this helps! Have a great day!

Answer:

4/9

Step-by-step explanation:

Answer:

Undefined

Step-by-step explanation:

Plugging in 3 for x and 4 for y we get:

6(3) + 4(4) = 36

multiplying we get

18 + 16 = 36
34 = 36

which is not true.

if this was helpful pls give me brainliest <3

The factor that is not a possible confounding factor is B. the expected sales for the year 2014.

A confounding factor is a third variable that influences or explains both the independent and dependent variables.

The independent variable here is the year while sales are the dependent variable.

However, confounding factors could include the number of new buildings constructed in 2013, which was not factored in by the architectural company and the state of the economy in 2013.

Thus, the expected sales for the year 2014 cannot be a confounding variable for the decreased sales in 2013 because it cannot explain the 2013 performance.

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A. the number of new buildings constructed

B. the expected sales for the year 2014

C the state of the economy

Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

C1(x) = C2(x).

Hence:

22 + x = 14 + 3x

2x = 8

x = 4.

4 movies would cause the two plans to have an equal monthly cost.

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When given 3 meters of cloth and it is to be divided in a ratio of 3:7 then one part will have 0.9 meters  and the other will have 2.1 meters.

The first thing to do is to find the denominator of the ratio by summing the two numbers in the ratio:

= 3 + 7

= 10

The first part of the cloth would be:
= 3 / 10 x 3 meters

= 0.3 x 3 meters

= 0.9 meters

The second part of the cloth would be:

= 7 / 10 x 3 meters

= 0.7 x 3

= 2.1 meters

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The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represents the number of months and y represents the total charge.

Scenario 1: DesTunes charges adults $15 per month.

Hence:

y = 15x

Scenario 2: DesTunes charges students a $20 sign-up fee and $5 per month, hence;

y = 5x + 20

The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20

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Answer:

Volume V ≈ 1481.3269 cubic inches

Step-by-step explanation:

Volume V of a cylinder is given by the formula

V = πr²h  where r = radius of the base of the cylinder and h the height

Here we are given the diameter, d = 5.9375 inches

Radius r = d/2 = 5.9375/2 = 2.96875 in

Height h = 53.5 in

V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches

Answer V ≈ 1481.3269 cubic inches

Answer:

Answers below

Step-by-step explanation:

To find per 20 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 40 (to get miles per 20 min)

=  20 miles / 160 minutes

_____________________________________________

To find per 15 miles

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 30 (to get miles per 15 minutes)

= 15 miles / 120 minutes

_____________________________________________

To find miles per minute

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 8 (to get miles per minute)

= 0.125 miles / 1 minute

_____________________________________________

To find miles per hour

= 26miles/ 208minutes / 26 (to simplify)

= 1mile / 8minutes / 2 (to simplify)

= 1/2mile / 4 minutes x 15 (to get miles per hour)

= 7.5 miles / 60 minutes

Answer:       5.1 x 10⁻¹ kg

To find the mass of water in the bottle, we can multiply the mass of one molecule by the number of molecules.

By using dimensional analysis, or by cancelling out units, we can figure out what to multiply or divide. Dimensional analysis uses fractions written with units. Dividing the same unit cancels out units we don't need.

To solve:

We are looking for the mass of H₂O in the bottle.

The units we need in the answer are:      [tex]\displaystyle{ \frac{kg}{bottle} }[/tex]

The question tells us:

Our equation puts the fractions in an equation, making them multiply to get the units we need.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}\ =\ \frac{kg}{bottle}[/tex]

Why is this equation correct?

Remember that dividing the same unit will cancel them out. In the equation, we have H₂O in a numerator and H₂O in a denominator. So, H₂O will cancel out. In the end, we will only have kg in the numerator and bottle in the denominator.

Take the equation we wrote. Now that we know our equation gives us the right units, we only need the front part.

[tex]\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1\ H_{2}O} \ *\ \frac{(1.7*10^{28}\ H_{2}O)}{1\ bottle}}[/tex]

Cancel out H₂O:

[tex]=\displaystyle{ \frac{(3 * 10^{-29}\ kg)}{1} \ *\ \frac{(1.7*10^{28})}{1\ bottle}}[/tex]

Simplify the equation:

[tex]=\displaystyle{ \frac{(3 * 10^{-29})*(1.7*10^{28})\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3 * 10^{-29}*1.7*10^{28}\ kg}{1\ bottle}[/tex]

Use exponent rules to multiply 10⁻²⁹ with 10²⁸:

[tex]=\displaystyle{ \frac{3 *1.7*10^{28-29}\ kg}{1\ bottle}[/tex]

[tex]=\displaystyle{ \frac{3*1.7*10^{-1}\ kg}{1\ bottle}[/tex]

Multiply within the numerator to simplify:

[tex]=\displaystyle{ \frac{5.1*10^{-1}\ kg}{1\ bottle}[/tex]

∴ The mass of water in the bottle is 5.1 x 10⁻¹ kg.

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Answer:

The Ratios, Rate and unit rate are used to solve many real-world problems.

Step-by-step explanation:

As a ratio is a comparison of two numbers or measurements.

A rate is also a ratio in which the two terms are in different units.

A unit rate means a rate for one of something

Jane is 2x+3 years old. (answer)

In this case, we can use Kay as the base/foundation in this problem. Kay is x years old. Mary is twice as old as Kay, making Mary 2 times x or 2x. We are solving for Jane. Jane is 3 years older than Mary, who we know is 2x. We can add on 3 years making the final expression for Jane's age: 2x+3. Since we do not know Kay's age, or x, we cannot solve this problem any further.

Answer:

y = -2

x = 9

Step-by-step explanation:

x - 7y = 23

8x - y = 74

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

Extra:

(x - 7y = 23) -8

-8x + 56y = -184

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

-8x + 56y = -184

8x - y = 74

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

55y = -110

÷55   ÷55

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

y = -2

x - 7y = 23

x - 7(-2) = 23

x + 14 = 23

   -14    -14

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

x = 9

I hope this helps!

Answer:

14

Step-by-step explanation:

To work out the lowest common multiple, we first:

7, 14, 21, 28...

14, 28...

The common multiples of 7 and 14 are 14, 28 etc, but the LEAST (or lowest) common multiple is 14.

Hope this helps.

Answer:

x> - 4

Step-by-step explanation:

In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them.

Answer:

20

Step-by-step explanation:

We need to determine what fraction of the container 6 gallons is. We know the difference between 2/5 and 7/10 is 6 gallons, so all we have to do is solve for 7/10 - 2/5. The common denominator is 10, as both 5 and 10 are factors of 10. 10/5 is 2, so we multiply the numerator of 2/5 by 2.

7/10 - 4/10 = 3/10

We now know that 6 gallons is 3/10 of the container. Now we solve.

10/3 = 3 1/3

So:

6 x 3 1/3 = 20

Answer:

20 gallons.-

Step-by-step explanation:

Let x be the number of gallons that the container holds.

The we have the equation

2/5 x + 6 = 7/10 x

Multiply through be 10

4x + 60 = 7x

3x = 60

x = 20.

The claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.

a) In home games, the Spelman college won 10 wins whereas Morehouse College won only 9 games.

So, Spelman College has a better team than Morehouse College in home games.

b ) In Away games, Morehouse College won 56 games whereas Spelman College only won 12 games. So, Morehouse College has a better team than Spelman College in Away games.

c ) In total, Spelman College has won 22 games and lost 23 games. The ratio of win is to lose is 22 : 23 that is it won 0.96 games against it lost 1 game. In total, Morehouse College won 65 games and lost 39 games. The ratio of win it to lose is 65 : 39 that is it won 1.67 games against the 1 game it lost.

So, the claim of Morehouse College makes more sense.

Therefore, we get that the claim made by Morehouse college make more sense as their ratio of winning a game than losing it is higher.

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Rawr!~ Allow me to help you today!

Answer:

[tex]V=\frac{2}{5}[/tex] cubic units!

Step-by-step explanation:

Step 1: Draw the carton (Carton is in the image)

Step 2: Calculate the volume V

[tex]V=LWH[/tex]

[tex]V=\frac{8}{3}[/tex] × [tex]\frac{1}{8}[/tex] ×[tex]\frac{6}{5}[/tex]

[tex]V=\frac{2}{5}[/tex] cubic units

I hope this helps you! <3

AshTheNeko

Answer:

f=-5

Step-by-step explanation:

Step-by-step explanation:

Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.

b. The  number of successes in the Washington sample were 4740 .

The number of  failures in the Washington sample is 1,260

c. the 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement "Employers should be required to pay men and women the same salary for the same job" is 0.018 to 0.068.

(b) Number of successes and failures in the Washington sample:

Total number of respondents in the Washington sample: 6,000

Percentage who agreed with the statement: 79%

Number of successes = 79% of 6,000

= 0.79 * 6,000

= 4,740

Number of failures = Total - Number of successes

= 6,000 - 4,740

= 1,260

(c)

confidence interval = (p1 - p2) ± Z * √((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))

p1 = Proportion of successes in the Washington sample

p2 = Proportion of successes in the Atlanta sample

n1 = Size of the Washington sample

n2 = Size of the Atlanta sample

Z = Z-score for the desired confidence level = 1.96

confidence interval = (0.79 - 0.74) ± 1.96 * √((0.79 * (1 - 0.79) / 6000) + (0.74 * (1 - 0.74) / 4800))

confidence interval = 0.05 ± 1.96 * √((0.79 * 0.21 / 6000) + (0.74 * 0.26 / 4800))

confidence interval = 0.05 ± 1.96 * √(0.00013815 + 0.0001244583)

confidence interval = 0.05 ± 1.96 * √(0.0002626083)

Lower bound of the confidence interval (DC - Atlanta)

= 0.05 - 0.0317226549

=  0.018

Upper bound of the confidence interval (DC - Atlanta)

= 0.05 + 0.0317226549

= 0.068

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