Ginger's baby weighed only 3 3/8 pounds when it was born. The doctor said it could not leave the hospital until it weighed 5 1/2 pounds. How many pounds must the baby gain before it can go home to Ginger ?
Solve in fraction form

In mathematics, a sequence is a list of numbers that are ordered in a particular way. Sequences can be finite or infinite, and they can be increasing, decreasing, or neither. In this lesson, we will discuss four sequences and their convergence or divergence.

1. The sequence (an) = n!/nⁿ converges to 1 as n approaches infinity.

2. The sequence (an) = \(\frac{\ln(n)^\pi}{\sqrt{n}}\) diverges.

3. The sequence (an) = ln(n²+1) + 1/ln(n+1) converges to 1.

4. The sequence (an) = n²(1-cos(1/n)) converges to 0.

1. The sequence ( \(\left{a_{n}\right}\)) where ( \(a_{n}=\frac{n !}{n^{n}}\) ) converges to 1.

This can be shown using the Stirling approximation, which states that

\(n! \approx \sqrt{2 \pi n} \left(\frac{n}{e}\right)^n\)

Substituting this into the definition of ( \(a_{n\)} ), we get

\(a_{n} \approx \frac{\sqrt{2 \pi n} \left(\frac{n}{e}\right)^n}{n^n} = \frac{1}{\sqrt{2 \pi}}\)

As n approaches infinity, the value of ( \(a_{n}\) ) approaches 1.

2. The sequence ( \(\left{a_{n}\right}\)) where ( \(a_{n}=\frac{(\ln n)^{\pi}}{\sqrt{n}}\) ) diverges.

This can be shown using the fact that the logarithm function is unbounded, which means that for any positive number k, there exists a natural number n such that ln(n) > k. This means that for any positive number M, there exists a natural number N such that ( \(a_{N}=\frac{(\ln N)^{\pi}}{\sqrt{N}} > M\) ). This shows that the sequence ( \(\left{a_{n}\right}\) ) does not have a limit, and therefore diverges.

3. The sequence ( \(\left{a_{n}\right}\) ) where ( \(a_{n}=\ln(n^2+1)+\frac{1}{\ln(n+1)}\)) converges to 1.

This can be shown using the fact that the logarithm function is continuous and increasing, which means that for any two real numbers x and y, ln(x) < ln(y) if and only if x < y. This means that for any natural number n, the sequence ( \(a_{n}=n^2(1-\cos(1/n))\)) is increasing. Since the sequence is increasing, it must converge to a limit. The limit of the sequence is the value of the sequence at the limit point, which is 1.

4. The sequence ( \(\left{a_{n}\right}\)) where ( \(a_{n}=n^2(1-\cos(1/n))\) ) converges to 0.

This can be shown using the fact that the cosine function oscillates between -1 and 1. This means that for any natural number n, the value of ( \(a_{n}\) ) is between 0 and n². Since the sequence is bounded, it must converge. The limit of the sequence is the value of the sequence at the limit point, which is 0.

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Mean is used to measure the center of a set of values. It is good for summarizing values which are generally pretty similar to each other.

Mean is more usually referred to as the average. It is calculated by adding up all of the values and dividing by the total number of values. It is a good way for summarizing the center of values which are commonly very similar to each other.

The mean is the most often used measure of central tendency since it uses all values in the data set to give us an average. For data from skewed distributions, the median is better than the mean because it is not influenced by large values.

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Although part of your question is missing, you might be referring to this full question: _________ is used to measure the center of a set of values. It is good for summarizing values that are generally pretty similar to each other.

Answer:

slope-intercept form: y=5x-3 point-slope form: y-7=5*(x-2)

Step-by-step explanation:

Y-y1=m(x-x1)

plug in the values and you get y=5x-3

\(\huge\boxed{\mathcal{HELLO!:)}}\)

Since we are given the slope of the line and a point that it passes through, we can easily determine the equation of the line.

First of all, we need to write it in Point-Slope Form:

\(\huge\boxed{\boxed{\rm{y-y1=m(x-x1)}}}\)

Where y1 is the y-coordinate of the point, m is the slope, and x is the x-coordinate of the point.

Plug in the values and solve:

\(\huge\rm{y-7=5(x-2)\)

\(\rm{y-7=5x-10\)

\(\rm{y=5x-10+7}\\\rm{y=5x-3\)

\(\huge\boxed{\mathbb{ANSWER:{\boxed{\bold{y=5x-3}}}}}\)

\(\bigstar\star\) Hope it helps! Enjoy your day!

\(\rm{FabulousKingdom:)\)

The possible side lengths of rectangle B are 12 cm and 7 cm, or 9 cm and 5.25 cm, etc.

The side length of rectangle B is calculated as follows;

Side length of rectangle A = 6 cm and 3.5 cm

If the two rectangles are proportional, the possible side lengths of rectangle B is calculated as follows;

Length of B = 2 x 6 cm = 12 cm

Width of B = 2  x 3.5 cm = 7 cm

or

Length of B = 1.5 x 6 cm = 9 cm

Width of B =1.5  x 3.5 cm = 5.25 cm

Thus, the side lengths of rectangle B will be increasing or decreasing at equal proportion.

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If x is the largest side :

If 4.1 is the greatest side :

Range of possible sizes for side 'x' :

Answer:

The answer is "descriptive statistics".

Step-by-step explanation:

Descriptive statistics are short descriptive factors that add up a production set, that can be either a reflection of a whole or a sample population. It is broken down into cumulative frequency measurements and variance measurements. The study uses descriptive statistics to explain the profile of the respondents. People give simple summaries about the sample as well as the actions.

Answer:

12.2 feet

Step-by-step explanation:

The key to this problem is trigonometry.

Imagine a right triangle. With a height, 10 ft (representing the tree's height), and a base of 7 ft (representing the horizontal distance to the worm).

Now the hypoteneuse length, or otherwise the distance from the worm is unknown.

So this is where we can use the pythagorean theorem.

\(a^2 + b^2 = c^2\)

\(c\) here is the hypoteneuse length, and \(a\) and \(b\) are the other lengths of the triangle.

Since we know a and b we can solve for c.

But first we will square root both sides of the equation to get \(c\) and not  \(c^2\).

\(\sqrt{a^2 + b^2} = c\)

Now just plug in our values for a and b respectively. (It doesn't matter what number replaces a or b, just make sure you are replacing a and b with the 2 known values) Calculate.

\(\sqrt{10^2 + 7^2} = \sqrt{100 + 49} = \sqrt{149} = 12.206....\)

Round to the nearest tenth.

\(12.2\) feet

Answer:

help on what???????????

HOW CAN I HELP U!??

To find where p is increasing, we must decide where p' = 1.7p(1 − p/5600) is positive. Assuming that p > 0 always, then we need (1 − p/5600) > 0. Therefore, p' is positive whenever p < 5600.

In other words, the function p is increasing whenever the value of p is less than 5600. This is because the derivative p' is positive in this range, meaning that the function p is increasing. As soon as p reaches 5600, the derivative p' becomes negative, meaning that the function p is decreasing.

So, the answer is that p is increasing whenever p < 5600.

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answer here!

sry it is a bit messy

Answer:

1) 11001 base 2

2)133 base 5

1) To convert base 10 into base 2

25/2= 12remainder 1

from this point on, the remainders will be replaced by r

12/2= 6r0

6/2=3r0

3/2=1r1

1/2=0r1

The remainders are then written down from the bottom up

= 11001

2) To convert 101011 base 2 into base 5

101011= 1×2⁵ + 0×2⁴+ 1×2³+ 0×2² + 1×2¹ + 1×2⁰

=1×32 + 0×16 + 1×8+ 0×4+1×2+1×1

=32+0+8+0+2+1

=43 base 10

Then convert 43 base 10 to base 5

43/5=8r3

8/5=1r3

1/5=0r1

=133 base 5

Well based on the info given I’d say you would expect to see about 14 more.

Answer:

11 1/2 miles per hour is the answer I believe

The data are listed in ascending order to be:

MEAN

The mean is the average of a data set. This can be calculated using the formula:

From the question, we can calculate the mean to be:

The mean is 33.

MEDIAN

The median is the middle of the set of numbers.

The middle terms are 40 and 42. Therefore, the median will be the average of the two numbers:

The median is 41.

MODE

The mode is the most common number in a data set.

The modes of the data are 3, 18, 19, 40, 42, 43, 48, and 51.

The solutions to the given initial value problem are:

x(t) = c₁\(e^{2\sqrt{2}t }\) + \(e^{-2\sqrt{2}t }\)

y(t) =-\(e^{12it\) + \(e^{-12it\)

Here, we have,

To solve the given initial value problem, we have the following system of differential equations:

dx/dt = 6x + y (1)

dy/dt = -4x + y (2)

Let's solve this system of differential equations step by step:

First, we'll differentiate equation (1) with respect to t:

d²x/dt² = d/dt(6x + y)

= 6(dx/dt) + dy/dt

= 6(6x + y) + (-4x + y)

= 36x + 7y (3)

Now, let's substitute equation (2) into equation (3):

d²x/dt² = 36x + 7y

= 36x + 7(-4x + y)

= 36x - 28x + 7y

= 8x + 7y (4)

We now have a second-order linear homogeneous differential equation for x(t).

Similarly, we can differentiate equation (2) with respect to t:

d²y/dt² = d/dt(-4x + y)

= -4(dx/dt) + dy/dt

= -4(6x + y) + y

= -24x - 3y (5)

Now, let's substitute equation (1) into equation (5):

d²y/dt² = -24x - 3y

= -24(6x + y) - 3y

= -144x - 27y (6)

We have another second-order linear homogeneous differential equation for y(t).

To solve these differential equations, we'll assume solutions of the form x(t) = \(e^{rt}\) and y(t) = \(e^{st}\),

where r and s are constants to be determined.

Substituting these assumed solutions into equations (4) and (6), we get:

r² \(e^{rt}\) = 8 \(e^{rt}\) + 7 \(e^{st}\) (7)

s² \(e^{st}\) = -144 \(e^{rt}\) - 27 \(e^{st}\)(8)

Now, we can equate the exponential terms and solve for r and s:

r² = 8 (from equation (7))

s² = -144 (from equation (8))

Taking the square root of both sides, we get:

r = ±2√2

s = ±12i

Therefore, the solutions for r are r = 2√2 and r = -2√2, and the solutions for s are s = 12i and s = -12i.

Using these solutions, we can write the general solutions for x(t) and y(t) as follows:

x(t) = c₁\(e^{2\sqrt{2}t }\) + c₂\(e^{-2\sqrt{2}t }\) (9)

y(t) = c₃\(e^{12it\) + c₄\(e^{-12it\) (10)

Now, let's apply the initial conditions to find the specific values of the constants c₁, c₂, c₃, and c₄.

Given x(0) = 1, we substitute t = 0 into equation (9):

x(0) = c₁\(e^{2\sqrt{2}(0) }\) + c₂\(e^{-2\sqrt{2}(0) }\)

= c₁ + c₂

= 1

Therefore, c₁ + c₂ = 1. This is our first equation.

Given y(0) = 0, we substitute t = 0 into equation (10):

y(0) = c₃e⁰+ c₄e⁰

= c₃ + c₄

= 0

Therefore, c₃ + c₄ = 0. This is our second equation.

To solve these equations, we can eliminate one of the variables.

Let's solve for c₃ in terms of c₄:

c₃ = -c₄

Substituting this into equation (1), we get:

-c₄ + c₄ = 0

0 = 0

Since the equation is true, c₄ can be any value. We'll choose c₄ = 1 for simplicity.

Using c₄ = 1, we find c₃ = -1.

Now, we can substitute these values of c₃ and c₄ into our equations (9) and (10):

x(t) = c₁\(e^{2\sqrt{2}t }\) + c₂\(e^{-2\sqrt{2}t }\)

= c₁\(e^{2\sqrt{2}t }\) + (1)\(e^{-2\sqrt{2}t }\)

= c₁\(e^{2\sqrt{2}t }\) + \(e^{-2\sqrt{2}t }\)

we have,

y(t) = c₃\(e^{12it\) + c₄\(e^{-12it\)

= (-1)\(e^{12it\) + (1)\(e^{-12it\)

= -\(e^{12it\) + \(e^{-12it\)

Thus, the solutions to the given initial value problem are:

x(t) = c₁\(e^{2\sqrt{2}t }\) + \(e^{-2\sqrt{2}t }\)

y(t) =-\(e^{12it\) + \(e^{-12it\)

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Answer:

His answer was correct:

(200*0.09)=18

18*16=288

200+288=488

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

-2 - 10h = -11h - 20

+ 2

- 10h = -11h - 18

+ 11h

h = -18

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

Step-by-step explanation:

-2-10h=-11-20, take -10 to the other side.

-2= -1-20, take 20 to the other side.

-18=-1h

-ve and -ve is pos.

h=18

positive 18

Answer:

∆ACD≅∆BCD                              definition of a segment bisector

Step-by-step explanation:

I think this is the only way to prove it in one reason

Answer:

Lauren

Step-by-step explanation:

1/2 is Erin

3/4 is Lauren

Answer:

1/2 for Eric and 6/8 for lauren

Eric: 1/2 = 4/8

Lauren: 6/8

Lauren was more succesful

Step-by-step explanation:

There are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.

To count the number of arrangements of 12 people with Dr. Tucker and Dr. Stanley positioned 3 apart, we can treat Dr. Tucker and Dr. Stanley as a single block of two people, and then arrange the resulting 11 blocks in a row.

Since Dr. Tucker and Dr. Stanley can occupy any of the 10 possible positions (the first two positions, the second and third, and so on up to the last two positions), there are 10 ways to form this block.

After the block is formed, we are left with 10 remaining people to arrange in the remaining 10 positions. There are 10! ways to arrange these people, so the total number of arrangements is:

10 x 10! = 3,628,800

Therefore, there are 3,628,800 ways to arrange 12 distinct people in a row so that Dr. Tucker is 3 positions away from Dr. Stanley.

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The solution to the system of equations is (3, 1, 2).

We have to find the solution of given system of equations.

Given system of equations are:

X – 2y + z = – 2 y + 2z = 5 x + y + 3z = 9 X = y = z =

To find the value of x, we need to convert the given equations into standard form

.x - 2y + z = -2   ------------(1)

y + 2z = 5   ------------(2)

x + y + 3z = 9 ------------(3)

From equation (2), we get y = 5 - 2zy = (5 - 2z)

Putting this value of y in equation (1), we get:

x - 2(5 - 2z) + z = -2x - 10 + 4z + z = -2x + 5z = 8         ------------(4)

From equation (3), we get x + (5 - 2z) + 3z = 9x - 2z = 4          ------------(5)

Multiplying equation (4) by 2 and adding with equation (5), we get:2x + 10z = 16 + 4x - 8z2x - 12z = -16         ------------(6)

Adding equation (4) and equation (5),

we get:x - 2z + z = -2 + 4x - 2z + 4z = 8 + 4x2x + 2z = 10x + z = 5          ------------(7)

Adding equation (5) and equation (6), we get:4x - 10z = -204x - 5z = -10z = 2

Putting z = 2 in equation (7), we get:x + 2 = 5x = 3

Putting x = 3 and z = 2 in equation (2), we get:y + 2(2) = 5y = 1

The solution of given system of equations is x = 3, y = 1 and z = 2.

Hence, x = 3, y = 1 and z = 2.

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the cost of the bike before tax

514.1/106%=$485

Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V and it can be determined by using the rate of interest formula.

Given that,

Dave is considering two loans.

Loan U has a nominal interest rate of 9.97%, and Loan V has a nominal interest rate of 10.16%.

If Loan U is compounded daily and Loan V is compounded quarterly.

We have to determine,

Which loan will have the lower effective interest rate, and how much lower will it be?

According to the question,

The effective interest rate is determined by the formula;

\(= \left(1+\dfrac{r}{t} \right )^t\)

Loan U has a nominal interest rate of 9.97%,

Loan U is compounded daily,

Then,

The effective annual multiplier for loan U is,

\(= \left(1+\dfrac{0.997}{365}\right)^{365}\\\\= (1+0.0027)^{365}\\\\= (1.0027)^{365}\\\\= 1.104824\)

And Loan V has a nominal interest rate of 10.16%,

and Loan V is compounded quarterly.

Then,

\(= \left(1+\dfrac{0.1016}{4}\right)^{4}\\\\= (1+0.0254)^{365}\\\\= (1.0254)^{365}\\\\= 1.105537\)

Therefore,

Loan V has a higher effective rate by,

\(=1.105537 -1.104824 \\\\= 0.000713 \\\\= 0.0713%\)

Hence, Loan U  will have a lower effective interest rate, and 0.0713 lower percentage points lower than Loan V.

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The phrase "number of values for which a certain condition holds" is referred to as multiplicity. The phrase, for instance, can be used to describe the magnitude of the totient valence function or the frequency with which a given polynomial equation has a root at a specific location.

Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.

This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.

Hence ,Multiplicity means the quality or state of being multiple or various. and

the number of components in a system (such as a multiplet or a group of energy levels)

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Let z_0 be a root of a function f, and let n be the least positive integer n such that f^((n))(z_0)!=0. Then the power series of f about z_0 begins with the nth term,

f(z)=sum_(j=n)^infty1/(j!)(partial^jf)/(partialz^j)|_(z=z_0)(z-z_0)^j,

and f is said to have a root of multiplicity (or "order") n. If n=1, the root is called a simple root '

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

The image point is located at (16, 4).

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that, a point (8, 2) is dilated using a scale factor of 2.

A point (x, y) when dilated by a scale factor of k changes to (kx, ky).

Point (8, 2) will become,

(8 × 2, 2 × 2) = (16, 4).

Hence the dilated point is (16, 4).

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The given vector-valued function is\(r(t) = f(t) × g(t)\), where \(f(t) = t^3i − tj − tk\) and\(g(t) = 3ti + t^2j − (t + 8)k.\)

To find the domain of the vector-valued function, we need to determine the values of t for which both f(t) and g(t) are defined.

For f(t), there are no restrictions on the domain since it is defined for all real values of t.

For g(t), we need to consider the denominator (t + 8) in the k-component. To avoid division by zero, we set t + 8 ≠ 0 and solve for t: t ≠ -8.

Therefore, the domain of the vector-valued function r(t) is all real numbers except t = -8.

Main answer: The domain of the vector-valued function

\(r(t) = f(t) × g(t) is (-∞, -8) U (-8, ∞).\)

The domain of the vector-valued function \(r(t) = f(t) × g(t)\)can be found by determining the values of t for which both f(t) and g(t) are defined. The function\(f(t) = t^3i − tj − tk\)is defined for all real values of t since there are no restrictions on its domain.

However, for the function \(g(t) = 3ti + t^2j − (t + 8)k\),

we need to consider the denominator (t + 8) in the k-component. To avoid division by zero, we set t + 8 ≠ 0 and solve for t: t ≠ -8. Therefore, the domain of g(t) is all real numbers except t = -8. Finally, to find the domain of r(t), we need to consider the intersection of the domains of f(t) and g(t), which is (-∞, -8) U (-8, ∞).

The domain of the vector-valued function \(r(t) = f(t) × g(t) is (-∞, -8) U (-8, ∞).\)

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Answer:

Sushil got 15 sweets

Step-by-step explanation:

we can use law of indices property as shown below

a:b:c = ax:bx:cx

that if we multiply each term of ratio by same number , the ratio does not change

____________________________

given

Malachy, Sushil and Fiona share some sweets in the ratio 1:3:1.

let

Malachy gets 1x sweets

sushil gets 3x sweets

Fiona gets 1x sweets

but given that

Malachy got 5 sweets

thus

1x = 5

x = 5

Sushil got 3x sweets = 3*5 = 15 sweets.

Sushil got 15 sweets.

Answer:

=−5x−3

Step-by-step explanation:

Let's simplify step-by-step.

−x−x−3x+2−5

=−x+−x+−3x+2+−5

Combine Like Terms:

=−x+−x+−3x+2+−5

=(−x+−x+−3x)+(2+−5)

=−5x+−3

brainliest please?

Answer:

5yds

Step-by-step explanation:

\(a^{2} +b^{2} =c^{2}\)

\(4^{2} +3^{2} =c^{2}\)

16+9=\(c^{2}\)

25 = \(c^{2}\)

\(\sqrt{25\) = c

5= c

5 yds