Determine whether the sequence converges or diverges. If itconverge, find the limit.
an = ln( 2n2 + 1 ) - ln( n2 +1 )
I know the answer is ln 2 but I need some help getting there.Thanks!

Answer:

Exact Form:

51/4

Decimal Form:

12.75

Mixed Number Form:

12 3/4

Step-by-step explanation:

The percentage of people with blood pressure between 115 and 165 mm is 68.27% (closest to option e). The percentage of people with blood pressure between 140 and 165 mm is 89.4% (closest to option b). The percentage of people with blood pressure over 165 mm is 10.6% (closest to option a).

To solve this problem, we can use the properties of the normal distribution, which is a continuous probability distribution that is often used to model real-world data. In particular, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentages of people with blood pressure within certain ranges. The empirical rule states that, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean. Approximately 95% of the data falls within two standard deviations of the mean. Approximately 99.7% of the data falls within three standard  deviations of the mean. Using this rule, we can estimate the following  percentages: The percentage of people with blood pressure between 115 and 165 mm: First, we need to find the z-scores for the lower and upper limits of the range: z_lower = (115 - 140) / 20 = -1.25.

z_upper = (165 - 140) / 20 = 1.25

We can then use a standard normal distribution table or a calculator to find the areas under the curve corresponding to these z-scores:

P(-1.25 < Z < 1.25) = 0.7887 - 0.1056 = 0.6831

So, approximately 68.31% of people have blood pressure between 115 and 165 mm.

The percentage of people with blood pressure between 140 and 165 mm: In this case, the lower limit is equal to the mean, so we only need to find the z-score for the upper limit: z_upper = (165 - 140) / 20 = 1.25

Using the same approach as before, we get:

P(Z < 1.25) = 0.8944

So, approximately 89.44% of people have blood pressure between 140 and 165 mm. The percentage of people with blood pressure over 165 mm:

In this case, we only need to find the area to the right of the upper limit:

P(Z > 1.25) = 0.1056

So, approximately 10.56% of people have blood pressure over 165 mm.

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Complete Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%

b. 89.4%

c. 39.4%

d. 78.8%

e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.

___ The percentage of people with blood pressure between 140 and 165 mm.

___ The percentage of people with blood pressure over 165 mm.

If we assume a power-law relation T = b×aⁿ, the linear regression that needs to be analyzed is : (d) log(T) vs log(a)  .

The Linear Regression between the two quantities do we need to analyzed is log(T) vs log(a)  because when we take the logarithm of both sides of the power-law equation,

we obtain log(T) = n × log(a) + log(b), which is a linear equation in logarithmic form.

So , By performing linear regression on log(T) vs log(a), we can estimate the values of n and log(b), and then use these estimates to obtain estimates of b and n in the original power-law equation.

The given question is incomplete , the complete question is

If we assume a power-law relation T = b×aⁿ, the linear regression between which two quantities do we need to analyze?

(a) T vs a ;

(b) log(T) vs a ;

(c) T vs log(a) ;

(d) log(T) vs log(a) .

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Answer:

420

Step-by-step explanation:

35 x 12 = 420

Answer:

420

Step-by-step explanation:

Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?

The fraction left to pay for the birthday party is 17/30.

The calculation is as follows:

1 * 1/4 = 1/4 … (1)

1/4 * 2/3 = 2/12 … (2)

2/12 * 1/10 = 2/120 … (3)

Fraction left to pay:

= 1 - (1/4 + 2/12 + 2/120)

= 1 - (30/120 + 20/120 + 2/120)

= 1 - (52/120)

= 1 - 13/30

= 30/30 - 13/30

= 17/30

Thus, the fraction left to pay for the birthday party is 17/30.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

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Answer: Distance traveled by bus in one second=414.23=18 meters. Car travels faster.It travels 4 meter more in one second than bus

Answer:

Step-by-step explanation:

2 + 2 = 5

Step 1: Find the gradient/slope

Gradient and slope are interchangeable words. To find the gradient/slope we need to use two points that we know are on the line and the following formula: (y2 - y1) / (x2 - x1)

Point 1 = (0,1)

Point 2 = (3,13)

Gradient = (13 - 1) / (3 - 0)

Gradient = 12 / 3

Gradient = 4

Step 2: Find the y-intercept

We can use the slope-intercept form to find the y-intercept. To do so, we plug in the gradient and one of the points on the line. You can pick either point to plug in here!

Slope-intercept form: y = mx + b

-m is the gradient

-b is the y-intercept (that we are trying to find)

13 = 4(3) + b

13 = 12 + b

b = 1

Step 3: Put it all together in slope-intercept form

Now that we have the slope and y-intercept, all that's left to do is plug in the values.

y = mx + b

y = 4x + 1

Answer: y = 4x + 1

Hope this helps!!

The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart.

It is composed of three atomic orbitals: one s-orbital and two p-orbitals. The s-orbital is spherical in shape, while the p-orbitals are composed of two lobes that are directed at an angle of 120 degrees apart. The combination of these three orbitals forms a hybrid orbital that is shaped like a flat trigonal planar, with a bond angle of 120 degrees. This hybrid orbital is known as the sp2 hybrid orbital.

The "s" in sp2 stands for the s-orbital, which is a single, spherical orbital. The "p" represents the two p-orbitals, which have two lobes and form an angle of 120 degrees with each other. The "2" in sp2 indicates that two p-orbitals are involved in the hybridization process. The hybridization of the s and two p-orbitals creates the sp2 hybrid orbital, which is trigonal planar in shape.

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Answer:

13×2=26

Maybe i can help u a little

Answer:

teo is 18 and Richard is 31

Step-by-step explanation:

hope it helps you

please mark me as brainlist

Answer:

π radians

Step-by-step explanation:

The angle subtended at the centre by an arc, has the same measure as the arc subtending it, then

angle subtended = measure of arc = π radians

By applying Pythagoras' theorem, the length of x is equal to 10 units.

In Mathematics and Geometry, Pythagorean's theorem is modeled or represented by the following mathematical equation (formula):

x² + y² = z²

Where:

x, y, and z represents the length of sides or side lengths of any right-angled triangle.

Based on the information provided about the side lengths of this right-angled triangle, we have the following equation:

x² = y² + z²

x² = 8² + 6²

x² = 64 + 36

x = √100

x = 10 units.

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Answer: x = 1/3

Step-by-step explanation:

5/x - 9/x = -8 - 4

-4/x = -12

x = -4/-12

x = 1/3

Answer:

-19

Step-by-step explanation:

symbolab- a website that you enter an equation in and it solves it for you it's free and no videos or anything :)

Answer:

potential to kinetic energy

The inverse Laplace transform of F(s) = -2/s + e^-4x/s^2 - 3 e^-4x/s as a function of x is f(x) = u(x - 4) x - 2 - 3 u(x - 4).

The correct answer is d) f(x) = u(x - 4) x - 2 - 3 u(x - 4)

To find the inverse Laplace transform of F(s), we need to use partial fraction decomposition and the Laplace transform tables.

F(s) = -2/s + e^-4x/s^2 - 3 e^-4x/s
= (-2/s) + (e^-4x/s^2) - (3e^-4x/s)

Using partial fraction decomposition, we can write:

-2/s = -2(1/s)
e^-4x/s^2 = 1/2(e^-4x)(s^-1)^2
-3e^-4x/s = -3(e^-4x)(s^-1)

Now, using the Laplace transform tables, we know that the inverse Laplace transform of 1/s is u(t), the unit step function. The inverse Laplace transform of (s^-1)^2 is (1/2)t(e^(-4t)u(t)), and the inverse Laplace transform of (s^-1) is u(t).

Therefore, the inverse Laplace transform of F(s) is:

f(x) = -2u(x) + (1/2)(x-4)e^(-4(x-4))u(x-4) - 3e^(-4(x-4))u(x-4)

Simplifying this expression, we get:

f(x) = u(x-4)(5x-22) - 2u(x)

Comparing this expression with the given options, we see that the correct answer is (d) f(x) = u(x - 4) x - 2 - 3 u(x - 4).

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Answer:

A = 80   S =70

Step-by-step explanation:

#Adults tickets = A

#Students tickets = S

A + S = 150

5A (means the price is $5 times the number of Adult tickets) equals the total amount for all of the Adult tickets altogether

3S (means the price is $3 times the number of Student tickets) equals the total amount for all of the students tickets altogether

5A + 3S = 610    (Means adding the total of all the student tickets plus adult tickets will equal $610 for all tickets sold)

Using both equations now, you can use substitution or elimination to solve for one of the variables. Then you can use the variable to substitute to solve the remaining one.

A + S = 150

5A + 3S = 610

Substitution:

A = 150 - S  (Rearrange the first equation by moving S to the other side)

Substitute into the other equation

5 (150 - S) + 3S = 610

750 - 5S + 3S = 610      Combine like terms :    -2S = -140

Solve for S = 70

Substitute into A + S = 150        A + (70) = 150

A = 80

Answer:

k=.25068

Step-by-step explanation:

450 = 100 \(e^{6k}\)

4.5 =   \(e^{6k}\)

ln(4.5) = 6k

k= ln(4.5)/6

k=.25068

The number of bacteria after 13 hours will be 2579.

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."

Given that a biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favourable growth medium. Six hours later, he measures 450 bacteria.

The bacteria after 13 hours will be calculated as,

\(N=100(e)^{13\times 0.25)\)

\(N = 100\times e^{3.25}\)

N = 2579.

Therefore, the number of bacteria after 13 hours will be 2579.

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Answer:

Step-by-step explanation:

Given expression:

Solving for p:

Answer:

Step-by-step explanation:

here you go mate

step 1

- 10p + 3(8 + 8p) = -6(p - 4)  equation

step 2

- 10p + 3(8 + 8p) = -6(p - 4)  simplify by distributing

14p+24=-6p+24

step 3

14p+24=-6p+24  subtract 24 from each sides

20p=0

step 4

20p/20=0/20  divide both sides by 20

answer

p=0

The probability that both the people own a dog is 0.3364  .

Probability of an event E is defined as the number of favorable cases divided by total number of cases .

denoted by ,

P(E) = \(\frac{number.of.favorable.cases}{total.number.of.cases}\)

In the question , it is given that the

percentage of people  owning a dog = 58%

Probability of selecting a dog at random = 58/100 = 0.58

If we select two people at random then

the probability that both people will own a dog will be ,

P(both own a dog) = P(first person own a dog)*P(second person own a dog)..........as owning a dog is an independent event

= 0.58*0.58

= 0.3364

Therefore , the probability that both the people own a dog is 0.3364 .

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Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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Answer:

5 1/10

Step-by-step explanation:

Convert all integers to decimals.

6.1

5.4

5 1/10 = 5.1

6 7/10 = 6.7

The smallest number frrom the list is 5.1 or 5 1/10.

Answer:

5 1/10

Step-by-step explanation:

Convert to the same format, IE. decimals so you can compare like numbers.  The other numbers are:

6.1

5.4

5.1      (1/10 = 0.1)

6.7      (7/10 = 0.7)

So, from least to greatest they are:

5.1

5.4

6.1

6.7

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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False. The correlation coefficient can vary between -1 and 1, and it can be negative.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive. A value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable increases proportionally. A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases proportionally. A correlation coefficient of 0 indicates no linear relationship between the variables.

Therefore, the statement that the correlation coefficient varies between 0 and 1 and can never be negative is false. The correlation coefficient can indeed be negative, indicating a negative relationship between the variables. It is important to note that the correlation coefficient only measures the strength and direction of the linear relationship between the variables and does not capture other types of relationships, such as non-linear or causal relationships.

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The correct answer is (a) fixed number of trials because there is no fixed number of trials in this case.

The doctor has the patients flip the coins until the end of the session, and then asks them to report the number of heads they got. Which of the following conditions for using the binomial model is not satisfied?The doctor has coins with a 50% chance of coming up heads. The doctor has patients flip the coins until the end of the session. The patients will then report how many heads they got. Which of the following conditions for using the binomial model is not met?The condition that is not satisfied for the use of the binomial model is a fixed number of trials. Since there is no fixed number of trials, the doctor may have to flip the coins several times. It is essential that the number of trials is fixed so that the binomial model can be used properly.In a binomial experiment, there are a fixed number of trials, each trial has two possible outcomes, the trials are independent, and the probability of success is the same for each trial. If any of these conditions are not met, the binomial model cannot be used. Therefore, the correct answer is (a) fixed number of trials because there is no fixed number of trials in this case.

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Answer:

option 2

Step-by-step explanation:

2(x + 6) > - 6(x + 1) + 2 ← distribute the parenthesis on both sides

2x + 12 > - 6x - 6 + 2

2x + 12 > - 6x - 4 ( add 6x to both sides )

8x + 12 > - 4 ( subtract 12 from both sides )

8x > - 16 ( divide both sides by 8 )

x > - 2

the graph will have an open circle at - 2, with arrow pointing right

this is indicated in option 2

Answer: 11

Step-by-step explanation:

There is the average decrease in temperature which is -2.5 degrees per hour.

For the given data:

So,

Difference in temperature =  32.7 - 45.2

                                            =  -12.5

Total time from 8:00 pm to 1:00 am = 5 hours.

Then,

Average change in temperature per hour = -12.5 / 5 = -2.5 degrees.

Thus, there is the average decrease in temperature which is -2.5 degrees per hour.

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The distance between two points of coordinates (x₁, y₁ ) and (x₂, y₂) is calculated using the formula:

The water system management of Greenville needs to take action to reduce the amount of lead in the water because more than 10% of the samples have amount of lead greater than or equal to 15ppb.

A histogram is a representation of the data because it shows the amount of lead in each number of sites.

Site A = 10/75 × 100

= 0.133333333333333 × 100

= 13.33%

Site B = 20/145 × 100

= 0.137931034482758 × 100

= 13.79%

Site C = 30/15 × 100

= 2 × 100

= 200%

A histogram is the graphical representation of numerical data in the form of upright bars, with the area of each bar representing frequency.

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Answer:

admission price of each parent = $7.5

admission price of each child = $15

Step-by-step explanation:

x = admission price of each parent

y = admission price of each child

Robinson family:

2x + 4y = 75

Moore family:

2x + 3y = 60

2x + 4y = 75 (1)

2x + 3y = 60 (2)

Subtract (2) from (1)

4y - 3y = 75 - 60

y = 15

Substitute y = 15 into (1)

2x + 4y = 75

2x + 4(15) = 75

2x + 60 = 75

2x = 75 - 60

2x = 15

x = 15/2

x = 7.5