Determine the limits of each of the following sequences, if they exist, or explain why the sequence diverges. You must indicate if you use any standard limits, continuity or l'Hopital's rule. an = (n + 2)^2n/(n^2 - n - 6)^n bn = cosh(3/n) - 1/sinh(2/n) Verify your answers for both limits >>using MATLAB

The correct option: C.) 3.75 x 10^6 m.  The size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.

The size of one smaller cell : 2.5 x 10^-9 m.

The size of other larger ball: 1.5 x 10^3 times larger than first ball.

For the size of other larger ball:

Size = 2.5 x 10^-9 x 1.5 x 10^3

Size = 2.5 x 1.5 x 10^(-9+3)

Size = 3.75 x 10^6 m

Thus, the size of other larger cell is found as the 3.75 x 10^6 m , written in the scientific notation.

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The correct question is-

The size of a certain cell is 2.5 x 10^-9 m. Another cell is 1.5 x 10^3 times larger. How large is the larger cell in scientific notation?

A.) 4 x 10^-27m

B.) 4 x 10^-12m

C.) 3.75 x 10^6m

D. 3.75 x 10^-6m

The provided Product 9/10 * 20/21 has the simplest form, which is 6/7.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given a fraction multiplication 9/10 × 20/21

Simplification Using PEMDAS

=>  9/10 × 20/21

=> 9* 20 /21 *10

=> 6/7

Therefore, the simplest form of the given Product 9/10 × 20/21 is 6/7.

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The required simplified value of the given expression is [A × B] ×10².

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
=  A x 10 ×  B × 10

Applying distributive property, a (bc) = (ab) c
= A × B × 10 × 10

Applying associative property in the exponents of 10, 10 × 10 = 10²
= [A × B] × 10²

Thus, the required simplified value of the given expression is [A × B] ×10².

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The benefit of using a curve over a histogram is that, it is a useful tool for visualizing data distributions, curves provide a more detailed and flexible representation of the data and offer additional advantages in terms of resolution, flexibility, parametric modeling, and comparison.

Visualizing data is an essential aspect of understanding the underlying patterns and relationships. In data analysis, two popular ways of visualizing data are histograms and curves. While both of these visualization techniques serve the purpose of summarizing data, each of them has its unique benefits and limitations.

Resolution: One of the main benefits of using a curve over a histogram is that a curve provides a higher resolution representation of the data. A curve can capture finer details of the data distribution that might get lost in a histogram due to the binning process.

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Answer:

answer for the expression 5(–4+k) + –2(–3+–10k) is -5k - 6.

To arrive at this answer, we used the order of operations (PEMDAS) as follows:

Parentheses first: (–4+k) = k-4 and (–3+–10k) = –10k-3

Next, the multiplication: 5(k-4) = 5k-20 and -2(-10k-3) = 20k+6

Finally, the addition: -5k-20 + 20k+6 = -5k - 6 + 20k

And then we simplify further by combining the like terms:

-5k - 6 + 20k = -5k + 20k - 6 = 15k - 6

So the final answer is -5k -6

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The interquartile range (IQR) is a measure of spread in a dataset and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

The IQR of the ‘gre’ variable can be calculated using the formula IQR = Q3 - Q1. This tells us the range of values that lie between the 25th and 75th percentile.

In this case, the IQR of ‘gre’ is calculated to be 210 - 340 = 70. This means that 70% of the distribution data falls within the interquartile range of ‘gre’. This can be further visualized on a boxplot, which shows the median, upper and lower quartiles. The IQR is represented by the box and the whiskers that extend out from it, indicating the range of values that lie within the interquartile range.

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The percent increase in the height of the seedling is, 23%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A seedling Jeffery planted in 2009 was 5cm tall in 2010 it was 120 cm

i.e. increase in the height = 120-5

                                           =115 cm

now,

the percent increase in the height of the seedling is,

115/5*100

=23%

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The value of the original fraction is expressed as; 36/45

Let the numerator be x and let the denominator be y. Thus;

Original fraction = x/y

Reciprocal of fraction = y/x

x/y = 4/5

Cross multiply to get;

5x = 4y

4y - 5x = 0   -----(1)

The numerator is now increased  by 9 and the new fraction equals the reciprocal of the value of the original fraction. Thus;

(x + 9)/y = 5/4

Cross multiply to get;

4x + 36 = 5y

5y - 4x = 36    ------(2)

Multiply eq 1 by 4 and eq 2 by 5 to get;

16y - 20x = 0   -----(3)

20y - 20x = 180  ----(4)

Subtract eq 3 from 4 to get;

4y = 180

y = 180/4

y = 45

5x = 4y

x = (4/5) * 45

x = 36

Original fraction is; 36/45

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Step-by-step explanation:

To mentally divide by 0.1, 0.01 and 0.001, you can use the following tips:

Dividing by 0.1 is equivalent to multiplying by 10.

Dividing by 0.01 is equivalent to multiplying by 100.

Dividing by 0.001 is equivalent to multiplying by 1000.

The graph of the sequence may pass toward the vertical line test.

Functions are defined as a fundamental part of the calculus in mathematics. These are the special types of relations. A function is visualized as a rule, which gives a unique output for every input x.

Given the information that, he gives two away on day 1, four away on day 2, and eight away on day 3. He continues this pattern for 10 days.

Let x be the number of days and f(x) be the number of cards.

So, the pattern is

f(x)=2, when x=1

f(x)=4, when x=2

f(x)=8, when x=3

Then, the function will be f(x)=2ˣ

The equation of the graph is passing through a vertical line.

The vertical line test is a graphical method that determines whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.

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Answer:

Where are the choices?

Step-by-step explanation:

By the property of exponents, the value of the above equation is 2*10^7.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is the expression. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The sum of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

=1.2 x 10^5/6 x 10^-3

=(12/6)*10^7

=2*10^7

The value of given expression is 2*10^7 by property of exponents.

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The statement that best describes the graph of linear Inequality in two variables is a straight line graph. That is option A.

A linear Inequality is defined as the expression that can be used to represent the relationship between two variables using inequality symbols such as '<', '>', '≤' or '≥'.

When a linear Inequality between two variables are being represented in a graph, a straight line graph is obtained because the inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

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The marks in paper 2 would be 100.

Given is a pupil who scored 50 in his paper 1 exam got ill and missed paper 2.

Assume the equation of the line of best fit is of the form -

y = mx + c

Let {c} = 0

Now, for the point (1, 50), we can write -

50 = m

So, the equation will be of the form -

y = 50x

Now, for {x} = 2, we can write -

y = 100

Therefore, the marks in paper 2 would be 100.

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Marna thinks is wrong. Thus Marna's think is incorrect.

What is the percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent. The symbol "%" represents it.

Given that Marna thinks that about 35% of her mail is junk mail.

Thus out of 100 emails, 35 emails are junk.

Thus the ratio of regular emails to junk mail is

100:35

= 20:7

Again given that she gets about twice as much regular mail as junk mail.

Assume that the number of junk mail is x.

Then the regular mail is 2x.

Thus the ratio of regular emails to junk mail is

2x:x

=2:1

The ratio  20:7 ≠ 2:1

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Luna received 9 dollar for each pair of sneakers. She got total 18 dollars for her 2 pairs of sneakers. The equation which we can use to find the amount of money x= total money spent+ money remained.

It is given that, total pair of jumper sneakers she sold at the secondhand market = 2 pairs.

So, total sneakers= 4

Let, she got total x dollar for her jumpy sneakers.

So, here, total money spent= 12 dollars

total money left with her= 6 dollars

Hence, x= 12+ 6 dollars = 18 dollars.

So, total money she got = 18 dollars.

Money for each pair of sneakers= 9 dollars.

Equation for x= total money spent+ money left with her.

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Each person eats at least one fruit. Hence 39% of people eat both orange and apple using the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics. From the given data

n(O)=0.63

n(A)=0.76

n(A∪O)=1 as every person eats at least one fruit

n(A∪O)=n(A)+n(O)−n(A∩B)

1=0.63+0.76−n(A∩B)

n(A∩B)=1.39−1

n(A∩B)=0.39

A∩B=0.39×100=39

Hence 39% of people eat both orange and apple

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Answer:

[tex]\frac{2}{15}[/tex]

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] - [tex]\frac{1}{5}[/tex]

[tex]\frac{5}{15}[/tex] - [tex]\frac{3}{15}[/tex] = [tex]\frac{2}{15}[/tex]

Answer:

Jada's Coffee Shop used 1/3 of a carton of whole milk and 1/5 of a carton of nonfat milk on Saturday. Therefore, the amount of whole milk used was 2/3 of a carton, and the amount of nonfat milk used was 1/5 of a carton. The difference between the two is 2/3 - 1/5, which is equal to 7/15 of a carton. Therefore, Jada's Coffee Shop used 7/15 of a carton more whole milk than nonfat milk.

Height is a interval - level variable typically in statistics.

Height is typically considered an interval-level variable in statistics. This means that height has a meaningful zero point, but the difference between two height measurements does not have a meaningful interpretation. For example, if one person is 6 feet tall and another person is 5 feet tall, the difference of 1 foot is meaningful, but the ratio of their heights is not.

In contrast, ratio-level variables have a meaningful zero point and the ratio of two values also has a meaningful interpretation. For example, weight is a ratio-level variable because a weight of 0 pounds has a well-defined meaning, and the ratio of two weights (such as two people each weighing 150 pounds) is meaningful and can be compared.

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The two numbers that multiply to -60 and add up to -7 are:

[tex]-12,5[/tex]

We can multiply -12 by 5 and get -60:

[tex]-12\times5=-60[/tex]

We can also add -12 and 5 to get -7:

[tex]-12+5=-7[/tex]

So therefore, the two numbers that multiply to -60 and add to -7 are:

[tex]\fbox{-12 and 5}[/tex]

The percent change for this camera is 9.756%.

Markdown percentage is defined as the decrease in the price which is calculated as a percent of the selling price.

Given that,

Original selling price of the camera = $315

Selling price has been decreased to $287

Mark down percentage = (315 - 287) / 287

                                        = 0.09756

                                        = 9.756%

Hence the rate of the markdown percentage is 9.756%.

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The measure of ∠XYZ is 130°. Option C is the correct option.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. Sometimes it is stated to have exactly two sides that are the same length, and other times it is stated to have at least two sides that are the same length, with the latter version including the equilateral triangle as an exception.

Given that the length of YZ = YX and ∠YZX = 25°.

There is an agreement between two sides. The base of an isosceles triangle refers to the third side of the triangle, which is unequal to the other two sides. The two angles that are opposite the equal sides line up perfectly.

According to the property of the isosceles triangle:

∠YXZ = ∠YZX = 25°

The sum of all angles of a triangle is 180°.

Therefore,

∠YXZ + ∠YZX + ∠XYZ = 180°

25° + 25° +  ∠XYZ = 180°

50° +  ∠XYZ = 180°

∠XYZ = 180° - 50°

∠XYZ = 130°

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Ximena wants to decrease 350 by 4%, here the complete statement is:

350 × 4% = 14.

When the denominator is 100, percentages are really just fractions. We place the percent sign (%) next to the number to indicate that the number is a percentage.

Comparing two amounts while rebasing the second amount to 100 is the simplest way to use percentages. The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin term made its way into English. It was later abbreviated to %.

b)

= 350 × 4%

= 350 × (4/100)

= 14

19. a)

5 (x - 6) = 15

or, 5x - 30 = 15

or, 5x = 45

or, x = 9

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Answer:

16/2

Step-by-step explanation:

2 2/7  = 16/2

2 times 7 = 14 + 2 = 16/2

So, the answer is 16/2

Answer:

2 2/7 = 17/7

Step-by-step explanation:

The way I learnt it is that when you take 2 2/7 we just have to multply the denominator (7) by the whole number (2) which gives us 14 and then we have to add the numerator (2) which gives us our numerator which is 16 and the denominator stays the same meaning our answer would be 17/7. (It is the simplest form)

The initial amount a is 1250 and the rate of decay r is 0.865 (86.5%). When t = 3, the function h(t) = 1250(0.865)3 = 587.356. Rounded to the nearest tenth, the answer is 587.4.

To solve this exercise, you need to use the equation

h(t) = a(r)^t,

Where a is the initial amount and r is the rate of decay.

In this example,

Plugging in t = 3 into the equation gives

h(t) = 1250(0.865)^3 = 587.356.

To round this to the nearest tenth, you need to look at the number to the right of the decimal point, which is the 6 in 587.356. Since the 6 is 5 or greater, you need to round the 587.356 up to 587.4.

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Answer:

3+[tex]\frac{1}{4}w[/tex]  represents the distance ran on week w

The required number of songs that can be put in the final CD are 5 song.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A band expects to put 16 songs on their next CD. The band writes and records ​25% more songs than they expect to put on the CD. During the editing​ process, 75​% of the songs are removed.

According to the question,
Song added to CD = 16 + 25% of 16
                               = 20 songs

Song added to Final CD = 20 - 75% of 20
                                        = 5 songs

Thus, the required number of songs that can be put in the final CD are 5 song.

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Each polynomial given is associated with the given factoring technique in the second column. a. GCF b. grouping c. none d. the difference of two squares e. Sum and product f. Perfect square trinomial.

To factorize 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.

Each polynomial given is associated with the given factoring technique in the second column.

a. grouping

b. GCF

c. none

d. the difference of two squares

e. Sum and product

f. Perfect square trinomial

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Answer:

To find the apothem of a regular polygon, we can use the formula:

A = (ns^2)/(4tan(180°/n))

Where A is the area, n is the number of sides, s is the length of each side, and tan(180°/n) is the tangent of half of the central angle.

First, we need to find the number of sides of the polygon. To do this, we can use the formula for the sum of the interior angles of a polygon:

(n - 2)180° = 1080°

Solving for n:

n = 6

So the polygon has 6 sides.

Next, we can plug in the values we have into the formula for the apothem:

A = (6s^2)/(4tan(180°/6)) = 160

Expanding the right side:

A = (6s^2)/(4tan(30°)) = 160

Using the tangent identity:

A = (6s^2)/(4(√3/3)) = 160

Multiplying both sides by 4(√3/3) to isolate s^2:

4(√3/3)A = 6s^2

Expanding the left side:

4(√3)A/3 = 6s^2

Dividing both sides by 6:

2(√3)A/3 = s^2

Taking the square root of both sides:

s = √(2(√3)A/3)

Plugging in the value for A:

s = √(2(√3) * 160/3)

Calculating:

s = √(106.667) = 3.25

So the length of each side is 3.25 inches.

Finally, we can find the apothem using the formula:

a = s/2tan(180°/n)

Expanding the right side:

a = 3.25/2tan(30°)

Using the tangent identity:

a = 3.25/2(√3/3)

Dividing both sides by √3/3:

a = 3.25√3

Calculating:

a = 5.5

So the length of the apothem is 5.5 inches.