The ratio of a human's femur (thigh bone)
length to the person's height is approximately
1:4. If Thomas is 5.8 feet tall, about how long
would you expect his femur to be?

The option `I and III` can be completely eliminated.

Thus, the series that is convergent series is option `II only`. Answer: O II only

`(I) Σ I) n^10 1 + 53 n^12)/(8^n - 8)`

To apply the ratio test, we compute

a_{n+1}/a_n to get;`

lim (as n → ∞)

|a_{n+1}/a_n|

=53/8`

Since

`lim (as n → ∞)

|a_{n+1}/a_n|>1,`

the ratio test fails and thus the series Σa_n diverges.

Hence, option `I only` and option `I and III` can be eliminated.`

(II) Σ (n^4 + 3)/(3^n)`

To apply the ratio test, we compute

a_{n+1}/a_n

to get;`

lim (as n → ∞)

|a_{n+1}/a_n|

=lim (as n → ∞)

[(n+1)^4 + 3]/[3^{n+1}] * [3^n]/(n^4 + 3)

=lim (as n → ∞)

[(n+1)^4 + 3]/(3n^4 + 3)`

Dividing both numerator and denominator by `n^4`, we have

`lim (as n → ∞)

[(1+1/n)^4 + 3/n^4]/[3(1 + 1/n)^4]`

=1/3`

Since `lim (as n → ∞)

|a_{n+1}/a_n|<1,`

the ratio test holds and thus the series Σa_n converges.

Thus, option `II only` is correct.`

(III) Σ n^3 + n^2 + n`

= `lim (as n → ∞)

[(n+1)^3 + (n+1)^2 + (n+1)] - (n^3 + n^2 + n)

=lim (as n → ∞)

[3n^2 + 3n + 1]`

=∞

Since `lim (as n → ∞)

|a_{n+1}/a_n|>1,`

the ratio test fails and thus the series Σa_n diverges.

Hence, option `I and III` can be completely eliminated.

Thus, the series that is convergent is option `II only`. Answer: O II only

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143

Step-by-step explanation:

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Answer:

143

Step-by-step explanation:

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The value of k from the equation is k = -20

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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Answer:

a = 6

TV = 52

Step-by-step explanation:

TU + UV = TV

3a - 4 + 6a + 2 = 5a + 22

Add like terms in RHS

3a + 6a - 4 + 2 = 5a +22

9a - 2 = 5a + 22

Add 2 to both sides

9a  = 5a + 22 + 2

9a = 5a + 24

Subtract 5a from both sides

9a - 5a = 5a + 24 - 5a

       4a = 24

Divide both  sides by 4

4a/4 = 24/4

a = 6

TV = 5a + 22

     = 5*6 + 22

     = 30 + 22

TV = 52

The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.

The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.

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To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.

Given matrix D:

D = | k 0 0 |

| 3 k² k³ |

| 0 kª k³ kº |

| k k k |

| 0 0 0 |

| k¹⁰ |

The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

- 0(det | 3 k² k³ |

| 0 kª k³ |

| k k k |)

+ 0(det | 3 k² k³ |

| k k k |

| k k k |)

Simplifying further, we have:

det(D) = k(det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |)

Now, we can calculate the determinant of the 3x3 submatrix:

det | k³ k k |

| 0 k³ kº |

| 0 0 k¹⁰ |

This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:

det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº

Now, we can set det(D) equal to 1024 and solve for k:

k⁴+kº = 1024

Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.

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Answer:

150

Step-by-step explanation:

z^2. (x-y)

(5)^2. (9-3)

25. 6

150

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

Answer:

0.00558

Step-by-step explanation:

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

From the given information provided, in the basketball game Shreyansh made 2 foul shots and 6 field goals.

Let's denote the number of foul shots that Shreyansh scored by "x". According to the problem, he made three times as many field goals as foul shots, so the number of field goals he made is 3x.

We know that a field goal counts 2 points, so the total points Shreyansh scored from field goals is 2 times the number of field goals he made:

Total points from field goals = 2 × (number of field goals) = 2 × 3x = 6x

Similarly, we know that a foul shot counts 1 point, so the total points Shreyansh scored from foul shots is 1 times the number of foul shots he made:

Total points from foul shots = 1 × (number of foul shots) = 1 × x = x

According to the problem, the total points Shreyansh scored in the game is 14. Therefore, we can write an equation:

Total points = Points from field goals + Points from foul shots

Substituting the values we calculated earlier, we get:

14 = 6x + x

Simplifying and solving for x, we get:

7x = 14

x = 2

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Answer:

x(x + 3)

Step-by-step explanation:

x² + 3x ← factor out x from each term

= x(x + 3)

The population being studied in this scenario is the group of "students".

The type of study in this case is "observational".

To select the participants for the survey, the Math Department decides to use a "simple random sample" method.

The Math Library wants to understand which students are more likely to know about the homework help they offer. To gather the necessary information, they decide to conduct a study using a survey.

The type of study in this case is "observational". This means that the researchers will observe and collect data from the participants without intervening or manipulating any variables. They are interested in understanding the existing relationship between students' characteristics and their awareness of the Math Library's homework help.

To select the participants for the survey, the Math Department decides to use a "simple random sample" method. This involves using a random number generator to select 500 students from the list of students currently enrolled in math classes. By using a random sampling method, the researchers ensure that each student in the population has an equal chance of being selected, thus reducing bias and increasing the generalizability of the findings.

The choice of a simple random sample allows the researchers to obtain a representative subset of the student population. This method ensures that the selected sample is unbiased and provides a fair representation of the entire student population. By surveying a diverse group of students, the Math Library can gather information about various factors that may influence students' awareness of the homework help services.

Overall, by conducting an observational study using a simple random sample of students, the Math Library aims to gain insights into the factors that influence students' awareness of their homework help services. This information can then be used to develop targeted strategies to reach out to students who may benefit from the Math Library's resources.

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Option (A) Names of TV shows taped in New York are an example of qualitative data. Qualitative data is descriptive in nature and does not involve numerical values or measurements.

It deals with qualities or attributes that cannot be expressed numerically. In this case, the names of TV shows are characteristics that describe the nature of the data. Quantitative data, on the other hand, is numerical data that can be measured and expressed in numbers. A parameter is a measurable factor or variable that can be used to define a system, while statistics is a branch of mathematics that deals with data collection, analysis, and interpretation. In conclusion, since the names of TV shows are descriptive in nature and do not involve numerical values, they are an example of qualitative data.

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Answer:

sorry i dont know hope you get it

Step-by-step explanation:

Answer:

a = 50, b = -5, c = 5

Step-by-step explanation:

All of the boxes have to be equal to 125

box 1,

75 + 50 = 125

box 2,

120 - ( -5 ) = 120 + 5 = 125

box 3

\(5^{3}\) =5 * 5 * 5=  125

If this helped, mark me as the brainliest!

Thank You !

Answer:

all of this box has be equal to 5

Hope this helps

Answer:$25.80

Step-by-step explanation:

6.45/5 = 1.29

1.29 x 20 =25.80

Survey every 4th student who walks into the cafeteria.

Using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.

In addition to formal deduction, two more categories of logical thinking are frequently distinguished: induction and abduction.

The following can be explained if one has a precondition or premise, a conclusion or logical consequence, and a rule or material conditional that indicates the conclusion given the precondition.

Mathematical logic and philosophical logic are frequently used to support the claim that "when it rains, objects outside become wet.

The grass is outside, therefore: when it rains, the grass gets wet."

A finding of the rule is supported by inductive reasoning.

So, according to the given, we can easily guess that Kaylon is wrong because the shaded temperature is -°.

Therefore, using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.

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Answer:

i think u should first givr her discount by doing 20/100×3500=700 and than he will get 5 percent profit than here

3500-700=2800

now for 5 % profit

5/100*2800=140

hence

20% discount=700

5% profit =140

it might be wrong but here u go

The capability index that is most desirable is a. 1.00.

The capability index, often represented by Cp, is a measure of the capability of a process to consistently produce output within specified limits. It compares the spread of the process output to the width of the specification limits.

A capability index of 1.00 indicates that the process spread is equal to the width of the specification limits, indicating a high level of capability. This means that the process is able to consistently produce output that meets the desired specifications without significant deviation.

On the other hand, a capability index below 1.00 indicates that the process spread is wider than the specification limits, indicating a lower level of capability. In such cases, the process may have difficulty consistently meeting the desired specifications.

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Answer:

Mia has a bag that contains a letter block for each of the 26 letters of the alphabet. She draws a letter block from the bag, writes down the letter, and puts the block back in the bag. She repeats this 26 times. The results show that she drew a vowel (A, E, I, O, or U) 6 times.

Step-by-step explanation:

The best match is Mia has a bag that contains a letter block for each of the 26 letters of the alphabet option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

The theoretical probability of the event?

As we know,

The area of mathematics that deals with probability are called probability theory.

Probability theory tackles the idea in a rigorously mathematical way by expressing it through a set of axioms, despite the fact that there are many distinct probability interpretations.

Thus, the best match is Mia has a bag that contains a letter block for each of the 26 letters of the alphabet option (B) is correct.

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Answer:

\(\frac{35}{18}\)

Step-by-step explanation:

my suggestion on solving problems like this is to multiply by a fraction that equals "1" made up of the L.C.M of the fraction denominators (2,4,5 = 20)

\(\frac{20}{20}\) ..... the denominators will clear out leaving \(\frac{15 - 50}{12-30} = \frac{-35}{-18}\)

= 35/18

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\( \huge \sf\frac { \frac { 3 } { 4 } - \frac { 5 } { 2 } } { \frac { 3 } { 5 } - \frac { 3 } { 2 } } \\ \)

\( \huge \sf \frac{\frac{3}{4}-\frac{10}{4}}{\frac{3}{5}-\frac{3}{2}} \\ \)

\( \huge \sf\frac{\frac{3-10}{4}}{\frac{3}{5}-\frac{3}{2}} \\ \)

\( \huge \sf\frac{-\frac{7}{4}}{\frac{3}{5}-\frac{3}{2}} \\ \)

\( \huge \sf\frac{-\frac{7}{4}}{\frac{6}{10}-\frac{15}{10}} \\ \)

\( \huge \sf\frac{-\frac{7}{4}}{\frac{6-15}{10}} \\ \)

\( \huge \sf\frac{-\frac{7}{4}}{-\frac{9}{10}} \\ \)

\( \huge \sf-\frac{7}{4}\left(-\frac{10}{9}\right) \)

\( \huge \sf\frac{-7\left(-10\right)}{4\times 9} \)

\( \huge \sf\frac{70}{36} \)

\( \huge \boxed{ \bf\frac{35}{18}\approx 1.944..}\)

The given expression is 7x^3√6 + √12x^2 * (-√2x^2).

To simplify the expression, let's break it down step by step.

First, let's simplify the square roots:

√6 can be simplified to 2√6 because 6 = 2 * 3, and we can take out the square root of 2.

√12 can be simplified to 2√3 because 12 = 4 * 3, and we can take out the square root of 4.

Next, let's simplify the expression further:

7x^3 * 2√6 = 14x^3√6

Now, let's simplify the multiplication:

14x^3√6 * (-√2x^2) = -14x^5√12

Therefore, the simplified expression is -14x^5√12.

In summary, the expression 7x^3√6 + √12x^2 * (-√2x^2) simplifies to -14x^5√12.

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The largest value that f(4) can possibly be is 29.

The mean value theorem states that for a function f(x) that is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), there exists a number c in the open interval (a, b) such that:

f(b) - f(a) = f'(c)(b - a)

In this case, we are given that f(0) = -3 and that f'(x) ≤ 8 for all values of x. To determine how large f(4) can possibly be, we can use the mean value theorem with a = 0 and b = 4:

f(4) - f(0) = f'(c)(4 - 0)

Substituting the given values:

f(4) - (-3) = f'(c)(4)

f(4) + 3 = 4f'(c)

Since f'(x) ≤ 8 for all values of x, we can say that f'(c) ≤ 8. Therefore:

f(4) + 3 ≤ 4f'(c) ≤ 4(8) = 32

Therefore, we have:

f(4) ≤ 32 - 3 = 29

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Answer:

He has 445$ in his account

Step-by-step explanation:

First, if he has 470 in his account and he makes a check for 55,  470 - 55 = 415, then he made a deposit his account now holds 445$, thus your final answer is 445$ is the balance in his bank account.

Hope This Helps!

The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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Answer:Does this help?

Step-by-step explanation:

3/4 needs to have the same denominator as 8/12 so you can do this by multiplying the denominator by 3 and the top by 3 you get 9/12 When you convert them to percents you get , 3/4= 75% and 8/12= 66.666%