The following data values represent a population. What is the variance of the
values?
8, 10, 14,4
A. 14
B. 10
C. 9
D. 13

The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.

This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.

The probability of having exactly k people who favor the new building project out of 4 is given by:

P(X = k) = (4 choose k) * \(0.45^{k}\) * \(0.55^{4-k}\)

where (4 choose k) is the binomial coefficient.

To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:

P(X = 3) = (4 choose 3) * \(0.45^{3}\) * \(0.55^{1}\)

= 0.290384375

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Answer:

Cuál es el término de la decimotercera (13.a) posición? 2,−1,5,−3,8,−5.

Step-by-step explanation:

Vamos a encontrar el patrón que se repite en la secuencia, y vamos a ver que el decimo tercer termino es 20.

Tenemos la secuencia:

2, -1, 5, -3, 8, -5

Tomando la diferencia entre terminos consecutivos obtenemos:

-1 - 2 = -3

5 - (-1) = 6

-3 - 5 = -8

8 - (-3) = 11

-5 - 8 = -13

Lo que podemos ver ahi es que la proxima vez que sumemos, tenemos que sumar 3 unidades mas de las que restamos antes, y cuando restemos, debemos restar dos unidades mas de lo que restamos antes, este es el patron.

Es decir, el proximo termino es:

-5 + 16 = 11

El proximo termino es:

11 - 18 = -7

Y así, los siguientes terminos son:

-7 + 21 = 14

14 - 23 = -9

-9 + 26 = 17

17 - 28 = -11

-11 + 31 = 20

Este ultimo es el treceavo termino.

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Answer:

\((\frac{-1}{2},\frac{-5}{2})\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Endpoint (-3, -6)

Endpoint (2, 1)

Step 2: Find Midpoint

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X \sim B(n,p)

The probability that out of n trials, there'd be x successes is given by

\(\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Assume the random variable X has a binomial distribution with the given probability of obtaining success.

Then the number of trials and the probability of obtaining success will be

P(X ≤ 2), n = 4, p = 0.2

Then we get

\(\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536\)

Then the cumulative probability will be

\(\rm P(X\leq 2) = 0.9728\)

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Answer:

y+3=4(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=4(x-1)

y+3=4(x-1)

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

The computation of the profitability ratios for Western Bookkeeping and Tax Service is as follows:

Profitability ratios are the financial ratios that evaluate an entity's ability to convert its earnings (revenue) into profit versus different criteria.

Some of the common profitability ratios include:

Stockholders' equity = $442,600

Total assets = $640,000

Net sales = $480,000

Net income = $36,000

Profit margin ratio = Net income/Net Sales x 100

= $36,000/$480,000 x 100

= 7.5%

= 8%

Return on equity ratio = Net income/Shareholders' Equity x 100

= $36,000/$442,600 x 100

= 8.13%

= 8%

Asset turnover ratio = Net Sales/Total Assets

= $480,000/$640,000

= 0.75

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Answer:

proton is the word you're looking for.

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

  41,850

Step-by-step explanation:

The 4th digit from the left is in the 10s place, so you need to round to that place. This requires rounding up, since the 1s digit is more than 4.

  41,850 . . . . to 4 significant figures

The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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9514 1404 393

Answer:

Step-by-step explanation:

It works well when making a Venn diagram to start in the middle (6 carried all three), then work out.

For example, if 10 carried early and extra-late, then only 10-6 = 4 of those trucks carried just early and extra-late.

Similarly, if 30 carried early and late, and 4 more carried only early and extra-late, then 38-30-4 = 4 carried only early. In the attached, the "only" numbers for a single type are circled, to differentiate them from the "total" numbers for that type.

__

a) 15 trucks carried only late

b) 24 trucks carried only extra late

c) 4+15+24 = 43 trucks carried only one type

d) 38+67+56 -30-28-10 +6 +6 = 105 trucks in all went out

Answer:

28

Step-by-step explanation:

SOLUTION

Step 1 :

In this question, we are told that :

A book editor was proofreading a draft of a novel.

She found that the number of errors on each page of the book was normally distributed, with the mean number of errors on a page as 8 and a standard deviation of 1.

If 82 pages had between 7 and 9 errors.

We are meant to find the approximate total number of pages in the book.

Step 2 :

CONCLUSION:

The approximate total number of pages in the book = 120 pages.

The equation of the graph g(x)  is \(3^{x-6}\)

What is a graph ?

A diagram that shows how a variable's variation compares to that of one or more other variables, such as a collection of points, lines, line segments, curves, or areas. all points whose coordinates satisfy a specific relation;

In mathematics, the word "graph" has (at least) two distinct meanings. A function graph or "graph of a function," also known as a plot, is referred to as a "graph" in elementary mathematics. A graph is a set of points and the connections between some subset of those points and their lines, which may or may not be empty.

The translation of the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

If the graph of the function  f(x) = 3^x is translated 6 units to the right , then the function becomes

g(x) = f(x - 6)

     = \(3^{x-6}\)

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The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Problem 1

Reason: We start at 0 and move 4 units left. This is represented by 0+(-4) or 0-4. That simplifies to -4. Then add on 7 to move 7 units to the right to arrive at 3 as the final destination.

=============================================

Problem 2

Reason: We start at 0 and move 8 units to the right. That is represented by +8 or simply 8. Then the +3 will move us 3 more units to the right to get to 11 on the number line. This is one visual way to see why 8+3 = 11.

Answer: 14

Step-by-step explanation: (3+8)*(10-8) = 14

Note that in question 28 above:

X = 56° (Alternative Angles)

Y = 124° (Angles in a straight line)

Z = 81° (Sum of angles in an irregular parallelogram).

in Question 29,
x = 126° (Co-interior angles and Bisector theorem).

Question 28: Note that the sum of angles in an irregular parallelogram always equal 360°. Since X and 56° are alternate angles and are therefore congruent, and Y and 56° are on the same line and therefore sum up to 180°, resulting in Y being equal to 124°, then we have three interior angles of an irregular parallelogram:

∠X = 56°

∠Y = 124°; and

∠99° (As given), which is co-interior with ∠Z

Thus whether by the Co-interior principle where two co-interior angels sum up to 180° or by sum of angles in an irregular parallelogram, we will still obtain a result where:

∠Z = 81°. That is

360° = 56 + 124 + 99 + ∠Z

∠Z = 360 - (56 + 124 + 99)
∠Z = 81°

OR

Using the Co-Interior angles theorem, we can state that:

∠Z = 180 - 99
∠Z = 81°

Question 29:
Recall that an angle bisector of a triangle's angle divides the opposing side into two portions that are proportionate to the triangle's other two sides, according to the angle bisector theorem.

Thus, we can state that 27° is half of the angle whose Co-interior is x.

Thus ∠x = 180 - (27*2)

∠x = 180 -54
∠x = 126°


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Answer:

1&2 are -2x^(3)+3x^(2)+x or Factored is −-x(2x^(2)-3x-1)

3&4 are 2x^(4)-3x^(3)-x^(2) or Factored is x^(2)(2x^(2)-3x-1)

5 is Yes

Step-by-step explanation:

1. (x+1*2x^(2)-x)(-1)

2x^(3)-x^(2)+2x^(2)-x(-1)

2x^(3)-3x^(2)-x(-1)

-2x^(3)+3x^(2)+x

−-x(2x^(2)-3x-1)

2. (2x^(2)-x*x+1*2x)(-1)

2x^(3)-x^(2)+2x^(2)-x(-1)

2x^(3)-3x^(2)-x(-1)

-2x^(3)+3x^(2)+x

−-x(2x^(2)-3x-1)

3. (x+1*2x^(2)-x)(x)

2x^(3)-x^(2)+2x^(2)-x(x)

2x^(3)-3x^(2)-x(x)

2x^(4)-3x^(3)-x^(2)

x^(2)(2x^(2)-3x-1)

4. (2x^(2)-x*x+1*2x)(x)

2x^(3)-x^(2)+2x^(2)-x(x)

2x^(3)-3x^(2)-x(x)

2x^(4)-3x^(3)-x^(2)

x^(2)(2x^(2)-3x-1)

5. (2x^(2)-x*x+1*2x)(x)=(x+1*2x^(2)-x)(x)

(2x^(2)-x*x+1*2x)(x)-2x^(2)-x=(x+1*2x^(2)-x)(x)-2x^(2)-x

(x+1)(x)=(x+1)(x)

(x+1)(x)-(x+1)=(x+1)(x)-(x+1)

X=X

To solve this question we will use the following diagram:

From the diagram, we get that the diameter of the semicircle is 8cm.

The perimeter of the figure is:

Substituting π=3.14 and simplifying we get:

Now, the area of the given figure is the area of the rectangle plus the area of the semicircle:

Substituting π=3.14 and simplifying we get:

Answer:

Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

The given graph represents a function, also notice that it is a one to one function because using the vertical line theorem we have that for all vertical lines it only intercepts the graph in just one point.

Answer:

A. x = -5

2(-5) + 10 = -3(-5) - 15

0 = 0

Answer:. h is 3h/2

k is h - 1/2

Step-by-step explanation:

Side h is half of 3h - 6.

Divide both terms by 2 So 3h/2 - 3

Side k is half of 2h - 1

Divide both terms by 2