Find the mean and population standar deviation for each data set.

Hours slept

Answer:

x < 5

Step-by-step explanation:

[tex]2x - 4 < 6[/tex]

[tex]2x < 10[/tex]

[tex]x < 5[/tex]

.........................................................

The slope of the line with the given coordinates (2,8) and (4,7.5) is -0.25.

Slope is simply expressed as change in y over the change in x.

Rise over run.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 2,8) )

Point 2( 4,7.5 )

To find the slope, plug the given x and y values into the slope formula and simplify.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 7.5 - 8 )/( 4 - 2 )

Slope m = ( -0.5 )/( 2 )

Slope m = -0.5 / 2

Slope m = -0.25

Therefore, the slope of the line is -0.25.

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No. of ways of selecting the 5 member committee by combination= 1981

What are the number of ways of selecting the 5 member committee ?

No. of women faculty in the mathematics department = 7

No. of men faculty in the mathematics department = 7

Total number of faculty members = 14

Condition - at least one woman must be on the committee

No. of ways of selection = C (14, 5) - C (7, 5)

We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]

Consider the total combination C (14, 5),

[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]              

Consider the combination of men C (7, 5) ,

[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]

No. of ways of selection = C (14, 5) - C (7, 5)

                                        = 2002 - 21

                                        =1981

No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981

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Answer:

Explanation:

The volume of a gas in a container varies inversely with the pressure on the gas

Let V represent volume

Let P represent Pressure

Rewrting the statement above Mathematically:

when V = 230 in³

P = 8 lb/in³

Substitute the value of P and V in the equation in order to ger k:

The number with 3,4 and 8 as its factors is 24

The least common multiple(LCM) can be defined as the smallest multiple that two or more numbers have in common

The Lowest Common Multiples of 3 are:3, 6, 9, 12, 15, 18, 21, 24, 27 and 30

The Lowest Common Multiples of 4 are:  4, 8, 12, 26, 20, 24, 28, 32, ...

The Lowest Common Multiples of 8 are: 8, 16, 24, 32, 40, 48, ...

From the Lowest Common Multiples above, 24 is the only number that is common among the multiples of 3,4 and 8

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According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.

The probability that mn has a units digit of 1 = 2/5

By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.

Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex],  [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).

We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).

We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is  [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].

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Answer:

$8 an hour and also requires a 40-hour week

Step-by-step explanation:

There were three different treatments: erythropoietin, darbepoetin, and no treatment. This selection exemplifies the principle of randomization principle.

In experiments, the word treatment refers to the use of a specific medicine, therapy, or condition that is controlled by the research to test the effect of the treatment on subjects. For example, if the researcher wants to find out the ideal amount of water for a plant to grow, the treatment would be the amount of water.

In the case presented, there are three treatments:

Randomization is the principle applied because the subjects are selected randomly for each of the groups and this reduces bias.

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Answer:

a. 4.2 - 2.8 = 1.4

b. 72.1 - 45.6 = 26.5

c. 82.2 - 41.3 - 29.2 = 11.7

d. 17.1 - 11.7 - 0.8 = 4.6

e. 29.2 - 12.5 - 0.9 = 15.8

f. 21 - 14 = 7

g. 71 - 37 - 18 = 16

h. 50 - 19 - 8 = 23

i. 92 - 57 - 16 = 19

j. 44 - 18 - 9 = 17

Answer:

0.49

Explanation:

Given the expression:

tan 26°

Evaluating using calculator

tan 26° = 0.4877

Hence the decimal rounded to the nearest hundredth is 0.49

Answer:

0.49 to nearest hundredth

Step-by-step explanation:

tan 26⁰ = 0.48773

Answer: n= -8

Step-by-step explanation:

1. -2 = -1 + [tex]\frac{n}{8}[/tex]

2. -1 =      [tex]\frac{n}{8}[/tex]

3. -8 = n

Answer:

40,60,80

Step-by-step explanation:

let 2x 3x and 4x

9x=180

x=20

2x=40

3x=60

4x= 80

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The probability that the experiment results in 9 or more successes = 0.0676

A binomial distribution is given by,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ  ,

where p is the probability of success and x is the random variable for success in n trials.

A binomial experiment has only two outcomes- success or failure.

Here, the number of trials, n = 10

Probability of success = 0.63

The probability for 9 or more success = P( X = 9, 10)

                                                               = P (X = 9) + P(X = 10)

So P( X = 9) =  ¹⁰C₉ (0.63)⁹ (1-0.63)¹⁰⁻⁹

                   = 10 x 0.0156 x 0.37

                   = 0.05772

and P(X = 10) = ¹⁰C₁₀ (0.63)¹⁰(1-0.63)¹⁰⁻¹⁰

                     = 1 x 0.009849 x 1

                     =  0.009849

Hence probability for 9 or more success = 0.05772 + 0.009849

                                                                    = 0.067569

                                                                    = 0.0676

The question is incomplete. Find the complete question below:

A binomial experiment with probability of success 0.63 and 10 trials is conducted. What is the probability that the experiment results in 9 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

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The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d

The constant of proportionality is 0.15.

Th amount the organisation will receive if dinner sales is $3600 is $540

The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.

A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.

The form of the linear equation would be:

total amount received by the organisation = percentage x amount the restaurant receives.

a = 0.15d

0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.

a = 0.15 x 3600

a = $540

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a. 2600 ways different samples are possible.

b. 0.11  is the probability that all 3 of the selected students are freshmen.

total student = 26

3 students are randomly selected  on group project

a.   the possible  different sample are

[tex]26 C_{3}[/tex] = [tex]\frac{26}{3 (26-3)}[/tex]

      =  [tex]\frac{26}{3 (23)}[/tex]

     = 2600 ways.

b.  13 students are freshmen  

Pr ( 3  selected students  is freshman)

[tex]\frac{13C_{3} }{26C_{3} }[/tex] = [tex]\frac{286}{2600}[/tex] = 0.11

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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Step-by-step explanation:

i don't knowhdjkedgeike

For all the given reactions there is a type name for it they are,

1. A + B → AB

2. AB → A + B

3. Hydrocarbon + O₂ → CO₂ + H₂O

4. AB + CD → AD + CB

All the above-mentioned chemical reactions are of the following types

1 → Synthesis

2 → Decomposition

3 → Combustion

4 → Replacement

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ANSWER:

STEP-BY-STEP EXPLANATION:

In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people

solving for x:

The width of the paper in the smaller notebook is 4 1/4 inches.

When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.

For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.

If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is

11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook

width of smaller notebook = 4 1/4 inches

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Answer:

1/x to the -8 power simplified would be x^8

Step-by-step explanation:

When there is a negative exponent you put the fraction under 1

[tex]\frac{1}{\frac{1}{x^{8} } }[/tex]  and its the same as x^8

The simplified expression is [tex]x^8[/tex].

Exponent is the power of the variable or constant to which it is raised.

The expression 1 over x is denoted by 1/x.

The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].

The exponents of the denominator change from negative to positive when they move from denominator to numerator.

[tex]\frac{1}{x^{-8}}=x^8[/tex]

Thus, the simplified expression will be x raised to the power 8.

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Answer: y=8x-58

Step-by-step explanation:

1. find the slope

Since the new line is parallel to the first one that means the slope of 8x will remain the same.

2. plug it into the point slope formula y-y1=m(x-x1)

which would look like

y-(-2)=8(x-7)

3. solve for y

y-(-2)=8(x-7)

y+2=8x-56

y=8x-58

The ordered pairs that could be included in the set so that the relation remains a function of x is  (-6, 1), (-1, 1).

For the given relation that is a function of x.

{(-5, 1), (-4, 1), (−3, 1), (−2, 1)}

As, from the definition of the function, the domain of the function will not repeat in the set.

Thus, (-6, 1), (-1, 1) is the ordered pairs that could be included in the set so that the relation remains a function of x.

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Given:

There is a density curve given in the question

Required:

We need to find for

Explanation:

Part a

We want to find P(X<1.6)

For this we just need to find the area below the curve until x=1.6, since we have a triangle we can do this:

Part b

For this case we want to find this probability:

P(X>4.8)

and we can complement rule and we got

Final answer:

0.04

0.64

Answer:

255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.

In linear equation, The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

What in mathematics is a linear equation?

5.5+6+7+10+7.5+8+9.5+9+8.5+8+7+7.5+6+6.5+5.5=111.5

Since there are 15 values,

           their mean is 111.5/15=7.43 which is very close to the mean.

A)A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes

D)The shape of the histogram can be approximated with a normal curve.

E)The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

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Answer:

[tex]x=\frac{-m-n+p}{-y+1}[/tex]

Step-by-step explanation:

EXPLANATION

Let's see the facts:

The increasing rate is:

The increasing rate is 1.67

In percentage this is:

The percentage of increasing is of 60%.

The number of coffee mugs that can be made is 12.

From the information, the pottery studio has 11 pounds of clay and it It takes 7/8 of clay to make a coffee mug.

The number of coffee mugs that can be made will be:

= Number of pounds of clay / Fraction used for each mug

= 11 / 7/8

= 11 × 8/7

= 88 / 7

= 12

There'll be 12 coffee mugs.

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Answer:

15

Step-by-step explanation: