Indicate in standard form equation of the line passing through the given 

Answer:

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg = 78.5%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Step-by-step explanation:

Complete Question

According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.

Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.

Solution

The Central limit theorem allows us to say

The mean of sampling distribution is approximately equal to the population mean.

μₓ = μ = 1.20 kg

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

σ = population standard deviation = 0.14 kg

N = sample size = 3

σₓ = (0.14/√3) = 0.08083

Percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, that is, percentage of all samples of three men with mean brain weights within 1.10 kg and 1.30 kg.

P(1.10 ≤ x ≤ 1.30)

We first normalize or standardize 1.10 and 1.30

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For 1.10 kg

z = (x - μₓ)/σₓ = (1.10 - 1.20)/0.08083 = -1.24

For 1.30 kg

z = (x - μₓ)/σₓ = (1.30 - 1.20)/0.08083 = 1.24

To determine the required probability

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

We'll use data from the normal distribution table for these probabilities

P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24)

= P(z ≤ 1.24) - P(z ≤ -1.24)

= 0.89251 - 0.10749

= 0.78502 = 78.502%

The sampling error is 0.08083, in terms of the sampling error, 78.5% of samples of three men will have mean brain weights within (1.24×sampling error) of the mean.

Hope this Helps!!!

Answer:

A)1/18

B)1/6

C)13/18

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW,

The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?

CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION

Answer:

g(x)= 1/4 |x-2| + 1

Step-by-step explanation:

line:

points on same line:

slope based on the points

And the line is moved to the right by 2 units:

So the function becomes:

Considering movement up by 1 unit as well:

This is the final of equation for the line.

Answer:

(-4,-7)

Step-by-step explanation:

Adding 1 to the x and subtracting 3 from the y we get

-5+1= -4

And

-4-3= -7

Answer:

A =12.56 m^2

Step-by-step explanation:

Find the area of a circle with radius 4

A = pi r^2

A = 3.14 * 4^2

A =50.24

Since this is 1/4 of the circle, multiply by 1/4

A = 1/4 * 50.24

A =12.56 m^2

Answer:

12.56

Step-by-step explanation:

the formula for the area of a circle is the following:

[tex]\pi r^{2}[/tex]

so divide that formula by 4 to get a quarter and plug in the radius for r.

[tex](\pi )(4^2)/4= 12.56[/tex]

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

--------------

(b)

Given

[tex]a_{n}[/tex] = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

------------------

Answer:

[tex]271.3 mm^3\\[/tex]

Step-by-step explanation:

We have to find the volume of the hole and subtract it from the volume of the cylinder.

The volume of a cylinder is given as:

[tex]V = \pi r^2h[/tex]

where r = radius

h = height

A cylindrical metal pipe has a diameter of 8.4 mm and a height of 10 mm.

Its radius is 4.2 mm. Therefore, its volume is:

[tex]V = 3.14 * 4.2^2 * 10 = 553.9 mm^3[/tex]

A hole cut out of the center has a diameter of 6 mm. Its height is also 10 mm.

Its radius is 3 mm. Therefore, its volume is:

[tex]V = 3.14 * 3^2 * 10 = 282.6 mm^3[/tex]

Therefore, the volume of metal in the pipe is:

[tex]553.9 - 282.6 = 271.3 mm^3[/tex]

Answer:

B

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Slope is: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points (2,8) and (-6, -8) .

[tex]m=\frac{-8-8}{-6-2} =\frac{-16}{-8}=2[/tex]

The slope is 2.

Answer: 360 cubic centimeters.

Step-by-step explanation:

Since it  has a base shaped like a square and we know that it has a side length of 6 cm then we could square it an multiply it by the height.

6^2 = 36  

36 * 10 = 360

Step-by-step explanation:

x and x+2 are the numbers

x(x+2)=143

x²+2x-143=0

x²+13x-11x-143=0

x(x+13)- 11(x+13)=0

(x+13). (x-11)=0

x+13=0. x=-13

x-11=0. x=11

Answer:

Dependent variable → bacteria cell increase or population

Independent variable → time variable

Step-by-step explanation:

An independent variable has direct effect on the dependent variable. The independent variable can stand on it own and it is not change by the other variable you are trying to measure. The independent variable have direct effect on the dependent variable.

A dependent variable is actually the variable being tested in an experiment. The dependent variable is actually dependent on the independent variable.

The dependent variable in this scenario is the bacteria cell increase or the bacteria cell multiplication.  The bacteria cell increase is dependent on the time . The time variable is the independent  variable as it can stand on it own .

Dependent variable → bacteria cell increase or population

Independent variable → time variable

Answer:

2

Step-by-step explanation:

Given the system of equations:

[Tex]x^2+y^2=9\\9x+2y=16[/tex]

Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].

The first equation is an equation of a circle centred at (0,0) with a Radius of 3.

The second equation 9x+2y=16 is a straight line equation.

A straight line can only intersect a circle at a maximum of 2 points.

Therefore the greatest possible number of solutions to the equations in the system is 2.

Answer:

2

Step-by-step explanation:

and jj is gay of outer banks

Answer:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Step-by-step explanation:

The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.

[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]

There are two different solutions:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):

[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]

[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]

Answer:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]

We are interested on this probability

[tex]P(X>65)[/tex]

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we find the z score for 65 inches we got:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Answer:

(A) [tex]y=-0.762+0.119x[/tex]

(B) If a country increases its life expectancy, the happiness index will increase.

(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Step-by-step explanation:

A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).

The output of the regression analysis are as follows:

a = -0.762

b = 0.119

r² = 0.8649

r = 0.93

(A)

The equation of the Least Squares Regression line of the form y = _ + _ x is:

[tex]y=-0.762+0.119x[/tex]

(B)

The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.

The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.

Thus, if a country increases its life expectancy, the happiness index will increase.

(C)

Compute the value of y for x = x + 3.5 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]

Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D)

Compute the value of y for x = 67 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]

Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Answer:

Step-by-step explanation:

For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written.  You'll need to understand the concept of "function" often in algebra and beyond.

What concepts (only the names) did you need to accommodate the concept of function in your mind?  input, output, rule, domain, range, mapping, variation (direct and inverse)

Simplest function:  y = c  (there's only one x-value and y equals that value)

In your day to day, is there any occurring fact that can be interpreted as a function?  An electronic parking meter:  the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.

Is it possible to view a function?  Sure.  Graph the function.

What strategy are you using to get the graph of a function?  Set up a coordinate plane.  Label the horizontal axis "x" and the vertical axis "y".  Choose x (input) values that are included in the domain of the function.  If the domain includes '0' you will be finding the 'y-intercept' of the function.  Write the input and output as a point:  (x, y).  Plot that point.  Choose other x values within the domain and calculate the corresponding y value for each.  Plot several more points and draw a line or a curve through them.  Of course there are more sophisticated strategies for graphing functions.  Remember:  If you're working with a function, there is never more than one output or y value for any particular input value.

Answer:

D (4,11)

Step-by-step explanation:

Answer: it’s d

x is just going up by 1 and y is going up by 2

Answer:

Slope is 4

slope of the line perpendicular to it: x=-1/4

Answer:

2, -1/2

Step-by-step explanation:

2m²-3m-2=0

2m² - 4m + 1m - 2=0

2m(m-2)+(m-2)=0

(2m+1)(m-2)=0

2m+1=0 ⇒ m= -1/2

m-2=0 ⇒ m=2

Answer:

if the diagonals of a parallelogram are congruent, then it's a rectangle (neither the reverse of the definition nor the converse of a property). If a parallelogram contains a right angle, then it's a rectangle (neither the reverse of the definition nor the converse of a property).

Step-by-step explanation:

Answer:

Step-by-step explanation:

24/3 - 4

8 - 4 = 4

Answer:

1. Option c

2. Option d

Step-by-step explanation:

This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.

This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.

Part A: The respondents are a voluntary response sample (Option C)

Part B: Responses may not reflect the opinions of the general population (Option D)

The total number of internet users = 1072

Percentage of the total number of people that chose to respond = 38%

Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.

Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.

In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples

The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population

Learn more on sampling methods here: https://brainly.com/question/16587013

Answer:

2.143

Step-by-step explanation:

An urn contains 8 black and;

6 pink balls.

5 balls are randomly drawn from the urn in succession, with replacement.

What is the probability that all the 5 balls drawn from the urn are pink?

The probability that all the 5 balls drawn is pink is 5 × 6/14 = 30/14 = 2.143 (rounded off to 3 decimal places)

The probability of drawing 5 pink balls is 0.271

Since the balls are replaced after each draw, the probability of drawing a pink ball each time is always  

6/14

=3/7

Since we are drawing 5 balls, the probability of drawing 5 pink balls with replacement is

[tex](3/7)^{5}[/tex]

≈0.2706

Rounding to 3 decimal places, the probability is  0.271

Learn more about probability here: brainly.com/question/32117953

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Answer:

#1

Step-by-step explanation:

The associative property of addition states that we can "flip" two expressions that are being added. Therefore, our answer is the first one because it can be rewritten as 3x + (-7y) which then is equivalent to -7y + 3x.

We have a right triangle and we're given the leg lengths.  

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

tan X = YZ / XZ = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as:

Answer:

21-25 = 4

26-30 = 3

Step-by-step explanation:

16-20 (4)= 17 17 17 18

21-25 (4)= 21 22 24 25

26-30 (3)= 26 27

30

31-35 (3)= 32 35 35

36-40 (5)= 36 37 37 38 39

41-45 (2)= 41 42

Answer:

$2350

Step-by-step explanation:

If 94 is 4%, multiply it by 25 to get $2350, or 100%

the cost of the item is $ 2350.

To find the cost of the item, we can set up an equation using the information given.

Let's denote the cost of the item as $ x.

According to the given information, the sales tax on the item is 4 % and is equal to $ 94. We can express this as:

0.04 x = 94

To solve for x, we divide both sides of the equation by 0.04:

x = tax on item / sales tax

x = 94 / 0.04

x = 2350

Therefore, the cost of the item is $ 2350.

Learn more about Sales Tax here

https://brainly.com/question/27608389

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Answer:

The minimum score that she must earn to get admitted is 523.

Step-by-step explanation:

As the scores are normally distributed, we can calculate the probability using the z-score.

The distribution has a mean of 420 and a standard deviation of 80.

We have to calculate the z-score z* that satisfies:

[tex]P(z>z^*)=0.1[/tex]

This happens for z*=1.28155.

Then, we can calculate the score as:

[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]

Answer:

it is the mode.

Step-by-step explanation:

i. e 5 is the most occuring number in the set of data listed above