What happens to the mean of the data set shown below if the number 20 is added to the data set?




A. The mean increases by 0.75.
B. The mean does not change.
C. The mean increases by 12.
D. The mean increases by 0.25.

Answer:

Step-by-step explanation:

If (8,2) and (0,0) are points on the line, the slope of the line is (2-0)/(8-0) = ¼.

y = ¼x

y = 1/4x is the equation of the  line passing through points (0, 0) and (8, 2)

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

slope of line passing through (0, 0) and (8, 2)

m=2/8

=1/4

Now let us find the y intercept in the equation.

2=1/4(8)+b

2=2+b

b=0

So equation will be y=1/4x.

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Answer:

A.

Step-by-step explanation:

Each mark is worth two. We are inbetween the first mark and 0 on the left. Half of two is one. and since we are in the left quadrant we know it to be negative. Looking down, we see that we are exactly one mark down. As a mark is two, ans that we are going down, this will be a negative two. That leaves us with the answer of (-1, -2)

Answer:

A. (-1,-2)

Step-by-step explanation:

just trust me...I promise it right

Answer:

Option C (25%) is the correct answer.

Step-by-step explanation:

Given:

Number of students,

= 120

Students responded high interest,

= 30

Students responded medium interest,

= 50

Students responded low interest,

= 40

Now,

The relative frequency will be:

= [tex]\frac{30}{120}[/tex]

= [tex]0.25[/tex]

or,

= [tex]25[/tex]%

Answer:

−2√85/85

Step-by-step explanation:

The required value of the cosθ is −2√85/85. Option D is correct.

Given that,
The value of cosθ given that (−2, 9) is a point on the terminal side of θ is to be determined.

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.

here,
horizontal run b = -2, vertical rise p = 9
Slant height,
h = √ -[2]² + [9]²
h = √4 + 81
h = √85
Now,
cosθ = b / h
cosθ = -2 / √85
cosθ = -2 √85/85

Thus, the required value of the cosθ is −2√85/85. Option D is correct.

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Answer:

the right answer would be C

Answer:

Step-by-step explanation:

You first need to find the surface area of a completely open cylinder. That formula is

[tex]SA=2\pi rh[/tex] Using 3.14 for π, we find the area of the material that is needed to make this pipe:

SA = 2(3.14)(1)(30)

SA = 188.49 square feet.

If it costs $3.50 per square foot and you have 188.9 square feet, we multiply the cost per square foot times the number of square feet:

188.49(3.50) = $659.40, choice B.

The expression cos240 degrees is equivalent to cos120 degrees

Answer: B. cos240°

Step-by-step explanation:

Took the Test/Exam on Edge

Answer:

28.0125 cm^2 rounded to 28.0 cm^2

Step-by-step explanation:

Area = a*b*sin(c)*1/2

Area = 7 * 13 * sin(38) * 1/2

Area = 91/2 * 0.61566...

Area = 28.0125...

Answer:

no solution?

Step-by-step explanation:

2(5)-5=5(5)+7+3(5)        <-- plug in 5

10−5=25+7+15

5=32+15

5=47

[tex] \underline{ \huge \mathcal{ Ànswér} } \huge: - [/tex]

Average of b and c is 8, that is

[tex]➢ \: \: \dfrac{b + c}{2} = 8[/tex]

[tex]➢ \: \: b + c = 16[/tex]

[tex]➢ \: \: c = 16 - b[/tex]

now let's solve for average of c and d :

[tex]➢ \: \: \dfrac{c + d}{2} [/tex]

[tex]➢ \: \: \dfrac{16 - b + 3b - 4}{2} [/tex]

[tex]➢ \: \: \dfrac{12 + 2b}{2} [/tex]

[tex]➢ \: \: \dfrac{2(6 + b)}{2} [/tex]

[tex]➢ \: \: b + 6[/tex]

Therefore, the average of c and d, in terms of b is : -

[tex] \large \boxed{ \boxed{b + 6}}[/tex]

[tex]\mathrm{✌TeeNForeveR✌}[/tex]

Answer:

b+6

Problem:

If the average of b and c is 8, and d=3b-4, what is the average of c and d in terms of b?

Step-by-step explanation:

We are given (b+c)/2=8 and d=3b-4.

We are asked to find (c+d)/2 in terms of variable, b.

We need to first solve (b+c)/2=8 for c.

Multiply both sides by 2: b+c=16.

Subtract b on both sides: c=16-b

Now let's plug in c=16-b and d=3b-4 into (c+d)/2:

([16-b]+[3b-4])/2

Combine like terms:

(12+2b)/2

Divide top and bottom by 2:

(6+1b)/1

Multiplicative identity property applied:

(6+b)/1

Anything divided by 1 is that anything:

(6+b)

6+b

b+6

Answer: correct answer is B.

Step-by-step explanation:

in the small triangle

taking 60 as reference angle

b = [tex]10\sqrt{3}[/tex]

so

tan 60 = p/b

[tex]\sqrt{3}[/tex] = p/([tex]10\sqrt{3}[/tex])

30 = p

so

[tex]h^2 = p^2 + b^2\\ = 30^2 + (10\sqrt{3} )^2\\\\ = 900 + 300\\ = 1200\\so h^2 = 1200\\then, h = \sqrt{1200} \\ = 20\sqrt{3} \\so\\in bigger triangle\\\\h = x[/tex](taking 45 as reference angle)

so

in bigger triangle

b = 20[tex]\sqrt{3}[/tex]

so

tan 45 = p/b

1 = p/(20[tex]\sqrt{3}[/tex])

p = 20[tex]\sqrt{3}[/tex]

so h^2 = p^2 + b^2

so

h^2 = (20[tex]\sqrt{3}[/tex])^2 +( 20[tex]\sqrt{3}[/tex])^2

= 1200 + 1200

h^2 = 2400

h =[tex]\sqrt{2400}[/tex]

=20[tex]\sqrt{6}[/tex]

so x = 20[tex]\sqrt{6}[/tex]

Answer:

See below

Step-by-step explanation:

-3x+2y = -6 [1]

-2x + y = 6 [2]

For [1], solve for X.

-3x + 2y = -6

-3x = -6 - 2y

3x = 6 + 2y

x = 2 + (2/3)y

Plug x into [2]

-2(2+(2/3)y) + y = 6

-4 - 4/3y + y= 6

-4/3y + y= 10

-1/3y = 10

y = -30

9514 1404 393

Answer:

  (x, y) = (-18, -30)

Step-by-step explanation:

When choosing to solve by substitution, it is convenient if one of the variables has a coefficient of 1 or -1. Here, y has a coefficient of 1 in the second equation, making it easy to rearrange that equation to give an expression for y:

  y = 2x +6 . . . . . add 2x to the second equation

Using this expression, we can substitute for y in the first equation:

  -3x +2(2x +6) = -6

  x + 12 = -6 . . . . . . . . . simplify

  x = -18 . . . . . . . . . . . subtract 12

  y = 2(-18) +6 = -30 . . . . substitute into the equation for y

The solution is (x, y) = (-18, -30).

Answer:

28 are in the larger class.

Step-by-step explanation:

50/2 = 25 xy

25+ 3 = 28 larger

25-3 = 22 smaller

x = 28

The larger class has 28 students, and the correct option is 28.

Let's assume the number of students in one class is x.

According to the given information, the other class has 6 more students than this class, which means the number of students in the other class is x + 6.

To find the total number of students, we add the number of students in both classes: x + (x + 6) = 50.

Combining like terms, we have: 2x + 6 = 50.

Next, we subtract 6 from both sides of the equation: 2x = 44.

Finally, we divide both sides of the equation by 2 to solve for x: x = 22.

So, there are 22 students in one class, and the other class has 22 + 6 = 28 students.

Therefore, the larger class has 28 students, and the correct option is 28.

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Answer: 12 x 6

Step-by-step explanation:

36/2=18

3x=18

x equal 6

6x2=12 as it is two times

Answer:

its the 4 one

Step-by-step explanation:

Answer:

There are 75 ways to form the committee.

Step-by-step explanation:

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:

[tex]T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75[/tex]

There are 75 ways to form the committee.

Answer:

  B.  x ≤ 1 or x > 6

Step-by-step explanation:

Subtract 8 and divide by 2. (Same steps for both inequalities.)

  2x +8 ≤ 10

  2x ≤ 2

  x ≤ 1

__

  2x +8 > 20

  2x > 12

  x > 6

The solution is x ≤ 1 or x > 6.

Answer:

1. >

2. <

3. =

4. <

Step-by-step explanation:

23.197 > 23.179

3 2/10 which is the same as,

3.2 < 3.243

30.423 = 30 423/1000

18.546 < 18 56/100

Answer: the answer is b

Answer:

The ratio between two values A and B is just the quotient between these two values:

ratio = A/B

a) $280 in 7m

Here the ratio is:

$280/7m = $40/m

This also can be read as:

$40 per meter.

b) 105 miles in 2 hours

Here the ratio is:

105mi/2h = 52.5 mi/h

This also can be read as:

52.5 miles per hour

c) $33 for 5lb

The ratio is:

$33/5lb = $6.6/lb

This can be read as:

$6.6 per pound.

d) 50 pages in 2 hours

the ratio is:

(50 pages)/2h = 25 pages/h

this can be read as:

25 pages per hour.

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

[tex]H_0: \mu \leq 384[/tex]

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

[tex]H_1: \mu > 384[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that [tex]\mu = 384[/tex]

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that [tex]n = 41, X = 387, \sigma = 23[/tex]

Value of the test statistic:

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

[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]

[tex]z = 0.835[/tex]

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

Answer:

Step-by-step explanation:

Total number of outcome are  

1320

.

Explanation:

It is apparent that there are  

12

ways in which the post of President can be filled. Once President's post is filled, there are  

11

ways to fill the post of Vice President and then  

10

ways to fill the post of Secretary,

Hence a total of  

12

⋅

11

⋅

10

or  

1320

ways or outcomes.

Answer:

1320

Step-by-step explanation:

Answer:

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they found employment, or they did not. The probability of a student finding employment is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation.

This means that [tex]p = 0.88[/tex]

Nine randomly selected students

This means that [tex]n = 9[/tex]

What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months?

This is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{9,6}.(0.88)^{6}.(0.12)^{3} = 0.0674[/tex]

[tex]P(X = 7) = C_{9,7}.(0.88)^{7}.(0.12)^{2} = 0.2119[/tex]

[tex]P(X = 8) = C_{9,8}.(0.88)^{8}.(0.12)^{1} = 0.3884[/tex]

[tex]P(X = 9) = C_{9,9}.(0.88)^{9}.(0.12)^{0} = 0.3165[/tex]

Then

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.0674 + 0.2119 + 0.3884 + 0.3165 = 0.9842[/tex]

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Answer:

[tex] \displaystyle 4[/tex]

Step-by-step explanation:

we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,

[tex] \displaystyle \rm W _{ garden} = 11 - 2[/tex]

simplify substraction:

[tex] \displaystyle \rm W _{ garden} = 9[/tex]

recall that, every single side of a square is equal to each other therefore the the area of the garden will be

[tex] \displaystyle {9}^{2} [/tex]

simplify square:

[tex] \displaystyle 81[/tex]

together the garden and path makes a square of every side length 11 ft saying that the area will be:

[tex] \displaystyle {11}^{2} [/tex]

simplify square:

[tex] \displaystyle 121[/tex]

the area of path will be the difference between the total area and the garden area therefore,

[tex] \displaystyle 121 - 81[/tex]

simplify addition:

[tex] \displaystyle 40[/tex]

to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:

[tex] \displaystyle \frac{40}{10} [/tex]

simplify division:

[tex] \displaystyle \boxed{\rm4}[/tex]

hence,

4 bags are needed to cover the path.

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

It was right for me

Answer:

Ungrouped data refers to the data that is first gathered from a study, it is a raw data that is, i.e it has not sorted into categories or grouped. To calculate the mean of ungrouped data we use the formula

Step-by-step explanation:

Answer:

e. All of the above statements are correct.

Option e is correct. All of the above statements are correct.

Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data

Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.

During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.

Hence, All of the above statements are correct, Option e is correct.

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Answer:

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

California:

Sample of 296 voters, 146 voted. This means that:

[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]

[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]

Colorado:

Sample of 215 voters, 127 voted. This means that:

[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]

[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]

Test if the population proportion of voter turnout in Colorado is higher than that in California:

At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So

[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]

At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So

[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 =  0.0975[/tex]

[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]

[tex]z = 2.2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.

Looking at the z-table, z = 2.2 has a p-value of 0.9861.

1 - 0.9861 = 0.0139.

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.