e. A set of observations has a mean of 9.0 and standard deviation 4.0. Another set of 20 observations has a mean of 10.0. Given the standard deviation of the combined set of 35 observations is 3.0, find the variance of the second set.

Answers

Answer 1

From the combined standard deviation, with the mean, and standard

deviation of the data sets, the required variance can be found.

[tex]\underline{\mathrm{The \ variance \ of \ the \ second \ set \ is} \ 4\dfrac{5}{28}}[/tex]

Reasons:

The given data information are;

Mean of the first set of observation, [tex]\overline x_1[/tex] = 9.0

Standard deviation of the the first set, σ₁ = 4.0

Sample size of second observation, n₂ = 20

Mean of second sample, [tex]\overline x_2[/tex] = 10

Standard deviation of the combined set, σ₁₂ = 3.0

Sample size of combined set of observation, n₂ = 35

Solution:

The number of elements in the second sample, n₁ = 35 - 20 = 15

The standard deviation of the combined set is given by the formula;

[tex]{\sigma_{12}} = \mathbf{\sqrt{\dfrac{n_1 \cdot \left ( \sigma^2_{1}-d_1^2 \right ) + n_2 \cdot \left ( \sigma^2_{2}-d_2^2 \right )}{n_{1}+n_{2}}}}[/tex]

Where;

[tex]\overline x_{12} =\mathbf{\dfrac{n_1 \cdot \overline x_1 +n_2 \cdot \overline x_2 }{n_1 + n_2}}[/tex]

Therefore;

[tex]\overline x_{12} =\dfrac{15 \times 9.0 +20 \times10.0 }{15 + 20} = \dfrac{67}{7}[/tex]

d₁ = [tex]\mathbf{\overline x_{12}}[/tex] - [tex]\mathbf{\overline x_1}[/tex]

[tex]d_1 = \dfrac{67}{7} - 9.0 = \dfrac{4}{7}[/tex]

d₂ = [tex]\mathbf{\overline x_{12}}[/tex] - [tex]\mathbf{\overline x_2}[/tex]

[tex]d_2 = \dfrac{67}{7} - 10.0 = -\dfrac{3}{7}[/tex]

Therefore;

[tex]3=\sqrt{\dfrac{15 \times \left ( 4.0^2-\left(\dfrac{4}{7}\right) ^2 \right ) + 20 \cdot \left ( \sigma^2_{2}-\left(-\dfrac{3}{7}\right) ^2 \right )}{15+20}}[/tex]

Solving gives;

[tex]Variance, \ \sigma^2_2 = \mathbf{\dfrac{{117} }{28}}[/tex]

[tex]\mathrm{The \ variance \ of \ the \ second \ set, \ \sigma_2^2} = \dfrac{{117} }{28} = 4\dfrac{5}{28}[/tex]

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Related Questions

I'm thinking of 2 numbers. Both numbers have the same absolute value. What number must be true about the 2 numbers?

Answers

Answer: they have the same number in them for example -4 and 4

Step-by-step explanation:

please help and explain how to solve these! Thanks

Answers

2. C
Slope = 40/8 = 5
Slope of graph c = 5/1 = 5

3. D
Slope = 9/3 = 3
Slope of graph d = 81/27 = 3

Step-by-step explanation:

Use the Pythagorean Theorem to find the missing sides in the triangles.

[tex]c^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

Q2. [tex]c^{2}[/tex] = 8^2 + 40^2

[tex]c^{2}[/tex] = 1664

c = [tex]\sqrt{1664}[/tex]

c = 8[tex]\sqrt{26}[/tex]

Find the missing sides of the other triangles and figure out which ones are the same.

Q3. Do the same thing as Q2.

What is the inverse of the function?
f(x) = 3^x + 1

f^-1(x)= log3 (x) +1
f^-1(x)= log3(x)-1

f^-1(x)=log3(x+1)

f^-1(x)=log3(x-1)

Answers

Answer:

f^-1(x)=logs3(x+1)

Step-by-step explanation:

Let y=f(x)

[tex]\\ \rm\Rrightarrow y=3^x+1[/tex]

Interchange

[tex]\\ \rm\Rrightarrow x=3^y+1[/tex]

[tex]\\ \rm\Rrightarrow lnx=ln(3^y+1)[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{ln(y-1)}{ln3}[/tex]

Again interchange

[tex]\\ \rm\Rrightarrow f^{-1}(x)=\dfrac{ln(x-1)}{ln3}[/tex]

Edward opens a new account and makes a deposit of $150. He then makes withdrawals of $10, $20 and $25, before depositing $30 more. What is the new balance?​

Answers

The new balance is $125
Explanation)
150-10-20-25 = 95
95 + 30 = 125
150 - 10 - 20 - 25 + 30 = 125
the new balance is $125 :)

Nathan usually drinks 32 ounces of water per day. He read that he should drink 56 ounces of water per
day. If he starts drinking 56 ounces, what is the percent increase? Round to the nearest percent.

Answers

Answer:

57 percent

Step-by-step explanation:

36 divided by 56 equals .57142 which rounds to 57

what is the x and y intercept of 18x-3y=15

Answers

Answer:

18(0) -3y = 15

-3y=15

now divide-3 from both sides

y= 15/-3

reduced is -5

y int = (0,-5)

18x-3(0)=15

18x=15

divide the 18 from both sides

x=15/18

reduced is 5/6

x int = 5/6

Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, how much take-home pay did Adjoa earn this past month?

Answers

Adjoa’s gross salary for last month was Ghc4,687.24. If Ghc421.78 was deducted from Adjoa’s salary pay, the take-home pay that Adjoa earn in the past month is Ghc4,265.46

The gross salary is the amount received by an individual prior to the deduction of the taxes.

Given that:

Adjoa's gross salary for last month = Ghc4,687.24and Ghc421.78 was deducted from Adjoa's salary pay.

Then, the take-home that Adjoa earned in the past month is calculated by removing the amount deducted from her gross salary.

i.e.

= Ghc4687.24 - Ghc421.78

= Ghc4,265.46

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Which equation, when solved, results in a different value of x than the other three? O -7-9-20 0 + 5 3 7 X=-20 4 O 3 4. - (b)*--20 +7(49-2-06-4) 8 O ​

Answers

Answer:

1

Step-by-step explanation:

Find the quotient or 4/5 and 6/7 give ur answer as a fraction in simplest form

Answers

Answer:

14/15

Step-by-step explanation:

Let me know if i got it right if not I'm sorry :(

The required quotient would be 14/ 15 which is a fraction.

What is the Quotient?

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

We have been given that two numbers are 4/5 and 6/7

To determine the quotient or 4/5 and 6/7

⇒ 4/5 ÷  6/7

⇒ 4/5 / 6/7

Reciprocal the term of denominator,

⇒ 4/5 × 7/6

Apply the multiplication operation,

⇒ 28 / 30

Reduce the above fraction to the simplest form

⇒ 14/ 15

Therefore, the required quotient would be 14/ 15 which is a fraction.

Learn more about the quotient here:

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#SPJ2

ANSWER LAST QUESTION PLZZZ

Answers

Step-by-step explanation:

what ask you ask you not ask any question please write your question please mark me brainlist

F(x)= 2x^3 + 5x^2 -x -6 is divided by x+1

What is the remainder and is it a fraction?

Remainder: 0 or -2
Is it a factor: yes or no

Answers

Step-by-step explanation:

substitute x= -1 into the equation to get the remainder

remainder= -2

the remainder is not a fraction

no, it is not a factor since its remainder is not zero


What is the distance between -33 and -18.5 on a number line

Answers

Step-by-step explanation:

The distance between two numbers in a number line is obtained by subtract the two numbers. The order of the subtraction starts with the number a bigger value followed by the number with the smaller value. For example,

x

and

y

are the two numbers and

x

y

, then the correct order should be

x

y

.

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

Given the numbers

7

and

11

on the number line, find the distance between the two numbers.

Solution:

Since

7

is...

13.5

absolute value ig

8) What is the area of a polygon with vertices
A(-2,4), B(4,4), C(7,0) and D(-5,0)?
(A) 48
(B) 42.5
(C) 36
(D) 24

Answers

Answer:

[C] 36.

Step-by-step explanation:

the given polygon is trapezoid, where its bases are AB and CD.

The required area can be calculated using the formula: A=0.5(AB+CD)*h, where h - height of the ABCD.

The lengths are: AB=6; CD=12; h=4, then the required area:

A=0.5(6+12)*4=36

-1/3x-1/6=2/9 solution

Answers

Answer:

-1  1/6

Step-by-step explanation:

Use a common denominator first to convert all the fractions so they can be easily added or subtracted.

Common denominator is 18 since 3, 6, and 9 can all evenly divide into 18

1/3 = 6/18

1/6 = 3/18

2/9 = 4/18

So now you have

-6/18x - 3/18 = 4/18

add 6/18x to both sides so you can make the number with the variable positive

6/18x - 6/18x - 3/18 = 4/18 + 6/18x simplifies to - 3/18 = 4/18 + 6/18x

subtract 4/18 from both sides

- 3/18 - 4/18 = 4/18 - 4/18 + 6/18x simplifies to - 7/18 = 6/18x

Divide both sides by 6/18 so x is alone on the one side

( - 7/18) / ( 6/18) = ( 6/18x) / ( 6/18)  simplifies to ( - 7/18) / ( 6/18) = x

When you divide a fraction by a fraction, the bottom fraction gets flipped over then you multiply the two new fractions straight across

so the new equation looks like this

- 7/18 times 18/6 and you multiply -7 x 18 = -126 and the bottom is 18 times 6 = 108    you now have  -126/108

x = -126/108  which simplifies to - 1  18/108  which can still be simplified more to -1  1 / 6   since 108 can be divided by 18 that gives you 6.

What are the characteristics of the graph of the inequality x < 4.5?

The ray will move to the left.
It will use a closed circle.
It will use an open circle.
The ray will move to the right.

Answers

Answer:

see explanation

Step-by-step explanation:

Given x < 5

The graph will have an open circle at 5 indicating that x is not equal to 5, which would be a closed circle.

The ray will move to the left since values less than 5 are to the left of 5

Answer:Please see explanation

Step-by-step explanation:

What are the characteristics of the graph of the inequality x < 4.5?

The answer is The ray will move to the left.

It will use an open circle.

Please votes me 5 stars,1 heart,and mark as brainliest. Thanks

Juanita is tying ribbon on gift bags. She has 24 feet of ribbon and each gift bag uses 0.75 foot of ribbon. The function

r = 24 -0.75g represents the amount of ribbon r Juanita has left after tying ribbon on g gift bags. Find the zero of the function. Describe

what this value means in the context of this situation

The zero of the function is at ___. This represents that after tying ribbon on ____ gift bags, Juanita will have ____ feet of ribbon left.

Answers

The zero of the function is at 32 gift bags. This represents that after tying ribbon on 32 gift bags, Juanita will have zero feet of ribbon left.

According to the question;

The function r = 24 -0.75g represents the amount of ribbon r Juanita has left after tying ribbon on g gift bags.

The zero of the function is at, r = 0.

Therefore;

0 = 24 -0.75g

g = 24/0.75

g = 32.

This value means that after tying 32 gift bags, Juanita will have zero feet of ribbon left.

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MC)
The equation represents Function A, and the graph represents Function B:
Function A
f(x) = 6x-1
Function B
4
3
2
1
- 2
-3
-4
-5
-6
Which equation best compares the slopes of the two functions?
Previous Question

Answers

Take 2points on graph

(0,1)(1,4)

[tex]\\ \sf\longmapsto slope=m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{4-1}{1-0}[/tex]

[tex]\\ \sf\longmapsto m=3[/tex]

def is a right triangle.

Answers

Answer:

false

Step-by-step explanation:

I am not sure about it if correct pls no mark me as brainliest tq

It’s not a right angle, the length is not the same

5) How many gal. of a 65% saline solution
must be mixed with 8 gal. of pure water to
make a 25% solution?

Answers

I bell 2 gallons must be added. But if it’s wrong sorry :(

Find the properties of the parabola with the equation (x - 1)^2 = (y - 1). Leave answers in fractional form.

Directrix

y = 5/4
x = 3/4
y = 3/4

Answers

Answer:

B

Step-by-step explanation:

I hope i helped and ur welcome

Prime numbers have, less than two factors, more than two factors, exactly two factors, less than or equal to two factors.​

Answers

Answer:

exactly 2

Step-by-step explanation:

Prime numbers, the way I was taught to answer this question, has less than 2 factors. The reason is that 1 is considered a factor. However, I think the definition has changed and a prime has exactly two factors -- 1 and itself. 11 is a prime number: only 11 and 1 will divide into it.

Answer:

C exactly two factors.

Step-by-step explanation:

its 2 factors since 1 is considered a factor and 11 is a prime number so it be 2.

Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?

Answers

Step-by-step explanation:

Based on the given conditions,

[tex] formulate: 1.6\% \times 40000 \times 12 \div 12

[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}

[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}[/tex]

[tex]Reduce the fraction: 2 \times320

[tex]Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]

Answer 640

Answer:

[tex]\sf\longmapsto \: 640[/tex]

Step-by-step explanation:

Based on given cases:

[tex] \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12[/tex]

Reduce the fraction:

[tex] \sf \longmapsto \: \dfrac{2 \times 40000}{125}[/tex]

[tex] \sf \longmapsto \: 320 \times 2[/tex]

Calculate the product/quotient:

[tex] \sf\longmapsto \: 640[/tex]

How do you write 3.707 x 10-8^-8 in standard form? ASAP BRAINLIST ​

Answers

.00000003707 I believe

place the boxes in the correct location this Math problem 15 points

Answers

Answer:

but where is the question please type your full questions

Do you have a picture

Carpenter Chalberg is building a new wall in his house. The wall is 8 feet long and 8 feet tall. The wall will be framed with wood and also have studs (vertical supports) at least every 18 inches. The wall has no doors or windows. He is looking to purchase enough 8 foot boards of wood to make the wall’s frame. How many boards will Carpenter Chalberg need?

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

For studs 16" O.C., Chalberg will need 9: one at the beginning of each of the 16" spaces in the 96" width of the wall, and one at the end. That's a total of 6+1 = 7 studs.

The top and bottom edges of the wall are each 8', so will require 1 more board each.

The total number of boards Chalberg needs is 9.

PLEASE HELP! I Would appreciate it

Answers

Quick answer: 0.2908, or %29.0816.

Long answer: So this question is a probability problem, so we take the number we’re looking for and divide it by the whole. Which in this case would be 285/980 Getting us 0.290816326530612 which can be rounded to 0.2908, or in percentage form %29.0816.

Please mark brainliest

do
any one need points​

Answers

Thanks for the points appreciate it hope you have a good day

Determine the domain and the range of the function.
f = {(4, 8),(19,-3),(33, 8),(54,3)}
The domain is {}.

Answers

Answer:

By definition: domain is set of x coordinates = {4, 19, 33, 54}, By definition: range is set of y coordinates = {8, -3, 8, 3} = {8, -3, 3}  

Step-by-step explanation:

will mark brainlest answer the question in the picture linked below
and explain as well

Answers

Answer:

¹⁰√4

Step-by-step explanation:

4^(2/5*1/4)

4^(1/10)

¹⁰√4

The functions f and g are defined as follows.
f(x)=-3x-1
3
g(x)=2x? +2
Find f (2) and g(-2).
Simplify your answers as much as possible.

Answers

>> Answer :

__________

[tex] \: [/tex]

f(x) = -3x - 1

g(x) = 2x + 2

Soo :

f(2) :

f(2) = -3(2) - 1

f(2) = -6 - 1

f(2) = -7

.

g(-2) ;

g(-2) = 2(-2) + 2

g(-2) = -4 + 2

g(-2) = -2

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