The mean of a set of 6 integers is 30. When one of the numbers is removed, the new mean is 34. What was the number that was removed?

Answers

Answer 1

Given:

The mean of a set of 6 integers is 30.

If one of the numbers is removed, then the new mean is 34.

To find:

The removed number.

Solution:

The formula for mean is

\(\text{Mean}=\dfrac{\text{Sum of observations}}{\text{Number of observations}}\)

The mean of a set of 6 integers is 30.

\(30=\dfrac{\text{Sum of 6 observations}}{6}\)

\(30\times 6=\text{Sum of 6 observations}\)

\(180=\text{Sum of 6 observations}\)

If one of the numbers is removed, then the mean of remaining 5 numbers is 34.

\(34=\dfrac{\text{Sum of 5 observations}}{5}\)

\(34\times 5=\text{Sum of 5 observations}\)

\(170=\text{Sum of 5 observations}\)

Now,

Removed number = Sum of 6 observations - Sum of 5 observations

                              = 180 - 170

                              = 10

Therefore, the removed number is 10.


Related Questions

If you select one card at random from a standard deck of 52 cards, what is the probability of that card being a 3, 4, OR 5?

Answers

Since we have four three cards, four four cards and four five cards, this means that we have 12 possibilities out of 52; that is the probability is:

\(P=\frac{12}{52}=\frac{3}{13}\)

Therefore the probability is 3/13

Express 156 as the product of primes.

Answers

Answer:

Step-by-step explanation:

Divide the numbers by only the prime numbers.

After u have done completing as in the attached picture:

you have to write :

156 = 2 × 2 × 3 × 13

Express 156 as the product of primes.


What is the tangent ratio for
• 4/3
• 5/4
• 5/3
• 3/4

What is the tangent ratio for 4/3 5/4 5/3 3/4

Answers

Answer:

Try the answer 5/3

or in other words C.

In a​ poll, 1 comma 002 men in a country were asked whether they favor or oppose the use of​ "federal tax dollars to fund medical research using stem cells obtained from human​ embryos." Among the​ respondents, 48​% said that they were in favor. Identify the population and the sample. What is the population in the given​ problem? Choose the correct answer below. A. 48​% of the 1 comma 002 men selected B. The 1 comma 002 men selected C. All men in the country D. 48​% of all men in the country Identify the sample for the given problem. Choose the correct answer below. A. 48​% of the 1 comma 002 men selected B. The 1 comma 002 men selected C. 48​% of all men in the country D. All men in the country

Answers

Answer:

Population: all men in the country

Sample: the 1,002 men selected

Step-by-step explanation:

The population describes the people/group of people involved.

The sample describes a portion taken out of the population.

Thus, in this case study, the population is all men in the country

The sample is the 1,002 men selected.

can someone help me, im straggling a lil bit.

can someone help me, im straggling a lil bit.

Answers

Answer:

J

Step-by-step explanation:

what is 5/6 x 3 in fraction form?

Answers

Answer:

The answer is 5/2

Step-by-step explanation:

5/6 times 3

15/6=

5/2

The fraction form of (5/6)×3 after simplification is  5/2.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, (5/6)×3.

= (5/6)×(3/1).

Now in fraction multiplication, we simply multiply the numerator with the numerator and the denominator with the denominator.

= (5×3)/(6×1).

= 15/6.

= 5/2.

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Every night, Doug drops any coins remaining in his pocket into a glass jar. Yesterday, Doug looked at how full the jar was and estimated he had $25. After he opened the jar and counted the coins, he found that the actual total was $30.60. What is the percent error for his estimate?

Answers

The percent error for his estimate is 22.4%.

His estimated value = $25

Actual value he found = $30.60

Percent error(δ) = \(|\frac{V_{A} - V_{E}}{V_{E} }|*100\)

where \(V_{A}\) = Actual value

           \(V_{E}\) = Expected value

Percent error (δ) = \(|\frac{30.60-25}{25}|*100\)

                            = \(\frac{5.6}{25}*100\)

                            = 5.6 * 4

                            = 22.4%

Hence, the percent error is 22.4%

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Identify the slope (m) and y-intercept (b) of each linear equation.
52. 3x+4y=24

Answers

Answer:

Step-by-step explanation:

  [1]    3x - 4y = -24

  [2]    -x - 16y = -52

Graphic Representation of the Equations :

   -4y + 3x = -24        -16y - x = -52  

 

Solve by Substitution :

// Solve equation [2] for the variable  x

 [2]    x = -16y + 52

// Plug this in for variable  x  in equation [1]

  [1]    3•(-16y+52) - 4y = -24

  [1]     - 52y = -180

// Solve equation [1] for the variable  y

  [1]    52y = 180

  [1]    y = 45/13

// By now we know this much :

   x = -16y+52

   y = 45/13

// Use the  y  value to solve for  x

   x = -16(45/13)+52 = -44/13

Solution :

{x,y} = {-44/13,45/13}

Find each Value

m∠A =

Find each ValuemA =

Answers

Answer:

75 degrees

Step-by-step explanation:

since this figure has four sides we can figure out the measure of the interior angles by using the formula, (n-2)*180, where 'n' = number of sides

(4-2)180 = 2(180) = 360

also, we know that since AB is parallel to DC that the figure is a rhombus where adjacent angles are supplementary

therefore, we can find 'x' by writing this equation:

12x - 3 + 9x - 6 = 180

simplify:

21x - 9 = 180

21x = 189

x = 9

also, we know that opposite angles in a rhombus are equal so if we substitute '9' for 'x' in angle C we will know the measure of angle A:

m<A = 9(9)-6

m<A = 81-6

m<A = 75 degrees

please please help!! and if you could show work too that would be amazing!!!

please please help!! and if you could show work too that would be amazing!!!

Answers

First you would add the two angles together to get 105. The. you do 180-105 to get 75. That is the missing angle. From there you would correspond the angles with the sides. Therefore the answer is Angle AB, angle BC, angle CA. these are in order from shortest to longest

Answer:

AB, BC, AC

Step-by-step explanation:

Hi there,

In order to solve this problem, we should know that the longest side of the triangle is always opposite of the largest angle in a triangle. The first step is to find the angle measures. We are given the measures of ∠A and ∠C.

To find m∠B, just subtract the sum of the other angles and subtract the value from 180.

m∠A + m∠C + m∠B = 180°

65° + 40° + m∠B = 180°

105° + m∠B = 180°

m∠B = 75°

Now that we know all of the angle measures, we can identify the the lengths of the sides from least to greatest by looking at the angle value. The greater the angle measure, the longer the opposite side would be.

m∠A = 65° ⇒ opposite of side BC = medium side

m∠B = 75° ⇒ opposite of side AC = longest side

m∠C = 40° ⇒ opposite of side AB = shortest side

Hope this explanation helps. Cheers.

fwweee points hmu cause why not

Answers

Answer:

thank you

Step-by-step explanation:

no

body

needs

your

free point

be serious

Im confused on #6...help anyone?

Im confused on #6...help anyone?

Answers

Answer:

Step-by-step explanation:

Using elimination means you either add the two equations together or subtract them. You can first multiply the second equation by 2, so you get 4x - 6y = 24. Then you add the two equations together to get 9x = 42. Then you solve for x and then you can solve for y.

A boat heading upstream (against the current) has a net speed of 80 mph, if the same boat heads downstream its speed is 110 mph. What is the speed of the current assuming it is less than the speed of the boat.

Answers

Answer:

The speed is 30mph

Step-by-step explanation:

what is(4c⁶)² x (3a⁴)-³ x 2​

Answers

Your answer with be 12c6 a4 -6
Hopes this helps.

For Gardyloo Manufacturing, the true proportion of accounts receivable with some kind of error is .20. If an auditor randomly samples 225 accounts receivable, what is the approximate normal probability that more than 39 will contain errors?

Answers

Therefore, The approximate normal probability that more than 39 accounts receivable will contain errors is 2.28%.

The problem involves calculating the probability of finding errors in a sample of accounts receivable. We know that the true proportion of accounts receivable with errors is 0.20. The sample size is 225 accounts receivable. We want to find the probability of finding more than 39 accounts with errors. We can use the normal distribution formula to calculate this probability. By converting the problem to a standard normal distribution, we can use a z-score table to find the probability. The probability is approximately 0.0228, or 2.28%. This means that there is a 2.28% chance of finding more than 39 accounts with errors in the sample.

Therefore, The approximate normal probability that more than 39 accounts receivable will contain errors is 2.28%.

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What is Santon’s goal?

Answers

Anno one came answer that without numbers

Step-by-step explanation:

Answer:

Although Stanton remained committed to efforts to gain property rights for married women and ending slavery, the women's suffrage movement increasingly became her top priority. Stanton met Susan B

Step-by-step explanation:

Which of the following are reasonable models of the spread of a disease
among a finite number of people:
(1) dN|dt = ON
(2) dN/dt = Q(N, - N)
(3) dN]dt = Q(N - Nr),
where N is the number of infected individuals and My is the total population.

Answers

dN/dt = Q(N - Nr), introduces the concept of a recovery rate (r) by subtracting Nr from the infected population (N).

What does the term "dN/dt" represent in these models?

Among the given options, (2) and (3) are reasonable models of the spread of a disease among a finite number of people.

Option (1), dN|dt = ON, does not provide sufficient information or context to accurately represent the spread of a disease.

Option (2), dN/dt = Q(N, - N), suggests that the rate of change of infected individuals (dN/dt) depends on the current number of infected individuals (N) and the difference between the total population (M) and the infected population (-N).

This model incorporates the concept that the disease spreads within the population and also accounts for the impact of susceptible individuals.

Option (3), dN/dt = Q(N - Nr), introduces the concept of a recovery rate (r) by subtracting Nr from the infected population (N). This model considers the impact of both the spread and recovery processes, providing a more comprehensive representation of disease dynamics.

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Hello! please help ! Find the exact perimeter of hexagon A B C D E F plotted below.

Hello! please help ! Find the exact perimeter of hexagon A B C D E F plotted below.

Answers

Answer:

23 + \(\sqrt{29}\) + \(\sqrt{58}\)

Step-by-step explanation:

538.6 − ____ is about 500. Write a decimal that when rounded to the nearest whole number makes the equation true.
A. 75.4
B. 53.8
C. 37.8
D. 8.6

Answers

Answer:

C

Step-by-step explanation:

538.6 - 75.4 = 463.2

538.6 - 53.8 = 484.8

538.6 - 37.8 = 500.8

538.6 - 8.6 = 530

C is closets to 500 so it has to be 500.8

A side of the triangle below has been extended to form an exterior angle of 134°. Find
the value of x.

A side of the triangle below has been extended to form an exterior angle of 134. Findthe value of x.

Answers

Check the picture below.

A side of the triangle below has been extended to form an exterior angle of 134. Findthe value of x.

write the equation of the line that passes through the given points. (0,-1) and (-11,-4)

write the equation of the line that passes through the given points. (0,-1) and (-11,-4)

Answers

Answer:

Line equation

y=0.2727272727272727x−1                Slope 0.27         Intercept   -1

Step-by-step explanation:

Grant just joined a new gym and signed up for a one-year membership. Membership fees can be paid in 12 monthly payments of $55, due at the beginning of each month or in one payment today. If the appropriate interest rate is 10%, how much should he pay today for the annual membership?

Answers

Grant should pay approximately $211.96 today for the annual membership, considering an interest rate of 10% and the option to pay in 12 monthly installments of $55 each.

To determine how much Grant should pay today for the annual membership, we need to calculate the present value of the 12 monthly payments of $55 each, considering an interest rate of 10%.

The present value (PV) can be calculated using the formula:

PV = C * (1 - (1 + r)^(-n)) / r

Where:

C = the monthly payment amount ($55)

r = the monthly interest rate (10% / 12 = 0.00833)

n = the number of payments (12)

Plugging in the values into the formula, we can calculate the present value:

PV = 55 * (1 - (1 + 0.00833)^(-12)) / 0.00833

PV ≈ 55 * (1 - 0.6806) / 0.00833

PV ≈ 55 * 0.3194 / 0.00833

PV ≈ 211.96

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the compounding of this question

the compounding of this question

Answers

50,000 of 50% right rose

6(3h-4) = 18h + _________

Answers

Step-by-step explanation:

6(3h - 4) = 18h + (-24) = 18h -24

how do u do thissss??
reflect this shape in the line y=x :)​

how do u do thissss??reflect this shape in the line y=x :)

Answers

Answer:

the x-coordinate and y-coordinate change places.

Step-by-step explanation: so you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).

Solve for B. N=-m^2+3d/b

Solve for B. N=-m^2+3d/b

Answers

Answer:

b = 3d/n+m^2

Step-by-step explanation:

Is xxx greater than, less than, or equal to 110^\circ110

110, degrees?

Is xxx greater than, less than, or equal to 110^\circ110 110, degrees?

Answers

The angle z is equal to 110° by vertically opposite angles. Hence, the correct option will be C. z = 110°.

What is vertically opposite angles?

The vertically opposite angles are those angles that are opposite one another at a specific vertex and are created by two straight intersecting lines.

Given;

The one angle is given as 110°.

So, angle z will be equal to 110° by vertically opposite angles.

Hence, the correct option will be C. z = 110°.

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kylie uses the number 400 to represent a location 400 miles north of the equator she uses the number- 2000 to represent a location 2000 miles south of the equator which number would represent what number would represent a location on the equator

Answers

Answer:

0

Step-by-step explanation:

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.

Given-

Kylie uses the number 400 to represent 400 miles north of the equator.

Kylie uses the number -2000 to show 2000 miles south of the equator.

What is the direction?

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.

As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.

Which of the following parts does not belong to a theoretical:
A. The hypotheses corresponding to the model
B. The operationalization of the used constructs of the model
C. A logical explanation of the relationship within a model
D. A graphical respresentation of the model

Answers

The operationalization of the used constructs of the model is not typically considered a part of the theoretical aspects of a model. The correct option is (B).

Operationalization refers to the process of defining and measuring the variables or constructs in a study. It involves turning abstract concepts into observable and measurable variables.

On the other hand, the theoretical parts of a model typically include:

A. The hypotheses corresponding to the model: This refers to the specific statements or predictions derived from the theoretical framework of the model.

Hypotheses provide testable expectations about the relationships between variables in the model.

C. A logical explanation of the relationship within a model: This involves providing a theoretical rationale or logical explanation for the expected relationships between variables in the model.

It is the theoretical framework that underlies the model and helps in understanding the underlying mechanisms or processes.

D. A graphical representation of the model: Graphical representation, such as diagrams or visual models, can be used to depict the structure or relationships within a model. It helps in visualizing the connections between variables and understanding the overall framework.

Therefore, B. The operationalization of the used constructs of the model does not belong to the theoretical parts of a model.

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82.8 cm measured to the nearest tenth of a cm.

Answers

Answer:

80.0 cm

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

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