1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
GaryK [48]
3 years ago
5

A collection of 5 positive integers has mean 4.4, unique mode 3 and median 4. If an 8 is added to the collection, what is the ne

w median. Express your answer as a decimal rounded to the nearest tenth.
Mathematics
1 answer:
Sphinxa [80]3 years ago
8 0

9514 1404 393

Answer:

  4.5

Step-by-step explanation:

It appears the 5 integers must be {3, 3, 4, 5, 7}.

For the mode to be unique, there must be more than one '3', and there cannot be any other repeated numbers. For 4 to be the median, it must be the 3rd-highest number. Then the remaining numbers must be integers greater than 4 with a sum of 12 for the mean to be 4.4.

When 8 is added to the collection, the median is now the average of 4 and 5, so is 4.5.

The new median is 4.5.

_____

<em>Comment on vocabulary</em>

<u>mean</u>: the sum of numbers divided by the number of numbers. 5 numbers with a mean of 4.4 will have a sum of 5×4.4 = 22.

<u>median</u>: the middle number of a collection of an odd number of numbers, when sorted from lowest to highest. It is the 3rd number of a group of 5 numbers. When there are an even number of numbers in the group, the median is the average of the middle two in the sorted list. Here, that means the 3rd number in the list of 5 is '4'. When 8 is added, 4 becomes one of the numbers contributing to the average that will be the new median.

<u>mode</u>: the member of the group that appears the most times. When the mode is unique, it means there are no other numbers repeated as often. Here, we know the 3rd number (of 5) is 4, so there can only be two numbers '3' in the collection. That 3 is the unique mode means no other numbers are repeated at all.

You might be interested in
Angel lives 3 3 4 blocks to the east of school. Tyrone lives 7 1 4 blocks to the west of Angel. Nadeem lives 8 blocks to the eas
Vladimir79 [104]

Answer:

3 1/2

Step-by-step explanation:

Given that:

Angel lives 3 3/4 blocks to the east of school

Tyrone lives 7 1/4 blocks to the west of Tyrone

Nadeem lives 8 blocks to the east of Tyrone.

Determining each of their homes in terms of distance from school :

Angel = 3 3/4 blocks from school

Tyrone = 7 1/4 blocks to the west of angel

Hence, distance from school will be :

7 1/4 - 3 3/4 = 3 1/2 blocks to the west of school

Nadeem = 8 blocks to the east of Tyrone :

Distance from school will be:

8 - 3 1/2 = 4 1/2 to the east of school.

Hence, 3 1/2 to the west of school is the closet distance of the three.

Hence, Tyrone lives closest to school

8 0
2 years ago
5 Which equation describes a line of symmetry for the figure shown? -4 3 O y = x 2 O x = 0 2 B O y = -2 4 4 6 O y = 0 -2 -3 7 ch
BaLLatris [955]

Answer:

y = 0

Step-by-step explanation:

The line y = 0 is cutting your triangle in half with perfect symmetry.

3 0
3 years ago
Maria and her family drove 885 miles on their summer vacation. The first 8 on the left in this number has a ____ of 800
Rudiy27
The first 8 on the left in this. umber has a VALUE of 800. :)
5 0
2 years ago
Read 2 more answers
An arc of a circle is 3πm long, and it subtends an angle of 72° at the center of the circle. Find the radius of the circle.
Artist 52 [7]

Answer:

7.5 m

Step-by-step explanation:

circumference = 360/72 × 3π = 15π

so the radius of the circle =

15π / 2π = 7.5 m

7 0
3 years ago
The perimeter of a rectangular garden is 290 feet. If the width of the garden is 62 feet, what is its length?
olga2289 [7]

Answer:

83

Step-by-step explanation:

Remember that the perimeter of a rectangle is two times the width plus two times the length. In other words:

2W + 2L = P

We know that the perimeter is 290 and the width is 62. We can plug these into the equation and solve for L.

2(62) + 2L = 290

124 + 2L = 290

Subtract 124 from both sides.

2L = 166

Divide both sides by 2.

L = 83

So now we know that the length is 83 feet.

I hope you find my answer and explanation to be helpful. Happy studying.

5 0
3 years ago
Read 2 more answers
Other questions:
  • THE HORROR! HELP!!!!!
    10·2 answers
  • Nsjsjs. bbhjjjjjjjjhhhhhhhh
    10·1 answer
  • I spent 25 Points, PLEASE HELP! In a graph, x represents the number of months since a business opened, and y represents the tota
    15·2 answers
  • A patio at the front of the school is a quadrilateral with 4 right angles and 4 congruent sides. What type of quadrilateral is i
    15·2 answers
  • 4. Exercise 8.1.10 (2 points)(a) Find a recurrence relation for the number of bit strings of positive lengthnthat containthe bit
    14·1 answer
  • Eliminate the parameter. X=t^2+1, y=t^2-1
    9·1 answer
  • I need the answer. Please help.
    15·1 answer
  • The m∠1 is the 63° angle. What is the measure of angle 1? degrees
    6·2 answers
  • A 22 ft ladder is set up 6 feet from the base of the building. How far up the building does the ladder reach. Round to the neare
    11·2 answers
  • If i can finish 1 class every 2 days how many days would it take to finish 42 classes
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!