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
podryga [215]
3 years ago
5

The mean of a particular set of 7 numbers is 4. Six of the numbers in the set are known: 1,2,2,5,7,and 8.

Mathematics
1 answer:
Setler [38]3 years ago
8 0
\dfrac{1+2+2+5+7+8+x}{7}=4\\
\dfrac{25+x}{7}=4\\
25+x=28\\
\boxed{x=3}

You might be interested in
Why is 3/8 bigger than 3/12​
Stolb23 [73]

Answer:

3/ 8  is greater than  3/ 12 because if you cross multiply 12 times 3 is 36 and 3 times 8 is 24

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
2x-7/3-5x+4/5=-x-4/30
Strike441 [17]

Answer:

Exact form: -7/10

Decimal form: -0.7

Step-by-step explanation:

Isolate the variable by dividing each side by by factors that don't contain the variable.

5 0
3 years ago
3,6,11,18,27,38
MakcuM [25]

Answer:  The pattern is x^2+2

where x is the term number

Example: the 5th term is 27 because x = 5 leads to x^2+2 = 5^2+2 = 27

=================================================

Explanation:

  • The jump from 3 to 6 is +3
  • The jump from 6 to 11 is +5
  • The jump from 11 to 18 is +7
  • The jump from 18 to 27 is +9
  • The jump from 27 to 38 is +11

The pattern of jumps is: 3, 5, 7, 9, 11

Those increments are going up by 2 each time.

Since we have a consistent pattern of increments, this means that the sequence follows a quadratic model.

Quadratics are stuff like x^2+7x+10 or 3x^2-7. The leading term has an exponent of 2.

-----------

If x is the term number and y is the term itself, then we have these points

(1,3)

(2,6)

(3,11)

(4,18)

(5,27)

(6,38)

The x coordinates increase by 1 each time. The y coordinates are the terms given by your teacher.

Pick exactly 3 of those points. I'll pick the first 3.

Why 3? Because we'll have 3 unknowns to solve for, in which we'll need 3 equations.

  • Plug (x,y) = (1,3) into y = ax^2+bx+c, then simplify. You should get the equation a+b+c = 3
  • Repeat for (x,y) = (2,6) and you should get 4a+2b+c = 6
  • Repeat for (x,y) = (3,11) and you should get 9a+3b+c = 11

-----------

We have this system of equations

\begin{cases}a+b+c = 3\\ 4a+2b+c = 6\\9a+3b+c = 11\end{cases}

There are a number of methods to solve this system. Substitution is what I'll go for.

Solve the first equation for c

a+b+c = 3

c = 3-a-b

Then use substitution.

4a+2b+c = 6

4a+2b+(3-a-b) = 6

3a+b+3 = 6

3a+b = 6-3

3a+b = 3

and

9a+3b+c = 11

9a+3b+(3-a-b) = 11

8a+2b + 3 = 11

8a+2b = 11-3

8a+2b = 8

We now have this reduced system of equations.

\begin{cases}3a+b = 3\\8a+2b = 8\end{cases}

I'll skip the steps as this solution is getting very lengthy as it is. The basic idea is to use substitution again. You should find that a = 1 and b = 0 form the solution set here.

Use those values to find c

c = 3-a-b

c = 3-1-0

c = 2

-----------

To summarize the previous section, we have these solutions:

a = 1, b = 0, c = 2

Therefore the equation y = ax^2+bx+c becomes y = 1x^2+0x+2 aka y = x^2+2. This lets us find any term.

Let's test it out.

  • If x = 1, then y = x^2+2 = 1^2+2 = 3
  • If x = 2, then y = x^2+2 = 2^2+2 = 6
  • If x = 3, then y = x^2+2 = 3^2+2 = 11

And so on. I'll let you test the other x values (4 through 6).

Another way to confirm the answer is to subtract 2 from each item in the original set {3,6,11,18,27,38} and you'll end up with {1,4,9,16,25,36}. This is the list of perfect squares. It shows that term x is simply x^2 but add on 2 so things are adjusted accordingly.

Side note: you can use a tool like GeoGebra or WolframAlpha to quickly solve the system of equations. However, I recommend it only as a means to check your answer rather than do the work for you.

7 0
2 years ago
How many pints are in 15 gallons
lesya692 [45]
There 60 pints in 15 gallon
6 0
3 years ago
Read 2 more answers
This is urgent 1. In a picture, there are 40 monkeys, and 60% of the monkeys are in the trees.
V125BC [204]

Answer:

There are 60 monkeys in the Zoo

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • How to write 15,409 in word form
    13·2 answers
  • 2. there are two phone plans. One plan a $28 monthly fee, and cost 9 cents per minute. The second plan is 13 cents per minute, a
    6·1 answer
  • Given the equations f(x) = x + 4 and d (x) = 2x + 5, find: f (1) + d (2)
    14·1 answer
  • A web site was hit 300 times over a period of 15 days Show that over some period of 3 consecutive days, it was hit at least 60 t
    12·1 answer
  • Rotate a semicircle around a line through the endpoints of the semicircle.
    5·1 answer
  • Please help asap || brainliest + 15 points
    9·2 answers
  • A friend asks to borrow $250 for 18 months and agrees to pay 12% annual simple interest. How much interest will you earn? Round
    6·1 answer
  • Is 23/48 less than 1/2
    5·2 answers
  • Find the value of x for the right triangle. Round your answer to the nearest hundredth.
    15·1 answer
  • Given:
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!