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DochEvi [55]
2 years ago
13

Find a rational number halfway between 7/8 and 6/7

Mathematics
1 answer:
algol [13]2 years ago
8 0
<h3>Answer: 97/112</h3>

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

How to get this answer:

Midpoint formula: (A+B)/2 = C

A and B are the endpoints with C as the midpoint

A = 7/8

B = 6/7

A+B = 7/8 + 6/7

A+B = 49/56 + 48/56

A+B = (49+48)/56

A+B = 97/56

(A+B)/2 = (97/56) divided by 2

(A+B)/2 = (97/56) times (1/2)

(A+B)/2 = (97*1)/(56*2)

(A+B)/2 = 97/112

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Mai bought eleven 12-ounce bags of
ella [17]

Answer:

8.25 pounds

Step-by-step explanation:

When you multiply 12 and 11 you get 132. So then you would have to divided the total amount of ounces by 16 to get the amount of pounds

5 0
1 year ago
Solve the system of linear equations using multiplication.
Anna71 [15]

Answer:

(8,-1)

Step-by-step explanation:

The given system is:

3x+3y=21

6x+12y=36

Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.

This gives me the system:

x+y=7

x+2y=6

We could solve the first equation for x and replace the second x with that.

Let's do that.

x+y=7

Subtract y on both sides:

x=7-y

So we are replacing the second x in the second equation with (7-y) which gives us:

(7-y)+2y=6

7-y+2y=6

7+y=6

y=6-7

y=-1

Now recall the first equation we arranged so that x was the subject. I'm referring to x=7-y.

We can now find x given that y=-1 using the equation x=7-y.

Let's do that.

x=7-y with y=-1:

x=7-(-1)

x=7+1

x=8

So the solution is (8,-1).

We can check this point by plugging it into both equations.

If both equations render true for that point, then we have verify the solution.

Let's try it.

3x+3y=21 with (x,y)=(8,-1):

3(8)+3(-1)=21

24+(-3)=21

21=21 is a true equation so the "solution" looks promising still.

6x+12y=36 with (x,y)=(8,-1):

6(8)+12(-1)=36

48+(-12)=36

36=36 is also true so the solution has been verified since both equations render true for that point.

5 0
1 year ago
Read 2 more answers
A special 8-sided die is marked with the numbers 1 to 8. It is rolled 20 times with these outcomes:
horsena [70]

Answer:

One: B

Two: 60% and 10%

Step-by-step explanation:

Problem One

There are only two numbers in the sample of 40 that are under 26. Both are 25. If you find more, make the adjustment. There are 2 more that are exactly 26 but they are not counted because the directions say "less than 26."

So set up your proportion

x/2000 = 2/40                     Multiply both sides by 2000

x = 2/40 * 2000

x = 4000/40

x = 100

A

I don't know where 5 comes from. But it is not correct.

B

B should be the correct answer.

C

Exactly 100 pieces should be defective. That is the theoretical result. C is incorrect.

D

D is not correct. The sample size would not be 40. It would have to be 2000 for D to be correct. So D is wrong.

E

We have enough data to get an answer. E is incorrect.

Problem 2

The think you must NOT do is count 1 as being prime. The prime numbers are 2 3 5 7 between 1 and 8. They break down as follows.

  • Prime           Number of them
  • 2                         3
  • 3                         4
  • 5                         2
  • 7                         3

The total number of primes = 12

There are 20 numbers in the sample

The experimental probability of tossing a prime is 12/20 * 100% = 60%

The non primes are 2 3 5 7 which is 4 out of 8

4/8 * 100 = 50%

The experimental value is 10% more than the theoretical value.

Discussion

Note: the problem may be one. This all depends on what you have been told about 1. I am using the exact wording of prime here. 1 is not a prime. It is also not a composite. So it has to be counted as part of the non primes.


4 0
2 years ago
Read 2 more answers
Which system of equations can be used to find the roots of the equation 12 x 3-5x=2 x 2+x+6
kirill [66]

Answer:

Option (a) is correct.

The system of equation becomes

y=12x^3-5x\\\\ y=2x^2+x+6

Step-by-step explanation:

Given : Equation  12x^3-5x=2x^2+x+6

We have to construct a  system of equations that  can be used to find the roots of the equation 12x^3-5x=2x^2+x+6

Consider the given equation 12x^3-5x=2x^2+x+6

To construct a system of equation put both sides of the given equation equal to a same variable.

Let the variable be "y", Then the equation 12x^3-5x=2x^2+x+6

becomes,

12x^3-5x=y=2x^2+x+6

Thus, The system of equation becomes

y=12x^3-5x\\\\ y=2x^2+x+6

Option (a) is correct.

   

8 0
1 year ago
Read 2 more answers
Celine's Cereal Company is launching a new brand of cereal and she is considering two different sizes for the base of the boxes.
densk [106]

The dimensions of the base of Box 1 are x by 3x.


The base area of Box 1 is:

3x^2

6 0
1 year ago
Read 2 more answers
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