a number, half of that number, and one-third of that number are added. the result is 22. what is the number?

Answers

Answer 1
Answer: Let the number be x.

Half of that number  =  x / 2
One third of the number  =  x / 3

=  x / 2 + x / 3 = 22.  LCM  =  6.

= (3x + 2 x) / 6  = 22.

5x / 6 = 22.      Cross multiply

5x = 6 * 22.

5x = 132      Divide both sides by 5.

x =  132 / 5

x = 26.4

The number is 26.4.  Cheers.

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What is the solution to the system of equations? y=2/3x+3 x=-2

Answers

Answer:

x=-2,y=(5)/(3)

Step-by-step explanation:

The given system of equations is

y=(2)/(3)x+3...(i)\n\nx=-2...(ii)

Plugging the value of x from (ii) in equation (i) and find the value of y

y=(2)/(3)*(-2)+3\n\ny=(-4)/(3)+3\n\ny=(5)/(3)

Therefore, the solution of the system of equations is

x=-2,y=(5)/(3)

We are going to solve for x=-2, y=2/3x+3, y=2/3(-2)+3, y=5/3. Therefore, x=-2 and y=5/3

Three weeks ago John bought stock at 49 1/4; today the stock is valued at 49 7/8. We could say the stock is performing at which of the following?A. On par
B. Par equality
C. Above par
D. Below par

Answers

Rate at which John bought the stock 3 weeks ago = 49 1/4
                                                                                = 197/4
Rate at which John sold the stock today = 49 7/8
                                                                = 399/8
Amount of loss or gain made by John = (399/8) - (197/4)
                                                             = (399 - 394)/8
                                                             = 5/8
So, we can say that the stock performed a bit above par. the correct option is option "C".

The stock is performing above par. The correct option is C

What is Par value ?

Par value is the face value of a stock. It is the price that the company originally sold the stock for. The stock is said to be trading at par when its current market price is equal to its par value.

In this case, the stock was bought at 49 1/4, which is $49.25. Today, the stock is valued at 49 7/8, which is $50.625. This means that the stock has increased in value by $1.375, or 2.8%.

Therefore, The correct answer is C. Above par.

Learn more about Par value here : brainly.com/question/31579501

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Jamil finds that he reads 1/5 of his 115-page book in 1/4 hour

Answers

Answer:

He will read 92 pages in an hour going by the current rate at which he reads

Step-by-step explanation:

The complete question is as follows;

Jamil found that he reads 1/5 of his 115 - page book in 1/4 of an hour. At this rate how many pages does he read in an hour

We proceed as follows;

If he reads 1/5 of 115 in 1/4 hour

1/5 of 115 pages refer to 1/5 * 115 = 23 pages

This means that he reads 23 pages in quarter of an hour

So in an hours the number of pages he will read will be 23 * 4 = 92 pages

Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 π ).a.π and π/3
b.π, π/3, and 5π/3
c.1 and 2π/3
d.1, 2π/3, and 4π/3
e.1, π/3, and 5π/3

Answers

the answer is (b) all this value of x satisfy the equation

Answer:

Option  B

Step-by-step explanation:

\pi ,(\pi )/(3), and (5\pi )/(3)

10 POINTS. 1/7 written as a decimal is 0.142857 (this sequence repeats). What digit occurs in the 2012th spot after the decimal? Please explain.

Answers

1/7 = 0.142857142857142857142857142857142857142857142857142857 and so on

the pattern repeats

the first digit is 1
second digit is 4
third digit is 2
fourth digit is 8
fifth digit is 5
sixth digit is 7

and then the seventh digit is 1, and it repeats

so the six digits repeat again and again...

2012/6 = 335 2/6

It has a remainder of 2, which means that the 12th digit will be 4. because that is the second digit. After going 335 times the 6 digit patterns it will stop at the second digit which is 4.

Your answer is 4.

I hope you understood, it was kind of hard to explain :P

The geometric period was mostly characterized by

Answers

The geometric period was mostly characterized by diversity.