MATHEMATICS HIGH SCHOOL

Simplify. Assume that letters represent any real number.\sqrt[5]{x^5}

Rewrite without rational exponents, and simplify, if possible.

32^(3/5)

Answers

Answer 1
Answer: \sqrt[5]{x^5}=x\n\n32^(3)/(5)=\left(32^(1)/(5)\right)^3=\left(\sqrt[5]{32}\right)^3=2^3=8
Answer 2
Answer: 32^(3/5) = (2^5)^(3/5) = 2^(15/5) = 2^3 = 8.

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Find the missing endpoint given one endpoint and midpoint2)
endpoint- ( -4,1) midpoint-(-1,3)

Answers

endpoint: \ ( x_(2),y_(2))= (-4,1) , \n midpoint : \(x,y)=(-1,3) \n\nMindpoint \ Formula : \n (x,y)=\left ( (x_(1)+x_(2) )/(2), \frac{y_ {1}+y_(2) }{2} \right )\n\n(-1,3)=\left ( (x_(1)-4 )/(2), \frac{y_ {1}+1 }{2} \right )

\begin{cases} (x_(1)-4 )/(2)= -1 \ \ /\cdot 2 \n \frac{y_ {1}+1 }{2} =3 \ \ / \cdot 2 \end{cases}\n\n\begin{cases} x_(1)-4 =-2 \n y_ {1}+1 =6\end{cases}\n \n\begin{cases} x_(1) =-2+4 \n y_ {1} =6-1 \end{cases}\n \n\begin{cases} x_(1) =2\n y_ {1} =5 \end{cases} \n \nAnswer : \ second \ endpoint : \ (x_(1),y_(1))=(2,5)

Machine X makes 300 boxes in 3 mins and machine Y makes 300 boxes in 2 mins. With both machines working, how long will it take to make 300 boxes?

Answers

-- Machine-X takes 3 minutes for 300 boxes . . . 3/300 = 1/100 minute per box.
-- Machine-Y takes 2 minutes for 300 boxes . . . 2/300 = 1/150 minute per box.

-- 3/150 = 2/100 . . . In 3/150 second, they can make 5 boxes by working together.

-- They need to make 5 boxes (300/5) = 60 times.
-- They'll need to work for 60 times (3/150) minutes.

60 (3/150) = 180/150 = 1.2 minutes = 1 minute and 12 seconds.

The number of guests in a hotel per day resembles a normal distribution with a mean of 220 and standard deviation of 30. One day, the z-score of the number of guests was 2.3. How many guests did the hotel have on that day?

Answers

The hotel had 289 guests on the day in question. The z-score is a measure of how many standard deviations a data point is away from the mean of the distribution.

In this case, we are given that the number of guests in a hotel per day follows a normal distribution with a mean of 220 and a standard deviation of 30, and that the z-score of the number of guests on a particular day was 2.3.

Using the formula for z-score, we have:

z = (x - mu) / sigma

where x is the number of guests on the given day, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.

Substituting the given values, we have:

2.3 = (x - 220) / 30

Multiplying both sides by 30, we get:

69 = x - 220

Adding 220 to both sides, we get:

x = 289

Therefore, the hotel had 289 guests on the day in question.

Find out more about standard deviations

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What is the probability of winning a raffle if 500 tickets are sold and you get 5

Answers

Then the probability is 5/100

Choose the converse of the following statement.They are not left behind, if they are on time.

If they are not left behind, then they are on time.
If they are on time, then they are not left behind.
If they are not on time, then they are left behind.
If they are left behind, then they are not on time

Answers

The converse of a statement can be found by switching the hypothesis and the conclusion (the beginning and ending statements) of a phrase.

Therefore, we started with the statement 

"They are not left behind, if they are on time."

To find the converse of this statement, we just need to switch the position of the two pieces.

Therefore, the converse is 

"If they are on time, then they are not left behind."

You answer is the above statement or the second option.  

How is the process of finding equivalent ratios like the process of finding equivalent fractions?

Answers

It's generally the same, because each ratio can be written as a fraction and each fraction can be written as a ratio. For example:

1 : 2 = 1/2
5 : 7 = 5/7
3.5 : 4.3 = 3.5/4.3 = 35/43
etc.

Finding equivalent ratios is just multiplying or dividing both sides by the same number. Finding equivalent fractions is multiplying or dividing both numerator and denominator by the same number, so it's the same. For example:

1 : 2 = 2 : 4
1/2 = 2/4

5 : 7 = 10 : 14
5/7 = 10/14

3.5 : 4.3 = 7 : 8.6
35/43 = 70/86

etc.
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