2^a / 2^2 = 2^3 solve for a

Suppose you pick 6 different numbers in [10]. Prove that 2 of the numbers are next to each other. (Hint: use the pigeonhole prin

Masja [62]

Step-by-step explanation:

We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):

| 1 2 | 3 4 | 5 6 | 7 8 | 9 10 |

So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).

4 0

3 years ago

3.25 3 2/5 3 3/8 from least to greatest

kirza4 [7]

Answer:

3.25, 3 2/5 , 3 3/8 is the order from least to greatest

3 0

3 years ago

"

allsm [11]

Answer:

$\boxed{\text{15.8 cords}}$

Step-by-step explanation:

Step 1. Calculate the volume of the room

V = lwh = 5 yd × 5 yd × 3 yd = 75 yd³

Step 2. Convert cubic yards to cubic feet

3 ft = 1 yd

$V = \text{75 yd}^{3} \times \left(\dfrac{\text{3 ft}}{\text{1 yd}} \right)^{3} = \text{2025 ft}^{3}$

Step 3. Convert cubic feet to cords

128 ft³ = 1 cord

$V = \text{2025 ft}^{3} \times \dfrac{\text{1 cord}}{\text{ 128 ft}^{3}} = \textbf{15.8 cords}\\\\\text{You could fit }\boxed{\textbf{15.8 cords}} \text{ of wood into the room.}$

3 0

3 years ago

Please help please help

GalinKa [24]

Answer:

Here it is B

5 0

2 years ago

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes

vesna_86 [32]

Answer:

A) P=2.28%

B) P=28.57%

C) I expect 10 students to be unable to complete the exam in the alloted time.

Step-by-step explanation:

In order to solve this problem, we will need to find the respective z-scores. The z-scores are found by using the following formula:

$z=\frac{x-\mu}{sigma}$

Where:

z= z-score

x= the value to normalize

$\mu = mean$

$\sigma$ = standard deviation

The z-score will help us find the area below the normal distribution curve, so in order to solve this problem we need to shade the area we need to find. (See attached picture)

A) First, we find the z-score for 60 minutes, so we get:

$z=\frac{60-80}{10}=-2$

So now we look for the z-score on our normal distribution table. Be careful with the table you are using since some tables will find areas other than the area between the mean and the desired data. The table I used finds the area between the mean and the value to normalize.

so:

A=0.4772 for a z-score of -2

since we want to find the number of students that take less than 60 minutes, we subtract that decimal number from 0.5, so we get:

0.5-0.4772=0.0228

therefore the probability that a student finishes the exam in less than 60 minutes is:

P=2.28%

B) For this part of the problem, we find the z-score again, but this time for a time of 75 minutes:

$z=\frac{75-80}{10}=-0.5$

and again we look for this z-score on the table so we get:

A=0.1915 for a z-score of -0.5

Now that we got this area we subtract it from the area we found for the 60 minutes, so we get:

0.4772-0.1915=0.2857

so there is a probability of P=28.57% of chances that the students will finish the test between 60 and 75 minutes.

C) Finally we find the z-score for a time of 90 minutes, so we get:

$z=\frac{90-80}{10}=1$

We look for this z-score on our table and we get that:

A=0.3413

since we need to find how many students will take longer than 90 minutes to finish the test, we subtract that number we just got from 0.5 so we get:

0.5-0.3413=0.1586

this means there is a 15.86% of probabilities a student will take longer than 90 minutes. Now, since we need to find how many of the 60 students will take longer than the 90 available minutes, then we need to multiply the total amount of students by the percentage we previously found, so we get:

60*0.1586=9.516

so approximately 10 Students will be unavailable to complete the exam in the allotted time.

3 0

3 years ago

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