There are 14 chairs and 8 people to be seated. But among the 8. three will be seated together:
So 5 people and (3) could be considered as 6 entities:
Since the order matters, we have to use permutation:
¹⁴P₆ = (14!)/(14-6)! = 2,162,160, But the family composed of 3 people can permute among them in 3! ways or 6 ways. So the total number of permutation will be ¹⁴P₆ x 3!
2,162,160 x 6 = 12,972,960 ways.
Another way to solve this problem is as follow:
5 + (3) people are considered (for the time being) as 6 entities:
The 1st has a choice among 14 ways
The 2nd has a choice among 13 ways
The 3rd has a choice among 12 ways
The 4th has a choice among 11 ways
The 5th has a choice among 10 ways
The 6th has a choice among 9ways
So far there are 14x13x12x11x10x9 = 2,162,160 ways
But the 3 (that formed one group) could seat among themselves in 3!
or 6 ways:
Total number of permutation = 2,162,160 x 6 = 12,972,960
She invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
<h3><u>Distributions</u></h3>
Given that Sylvia invested a total of $27,000, and she invested part of the money in a certificate of deposit (CD) that earns 3% simple interest per year, she invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund that returns 2%, and she invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the end of 1 yr, to determine how much principal did she put in each investment, the following calculation must be made:
- 9000 x 0.07 + 3000 x 0.03 + 15000 x 0.02 = 630 + 90 + 300 = 1020
- 9900 x 0.07 + 3300 x 0.03 + 13800 x 0.02 = 693 + 99 + 276 = 1068
- 12,000 x 0.07 + 4,000 x 0.03 + 11,000 x 0.02 = 840 + 120 + 220 = 1,180
- 11400 x 0.07 + 3800 x 0.03 + 11800 x 0.02 = 798 + 114 + 236 = 1148
- 10800 x 0.07 + 3600 x 0.03 + 12600 x 0.02 = 756 + 108 + 252 = 1116
- 11160 x 0.07 + 3720 x 0.03 + 12120 x 0.02 = 781.2 + 111.6 + 242.4 = 1135.2
- 11190 x 0.07 + 3730 x 0.03 + 12080 x 0.02 = 783.3 + 111.9 + 241.6 = 1136.8
- 11250 x 0.07 + 3750 x 0.03 + 12000 x 0.02 = 787.5 + 112.5 + 240 = 1140
Therefore, she invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
Learn more about distribution in brainly.com/question/10250387
Answer:
Can i have brainliest
The second one
The third one
and the last ones
Step-by-step explanation:
The x values are opposite
and the y stay the same
Like all problems that involve images within the question, we should definitely try to draw this out. In the picture above, I have done this.
Now, we can see that this is just a simple proportion problem. For every 2.5 cm of height of the flower, we are 2 cm from the opening, or aperture. For every 20 cm of height, how far are we? We can set up the problem like this:
20 ............2.5
-------- = ---------
...x ............. 2
where x is the unknown distance to the aperture from the flower. Now, we just need to get x by itself. A typical way of solving something like this is by doing "butterfly multiplication" which is really just a shortcut haha. Anyway, I can rewrite that equation ^ as:
20×2 = 2.5 × x
Then, to solve for x, we would divide both sides by 2.5. (If you don't know why that is, please let me know and I'll elaborate).
We would then have:
20×2
------- = x
2.5
Which then simplifies to:
x = 16
Try using the same logic for your second question, and if you get stuck, I'd be happy to help! please let me know if any of this doesn't make sense. :)
Answer:
x>-4 x≤-8
Step-by-step explanation: