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vodomira [7]
3 years ago
10

The triangular arrangement of numbers shown is known as Pascal's triangle. Use inductive reasoning to find the 6 missing numbers

.

Mathematics
1 answer:
denis-greek [22]3 years ago
3 0

Answer:

1 5 10 10 5 1

Step-by-step explanation:

The complete question has been attached as an image.

Looking at the triangle, we see a pattern. The first level we have 1, in the next level we have 1 1, the next evel we have 1 2 1, the next level we have 1 3 3 1 and so on. From here, we see that to get the numbers of the next level, we have to write 1 as the first number, then add 1 to the next number after it in the previous level to get the second number in the next level then add the second number of the previous level to the next number beside it to get the third number in the next level and so on until you get to the last number before 1 in the previous level, add that number to 1 to get the second to the last number in the next level and finally put 1 as the last number in the next level. Now, we have

1 4 6 4 1

1 5 10 10 5 1

And that is the required set of numbers.

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=20/3
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Which of the following expressions are equivalent
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It’s 2 and 3 bc 6a+12 and then 3(2a+4) and you need to distribute for that so 3 times 2a equals 6a and 3 times 4 equals 12 so you get 6a+12
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A swimming pool is to be drained. The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. Su
Gala2k [10]

Answer: it will take 9 hours to empty the pool.

Step-by-step explanation:

The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is

30 × 18 × 4 = 2160 ft³

If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence(initial amount of water in the pool when completely full).

d represents the common difference(rate at which it is being pumped out)

n represents the number of terms(hours) in the sequence.

From the information given,

a = 2160 degrees

d = - 216 ft3

Tn = 0(the final volume would be zero)

We want to determine the number of terms(hours) for which Tn would be zero. Therefore,

0 = 2160 - 216 (n - 1)

2160 = 216(n - 1) = 216n + 216

216n = 2160 - 216

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8 0
3 years ago
17/6 as a mixed number
natta225 [31]


just divide 17 by 6 and you'll get your mixed number:

2 5/6

8 0
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Two different simple random samples are drawn from two different populations. The first sample consists of 30 people with 16 hav
Furkat [3]

Answer:

  • There is no significant evidence that p1 is different than p2 at 0.01 significance level.
  • 99% confidence interval for p1-p2 is  -0.171 ±0.237 that is (−0.408, 0.066)

Step-by-step explanation:

Let p1 be the proportion of the common attribute in population1

And p2 be the proportion of the same common attribute in population2

H_{0}: p1-p2=0

H_{a}: p1-p2≠0

Test statistic can be found using the equation:

z=\frac{p2-p1}{\sqrt{{p*(1-p)*(\frac{1}{n1} +\frac{1}{n2}) }}} where

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  • p2 is the sample proportion of the common attribute in population2 (\frac{1337}{1900} =0.704)
  • p is the pool proportion of p1 and p2 (\frac{16+1337}{30+1900}=0.701)
  • n1 is the sample size of the people from population1 (30)
  • n2 is the sample size of the people from population2 (1900)

Then z=\frac{0.704-0.533}{\sqrt{{0.701*0.299*(\frac{1}{30} +\frac{1}{1900}) }}} ≈ 2.03

p-value of the test statistic is  0.042>0.01, therefore we fail to reject the null hypothesis. There is no significant evidence that p1 is different than p2.

99% confidence interval estimate for p1-p2 can be calculated using the equation

p1-p2±z*\sqrt{\frac{p1*(1-p1)}{n1}+\frac{p2*(1-p2)}{n2}} where

  • z is the z-statistic for the 99% confidence (2.58)

Thus 99% confidence interval is

0.533-0.704±2.58*\sqrt{\frac{0.533*0.467}{30}+\frac{0.704*0.296}{1900}} ≈ -0.171 ±0.237 that is (−0.408, 0.066)

7 0
3 years ago
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